- Email: [email protected]
The Automatic Task Solution in an Information-control Complex of a Distributed System
CliP\! ig lu ([) I F.\L \)i gi1.d CIIIIIIHII('I' .\J>p iil; ltin[l . . HI 1'1III l·........ ( :111 111'111 . \ ·il·1l11,1. .\I' . . tri ,1, I ~ I~ .~)
THE AUTOMATIC TASK SOLUTION IN AN INFORMATION-CONTROL COMPLEX OF A DISTRIBUTED SYSTEM J.
Ulicny, O. Moravcik, Z. Knilova, L. Poljakova and L. Drab I: i({/!l1 1// I: 'I/.!...'/')!('( I/')!.!.!' l
(101/1r.
S /o; '11l /'n/III/I'I// { ',I/', ', '/ 1/11 . If 1111/ 1/11t '11.
( ,':('(//01/(1 ; 'Id,'/tl
ABSTRACT The article deals with the structure and mode of operation of an information-control complex of a system with fully automatized acquisition, processing and utilization of information on problem environment. In this information-control complex the internal model of problem environment within which the system operates is described in the first-order lo gi c. Methods of automatic theorem proving representing knowledge on the f orms and ways of the solution of control problems of a distributed system with hierarchical structure are used in the solution of the tasks of inf ormation-control complex. The simulation of one subsystem is illustrated in the conclusion, g iving more detailed explications as the mode of operation typical for the complex as a whole. Keywords. Information-control complex; situation recognition system; automatic task solution system; supervis ~ry control system; solution implementation system; knowledg e representation, input situation; twolewel hierarchical structure production system.
INTRODUCTOhY
P~MARKS
Forei gn forecasts of the development of control compu t ers and their applications suggest that by the end of the present century they will be most extensively used in the so-called expert systems processing human knowledge and using it to solve tasks of different nature. Consequently, problems involved in the automation of the solution of control tasks on the basis of representation of knowledge and experience accumulated during i ndivi du al control of distributed systems (u l j cr~ and Drab , 1982 ; U li~ nj,Thuan,Balaz and Dra b , 1983 ). Attempts at the automation of intellectual activity in the solution of different types of tasks are not recent. In the past they involved primarily computer-aided design of control systems. The main drawback of such attempt s was their low sensi bil ity and adaptability to changes in their environment and their intrinsic characteristics. They were represented especially by the socalled interpretation systems which had the character of "program control systems". The control of a distributed system by means of a control computer dependes, as it is known, first of all on the information availability to the sub j ect controlling the operation of the the system as a whole.lnformation available to the subject building computer programs chang es a~ a function of chang es in the impact of t he environment on the controlled system and chang es in the contrOl-system structure. An attempt at the automation of sUbject's activity connected with the construction of programs for control computers in rela-
tion to above changes is the main theme of our study. The information-control complex (ICC) of a distributed system denotes a whole complex of systems which carry out the control of a di stributed system in conformity with the given c ontrol objective depending on changes in the impact of the environment on the controlled system (Fig.1). The advantages of the proposed I CC of a distributed system consist, as compared to the existing and comparable systems, in its a bi lity to respond more flexibly not only to chang es in the values of environment paramete r s (such chang es do not usual:~ call fo r the modification of the selec: ed cutl trol program, but only for the modification of input data for this program) but also to chang es in the overall character of the environment whi ch - i n distributed production system - may involve e. g . exceptional and emergency situations, change s in the plan, economy measures concerning material and energy savings, etc. The proposed system can also change the control rule on the basis of changes having previously affected the system and thus also the control system structure in the case that the previously adopted measures had not been sufficiently efficient. We shall consider a distributed system represented by a control system with two-lewel hierarchical structure and a controlled system represented by the process of production (Fig. 2) . The control system cons~s~s of the centre So.and subsystems S. (l. - 1, 2, .•. , N) wnl.ch have a relat!ve decision-making authority in the sense of (Mesarovic, Macko and Takahara, 1970;, Uli~ny and Drab , 1982 ; Uli~nj, Thuan, Balaz and Drab, 1963) .
J L'iiclI\ The implementation of knowledge representation results in a sUbstantial improvement of the control-task solving system. FUNCTIONAL ACTIVITY OF THE OF A DISTRIBUTED SYSTEM
ICC
From the cybernetic point of view, the ICC consists of the following systems (Fig. 3): a) intellectual system b) sensory system c) control system Information flows between individual ICC systems are evident from Fig. 1. The task of the situation recognition system of input information, changes in the parameters of internal structure of both the control and the controlled systems affecting the selection of the method for control-task solution and implementation of this solution. Input situations ~ are generated in the system as sets of assertions characterizing the situation at the system input at any given point in time. Each input situation is transformed into the language of the first-order predicate calculus and the input situation image ~ is thus generated , representing one of the inputs to the automatic task solution system (ATSS). The ATSS assigns an appropriate method of control task solution to the input situation image and using other i nformation concerning the task determines its solution and mode of distribution of solution elements among the elements of the hierar chical system. The role of the solution implementation system (SIS) is to transform the solution of the task and its distribution into physical variables ~ affecting directly the process of production. If the ATSS is designated as the ICC of a distributed system, the supervisory control system (SCS) will represent a body superior to all the ICC systems. At the planning stage, i.e. during the decision~ma king process, a so-called expected result is determined. The achievement of this result is supervised by the SCS during the plan (solution) implementation stage, i. ~ . at the period of control exertion. Deviations from the expected result can generally occur as a result of changes to the input situation having taken place during the plan implementation stag e . In such case, a modification of the solution is expected from the ATSS. If the SCS does not receive the modification of the solution from the AT SS in time, it addresses directly the coordinator by means of the question-answering dialog system (DSQA). The SCS also handles emergency situations. By means of the DSQA the coordinator has the possibility of controlling the SCS and thus the distributed system as a whole. The SCS is incorporated as a feedback member using information on output variables of the process, input situations and information from other systems of the distributed system, i.e. SRS, ATSS and SIS.
1'1 Id.
Thuan, Balaz and Drab, 198 3): fcC'): 0(1 0 ' 1 1 , 1 2 , 1 , I 4 ;'t") 3
( 1)
Individual components of the input situation represent the influence of the environment on the system, information availability to the centre concerning the functional activity of the subsystem, interactions between the subsystemsat the same level of the hierarchical structure of system control, etc. The situation recognition system (SRS) represents the i nput part of the lee which is interconnected to the controlled process and which g enerates the image of input situation ~ for the AT SS and/or ses needs. The SRS provides for the following main functions: a) acquisition of input inf ormation on the tasks and possibilities of the hierarchical production system assigned by the superior body (10)' on the influence of the outside environment on the hierarchical produc tion system (1 1 ), on internal influences within the hierarchical production system (I ), on information concerning the functional activity of S . subsystems available to the centre ~of hie r a r chical production system So (1 ) and on interactions between and 3 information availability of subsystems at one and the same level of the hierarchical system of pro duction (1 ) 4 b) generation of information 1 0 to 14 and of macro information to the data according to their significance and necessity for individual lee systems and the generation of the orig inal of input situation c) g ener ation of input situation images according to defined criteria d) comparison of input situation images to hypothetical input situation images e) ensuring a two-mode operation of the SRS for the planning stage and for the plan i mplement at i on stag e f) identification of extraord i nary situations within the controlled system g) building of informations for databank. The SRS also performs autonomous supervisory activity and is able to respond to external supervisory instructions from the SeS.The focus in the SRS is on mastering the functional activity of the distributed control system under conditions of uncertainty. The declarative form of the representation of knowledge concerning the functional activity of a distributed system controls the inflow of information for decision making process within the ATSS. Such information larg ely determines a correct functioning of the whole information-control complex of the distributed system. Automatic Task Solution System
Situation Recognition System Hereafter, the term of input situation will denote an ordered set of information at the input to the system within a given control period (Uli~nY and Drab, 1982; Uli~nY,
The complexity of the solution of a control task at the level of a centre of a hierarchical production systems is generally entailed by the score of possible task definitions. The control task fulfilment is
ultimately reduced to the application of a certain sequence of operators (standard procedures) with the given values of parameters and constants. The development of such sequences for all possible combinations of the modes of the definition of U, X, Z sets expressing the allowed space of control, shapes of goal functions and limiting conditions as well as the activity of system elements, storage of these sequences in the memory of the control computer and their scanning at each instance of changing character of task definition, these are apparently not suitable ways of the solution of the pro blem. The ATSS solves the control task by stages, using first the most g eneral, later a more detailed information on task definition (Fig. 4). Data on the control task under implementation, flowing to the ATSS from the SRS, are therefore grouped into three levels according to their degree of detailedness: 1) lj; - input situation imag e - file of logical expressions of the type "p is given (known), where p is e.g. a set of U, X, Z, eventually Xo parameter values, limiting condition f and the like, without any more detailed information on the form of the sets and functions and on parameter values 2a) A - characteristic of the parts of p definition from the ~ image expresses the shape of the goal function, mode of U, X, Z set definition, form of other limiting conditions, etc. using the formula CHAB(go' U, X, Z, ... ) 2b)
3)
- conditions of activity of hierarchical system elements expressed through the formula CONDACT (NO, SO' Si)' giving the degree of autonomy of subsystem decision making
SS -
concrete values of parameters and of the control task.
