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Problems of High Level Control in Man
Copyright © IFAC Control Science and Technology (8th Triennial World Congress) Kyoto. Japan . 1981
PLENARY PAPERS
PART B
PROBLEMS OF HIGH LEVEL CONTROL IN MAN G. Vossius Institute of Biomedical Engineering, University of Karlsruhe, Karlsruhe, Federal Republic of Germany
Abstract. The control concept used in man at lower levels might be already very spezialized. In addition the higher controls are not only capable of adaptively adjusting the parameters of the dependent loops but also of changi ng the cont ro 1 st rategy. I n order to fu lfi 1 thei r task the hi gher centers have at first the momentary effective measurement vector from fuzzy coupled receptor arrays and must establish sufficiently a qualitative and quantitative reference system, because man has no built-in scheme of the internal and external sphere. Only after achieving this, may the control functions be executed. To evaluate the functional concept and the quality of control, especially at higher levels, for instance the principles of observability and controllability ought to be helpful too, because their requirements mi ght not always be fulfil 1 ed. This enforces other strategies of control which may restrict the performance of the system.
Keywords. Adaptive control; identification; selforganisation; optimal control; biocontrol; observability and controllability; fuzzy systems. I NTRODUCTI ON The last two plenary papers presented in 1975 and 1978 looked upon the characteristcs of an external control situation, for instance man-machine or socio-technical systems. This lecture was initiated by the IFAC-workshop which took place at Karlsruhe in 1979. The topic of that workshop was the funct i ona 1 structu re, the concepts of control effective within man itself. The goal was to screen the known facts clearing mi nor open quest ions and to specify centers of gravity which might permit better insights in the requirements and potentials the organism needs to execute the spectrum of control it is capable of. The main aspects of th i s topi c bei ng brought up in the course of the workshop or bei ng pert inent generally are discussed in the following. In this connection the talk is concerned mainly with the physiological sphere not considering other aspects, as for instance the psychological one.
THE MAIN FUNCTIONAL COMPONENTS OF BIOLOGI CAL CONTROL SY STEMS The organi sat i on of cont ro 1 in man may be subdivided in a horizontal or a vertical. In a horizontal ordering you can differentiate the wellknown levels of: - Feed forward control respectively stabilisation e.g. the different modes of reflexes or the buffering systems and so forth. - The "simple" feedback loop with fixed parameters. - The adaptive control loop. which might be equipped already with the capability to store former conditions of operation, called in this context learning. - Following is the level of process identification and establ ishing the appropriate cont ro 1 mode. The organism is not only confronted with a changing environment but also with a not-
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fixed somewhat floating inner world . In addition at each level the organism often has the task to coordinate a more or less large number of control loops stabi 1 ising various physiological functions . - This task is executed by selforganizing systems, being able to identify their own frame of organization, and to project the st ructure of superi or cont ro 1 in connect i on wi th requ i rements imposed by the outer world. - All of th i s can be topped by the genera 1 but a bit blurred scheme of a multi level-multi - goal system, introduced about t\~O decades ago by MESAROVIC . Compared with technical systems the organism has a few more problems to solve in order to execute its control; for examp1e: - The measurement devices, the receptors, have often a rather limited range and their characteristic is a powerfunction . In addition the material embedding the receptors di s torts the phys i ca 1 or chemical signal,the mechanical coupling is sliding . Therefore nature uses receptor a rrays rather than si ngl e receptors, to enhance the range and prec is i on of the measurement. The appropriate statical and dynami ca 1 signa 1 vector has to be computed on - l i ne . - A long evolutionary process in our scientific thinking was required to separate the different physical and chemical modalities, their scaling, and - if possible establishing an absolute reference poi nt. In man nature has taken care of the separation of modalities by the constructi on of the receptors (transducers) . The scaling is apparrently not built in, there doesn't exist a quantification system . Consequently the organism has on all levels to establ ish procedures which link the physical and chemical quantities, pictured as time intervals of nervepulses - in most of the cases in a nonli near manner- to an i nterna 1 ana 1ogous reference system . This includes the ability to build up reference extracting systems and update them continously . For the control loops the reference point of operation has to be determined . - The existence of life is tied to working controls . One ,of the requirements for con trol is an urli irectional flow of informa-
tion . In the single cell this ul1directional information flow is secured for instance by about 500 to 3000 enzymes steeri ng the bi 0chemical processes . Within the nervous system the biochemical component of the synaptic transmission has especially evolved to enforce the unidirectionality. Above the unidirectional flow of information and the introduction of the set point the operational conditions of control in man has to be defined in a much broader sense up to the 1ay out of the total concept of the central multifunctional control. This needs as a supposition a reference frame of the externa 1 and i nterna 1 worl d. The reference system has to be fed by an equivalent system extracting the informat ion assembled by the receptors through more and more sophisticated procedures. To fu lfi 11 these tasks each doma i n has to have a good logic structure in itsel f, separating one from the other. Therefore the functional structure of the organism may be subdivided also in a vertical manner, which might be called domains: - Domain of measurement with extraction of the effective vector - Domain