Mechanism of Intelligent Behavior of Systems with Dynamic Properties

Copyright @ IFAC Modelling and Control in Biomedical Systems, Karlsburg/Greifswald, Germany, 2000

MECHANISM OF INTELLIGENT BEHAVIOR OF SYSTEMS WITH DYNAMIC PROPERTIES

Dr. Vladimir N. Pilishkin

Department of Automatic Control, Bauman Moscow State Technical University, Nikoloyamsky per., 2-84, Moscow 109004, Russia, phone/fax: +7 (095) 912-34-02: email: pilishkim1.'hotmail.com

Abstract: The presented approach allows the system with intelligent properties (with various type of origin) to form the general dynamic model and, with its help, to define the system structure and parameters. The approach is based on introduction of an intelligent environment according to the appropriate structure, which, as well as the system itself, functions according to structural-algorithmic functioning mechanism, which assumes that the general behavior of system is determined by the current situation. The structural scheme of the functioning mechanism, the dynamic model of the entire system and the major relationships are presented. Copyright © 2000 IFAC Keywords: Intelligent system, intelligent feedback. intelligent environment

includes C(t) - current target; D(t) - current system model, 8(t) - current environment (~to).

INTRODUCTION A broad range of systems is known for a certain duality of their physical nature. First, they can be referred as dynamic systems, i.e. their math models are described by differential equations. On the other hand, these systems possess logical functioning base, which is apparently connected with their physical properties. Such systems include various biological systems. systems with artificial organs, etc.

Then..

Stet) = (C(t),D(t), 8(t))

(1)

If Stet) is determined for V t~t). then the controls set Ust (t) is determined. In case a certain control function u(-) eo Ust(t), the disturbed situation is as follows:

St(t)

Study of these systems via traditional dynamic models does not reveal the complete mechanism of their behavior. The presented approach takes into account the diversity of physical properties of these systems as well as reflects their dynamic according to the intelligent control.

= St(t) + Mt

(2)

Where the disturbance value !J. St may depend on the uncertainty of D(t), 8(t) factors as well as on the target CCt) uncertainty. The uncertainty !J. C(t) may depend on the target CCt) uncertainty as well as on wrong control function choice. so that the real situation Stet) differs from the current one. So that. for the class of systems under study, the following rule of acceptable control function choice may be formulated: for each time point, the acceptable control function u=u(·) should be chosen, so that the following relationship would be satisfied:

STATEMENT OF THE PROBLEM The dynamic systems with intelligent properties are under study. It is assumed that. in general, the behavior of an arbitrary system is determined by the current situation Stet). Stet) is a group, which

255

Mt

E

!lR(t),t

~

to

THE GENERAL FUNCTIONING MECHANISM OF SYSTEMS WITH INTELLIGENT PROPERTIES

(3)

Where tlR(t) is a certain small region of the nullsituation «0,0.0», in particular, t1R(t) == <0,0,0>. Given these conditions, the problem under study can be restated as:

To be more precise, we assume that a system under study is described within a certain state space H. Besides, according to intelligent properties definition. we believe that the system's self-description formulates according to intelligent environment S. which contains the procedure of the desired svstem' s behavior. '

By forming the acceptable control function u('), it is necessary to provide the dynamic behavior of the system, so that the following relationship holds:

Mt

E

!lR(t)

(4)

So that, to solve this problem. it is assumed that the arbitrary intelligent systems, including dynamic ones, function according to mutual reflection of state space H and intelligent environment S, which forms the dynamics procedure. Intelligent environment S is a diversity of elements S, which provide the situation and the acceptable current situations set (4). Then. the control algorithm is formed providing the acceptable error value tlSt (i.e. (3». The presented functioning mechanism is called structuralalgorithmic functioning mechanism, and. according to (Pilishkin, PupkoY, 1997), it can be presented as follows:

The intelligent properties of a system mean that the system itself can recognize the character of its functioning in state space (or in the space, in which the system's model was formulated). Using this selfdefinition, the control formula u = chosen.

U(.)

should be

5

P

P 6

H

s

9

10

Fig I. Structural-algoritlunic functioning mechanism

2'in

f - - - - r - - - - - - r - - - IntellIgent feedback

-

0 -

-

-

where SI. SIn SIc. SI; - the true predefined realizations of current and corrected situations,

defines the influence of A onto StO; "5" characterizes the situation Stc formation. Because the true

respectively~

- S-reflections of Stn

situations~

the predicted corrected

situation StD and assumed situations St n are not the same, then their reflections Sr~s and Sr;s are different, and, according to "5" and"?", we can form an error E:s between them, using which ("8") we can build the correction algorithm ("9")

51; .5I~ 5In. 51; : 51;s

situation in S; A As - the control algorithm and its Sreflection, E:s - the error between predicted and corrected situations in S, i.e.