constant~
The first-level data are used by the first stage of the ATSS to search for a suitable method of functional activity (mechanism) MFA i.e. method of the solution of control task m and of the mode of distribution of solufion elements within the hierarchical production system, called control strategy s • This outcome of the first AT SS level, complemented with the secondlevel data in the task, constitutes a socalled type model of functional activity of the control system which serves the second ATSS level as a source of information in looking for the sequence of operators lRiS and tF jJ. The application of operator sequence R. using the third-level data by the last ATSS block yields the solution of the control task which, together with the operator sequence £Fjl(the application of the latter will provide for the distribution of solution elements to the respective elements of the hierarchical system), is an o~tput from the ATSS - functional activity ~ instruction designated for the SIS.
mj,
The ATSS algorithm employs still another mode of classification of input situation images, i.e. according to specified characteristic features (predicate calculi in 0/
image, incidence of certain concrete predicate in 'f etc.). An analogical method is also used to classify the conditions for the applicability of functional activity methods. These conditions are represented by the list of assertions which need to be contained in the input situation image 'f if the g iven method is to be applicable for the solution of the control task. The task of the first ATSS level is to look in the set of functional activity methods for a method suitable for the given input situation f, i.e. which complies with feasability conditions at the given input situation image f5 and which can use all information contained in the input situation image. The algorithm contains elements of learning. Before it starts scanning the file of functional ac t ivity methods it verifies whether a similar input situation image has not already occured during the previous stages of control task solution. If the search yields a positive result, the method ascribed to the given image is retrieved from the file and the next step is the construction of the functional activity model. In the case of a negative result, the retrieval mechanism gradually narrows the set of functional activity methods down to a subset of identical-characteristics methods with characteristics of input information image and selects the suitable method out of this subset, using automatic theorem proving. The newly formed pair ( , , mq) is regi stered in the databank and the name of the method chosen is announced to the block in which the type model of functional activity is developed. The second AT SS level employs a similar mode of learning as the first one. If during the previous ATSS activities there has been a type model of functional activity which is identical with the model currently examined, the respective operator sequences tRiT , '\.F j~ are retrieved from the databank. If not, the type model of functional activity M~ is divided into two parts: image of metnod mr plus characteristics of the the task CHAR and image of strategy sr plus conditions of CONDACT activity. The first part of the model serves to .determine the operator sequence tRi!, the determination of which simultaneously yields the image ~ of the initial distribution of the results of control task solution within the hierarchical system which is a part of the initial model of functional control strategy ()~. The i 'c. " of the functional activity type model is used to build the target model of control strategy()+. The comparison be+ r tween \Ay and G'" r leads to the task of searching for the operator sequencetFjl,the application of which will result in the transformation of the initial model to the target one. The last step of the ATSS is the application of operator sequence lRiJ to the method of control mr using the third-level data on the control task. Its outcome is the concrete solution of the assigned task of control which, together with the operator sequence LF . ~,represents the AT SS outJ.>
J
l'Iic1l\' 1'1 Il l.
put submitted to the SIS. Supervisory Control System Two main problem areas (UlicnY, Thuan, Balaz and Drab, 198 J) are considered in our model of the control of the hierarchical production system under conditions of uncertainty: a) discrete adoption of solutions at the planning stage, b) continuous control of production system at the plan i mplementation stag e. This structure of the control system is reflected also in the structure of the information-control complex. The decision making responsibility at the planning stag e rests with the ATSS. Other components of the ICC operate in real time and provide for the implementation of solution, supervisory and inspection functions. The ICC task is to ensure the feed back within the ICC and communication with the operator - i.e. per son connected with the ICC by means of a dialogue endowed with the autority and possibility of influenc i ng the I CC operation. The SCS is activated in two alternative ways: a) by the operator - person - in the event of malfunctioning of the ICC or if inclusion or exclusion of certain system function is required, b) through the change in external situation. We shall not as yet deal with the former possibility, as its implementation largely depends on the specific ICC implementation. If there has been a change in the external situation, it must be analyzed by the SCS and - in the event of a so-called emergency situation - directly handled through the inclusion of the emergency program for processing. In the non-emergency situation it activates the AT SS which chooses a suitable functional activity method and submits it to the SIS. The supervisory control system thus fulfils three elementary functions: a) communication with the operator, b) control in emergency situations, c) supervision of operator sequence performance. Solution Implementation System The solution implementation system is a program system closely interconnected with the ATSS, SRS and SCS. The SIS is activated in two ways: - by the automatic task solution system if the latter reached a certain solution, - by the supervisory control system if the need has arisen for implementing alternative solutions as a result, e.g., of unexpected or emergency situations. For supervision reasons, the system of solution implementation must inform the supervisory control system on its activities. In the process of implementation of the solution having been generated by the ATSS system, an account must be taken of failures which might prevent solution implementation. As a result, the SIS must inform the ses on such possibilities and the latter either coordinates the computation or works out alternative solutions itself. The main task of the SIS is to implement solutions obtained by the ATSS. Information provided to the SIS from the ATSS is twofold - sequence of operators securing con-
trol strategy and control methods. If we assume that the controlled system has a two-level hierarchical structure and consists of a higher control system - centre and of control subsystems of a lower level and of the controlled process, it will become evident that the IF . ~ operators will have to secure the distribution of solution results both in time and space of the controlled system. In other words, the results must reach the ri ght place at the right time. The Fi g . 1 sugg ests that the pro g ram block of SIS is placed between the external environment, i.e. controlled system and the SCS and ATSS systems. In addition to the communication between the ATSS and ses it thus must also secure the communication with the external environment consisting in the ou~ put of data to the facilities of the external environment, •• e. with production. This means that information must also flow in the opposite direction, i.e. from the external environment to the SIS. It is likely that the input-output operation as well as information on the state of the facility before or a f ter the operation w' l l b e I ndirect, i.e. performed through th ~ operational system of the computer verifying the justification of the input-output operation through the facility owner, etc. and having at its disposal the program unit controlling the respective facility. Thus, the interconnection to the computer operating system in this respect is very tight. Requirements for the SIS can be summarized as follows: - communication with other prog rams - knowledge of the interpretation of operators of control strategy and control method - different possibilities of program starting - ability of communication with the external e~vironment. The fulfilme.t of the above requirements calls for a very close cooperation with the operating system of the computer and the SIS must be therefore prog rammed in the combination of higher and lower prog ramming languages. The higher programming language will be used to program global organizational al gorithmus and the lower one, e. g . the language of symbolic address will be used to write certain frequencly repeated al goritms and some subprograms calling special parts of the operating system which will be oriented to the cooperating higher prog ramming language. ILLUSTRATION
OF
AT SS
SIMULATION
The simulation of the ATSS activity within the ICe system on the digital computer in the solution of tasks of the control of production system operating under conditions of uncertainty is described below. Let us c.asider a hierarchical production system consisting of the centre So and subsystems S. (i = 1,2, .•• , N). Let us assume that lthe functions of effectiveness of operation of the centre and of the subsystems are known, assigned e.g. by superior bodies of the system. The goal function of the centre can be written as follows:
,j ~ J(J
ThL' .-\utolllatic Task Solutioll
where P(~,Z'~) is the production function of the system and GO is the function of the effectiveness of system operation. Let us assume that the production fuction of the system is a vector function of production functions of the subsystems, i.e. that: P = f(P l , P 2 , ••• ,P N) • Let the variables of function GO be: ~ E: U ~ = (u l ' Z E.X Z = (Xl' 2 E: ~ = (z\ ' ~ N 'Vx . X xi ~ Xi ,L..., l. i=l N 2i 2 zi E: 2.l. i=l
6
...