of establishing the reference in quality and quantity - Domain of prediction - Domain of control The division in these domains is to a certain extent schematic and arbitary. The question which specific function, e. g. the id entification or the modelling is to be attributed to which domain is largely dependent on the actual structure of the specific system, or vice versa: The tasks outlined in different domains might very well be executed combined in one functional block. THE FUNCTIONAL STRUCTURE OF BIOLOGICAL CONTROL SYSTEMS One of the most promi nent cha racteri st i cs of biological control seems to be that on one side it behaves rather sloppily . The control is lined up just enough to fulfil the oncorrmi ng demands, not ca ri ng too much about such requirements as robustness or quality . The internal controls and the reserve capacity of an untrained subject therefore soon fail when the subject is suddenly exposed to forceful demands . On the other si de the same control systems wi 11 organize themselves very efficiently, if
Problems of High Level Control
the training takes place slowly giving them the chance to do so . This multi various face of biological control, depending on the si tuation and the prehistory man lives in, makes it so difficult for the researcher to evaluate the concept realizing the control as a certain body function . In the analysis of biological systems the researcher evaluated therefore at fi rst the class i ca 1 input - output re 1 at i onsh i p and deri ved from it a linear black box model. In most cases these models have been not only incorrect for drastic phYSiological or pathological changes of the internal status of the subject or of the environment but valid just for a very limited range. The biological systems incorporate essential nonlinearities . Therefore phYSiologists started conducting the analysis more closely in accordance with the physiological function to prove experimentally the assumptions made in the process of modelling with good success . As an example for analysis conducted by ROBINSON et.al. mi ght be cited: Focussing on a new target the eye executes fast movements, so - ca 11 ed saccades, wi th great pr ecision . The question arises wether these saccades are carried out in an open l oop manner, with the brai n centers creating their commands very conSistently, or wether cont ract i on of the externa 1 eye mus cels is controlled. In recording the activi ty of the specific nerv cells by means of microelectrodes ROBINSON found, that the difference between the nerve pul se command signal and the signal effecting the contraction of the eye muscels is fed into a so called burst generator, nerve cells responding to small error signals with very high rates of firing similar to a differentia tion and a limiting characteristic for larger magnitudes of error. An integration of the burst sequence leads to the contraction signal and represents the eyeposition signa 1 for compari son with the command signal, thus cloSing the loop . Using this circuit the eye may be moved fast even for sma 11 errors whereas for 1 arge errors the limiting characteristic prevents the muscels from being damaged by too forceful contraction . Because of the very high gain factor of the burst cells, the circuit tends to be unstabl e. Therefore the loop should be opened at rest by a switch which has to be closed synchronously with the command signal. So-called tonic nerve cells
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a 1ways reproduce a nerve pu 1se sequence corresponding to the last command signal holding the eye in position (neglected in Fig.l) Fig.1 presents the basic scheme of the control loop (after ROBINSON) . u(t} com mandsignal; C Comparison; S Switch; eB(t} output of burst cells BC; I integrator . This loop has a rather simple configuration with no need to change its parameters . It shows also a very specific design well adjusted to its task . The latter might be true at this level, as is indicated by other examples: Therefore it is difficult to produce a general scheme or concept of biologi cal control applicable to a wide range of prob 1ems . That comp 1 i cates the ana lys i s of biological control systems. INTEGRATO~
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Control loop of the contraction of eye muscles (after Robinson) The last example demonstrated the control of the execution of the command signal, leaving the question undecided, how it is ass ured that the command si gnal itself for this lower loop has the appropriate magnitude . An analysis carried out by the author together with WERNER re vea 1ed that the ga in of this loop is adaptively controlled at the next level . The former loop was embed ded completely within the special nerve centers themselves . At this stage the error signal results from the position of the target on the ret i na of the eye . The poi nt of reference is the so-called fovea centra lis, the locus where the retina possesses the highest resolution. The task of the control loop is rather simple: The eyeball has to be turned exactly by the angle of the difference between the fovea central is and the picture of the target on the retina . The gain has a magnitude of "one" (Fig . 2) . The loop can be treated as a samp 1 ed data system since the saccadic eye movements
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occur at certain time intervals only. Experi ments conducted in open loop cond it i on by adding continously the eye position to the target proved the adapti ve control of the gain is achieved by dividing the difference of the last two samples of the eye position by the difference of the error yl e . At the first glance this fact is surprising. The necessity for the adaptive control becomes obvious, if one takes the conditions for the operation of the brain into account: Origina lly there existed no knowledge about any quantity in the brain. This knowl edge has a 11 to be ext racted by observing the various processes and comparing this observation with the result of its own reaction. The adaptive procedure used in this example achieves the extraction of the reference equivalent in a very simple and effective way without expressing it as a quantity and with the possibility of continous correction. In addition this procedure has the abi 1i ty to correct for certa in unwanted changes in the nervous centers 1ike dying nerve cells.