According to presented functioning mechanism the control formula choice is determined by elements of environment S, and the information about the real system behavior within H is used for correction of control algorithm. The algorithm As is used primarily for solving the task, and the correction algorithm Ks is necessary. in case this task can't be solved because of the situations being different. Therefore, the functioning mechanism of systems under study is formed of two parts: the first part is fully contained in H. and characterizes only dynamic properties of the system and, therefore, corresponds to dynamic level of functioning; the second part is fully contained in intelligent envirorunent S and characterizes the system's ability to form the acceptable control algorithm using self-detection of current situation (i.e., intelligent behavior) and corresponds to detection level of functioning.

Us - the algorithm of S - reflection of predicted

situations, i.e.

(6) p - the reflection operator H ~ S, providing a certain conformity, i.e. C is satisfied in H and Cs is satisfied in S~ ''1'', "2", "10" are the functioning order steps. Intelligent feedback is defined as the connection made with the intelligent envirorunent S in form of sequence of operations which provide the probable situation correction. In this case the sequence "5", ''7''. "8", "9" is an intelligent feedback.

In turn, this level can be divided onto the prediction sublevel, which forms the algorithm As and determines the situation Sf;s: and correction

If a system possesses intelligent properties, if can be assigned a certain intelligent environment S in accordance with operators ''1''-''9''. We will clarify the functioning of the system presented on fig. I. According to ''1''-''6'' in envirorunents, under operator P, the reflections of assumed situations are formed, which differ from the exact ones by unknown value of uncertainty. As a situation's reflection in S we can use the situation, which is an estimate of the true situation. According to "2" the situation Sf; induces the algorithm As, which

sublevel, which clarifies the situation Sr; . This control task stated generally, we will solve according to described above structural-algorithmic functioning mechanism for systems with intelligent properties.

INTELLIGENT FEEDBACK DESIGN

provides formation of Sf;s (see "4") using this relationship

The possible structure of system with intelligent properties can be described as follows. It uses the concept of functioning mechanism, presented on fig. I. The dynamic part of structural-algoritlunic mechanism determines the following part of the entire system structure:

(7)

where Sr s . Rs - are reflections of Sf and R from (4) which are obtained by reflection with the help of operator P onto the environment S. Besides, the following operations are processed simultaneously: '"3" reconstructs the algorithm A within H; "4"

257

co

, Us

Control reconstruction block

...

A

u

r----.

x

Dynamic level of the intelligent system

...

It "-

CU

,

IT,

X

U

Fig.2. Dynamic part of the general structure of system with intelligent properties where Us, 1I - are msx 1. mx I - dimensional control vectors in S and H accordingly, co - the environment's signal, x - is nx I - dimensional state vector, IT is XX I - dimensional vector of virtual variables or system parameters (virtual signal), i.e. of those variables or parameters can be used for model Dd reconstruction with any level of precision (using the virtual signal IT the assumed system model is reconstructed): xl' - is nux I - dimensional virtual or assumed system's state vector; CV - is a forming block for virtual state vector,

the reflection

D:

s of the assumed system's modeL

nu,

U Pn, Px form the reflections of signals X in S: E s forms the error signal Cs = cAx~,xps), K s - block of

correction of reflection

D'!.s

of the assumed modeL

<:Ps , (Os - are reflections of signals of target C and the environment e, which characterize the current states C and e; gs is a signal for the reflection D'!.s . The general structure of system with intelligent properties can be presented as follows:

Using the analogy for a dynamic part, and according to fig. I , the detection level of general system structure can be presented as follows:

Fig.4. The general structure of system with intelligent properties where I - the area of control algorithm design in S, 11 - the area of correction of the assumed model's reflection in S, III - the area of control of dynamic part of the system in state space H. So that, in L using the target, environment, and the model of the system, the control Us in environment S is formed. This control is assumed to be chosen if the target' s

Fig.3. The detection level of the general structure of system with intelligent properties where As - block of design of control algorithms is block of forming within the environment S:

Jt!.s -

258

reflection Cs is satisfied. In general, it can be assumed that Us is determined according to

performs the solution of the inequality (11), As is a stationary block, which forms the control Us using signals Il" COS, '+'S (which determines (10), or the function '+'s(-). The other types of stationary blocks As may also be used for control Us synthesis using other algebraic relationships. It is assumed that us<-) formation within a stationary block is performed on the same time scale within S (i.e. real time scale) However, in general case, this assumption may not be satisfied, since the character of us(') formation depends on a certain algorithm for solving the appropriate algebraic relationship (i.e. (11) For instance. the chosen algorithm may not allow to determine the straightforward formula for u,(·). but requires a numerical procedure to determine us<-): the time to perform this procedure is crucial for us (-) determination. Taking into account the duration of this numerical procedure, it can be substituted by a certain dynamic process of us<-) formation, which should correspond to he algorithm used within a block As. This question is not taken into account in this paper. but it is assumed that us(') is formed. within a block As, in real time scale for S