,
u. , ) I' XN) zN)
i = 1, ••• ,N
i = 1, .•• ,N
where U and X sets represent the mutually admissible area of solution of the centre and the subsystems. The goal function of the subsystem can be written as follows: gi(ui,xi,zi) = Gi(ui,xi,zi'P i ) where Gi is the function of the effectiveness of subsystem operation. Let us also assume that the system operates within a non-stationary environment. The influence of the environment of the hierarchical production system in our understanding denotes the influence of other systems S on the system S under examination and we assume that that both the Sand S have a common superior body. The environment of the hierarchical production system thus conceiv~d is of great importance in our concept1.on of the ICe, as the Z,(ZE 2) variable represents an indefinite-factor for our system S. Under the assumption that the system operates within a non-stationary environment we may deduce that the characteristics of this environment change from time to time. These changes then force the centre to revise its decision and thus to maintain the activity of the system close to the optimum. Consequently, we divide the functional activity of the hierarchical production system into periods a time interval T. Let ~ be th~ serial number of the period, then the t period of system operation will be given as follows: n'l;"= tt: t6{Tt/t+ l ) ••
TJ~t=t,2,
The control task is to make the hierarchical production system reach the optimum result, expressed through the value of the goal function of the centre gO(~'Z'~)' The mechanism (method) of the functional activity of the control system of a hierarchical production system based on the allocation of resources Ut' u 2 ' ••• , UN by the centre So to the subsystems Sl' S2' ""SN and on the selection of the values of resources XI' x ' ""xN by the subsystems themselves. 2 The result of the centre und thus of the system as a whole dependes on the selection of Xl "",xN values by the subsystems SI' ""~T and on information available to the centr~ So on the functional activity of the
subsystems (e.g. on what information the centre has on the models of subsystems control, whether it knows their decision-making rules gr whether the subsystems know one another s decision-making rules, eventually whether the subsystems know the decision-making model of the centre, etc.). From the aspect of optimality principle of g reat importance is also the question of priorities in decision-making and mutual information on solutions concerning individual elements of hierarchical production systems (if there is such information at all). Not less important is the question of information of hierarchical production system elements on the uncertainty factor after the adoption of the solution. The functioning of the system in the acquisition, processing and utilization of information in production process control will be examined in the following stages: a ) stage of data generation b) planning stage c) stag e of plan implementation. The first stage is characterized by the collection of information serving as background data for the adoption of solutions at the planning stage for the L:' period. The decisions are then implemented by the system at the stage of plan implementation which coincides in time with the time interval of the future period ~. The task of the hierarchical production system at the planning stage is to determine the solutions, i.e. to choose the values of variables u., i = 1, .•• ,N under conditions of uncertainty, before even the ~period of system operation. The task of the centre is solved by the ATSS. For sake of simplicity we shall assume a hierarchical system consisting of the centre So and two subsystems SI and S2' Let the goal functions of the centre and the subsystern~ be determined as follows: 2 I /2 ~2 1/2 2 gO(~'Z'~)= Cl diU 1.. x·z. 1. 1. - c 2 ( d 1.. u.l. x 1.. -P) i=1 i=l
2::
1/2 2 mix i , i = 1,2. gi (ut' Xi ' Zi ) = cdiu i xiz i 10 4 , c~ = 4, 10 4 , Cl = 3 Let: c = 2,4 10 , d 1= 0,7, d 2 = 0,9, ml = 1,2 10 4 ; m2 = 10 4 , P = 6 U = t(u\,u 2 ) : Ofu l{,5.104, 0!:-u 2'= 5 ,5. 104 , u 1+u 2 = 8 .10 4} X = l(x l ,x2 ) : 0f:xl~3.l 04 , OfX 2 ,=4.10 4}
.
.
2 = [ (Zl'Z2): l'-zl!. 2,
lfX 2 !,2j
Let us assume that the system operates within the period 'L -1 and the ATSS plans the control for the period~, i.e. it selects the value and the mode of allocation of an exogenous resource ~ to the subsystems SI and S2 so as to achieve the maximum of goal functIon gO(~,xlz), The ATSS solves this problem using artificial intelligence methods. Let the centre (and the ATSS as its representative) have the following informations on the situation in the hierarchical production system: - it knows the set 4r0f the uncertain factor;
J
tillt)
l ' li,1I\
- it knows the set Utof the exogenous resource; - it knows the goal function of the centre go(~'1£'~)
0 · - it knows the so 1 u t ~ons x 10 ,x?, 2 2 10 ,
x~=2,44
•
d
"I.
The situation recognition system supplies information of the type CHAR(gO'U,X,Z) and CONDACT(NO,SO,Si)' i.e. information on the characteristics of the goal function gO(~'
1£,~)1
lx=x
10 ).
The set of this informations represents the input information ~( ~ 1 the image of which is recorded by means of the predicates as follows: if(Zl = lEESETZ (Z:;), BESETU (U c ), BECRITERIONSO (eO)' BEVALUEX (xO)l In adopting the solution the ATSS works with the input situation image. It searchsthrough the databank to determine whether an identical input situation image has occured already during the previous stages. Let us assume that the given input situation image has not yet existed in the previous periods. The next step is to determine two characteris~ic symbolSYl et') and "f 2(1:) of the image 'f n"): ~1 (L) - characteristic symbol determining the predicate calculus number ~2(~) - characteristic symbol determining the list of different predicates of the ima~e if Ct') wi th respect to the image ~(T-l) i.e. the image of the preceding period. In our case there is 0('1 ('Cl = 4 and let y 2('t) =£BEVALUEXJ. In the respective databank the search is initiated for such method of functional activity (MFA) m2 the respective image of feasibility condi~ions of which p p (m~) has the predicate calculus equal to~~ and contains predicates from the list 11 2 (1;'). In ou~ cases these conditions are met by the MFA mf selected for confirmation. Feasibility conditions form the following theorem: PP(mi) (3~)BESETU (2:!l.J\ (3 g )BECRITEli.IONSO( g ).\ J\ 8~)BESETZ(~)!\ (:';1£1 )BEVALUEX(1£l) ,,-,PP(mi) : (.v~)(~g)(I/~)(lf1£l )~BESETU (~)V' V~BECRITERIONSO(g)V rvBESETZ( z)1I VrvBEVALUEX(Zl )J. Another task is to confirm the satisfiabi2 conditions with respect to lity of PF(m{) f(Y); the p . oof is performed using the resolution method,-1.e. proof of the non-satisfiability of pp with respect to axioms ~(tJ. The application of the resolution method to the following clauses: BESETZ(Z·rl BESETU (U'cl BECRITERIONSO(gO) BEVALUEX(1£O)
~pp(:ni): ....... BESETU(~)v ~BECRITERIONSO(g)v v,,-BESETZ(~) V~BEVALUEX(
x' )
yields an empty set - the clause. It means that the ch~sen method of functional activity m = m • Then follows the mechanism of lookin£ up the respective image of this method in the databank, and the MFA mf image is as follows:
0
and oa the activity of system elements. Let this information in our example be as follows: 0 - goal function g (u,x,z) for x=x is nonlinear with resBect-to the variable ~ and linear with respect to z - U area is defined with linear non-equations with nspect to ~ - Z area is defined with linear non-equations with respect to z. The following list-of clauses results: )1= CHAli.(gO'U,X,Z) = : {
NOTLlNEARF(gox, (ul ' u 2 ))} LlNEARF (gOX,(zl,z2)) LINEARG (U r ,(u 1 ,u 2 )) LINEARG
( Zt' (z 1 ' z 2) )
The type functional model of control is determined with the MFA, characteristics CHAR and conditions of activity CONDACT, Le.:
Mf(C)'{ ~~~:;~¥: ~:~~:: Si)) In our specific case:
",
OPTIMAL( (SO), (max,min), (U-r' Z'!:'), (u, , u 2 ,\ \ zl,z2),(gOx)) \
o
MC
0
0
AT(u 1 ,SO) AT(u 2 ,SO) AT(u, ,SI) NOTLINEARF (gox' (u 1 ' u 2 ) LINEARF(gOx,(z l ,z2) LlNEARG(U t , (u! ,u 2 ) LINEARG(Zt,(zl,z2)
0
;·
AT(u2,S2~ !