is much more difficult if not impossible. Although from the systems point of view it is quite obvious that a control loop has to have a set point, physiologists are questioning this part sometimes being unable to detect it. In the simplest way the set poi nt mi ght be gi ven as the cross i ng poi nt of the characterisics of the system's components. For such a system it would be valid that it is comp letely selfsustaining as poi nt ed out by WERNER . The prob le m is that such a system neither can be brought back to its operating point , be corrected by hi gher systemic i nfl uences incase of unwanted deviations nor may the set point be shifted if necessary in the collaboration withother systems. This situation is rather risky for the organis m. In any case this is admissible only if proc esses stabilizing themselves are incorporated in the system at crucial positions like biomedical reaction with a tendency towards a stable operating point. For the basic control of body temperature with its metabolic components such a stabilization mode might be true.
Fig.2 Adaptive control of the saccadic eye movement
Proceeding to the next level of control, signal analysis and interaction of different control pathways servi ng the same goal become more promi nent. A quantat i ve ana 1ysis of the eye tracking movement was carried out by GOUIS et al. This allows me to illustrate this level of control using the same system. The eye movement cons i sts of two components: A rapi d step 1i ke one, the saccades, you are already familiar with, and a slow continuous one, following the pattern of the target mov ement.
Fig.2 shows the scheme of the control loop of the saccadic eye movement. u(t) command signal; e(t) error; S sampler; eN error at saccade N; H hold with delay; G gain factor of the loop; LlYN calculation and hold of the difference of the last two eye positions; CEM loop for the control of eye muscle contraction (Fig .I ); EN actual eye position . I n the system dealt with so far the question of the set or reference point was to be answered very eas i ly. Nature took special care to establ ish it. In biological control systems, especially in the ones sustaining functions as circulation or body temperature, the defi nit i on of a set poi nt
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Problems of Hi gh Leve l Control
As ca n be seen in Fig . 3 , the continuous movement tries to trace and to predict the target pattern whereas t he saccades correct the error made by the continous system. Fig . 4 shows a scheme of the total system. The impo rtant functions of it wi 11 be expl ained brief ly. - The processing of the signal th r ough the retina and the following nervous centers creates a delay time of about 120 ms . In the continuous branch the signal is processed through a time window of 60 ms duration to calculate t he mean va l ue of the target's velocity . - A O- order track and hold stores the 1ast va 1ue for 60 ms incase of a saccade to prevent false compu{ion of the velocity. - A special characteristic limits the maxi mum speed of the continuous movement . - An adaptive Proportiona l -Integral - Controller adjusts the velocity of the continuous movement to the one of the signa 1 and to t he mode of operation, for instan ce during the tracking with artificia l externa l feedback . The magnitude of the branch output is weighted according to the apparent regu l arity of t he signal. - In the saccadic branch the decision has to be made wether an error wi 11 be corrected by a saccade or by changing the ve l ocity of the cont i nuous movement. The sac cade interupts the signa l processing in the continuous branch. - The magnitude of the correcting saccade is computed by taking into account the predicted velocity of the target movement and in order to mi nimi ze the mean error of the movement . According to this analysis the system is running on a clock cycle of about 60 ms, which is triggered by the beginning of the movement. The production of the continuous movement is decoupled from the target func tion by a prediction procedure, in this case rather simple, and then in addition adaptively controlled . Th i s concept seems to be va 1id for most of the human movements . The decision wether to correct an error by a saccade or the cont i nuous movement tak es into accou nt the pos i tion error and the velocity error, using an optimal strategy . This analysis demonstrates, that even for the rather simple task of persuing a target with 1 imited speed the organi srn has bui lt