(8) where B(·) is a certain operator, which possess the desired properties. which characterizes the rule of choice of control Us within the forming block As. As As. in particular, a stationary block can be used, i.e. which uses only algebraic operations to determine the desired control Us. For dynamic objects. the following general approach to stationary block formation can be used. We assume that a model s is described by

D:

where S E S is an element of intelligent environment (nsx I - dimensional vector). s = set') - trajectory in S; t' - true time of processes duration within S;.fs(-) is I1 s X 1 - dimensional vector-function, which provides the only solution to the Cauchi problem.

The structure of system with intelligent properties (SIP), which is presented on fig.4, is done according to an assumption of that the block As forms the control u,(·) which provides the reflection of target C. Then, to provide the target C, the correction of the area I should be performed. It can be easily done: however, this paper will not review this problem.

Then. according to a concept of functional-set belonging (Pilishkin, Pupkov. 1997). we can assume that arbitrary target Cs can be described via the following relationships: (10)

THE SIP DESIGN where ,+,,(.) is a certain scalar continuouslydifferentiable function. Using, for instance. the phase constraints approach (Pilishkin, 1998), we can that the desired control us (-) should satisfy the following:

(Vs'+'s,fs(s,us,fls,gs,cos,tJ)+ 'I1s E TQ&S

To design the structural- algorithmic mechanism for intelligent dynamic system, the following approach may be applied. It is assumed that both dynamic and intelligent parts of the system may be defined and put into the intelligent transducer. The relationships of these parts can be presented in Cauchi form:

~~ $0] (11)

1t S c. t~.

•

Dynamic parts: (12)

where

Vs \1' s

=[ 8\jf s

aS

I

...

8\jJ s oSn,

] T

is a gradient of where x, u, w - state. control and disturbance vectors, respectively.

function '+'s; (Vs'+' s,fJ - is a scalar product of I1 s dimensional vectors Vs'+', .fs in S; TQ,(t') - is a boundary of a set Qs(t') = {SES: '+'s(s. t') $ O}.

•

Intelligent transducer

x = [(X,X.lI.lIW. w,
The inequality (11) is algebraic with respect to the vector lis to be determined. Therefore. we use only algebraic operations to find Us' Then. if block As

259

x,

where ii - state and control vectors of the intelligent transducer, respectively, cp - signal of the control target, w - intelligent transducer disturbance vector.

then, according to (pilishkin, 1998), it can be shown that the following relationship must be true to provide (19):

The overall system equation.

+ ('V ;ca, J(x, x, u(x, x,t), l1(x, x,t), w, w,
.\" = F(X, U, W, CP,f),X(to) = X 0, t 2. to

('V xa, f(x, u(x, x,t), w,t» +

aa.

(14)

+-~o

at

v[x

where

t

,

xt ]E TQ(t), t? to (20)

.r =
where

(15)

iQ(t)

(vector-functions
The relationships obtained make possible the study of dynamic intelligent systems, as well as to analyze the target trend, to form the desired behavior using the appropriate control function. The presented structural algorithmic functioning mechanism can be used to solve the analysis and synthesis problems.

REFERENCES:

(17)

Pilishkin Y.N., Pupkov K.A. Development of intelligent system dynamic model, - 2nd IFAC Workshop on "New trends in design of control system", Smolenice, Slovak Republis 1997, p.p. 383386.

Then, the intelligent transducer can be presented as a certain combination of dynamic and intelligent components. i.e.

Pilishkin Y.N. "Robust control algorithms in intelligent systems", Vestnik MGTU, "Priborostroenie", NQ1, 1998,

(18)

where G - is a certain vector-function, intelligent parts models.

10 u. lu U

'b

.•

is assumed to be fixed. but predefined

function. which. once been chosen and remains

in(-)

describes the transducers ability to constant. form signals regardless its own dynamics. The function can change the current situation St(t). In case the accept table system behavior can be presented as cx.(X(t).t):S; O. t 2. to

(21)

CONCLUSION

Intelligent transducer has to form the environments and all applicable operations. The influence of the transducer onto the dynamic part (12) is made through the control function U. This can be taken into account by using the generalized control function:

u = D( X,f)

= {X : cx.(X,t) = o}

(19)

260