! I
In this specific case ste CONDACT conditions are empty. The clauses No. 1,3,4,5,6 are connected with the control method, clause No.2 and eventual clauses CONDACT are connected with the control strategy. The solution of the control task continues with the search for operator sequence R. which is capable of implementing the cont~ol method expressed through the formula: OPTIMAL«SO),(max,min),(UC,Z L)' (u 1 ,u 2 ,zl ,z2)' (gOx) under conditions CHAR. This type of m~ti pIe optimization can be broken down to two subtasks: a) OPTIMAL( (SO) , (min) , (Z'(") , (z 1 ' z 2) , ) -Ox) ) b) OPTIMAL ( (SO), (max), (Ut')' (u 1 ' u 2 ), (gox») The theorem proving method will be used to prove the satisfiability of the conditions of operator feasibility + SIMPL ( ( So ) , (min) , (ZrJ , (z, , z 2 ) , (g Ox) ) for the task a) and satisfiability of the conditions of feasibility for the operator ++
FEASIBL«SO),(max),(U~),(u1,u2),(gOx)
for the task b). Thus, R = + and R = ++ and the scheme of initiai distributfon of the future results of activities of opera-
lilll
RI and RL : o 0 0 VR = AT(z l ,SO) f\ AT(z2'SO) 1\ AT(u j ,SO)A 1 t\ AT(U ,SO) . 2 Now it is necessary to build ()~-thc initial cud.l ef the ."nt.ol strategy and
-
j
AT(Z~1
'so)l
G"~('t'): AT( Z:2' So)
AT(ul,SO ) Q
i,AT( u 2 , So). I
:i"'AT( u~ ,S OH' "" AT( u~, So \1'1 o . 0 \ "-AT(u l ,SI )\I"vAT(u 2 ,S2 .J The task of the search for operators for the strategy of control is transformed to the task of the search for operators {F~ for the fulfilment of the target modet '0 ;('\,;). We shall use the following operator scheme INF (A,k,B) - object "A" announces the parameter "k" for the object " B": - feasibility conditions PFi = AT(k,A) result of operator activlty - list of formul~ for elimination - list of formulae for inclusion AT(k,B).
r-.();Cn
I
CONCLUSION ~n conformity with the world-wide trend we e dvocate the suitability of ICC implementation for the control of distributed systems with hierarchical structure. We assume that individual subsystems of a distributed system have the attributes of active elementes and that in the decision-making process exists the priority of the centre in task solution. We point to a new formal approach towards the solution of the control task using elemnts of artificial intelli gence and to the appropriateness of the ICC supervision through the dialogue s~stem VSGA primarily in those cases when the lntervention of the active control element - the man - appears to be inevitable. The proposed heuristic mode of automatic selection of the method of functional act i vity of control system through the ATSS was simulated on the di gi tal computer EC 102 1 in the language LIS? :.5. Ne see the contribution especially in the fact that the ATSS system, as compared to the STRIPS system, reduces the initial information obtained from the environment in the direction of their processing and application for the needs of automatic solution of control tasks. To this end a system has been devised. The ATSS operates within the functional space of the nistributed system where it has to deal with the solution of functional tasks of multiple optimization and of conflicting relationships between active elements of the hierarchical production system.
The outc.,me of the above procedure is:
~I
:AT(zl ,SO)~
• 0 \AT(z'2'SO)~ T ;; +(tl=t (J 1 ,So)"
r
,
f. C~
[1 ;MEE: t--l
rT(U'2 'SO)~ IAT ( U"I,SI )~
l~T(J2,S2)" i
1 jS
The sequence of operators [R i! and F is submitted to the SIS and SCS where the concrete values are determined of the variables ul,uazl'z2' The calculation of lRh is made with the use of simplex method, that of R with the use of the feasible direction~ method. The application of the operator means in practice that a program is worked out which is allocated to the operator. After obtaining specific parameters and calling of respective programs, the following values had been received: z o1 -_ !,. z20 -_ I,. u 01 -_ 2, 9 1.10 4.,u 02 = 5 , 09 • . 10 4 2 for Xlo = 1,19.10 2 and x 20 = 2,44.10.
With these values the hierarchical productions system attains the effectiveness of g~ = 1,656.10 9 The calculated u~ and u~ values are then applied by the SIS and g~ proceeds to the SCS.
SRS - Situation Recognition System IMEE- Internal Model of External Environ ment AT SS- Automatic Task Solution System SCS - Supervisory Control System SIS - Solution Implementation System Fig. 1 - The principle scheme of the Information - Control Complex
J.
L1iclI\ 1'1 Ill.
--------,
SRS
.-------l :
L -_ _ _ _~~--~
-----,
I I
I
I I I I
I
I
I I
~
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ J1
HPS - Hierarchical production system So - The centre of HPS Si - The subsystem of HPS go ••• gN - the goal functions of the centre and the subsystems u i - the value of the centre source given to the subsystem S. the value of the su~system own source uncertain factor superior organ Fig. 2 - Hierarchical production system acting under conditions of uncertainty
r-------------------l 1
1
I I I
1~
control system
I
1
1
V
'-------_~
I
intellectual system
I
I
I _________________ I L ~
I -
information
1/1- task solution
'f-
information transformed to the first order logic
Fig. 3 - The cybernetics dismembering of the ICC
Ir~----·+L-----, 1
I
I I
I
~
Cl!
(IJ
~ '8 r:.c
~~
g >.
;! +>
H·... (IJ .....
~
G>O+>
I .~ f - I ~M I ..; ~ I ~
I
E
II
0. 0
~
The choice of the sui table functional activity method
I
I
I
i!
I : I I. I I I ~tagel : :
A~SS I I I
I! !
t~'
The creation of the - I I functional activity ~-~--1-J type model
I
I
1
I I
Hf
The looking for 11. 1 the operator succes- stagel sions I
1\Rd,~F.t1
application {'Po} 'J
I
I I 1 I f----r-..J Z
Y
L------h·-----J SIS Fig. 4 - The simplified scheme of the ATSS activity
REFERENCES Ernst,G.W. and Newell,A.(1969).GPS A Case Study in Generality and Problem Solving. Academic Press, Neww York and London. Fikes,R.E. and N.J.Nilson (1971). A new approach to the application of the theorem proving to the problem solving. In Proc.2nd Intern.Conf. on Artificial Intelligence, London. Mesarovic,M.D., D.Macko and Y.Takahara (1971). Theory of Hierarchical Multilevel Systems. Academ~c Press, New York and London. Uli~nY,J.(1978).VYznam simulacie a modelovania ~innosti hierarchickeho systemu v riadeni zlozitych systemov.lnforma~ne systemy,No.6. Uli~nY,J. and Drab,L. (1982) Adaptive method of strategy control synthesis of subsystems in hierarchical systems. In Proc. of the 4th FORMATOR S~posium on Mathematical Methods for Analys~s of Large-Scale Systems.Liblice near Prag. Uli~nY,J.,Thuan,N.T.,J.Balaz and Drab L.(1983). Automatic solutions projecting of controlling complex in automated control systems. In Proc. of the rd IFAC IFORS S osium Lar e-Scareand Appl~cat~ons.