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Fig . 4 Model of the combined eye tracking control system. up a rather sophisticated well structured control system with partitioning the func tions. Perhaps this keeps each function simp l er and easier to execute . On the other side the brain centers are very well able to coord i nate the different components and
G. Vossius
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to produce an optimal mode of operation if necessary. This example gi ves al so hi nts at the reason that the analysis of biological systems soon becomes so difficult and that the mode 11 i ng of the overa 11 input - output relation does not tell much about the true functional properties of the system, its strong and its weak points . Having analysed one stage of the system for the example outlined here the control of the combined continuous and saccadic eyemovement one discovers that the true inside in the capabilities of the system is transfered to the next stage: e. g. how is the optimal procedure for executing the cor recting saccades establ ished - and so on . PROBLEMS OF HIGH LEVEL CONTROL During the past decade physiologists and bioengineers were trying more and more to trace at least the qua l itative functional structure of the main physiological systems as circulation and respiration and their i nterdependences. As an examp 1e a scheme of the control of the body temperature and its connections to other systems is presented in detail by WERNER . The contro l task of pooling main body functions for an integra ted performance is at the order of multi level-multi-goal systems . But the difficulties arising from the attempt to analyse such a system can imagined by recall ing the complicated structure of the rather small control system for the eye tracking movement. Moreover the question arises wether the criteria appl ied so far to the pattern of ana lysis are sufficient . This is at least doubtful. As already mentioned above the fuzziness with which the measurements are taken is often neglected. (For large receptor arrays like the retina or the cochlea this aspect is especially analysed.) The continuous computation of the measurement vector significant for the system and the implementation of the reference system are achievements especially to be taken into accou nt. At the higher levels of control the formation of the reference is of another order than in the example of the saccadic eyemove ment. A high diver performing a triple so mersault and diving almost splashless into the water has to ha ve a complete i nterna 1 image of the diving pool and the dynamic diving path of his own body to execute the
dive correctly . On the other side normally the movements are conducted at 1east partially in a prograrrrned - predicted - manner. For fast movements the continuous control including the eye would be too slow because of delay times of the system. For instance while performing a tennis stroke it is a 1most i mposs i b1e to change the pattern of the stroke successfully . Only small correcti ons with the hand may be made . The prograrrrned execution of the movements has yet another cause. Playing tennis with a firm grip, arm and hand have still about 10 degrees of freedom left. A unique system measuring the position of the arm does not exist. The receptors are distributed all over the muscels and the joints. Therefore the complete observability is not given. On the motori c side the same is true for the controllability. This might be illustrated again for a tennis player . Without a trainer the player has a good chance to develop wrong patterns of movement severely limi ting his ability of playing. But he will be unable to recognize this fact . The trainer (and the videorecorder) circumvents the gap by correcting the false movement in an external loop while the internal one is missing . The nervous centers of motor control close the gap by building up a model, which has to be updated constantly through daily training. The limited to incomplete observability is not only a problem while executing the actual control task, but is as much a hurdle for the identification, the development of the internal models, the prediction, and the build-up of the reference . Therefore the training of the system of motor control as well as the one of basic physiological functions needs so much time . Despite this deficiency the control in and by man might be conducted in an optimal way . For instance CHOW and JACOBSON or HASTE showed that man is able to perform his movements in an energy or time optimal manner . Other valuable properties of biological sy stems as robustness or insensitivity to pa rameter changes and the stabi 1ity have not been given much attention so far. Physiological systems for instance must be stable, otherwise life would be impossible . But this stabi 1ity is not neccessari ly granted .
Problems of High Level Control in Man
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gai n factor. The blood pressure starts to oscillate with increasing amplitudes causing the patient finally to collaps. The 1i vi ng organism is a status referred to
G. Vossius
3608
by BERTALANFFY as an equi 1 i brium of exchange. The state of the living organism is, accordi ng to BERTALANFFY, an equ i 1 i bri urn of flowing exchange. This equilibrium is like the one of a pyramid balancing on its tip. Additionally the pyramid is not solid but consists of billions of parts more or less tightly interconnected with certain mainlines of a systemic structure. To keep the pyramid on its tip the equilibrium has to be controlled. But the observability is fuzzy and 1 i mi ted, as is the cont ro 11 abi 1 ity. In addition the partitions and the environments are always changing their states. To match these condit ions the control principles appl ied grew more and more sophisticated to keep the pyramid in line for the sake of the equi 1 i brium. The development of modern cont ro 1 theori es is now at a point, at which we corrrnence to gain an idea about the order of magni tude the core of biological control has achieved. But unless we know the functional principal of the core our role in solving the problems of biological control is like the one of man in PLATO'S parable of the cave.
REFERENCES
Allgemeine Neurophysiologie, ed . Gauer, Kramer, Jung (1980). Urban und Schwarzenberg, Miinchen. Bertalanffy, L.v. :(1942). Theoretische Biologie. Bd.II, Gebr. Borntraeger, Berlin. Bouis D., Vossius G.:(1978). Interpendence betvleen the Saccadi c and the cont i nous Eye Movement Control Systems. IFAC, Pergamon Press, S 489 - 493. Chow C.K ., Jacobson D.H.: (1971) Studies of human locomotion via optimal programming . Math . Biosciences, lQ 239 -306. Drischel H. :(1972). Einfiihrung in die Biokybernetik. Akademie -V erlag, Berlin . Haken H.:(1978).Synergetics. Springer, Berl in. Haste H. :(1976) The Complete Optimiza tion of a Human Motion . Math Biosciences, 28 . Kalman R. E. :(1961) On the General Theory of Cont ro 1 Systems. Auto mat i c and Remote Cont ro 1. Bd. I, S. 481 -492, Butterworth, London. Oldenbourg Verlag Miinchen . Lerner A. Y. : (1975) Fundamenta 1s of Cyberne tics. Plenum Press, London.
Mechelke K., Christian P.: (1958) Formen und Bedeutu ng a bnormer Rege 1ungs vorgange im Kreislauf. Kreislaufforschung, 47, 246 -2 60. Mesarovic M.D. :(1960) The Control of Multivariable Systems. New York. Mesarovic M.D.:(1968) System Theory and Biology. Springer Berlin. McRuer 0 . :(1978) Human Dynamics in Man-Machine Systems. IFAC, Pergamon Press,New York. Robinson D.A.:(1975) Oculomotor Control Signals. In: Basic Mechanisms of Ocular Motility pp. 373 -374, Pergamon Press Rosen R.:(1976) Optimality Principles in Biology. Butterworth, London. Stark L.: (1968) Neurological Control Systems. Plenum Press, New York. Thoma M.:(1973) Theorie linearer Regelungssysteme. Vieweg, Braunschweig. Vossius G.:(1974) Die Augen- und Kopfbewegungen als Verarbeitungsergebnis hoher organis. Systemstrukturen. Proc. of the 5th Congr. of the Dtsch.Ges.f.Kyb. Oldenbourg. Werner J. Vossius G.:(1972) Die Identifizierung der effektiven Riickkopplung der sakkadischen Augenbewegung durch das ZNS. Kybernetik,10, 98 -102. Werner J.: (1981) Control Aspects of Human Temperature Regulation. Automatica, in Press. Zypkin J.S.:(1970). Adaption und Lernen in kybernetischen Systemen . Oldenbourg Verl ag MUnchen.
PLENARY PAPERS
PART B
PROBLEMS OF HIGH LEVEL CONTROL IN MAN G. Vossius Institute of Biomedical Engineering, University of Karlsruhe, Karlsruhe, Federal Republic of Germany
Abstract. The control concept used in man at lower levels might be already very spezialized. In addition the higher controls are not only capable of adaptively adjusting the parameters of the dependent loops but also of changi ng the cont ro 1 st rategy. I n order to fu lfi 1 thei r task the hi gher centers have at first the momentary effective measurement vector from fuzzy coupled receptor arrays and must establish sufficiently a qualitative and quantitative reference system, because man has no built-in scheme of the internal and external sphere. Only after achieving this, may the control functions be executed. To evaluate the functional concept and the quality of control, especially at higher levels, for instance the principles of observability and controllability ought to be helpful too, because their requirements mi ght not always be fulfil 1 ed. This enforces other strategies of control which may restrict the performance of the system.