THE AUTOMATIC TASK SOLUTION IN AN INFORMATION-CONTROL COMPLEX OF A DISTRIBUTED SYSTEM J.
Ulicny, O. Moravcik, Z. Knilova, L. Poljakova and L. Drab I: i({/!l1 1// I: 'I/.!...'/')!('( I/')!.!.!' l
(101/1r.
S /o; '11l /'n/III/I'I// { ',I/', ', '/ 1/11 . If 1111/ 1/11t '11.
( ,':('(//01/(1 ; 'Id,'/tl
ABSTRACT The article deals with the structure and mode of operation of an information-control complex of a system with fully automatized acquisition, processing and utilization of information on problem environment. In this information-control complex the internal model of problem environment within which the system operates is described in the first-order lo gi c. Methods of automatic theorem proving representing knowledge on the f orms and ways of the solution of control problems of a distributed system with hierarchical structure are used in the solution of the tasks of inf ormation-control complex. The simulation of one subsystem is illustrated in the conclusion, g iving more detailed explications as the mode of operation typical for the complex as a whole. Keywords. Information-control complex; situation recognition system; automatic task solution system; supervis ~ry control system; solution implementation system; knowledg e representation, input situation; twolewel hierarchical structure production system.
INTRODUCTOhY
P~MARKS
Forei gn forecasts of the development of control compu t ers and their applications suggest that by the end of the present century they will be most extensively used in the so-called expert systems processing human knowledge and using it to solve tasks of different nature. Consequently, problems involved in the automation of the solution of control tasks on the basis of representation of knowledge and experience accumulated during i ndivi du al control of distributed systems (u l j cr~ and Drab , 1982 ; U li~ nj,Thuan,Balaz and Dra b , 1983 ). Attempts at the automation of intellectual activity in the solution of different types of tasks are not recent. In the past they involved primarily computer-aided design of control systems. The main drawback of such attempt s was their low sensi bil ity and adaptability to changes in their environment and their intrinsic characteristics. They were represented especially by the socalled interpretation systems which had the character of "program control systems". The control of a distributed system by means of a control computer dependes, as it is known, first of all on the information availability to the sub j ect controlling the operation of the the system as a whole.lnformation available to the subject building computer programs chang es a~ a function of chang es in the impact of t he environment on the controlled system and chang es in the contrOl-system structure. An attempt at the automation of sUbject's activity connected with the construction of programs for control computers in rela-
tion to above changes is the main theme of our study. The information-control complex (ICC) of a distributed system denotes a whole complex of systems which carry out the control of a di stributed system in conformity with the given c ontrol objective depending on changes in the impact of the environment on the controlled system (Fig.1). The advantages of the proposed I CC of a distributed system consist, as compared to the existing and comparable systems, in its a bi lity to respond more flexibly not only to chang es in the values of environment paramete r s (such chang es do not usual:~ call fo r the modification of the selec: ed cutl trol program, but only for the modification of input data for this program) but also to chang es in the overall character of the environment whi ch - i n distributed production system - may involve e. g . exceptional and emergency situations, change s in the plan, economy measures concerning material and energy savings, etc. The proposed system can also change the control rule on the basis of changes having previously affected the system and thus also the control system structure in the case that the previously adopted measures had not been sufficiently efficient. We shall consider a distributed system represented by a control system with two-lewel hierarchical structure and a controlled system represented by the process of production (Fig. 2) . The control system cons~s~s of the centre So.and subsystems S. (l. - 1, 2, .•. , N) wnl.ch have a relat!ve decision-making authority in the sense of (Mesarovic, Macko and Takahara, 1970;, Uli~ny and Drab , 1982 ; Uli~nj, Thuan, Balaz and Drab, 1963) .
J L'iiclI\ The implementation of knowledge representation results in a sUbstantial improvement of the control-task solving system. FUNCTIONAL ACTIVITY OF THE OF A DISTRIBUTED SYSTEM
ICC
From the cybernetic point of view, the ICC consists of the following systems (Fig. 3): a) intellectual system b) sensory system c) control system Information flows between individual ICC systems are evident from Fig. 1. The task of the situation recognition system of input information, changes in the parameters of internal structure of both the control and the controlled systems affecting the selection of the method for control-task solution and implementation of this solution. Input situations ~ are generated in the system as sets of assertions characterizing the situation at the system input at any given point in time. Each input situation is transformed into the language of the first-order predicate calculus and the input situation image ~ is thus generated , representing one of the inputs to the automatic task solution system (ATSS). The ATSS assigns an appropriate method of control task solution to the input situation image and using other i nformation concerning the task determines its solution and mode of distribution of solution elements among the elements of the hierar chical system. The role of the solution implementation system (SIS) is to transform the solution of the task and its distribution into physical variables ~ affecting directly the process of production. If the ATSS is designated as the ICC of a distributed system, the supervisory control system (SCS) will represent a body superior to all the ICC systems. At the planning stage, i.e. during the decision~ma king process, a so-called expected result is determined. The achievement of this result is supervised by the SCS during the plan (solution) implementation stage, i. ~ . at the period of control exertion. Deviations from the expected result can generally occur as a result of changes to the input situation having taken place during the plan implementation stag e . In such case, a modification of the solution is expected from the ATSS. If the SCS does not receive the modification of the solution from the AT SS in time, it addresses directly the coordinator by means of the question-answering dialog system (DSQA). The SCS also handles emergency situations. By means of the DSQA the coordinator has the possibility of controlling the SCS and thus the distributed system as a whole. The SCS is incorporated as a feedback member using information on output variables of the process, input situations and information from other systems of the distributed system, i.e. SRS, ATSS and SIS.
1'1 Id.
Thuan, Balaz and Drab, 198 3): fcC'): 0(1 0 ' 1 1 , 1 2 , 1 , I 4 ;'t") 3
( 1)
Individual components of the input situation represent the influence of the environment on the system, information availability to the centre concerning the functional activity of the subsystem, interactions between the subsystemsat the same level of the hierarchical structure of system control, etc. The situation recognition system (SRS) represents the i nput part of the lee which is interconnected to the controlled process and which g enerates the image of input situation ~ for the AT SS and/or ses needs. The SRS provides for the following main functions: a) acquisition of input inf ormation on the tasks and possibilities of the hierarchical production system assigned by the superior body (10)' on the influence of the outside environment on the hierarchical produc tion system (1 1 ), on internal influences within the hierarchical production system (I ), on information concerning the functional activity of S . subsystems available to the centre ~of hie r a r chical production system So (1 ) and on interactions between and 3 information availability of subsystems at one and the same level of the hierarchical system of pro duction (1 ) 4 b) generation of information 1 0 to 14 and of macro information to the data according to their significance and necessity for individual lee systems and the generation of the orig inal of input situation c) g ener ation of input situation images according to defined criteria d) comparison of input situation images to hypothetical input situation images e) ensuring a two-mode operation of the SRS for the planning stage and for the plan i mplement at i on stag e f) identification of extraord i nary situations within the controlled system g) building of informations for databank. The SRS also performs autonomous supervisory activity and is able to respond to external supervisory instructions from the SeS.The focus in the SRS is on mastering the functional activity of the distributed control system under conditions of uncertainty. The declarative form of the representation of knowledge concerning the functional activity of a distributed system controls the inflow of information for decision making process within the ATSS. Such information larg ely determines a correct functioning of the whole information-control complex of the distributed system. Automatic Task Solution System
Situation Recognition System Hereafter, the term of input situation will denote an ordered set of information at the input to the system within a given control period (Uli~nY and Drab, 1982; Uli~nY,
The complexity of the solution of a control task at the level of a centre of a hierarchical production systems is generally entailed by the score of possible task definitions. The control task fulfilment is
ultimately reduced to the application of a certain sequence of operators (standard procedures) with the given values of parameters and constants. The development of such sequences for all possible combinations of the modes of the definition of U, X, Z sets expressing the allowed space of control, shapes of goal functions and limiting conditions as well as the activity of system elements, storage of these sequences in the memory of the control computer and their scanning at each instance of changing character of task definition, these are apparently not suitable ways of the solution of the pro blem. The ATSS solves the control task by stages, using first the most g eneral, later a more detailed information on task definition (Fig. 4). Data on the control task under implementation, flowing to the ATSS from the SRS, are therefore grouped into three levels according to their degree of detailedness: 1) lj; - input situation imag e - file of logical expressions of the type "p is given (known), where p is e.g. a set of U, X, Z, eventually Xo parameter values, limiting condition f and the like, without any more detailed information on the form of the sets and functions and on parameter values 2a) A - characteristic of the parts of p definition from the ~ image expresses the shape of the goal function, mode of U, X, Z set definition, form of other limiting conditions, etc. using the formula CHAB(go' U, X, Z, ... ) 2b)
3)
- conditions of activity of hierarchical system elements expressed through the formula CONDACT (NO, SO' Si)' giving the degree of autonomy of subsystem decision making
SS -
concrete values of parameters and of the control task.