Keywords. Adaptive control; identification; selforganisation; optimal control; biocontrol; observability and controllability; fuzzy systems. I NTRODUCTI ON The last two plenary papers presented in 1975 and 1978 looked upon the characteristcs of an external control situation, for instance man-machine or socio-technical systems. This lecture was initiated by the IFAC-workshop which took place at Karlsruhe in 1979. The topic of that workshop was the funct i ona 1 structu re, the concepts of control effective within man itself. The goal was to screen the known facts clearing mi nor open quest ions and to specify centers of gravity which might permit better insights in the requirements and potentials the organism needs to execute the spectrum of control it is capable of. The main aspects of th i s topi c bei ng brought up in the course of the workshop or bei ng pert inent generally are discussed in the following. In this connection the talk is concerned mainly with the physiological sphere not considering other aspects, as for instance the psychological one.
THE MAIN FUNCTIONAL COMPONENTS OF BIOLOGI CAL CONTROL SY STEMS The organi sat i on of cont ro 1 in man may be subdivided in a horizontal or a vertical. In a horizontal ordering you can differentiate the wellknown levels of: - Feed forward control respectively stabilisation e.g. the different modes of reflexes or the buffering systems and so forth. - The "simple" feedback loop with fixed parameters. - The adaptive control loop. which might be equipped already with the capability to store former conditions of operation, called in this context learning. - Following is the level of process identification and establ ishing the appropriate cont ro 1 mode. The organism is not only confronted with a changing environment but also with a not-
360 I
360 2
G. Vossius
fixed somewhat floating inner world . In addition at each level the organism often has the task to coordinate a more or less large number of control loops stabi 1 ising various physiological functions . - This task is executed by selforganizing systems, being able to identify their own frame of organization, and to project the st ructure of superi or cont ro 1 in connect i on wi th requ i rements imposed by the outer world. - All of th i s can be topped by the genera 1 but a bit blurred scheme of a multi level-multi - goal system, introduced about t\~O decades ago by MESAROVIC . Compared with technical systems the organism has a few more problems to solve in order to execute its control; for examp1e: - The measurement devices, the receptors, have often a rather limited range and their characteristic is a powerfunction . In addition the material embedding the receptors di s torts the phys i ca 1 or chemical signal,the mechanical coupling is sliding . Therefore nature uses receptor a rrays rather than si ngl e receptors, to enhance the range and prec is i on of the measurement. The appropriate statical and dynami ca 1 signa 1 vector has to be computed on - l i ne . - A long evolutionary process in our scientific thinking was required to separate the different physical and chemical modalities, their scaling, and - if possible establishing an absolute reference poi nt. In man nature has taken care of the separation of modalities by the constructi on of the receptors (transducers) . The scaling is apparrently not built in, there doesn't exist a quantification system . Consequently the organism has on all levels to establ ish procedures which link the physical and chemical quantities, pictured as time intervals of nervepulses - in most of the cases in a nonli near manner- to an i nterna 1 ana 1ogous reference system . This includes the ability to build up reference extracting systems and update them continously . For the control loops the reference point of operation has to be determined . - The existence of life is tied to working controls . One ,of the requirements for con trol is an urli irectional flow of informa-
tion . In the single cell this ul1directional information flow is secured for instance by about 500 to 3000 enzymes steeri ng the bi 0chemical processes . Within the nervous system the biochemical component of the synaptic transmission has especially evolved to enforce the unidirectionality. Above the unidirectional flow of information and the introduction of the set point the operational conditions of control in man has to be defined in a much broader sense up to the 1ay out of the total concept of the central multifunctional control. This needs as a supposition a reference frame of the externa 1 and i nterna 1 worl d. The reference system has to be fed by an equivalent system extracting the informat ion assembled by the receptors through more and more sophisticated procedures. To fu lfi 11 these tasks each doma i n has to have a good logic structure in itsel f, separating one from the other. Therefore the functional structure of the organism may be subdivided also in a vertical manner, which might be called domains: - Domain of measurement with extraction of the effective vector - Domain of establishing the reference in quality and quantity - Domain of prediction - Domain of control The division in these domains is to a certain extent schematic and arbitary. The question which specific function, e. g. the id entification or the modelling is to be attributed to which domain is largely dependent on the actual structure of the specific system, or vice versa: The tasks outlined in different domains might very well be executed combined in one functional block. THE FUNCTIONAL STRUCTURE OF BIOLOGICAL CONTROL SYSTEMS One of the most promi nent cha racteri st i cs of biological control seems to be that on one side it behaves rather sloppily . The control is lined up just enough to fulfil the oncorrmi ng demands, not ca ri ng too much about such requirements as robustness or quality . The internal controls and the reserve capacity of an untrained subject therefore soon fail when the subject is suddenly exposed to forceful demands . On the other si de the same control systems wi 11 organize themselves very efficiently, if
Problems of High Level Control
the training takes place slowly giving them the chance to do so . This multi various face of biological control, depending on the si tuation and the prehistory man lives in, makes it so difficult for the researcher to evaluate the concept realizing the control as a certain body function . In the analysis of biological systems the researcher evaluated therefore at fi rst the class i ca 1 input - output re 1 at i onsh i p and deri ved from it a linear black box model. In most cases these models have been not only incorrect for drastic phYSiological or pathological changes of the internal status of the subject or of the environment but valid just for a very limited range. The biological systems incorporate essential nonlinearities . Therefore phYSiologists started conducting the analysis more closely in accordance with the physiological function to prove experimentally the assumptions made in the process of modelling with good success . As an example for analysis conducted by ROBINSON et.al. mi ght be cited: Focussing on a new target the eye executes fast movements, so - ca 11 ed saccades, wi th great pr ecision . The question arises wether these saccades are carried out in an open l oop manner, with the brai n centers creating their commands very conSistently, or wether cont ract i on of the externa 1 eye mus cels is controlled. In recording the activi ty of the specific nerv cells by means of microelectrodes ROBINSON found, that the difference between the nerve pul se command signal and the signal effecting the contraction of the eye muscels is fed into a so called burst generator, nerve cells responding to small error signals with very high rates of firing similar to a differentia tion and a limiting characteristic for larger magnitudes of error. An integration of the burst sequence leads to the contraction signal and represents the eyeposition signa 1 for compari son with the command signal, thus cloSing the loop . Using this circuit the eye may be moved fast even for sma 11 errors whereas for 1 arge errors the limiting characteristic prevents the muscels from being damaged by too forceful contraction . Because of the very high gain factor of the burst cells, the circuit tends to be unstabl e. Therefore the loop should be opened at rest by a switch which has to be closed synchronously with the command signal. So-called tonic nerve cells
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3603
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a 1ways reproduce a nerve pu 1se sequence corresponding to the last command signal holding the eye in position (neglected in Fig.l) Fig.1 presents the basic scheme of the control loop (after ROBINSON) . u(t} com mandsignal; C Comparison; S Switch; eB(t} output of burst cells BC; I integrator . This loop has a rather simple configuration with no need to change its parameters . It shows also a very specific design well adjusted to its task . The latter might be true at this level, as is indicated by other examples: Therefore it is difficult to produce a general scheme or concept of biologi cal control applicable to a wide range of prob 1ems . That comp 1 i cates the ana lys i s of biological control systems. INTEGRATO~
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Control loop of the contraction of eye muscles (after Robinson) The last example demonstrated the control of the execution of the command signal, leaving the question undecided, how it is ass ured that the command si gnal itself for this lower loop has the appropriate magnitude . An analysis carried out by the author together with WERNER re vea 1ed that the ga in of this loop is adaptively controlled at the next level . The former loop was embed ded completely within the special nerve centers themselves . At this stage the error signal results from the position of the target on the ret i na of the eye . The poi nt of reference is the so-called fovea centra lis, the locus where the retina possesses the highest resolution. The task of the control loop is rather simple: The eyeball has to be turned exactly by the angle of the difference between the fovea central is and the picture of the target on the retina . The gain has a magnitude of "one" (Fig . 2) . The loop can be treated as a samp 1 ed data system since the saccadic eye movements
C. Vossius
3604
occur at certain time intervals only. Experi ments conducted in open loop cond it i on by adding continously the eye position to the target proved the adapti ve control of the gain is achieved by dividing the difference of the last two samples of the eye position by the difference of the error yl e . At the first glance this fact is surprising. The necessity for the adaptive control becomes obvious, if one takes the conditions for the operation of the brain into account: Origina lly there existed no knowledge about any quantity in the brain. This knowl edge has a 11 to be ext racted by observing the various processes and comparing this observation with the result of its own reaction. The adaptive procedure used in this example achieves the extraction of the reference equivalent in a very simple and effective way without expressing it as a quantity and with the possibility of continous correction. In addition this procedure has the abi 1i ty to correct for certa in unwanted changes in the nervous centers 1ike dying nerve cells.