constant~
The first-level data are used by the first stage of the ATSS to search for a suitable method of functional activity (mechanism) MFA i.e. method of the solution of control task m and of the mode of distribution of solufion elements within the hierarchical production system, called control strategy s • This outcome of the first AT SS level, complemented with the secondlevel data in the task, constitutes a socalled type model of functional activity of the control system which serves the second ATSS level as a source of information in looking for the sequence of operators lRiS and tF jJ. The application of operator sequence R. using the third-level data by the last ATSS block yields the solution of the control task which, together with the operator sequence £Fjl(the application of the latter will provide for the distribution of solution elements to the respective elements of the hierarchical system), is an o~tput from the ATSS - functional activity ~ instruction designated for the SIS.
mj,
The ATSS algorithm employs still another mode of classification of input situation images, i.e. according to specified characteristic features (predicate calculi in 0/
image, incidence of certain concrete predicate in 'f etc.). An analogical method is also used to classify the conditions for the applicability of functional activity methods. These conditions are represented by the list of assertions which need to be contained in the input situation image 'f if the g iven method is to be applicable for the solution of the control task. The task of the first ATSS level is to look in the set of functional activity methods for a method suitable for the given input situation f, i.e. which complies with feasability conditions at the given input situation image f5 and which can use all information contained in the input situation image. The algorithm contains elements of learning. Before it starts scanning the file of functional ac t ivity methods it verifies whether a similar input situation image has not already occured during the previous stages of control task solution. If the search yields a positive result, the method ascribed to the given image is retrieved from the file and the next step is the construction of the functional activity model. In the case of a negative result, the retrieval mechanism gradually narrows the set of functional activity methods down to a subset of identical-characteristics methods with characteristics of input information image and selects the suitable method out of this subset, using automatic theorem proving. The newly formed pair ( , , mq) is regi stered in the databank and the name of the method chosen is announced to the block in which the type model of functional activity is developed. The second AT SS level employs a similar mode of learning as the first one. If during the previous ATSS activities there has been a type model of functional activity which is identical with the model currently examined, the respective operator sequences tRiT , '\.F j~ are retrieved from the databank. If not, the type model of functional activity M~ is divided into two parts: image of metnod mr plus characteristics of the the task CHAR and image of strategy sr plus conditions of CONDACT activity. The first part of the model serves to .determine the operator sequence tRi!, the determination of which simultaneously yields the image ~ of the initial distribution of the results of control task solution within the hierarchical system which is a part of the initial model of functional control strategy ()~. The i 'c. " of the functional activity type model is used to build the target model of control strategy()+. The comparison be+ r tween \Ay and G'" r leads to the task of searching for the operator sequencetFjl,the application of which will result in the transformation of the initial model to the target one. The last step of the ATSS is the application of operator sequence lRiJ to the method of control mr using the third-level data on the control task. Its outcome is the concrete solution of the assigned task of control which, together with the operator sequence LF . ~,represents the AT SS outJ.>
J
l'Iic1l\' 1'1 Il l.
put submitted to the SIS. Supervisory Control System Two main problem areas (UlicnY, Thuan, Balaz and Drab, 198 J) are considered in our model of the control of the hierarchical production system under conditions of uncertainty: a) discrete adoption of solutions at the planning stage, b) continuous control of production system at the plan i mplementation stag e. This structure of the control system is reflected also in the structure of the information-control complex. The decision making responsibility at the planning stag e rests with the ATSS. Other components of the ICC operate in real time and provide for the implementation of solution, supervisory and inspection functions. The ICC task is to ensure the feed back within the ICC and communication with the operator - i.e. per son connected with the ICC by means of a dialogue endowed with the autority and possibility of influenc i ng the I CC operation. The SCS is activated in two alternative ways: a) by the operator - person - in the event of malfunctioning of the ICC or if inclusion or exclusion of certain system function is required, b) through the change in external situation. We shall not as yet deal with the former possibility, as its implementation largely depends on the specific ICC implementation. If there has been a change in the external situation, it must be analyzed by the SCS and - in the event of a so-called emergency situation - directly handled through the inclusion of the emergency program for processing. In the non-emergency situation it activates the AT SS which chooses a suitable functional activity method and submits it to the SIS. The supervisory control system thus fulfils three elementary functions: a) communication with the operator, b) control in emergency situations, c) supervision of operator sequence performance. Solution Implementation System The solution implementation system is a program system closely interconnected with the ATSS, SRS and SCS. The SIS is activated in two ways: - by the automatic task solution system if the latter reached a certain solution, - by the supervisory control system if the need has arisen for implementing alternative solutions as a result, e.g., of unexpected or emergency situations. For supervision reasons, the system of solution implementation must inform the supervisory control system on its activities. In the process of implementation of the solution having been generated by the ATSS system, an account must be taken of failures which might prevent solution implementation. As a result, the SIS must inform the ses on such possibilities and the latter either coordinates the computation or works out alternative solutions itself. The main task of the SIS is to implement solutions obtained by the ATSS. Information provided to the SIS from the ATSS is twofold - sequence of operators securing con-
trol strategy and control methods. If we assume that the controlled system has a two-level hierarchical structure and consists of a higher control system - centre and of control subsystems of a lower level and of the controlled process, it will become evident that the IF . ~ operators will have to secure the distribution of solution results both in time and space of the controlled system. In other words, the results must reach the ri ght place at the right time. The Fi g . 1 sugg ests that the pro g ram block of SIS is placed between the external environment, i.e. controlled system and the SCS and ATSS systems. In addition to the communication between the ATSS and ses it thus must also secure the communication with the external environment consisting in the ou~ put of data to the facilities of the external environment, •• e. with production. This means that information must also flow in the opposite direction, i.e. from the external environment to the SIS. It is likely that the input-output operation as well as information on the state of the facility before or a f ter the operation w' l l b e I ndirect, i.e. performed through th ~ operational system of the computer verifying the justification of the input-output operation through the facility owner, etc. and having at its disposal the program unit controlling the respective facility. Thus, the interconnection to the computer operating system in this respect is very tight. Requirements for the SIS can be summarized as follows: - communication with other prog rams - knowledge of the interpretation of operators of control strategy and control method - different possibilities of program starting - ability of communication with the external e~vironment. The fulfilme.t of the above requirements calls for a very close cooperation with the operating system of the computer and the SIS must be therefore prog rammed in the combination of higher and lower prog ramming languages. The higher programming language will be used to program global organizational al gorithmus and the lower one, e. g . the language of symbolic address will be used to write certain frequencly repeated al goritms and some subprograms calling special parts of the operating system which will be oriented to the cooperating higher prog ramming language. ILLUSTRATION
OF
AT SS
SIMULATION
The simulation of the ATSS activity within the ICe system on the digital computer in the solution of tasks of the control of production system operating under conditions of uncertainty is described below. Let us c.asider a hierarchical production system consisting of the centre So and subsystems S. (i = 1,2, .•• , N). Let us assume that lthe functions of effectiveness of operation of the centre and of the subsystems are known, assigned e.g. by superior bodies of the system. The goal function of the centre can be written as follows:
,j ~ J(J
ThL' .-\utolllatic Task Solutioll
where P(~,Z'~) is the production function of the system and GO is the function of the effectiveness of system operation. Let us assume that the production fuction of the system is a vector function of production functions of the subsystems, i.e. that: P = f(P l , P 2 , ••• ,P N) • Let the variables of function GO be: ~ E: U ~ = (u l ' Z E.X Z = (Xl' 2 E: ~ = (z\ ' ~ N 'Vx . X xi ~ Xi ,L..., l. i=l N 2i 2 zi E: 2.l. i=l
6
...
,
u. , ) I' XN) zN)
i = 1, ••• ,N
i = 1, .•• ,N
where U and X sets represent the mutually admissible area of solution of the centre and the subsystems. The goal function of the subsystem can be written as follows: gi(ui,xi,zi) = Gi(ui,xi,zi'P i ) where Gi is the function of the effectiveness of subsystem operation. Let us also assume that the system operates within a non-stationary environment. The influence of the environment of the hierarchical production system in our understanding denotes the influence of other systems S on the system S under examination and we assume that that both the Sand S have a common superior body. The environment of the hierarchical production system thus conceiv~d is of great importance in our concept1.on of the ICe, as the Z,(ZE 2) variable represents an indefinite-factor for our system S. Under the assumption that the system operates within a non-stationary environment we may deduce that the characteristics of this environment change from time to time. These changes then force the centre to revise its decision and thus to maintain the activity of the system close to the optimum. Consequently, we divide the functional activity of the hierarchical production system into periods a time interval T. Let ~ be th~ serial number of the period, then the t period of system operation will be given as follows: n'l;"= tt: t6{Tt/t+ l ) ••
TJ~t=t,2,
The control task is to make the hierarchical production system reach the optimum result, expressed through the value of the goal function of the centre gO(~'Z'~)' The mechanism (method) of the functional activity of the control system of a hierarchical production system based on the allocation of resources Ut' u 2 ' ••• , UN by the centre So to the subsystems Sl' S2' ""SN and on the selection of the values of resources XI' x ' ""xN by the subsystems themselves. 2 The result of the centre und thus of the system as a whole dependes on the selection of Xl "",xN values by the subsystems SI' ""~T and on information available to the centr~ So on the functional activity of the
subsystems (e.g. on what information the centre has on the models of subsystems control, whether it knows their decision-making rules gr whether the subsystems know one another s decision-making rules, eventually whether the subsystems know the decision-making model of the centre, etc.). From the aspect of optimality principle of g reat importance is also the question of priorities in decision-making and mutual information on solutions concerning individual elements of hierarchical production systems (if there is such information at all). Not less important is the question of information of hierarchical production system elements on the uncertainty factor after the adoption of the solution. The functioning of the system in the acquisition, processing and utilization of information in production process control will be examined in the following stages: a ) stage of data generation b) planning stage c) stag e of plan implementation. The first stage is characterized by the collection of information serving as background data for the adoption of solutions at the planning stage for the L:' period. The decisions are then implemented by the system at the stage of plan implementation which coincides in time with the time interval of the future period ~. The task of the hierarchical production system at the planning stage is to determine the solutions, i.e. to choose the values of variables u., i = 1, .•• ,N under conditions of uncertainty, before even the ~period of system operation. The task of the centre is solved by the ATSS. For sake of simplicity we shall assume a hierarchical system consisting of the centre So and two subsystems SI and S2' Let the goal functions of the centre and the subsystern~ be determined as follows: 2 I /2 ~2 1/2 2 gO(~'Z'~)= Cl diU 1.. x·z. 1. 1. - c 2 ( d 1.. u.l. x 1.. -P) i=1 i=l
2::
1/2 2 mix i , i = 1,2. gi (ut' Xi ' Zi ) = cdiu i xiz i 10 4 , c~ = 4, 10 4 , Cl = 3 Let: c = 2,4 10 , d 1= 0,7, d 2 = 0,9, ml = 1,2 10 4 ; m2 = 10 4 , P = 6 U = t(u\,u 2 ) : Ofu l{,5.104, 0!:-u 2'= 5 ,5. 104 , u 1+u 2 = 8 .10 4} X = l(x l ,x2 ) : 0f:xl~3.l 04 , OfX 2 ,=4.10 4}
.
.
2 = [ (Zl'Z2): l'-zl!. 2,
lfX 2 !,2j
Let us assume that the system operates within the period 'L -1 and the ATSS plans the control for the period~, i.e. it selects the value and the mode of allocation of an exogenous resource ~ to the subsystems SI and S2 so as to achieve the maximum of goal functIon gO(~,xlz), The ATSS solves this problem using artificial intelligence methods. Let the centre (and the ATSS as its representative) have the following informations on the situation in the hierarchical production system: - it knows the set 4r0f the uncertain factor;
J
tillt)
l ' li,1I\
- it knows the set Utof the exogenous resource; - it knows the goal function of the centre go(~'1£'~)
0 · - it knows the so 1 u t ~ons x 10 ,x?, 2 2 10 ,
x~=2,44
•
d
"I.
The situation recognition system supplies information of the type CHAR(gO'U,X,Z) and CONDACT(NO,SO,Si)' i.e. information on the characteristics of the goal function gO(~'
1£,~)1
lx=x
10 ).
The set of this informations represents the input information ~( ~ 1 the image of which is recorded by means of the predicates as follows: if(Zl = lEESETZ (Z:;), BESETU (U c ), BECRITERIONSO (eO)' BEVALUEX (xO)l In adopting the solution the ATSS works with the input situation image. It searchsthrough the databank to determine whether an identical input situation image has occured already during the previous stages. Let us assume that the given input situation image has not yet existed in the previous periods. The next step is to determine two characteris~ic symbolSYl et') and "f 2(1:) of the image 'f n"): ~1 (L) - characteristic symbol determining the predicate calculus number ~2(~) - characteristic symbol determining the list of different predicates of the ima~e if Ct') wi th respect to the image ~(T-l) i.e. the image of the preceding period. In our case there is 0('1 ('Cl = 4 and let y 2('t) =£BEVALUEXJ. In the respective databank the search is initiated for such method of functional activity (MFA) m2 the respective image of feasibility condi~ions of which p p (m~) has the predicate calculus equal to~~ and contains predicates from the list 11 2 (1;'). In ou~ cases these conditions are met by the MFA mf selected for confirmation. Feasibility conditions form the following theorem: PP(mi) (3~)BESETU (2:!l.J\ (3 g )BECRITEli.IONSO( g ).\ J\ 8~)BESETZ(~)!\ (:';1£1 )BEVALUEX(1£l) ,,-,PP(mi) : (.v~)(~g)(I/~)(lf1£l )~BESETU (~)V' V~BECRITERIONSO(g)V rvBESETZ( z)1I VrvBEVALUEX(Zl )J. Another task is to confirm the satisfiabi2 conditions with respect to lity of PF(m{) f(Y); the p . oof is performed using the resolution method,-1.e. proof of the non-satisfiability of pp with respect to axioms ~(tJ. The application of the resolution method to the following clauses: BESETZ(Z·rl BESETU (U'cl BECRITERIONSO(gO) BEVALUEX(1£O)
~pp(:ni): ....... BESETU(~)v ~BECRITERIONSO(g)v v,,-BESETZ(~) V~BEVALUEX(
x' )
yields an empty set - the clause. It means that the ch~sen method of functional activity m = m • Then follows the mechanism of lookin£ up the respective image of this method in the databank, and the MFA mf image is as follows:
0
and oa the activity of system elements. Let this information in our example be as follows: 0 - goal function g (u,x,z) for x=x is nonlinear with resBect-to the variable ~ and linear with respect to z - U area is defined with linear non-equations with nspect to ~ - Z area is defined with linear non-equations with respect to z. The following list-of clauses results: )1= CHAli.(gO'U,X,Z) = : {
NOTLlNEARF(gox, (ul ' u 2 ))} LlNEARF (gOX,(zl,z2)) LINEARG (U r ,(u 1 ,u 2 )) LINEARG
( Zt' (z 1 ' z 2) )
The type functional model of control is determined with the MFA, characteristics CHAR and conditions of activity CONDACT, Le.:
Mf(C)'{ ~~~:;~¥: ~:~~:: Si)) In our specific case:
",
OPTIMAL( (SO), (max,min), (U-r' Z'!:'), (u, , u 2 ,\ \ zl,z2),(gOx)) \
o
MC
0
0
AT(u 1 ,SO) AT(u 2 ,SO) AT(u, ,SI) NOTLINEARF (gox' (u 1 ' u 2 ) LINEARF(gOx,(z l ,z2) LlNEARG(U t , (u! ,u 2 ) LINEARG(Zt,(zl,z2)
0
;·
AT(u2,S2~ !
! I
In this specific case ste CONDACT conditions are empty. The clauses No. 1,3,4,5,6 are connected with the control method, clause No.2 and eventual clauses CONDACT are connected with the control strategy. The solution of the control task continues with the search for operator sequence R. which is capable of implementing the cont~ol method expressed through the formula: OPTIMAL«SO),(max,min),(UC,Z L)' (u 1 ,u 2 ,zl ,z2)' (gOx) under conditions CHAR. This type of m~ti pIe optimization can be broken down to two subtasks: a) OPTIMAL( (SO) , (min) , (Z'(") , (z 1 ' z 2) , ) -Ox) ) b) OPTIMAL ( (SO), (max), (Ut')' (u 1 ' u 2 ), (gox») The theorem proving method will be used to prove the satisfiability of the conditions of operator feasibility + SIMPL ( ( So ) , (min) , (ZrJ , (z, , z 2 ) , (g Ox) ) for the task a) and satisfiability of the conditions of feasibility for the operator ++
FEASIBL«SO),(max),(U~),(u1,u2),(gOx)
for the task b). Thus, R = + and R = ++ and the scheme of initiai distributfon of the future results of activities of opera-
lilll
RI and RL : o 0 0 VR = AT(z l ,SO) f\ AT(z2'SO) 1\ AT(u j ,SO)A 1 t\ AT(U ,SO) . 2 Now it is necessary to build ()~-thc initial cud.l ef the ."nt.ol strategy and
-
j
AT(Z~1
'so)l
G"~('t'): AT( Z:2' So)
AT(ul,SO ) Q
i,AT( u 2 , So). I
:i"'AT( u~ ,S OH' "" AT( u~, So \1'1 o . 0 \ "-AT(u l ,SI )\I"vAT(u 2 ,S2 .J The task of the search for operators for the strategy of control is transformed to the task of the search for operators {F~ for the fulfilment of the target modet '0 ;('\,;). We shall use the following operator scheme INF (A,k,B) - object "A" announces the parameter "k" for the object " B": - feasibility conditions PFi = AT(k,A) result of operator activlty - list of formul~ for elimination - list of formulae for inclusion AT(k,B).
r-.();Cn
I
CONCLUSION ~n conformity with the world-wide trend we e dvocate the suitability of ICC implementation for the control of distributed systems with hierarchical structure. We assume that individual subsystems of a distributed system have the attributes of active elementes and that in the decision-making process exists the priority of the centre in task solution. We point to a new formal approach towards the solution of the control task using elemnts of artificial intelli gence and to the appropriateness of the ICC supervision through the dialogue s~stem VSGA primarily in those cases when the lntervention of the active control element - the man - appears to be inevitable. The proposed heuristic mode of automatic selection of the method of functional act i vity of control system through the ATSS was simulated on the di gi tal computer EC 102 1 in the language LIS? :.5. Ne see the contribution especially in the fact that the ATSS system, as compared to the STRIPS system, reduces the initial information obtained from the environment in the direction of their processing and application for the needs of automatic solution of control tasks. To this end a system has been devised. The ATSS operates within the functional space of the nistributed system where it has to deal with the solution of functional tasks of multiple optimization and of conflicting relationships between active elements of the hierarchical production system.
The outc.,me of the above procedure is:
~I
:AT(zl ,SO)~
• 0 \AT(z'2'SO)~ T ;; +(tl=t (J 1 ,So)"
r
,
f. C~
[1 ;MEE: t--l
rT(U'2 'SO)~ IAT ( U"I,SI )~
l~T(J2,S2)" i
1 jS
The sequence of operators [R i! and F is submitted to the SIS and SCS where the concrete values are determined of the variables ul,uazl'z2' The calculation of lRh is made with the use of simplex method, that of R with the use of the feasible direction~ method. The application of the operator means in practice that a program is worked out which is allocated to the operator. After obtaining specific parameters and calling of respective programs, the following values had been received: z o1 -_ !,. z20 -_ I,. u 01 -_ 2, 9 1.10 4.,u 02 = 5 , 09 • . 10 4 2 for Xlo = 1,19.10 2 and x 20 = 2,44.10.
With these values the hierarchical productions system attains the effectiveness of g~ = 1,656.10 9 The calculated u~ and u~ values are then applied by the SIS and g~ proceeds to the SCS.
SRS - Situation Recognition System IMEE- Internal Model of External Environ ment AT SS- Automatic Task Solution System SCS - Supervisory Control System SIS - Solution Implementation System Fig. 1 - The principle scheme of the Information - Control Complex
J.
L1iclI\ 1'1 Ill.
--------,
SRS
.-------l :
L -_ _ _ _~~--~
-----,
I I
I
I I I I
I
I
I I
~
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ J1
HPS - Hierarchical production system So - The centre of HPS Si - The subsystem of HPS go ••• gN - the goal functions of the centre and the subsystems u i - the value of the centre source given to the subsystem S. the value of the su~system own source uncertain factor superior organ Fig. 2 - Hierarchical production system acting under conditions of uncertainty
r-------------------l 1
1
I I I
1~
control system
I
1
1
V
'-------_~
I
intellectual system
I
I
I _________________ I L ~
I -
information
1/1- task solution
'f-
information transformed to the first order logic
Fig. 3 - The cybernetics dismembering of the ICC
Ir~----·+L-----, 1
I
I I
I
~
Cl!
(IJ
~ '8 r:.c
~~
g >.
;! +>
H·... (IJ .....
~
G>O+>
I .~ f - I ~M I ..; ~ I ~
I
E
II
0. 0
~
The choice of the sui table functional activity method
I
I
I
i!
I : I I. I I I ~tagel : :
A~SS I I I
I! !
t~'
The creation of the - I I functional activity ~-~--1-J type model
I
I
1
I I
Hf
The looking for 11. 1 the operator succes- stagel sions I
1\Rd,~F.t1
application {'Po} 'J
I
I I 1 I f----r-..J Z
Y
L------h·-----J SIS Fig. 4 - The simplified scheme of the ATSS activity
REFERENCES Ernst,G.W. and Newell,A.(1969).GPS A Case Study in Generality and Problem Solving. Academic Press, Neww York and London. Fikes,R.E. and N.J.Nilson (1971). A new approach to the application of the theorem proving to the problem solving. In Proc.2nd Intern.Conf. on Artificial Intelligence, London. Mesarovic,M.D., D.Macko and Y.Takahara (1971). Theory of Hierarchical Multilevel Systems. Academ~c Press, New York and London. Uli~nY,J.(1978).VYznam simulacie a modelovania ~innosti hierarchickeho systemu v riadeni zlozitych systemov.lnforma~ne systemy,No.6. Uli~nY,J. and Drab,L. (1982) Adaptive method of strategy control synthesis of subsystems in hierarchical systems. In Proc. of the 4th FORMATOR S~posium on Mathematical Methods for Analys~s of Large-Scale Systems.Liblice near Prag. Uli~nY,J.,Thuan,N.T.,J.Balaz and Drab L.(1983). Automatic solutions projecting of controlling complex in automated control systems. In Proc. of the rd IFAC IFORS S osium Lar e-Scareand Appl~cat~ons.