is much more difficult if not impossible. Although from the systems point of view it is quite obvious that a control loop has to have a set point, physiologists are questioning this part sometimes being unable to detect it. In the simplest way the set poi nt mi ght be gi ven as the cross i ng poi nt of the characterisics of the system's components. For such a system it would be valid that it is comp letely selfsustaining as poi nt ed out by WERNER . The prob le m is that such a system neither can be brought back to its operating point , be corrected by hi gher systemic i nfl uences incase of unwanted deviations nor may the set point be shifted if necessary in the collaboration withother systems. This situation is rather risky for the organis m. In any case this is admissible only if proc esses stabilizing themselves are incorporated in the system at crucial positions like biomedical reaction with a tendency towards a stable operating point. For the basic control of body temperature with its metabolic components such a stabilization mode might be true.
Fig.2 Adaptive control of the saccadic eye movement
Proceeding to the next level of control, signal analysis and interaction of different control pathways servi ng the same goal become more promi nent. A quantat i ve ana 1ysis of the eye tracking movement was carried out by GOUIS et al. This allows me to illustrate this level of control using the same system. The eye movement cons i sts of two components: A rapi d step 1i ke one, the saccades, you are already familiar with, and a slow continuous one, following the pattern of the target mov ement.
Fig.2 shows the scheme of the control loop of the saccadic eye movement. u(t) command signal; e(t) error; S sampler; eN error at saccade N; H hold with delay; G gain factor of the loop; LlYN calculation and hold of the difference of the last two eye positions; CEM loop for the control of eye muscle contraction (Fig .I ); EN actual eye position . I n the system dealt with so far the question of the set or reference point was to be answered very eas i ly. Nature took special care to establ ish it. In biological control systems, especially in the ones sustaining functions as circulation or body temperature, the defi nit i on of a set poi nt
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Problems of Hi gh Leve l Control
As ca n be seen in Fig . 3 , the continuous movement tries to trace and to predict the target pattern whereas t he saccades correct the error made by the continous system. Fig . 4 shows a scheme of the total system. The impo rtant functions of it wi 11 be expl ained brief ly. - The processing of the signal th r ough the retina and the following nervous centers creates a delay time of about 120 ms . In the continuous branch the signal is processed through a time window of 60 ms duration to calculate t he mean va l ue of the target's velocity . - A O- order track and hold stores the 1ast va 1ue for 60 ms incase of a saccade to prevent false compu{ion of the velocity. - A special characteristic limits the maxi mum speed of the continuous movement . - An adaptive Proportiona l -Integral - Controller adjusts the velocity of the continuous movement to the one of the signa 1 and to t he mode of operation, for instan ce during the tracking with artificia l externa l feedback . The magnitude of the branch output is weighted according to the apparent regu l arity of t he signal. - In the saccadic branch the decision has to be made wether an error wi 11 be corrected by a saccade or by changing the ve l ocity of the cont i nuous movement. The sac cade interupts the signa l processing in the continuous branch. - The magnitude of the correcting saccade is computed by taking into account the predicted velocity of the target movement and in order to mi nimi ze the mean error of the movement . According to this analysis the system is running on a clock cycle of about 60 ms, which is triggered by the beginning of the movement. The production of the continuous movement is decoupled from the target func tion by a prediction procedure, in this case rather simple, and then in addition adaptively controlled . Th i s concept seems to be va 1id for most of the human movements . The decision wether to correct an error by a saccade or the cont i nuous movement tak es into accou nt the pos i tion error and the velocity error, using an optimal strategy . This analysis demonstrates, that even for the rather simple task of persuing a target with 1 imited speed the organi srn has bui lt
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G. Vossius
3606
to produce an optimal mode of operation if necessary. This example gi ves al so hi nts at the reason that the analysis of biological systems soon becomes so difficult and that the mode 11 i ng of the overa 11 input - output relation does not tell much about the true functional properties of the system, its strong and its weak points . Having analysed one stage of the system for the example outlined here the control of the combined continuous and saccadic eyemovement one discovers that the true inside in the capabilities of the system is transfered to the next stage: e. g. how is the optimal procedure for executing the cor recting saccades establ ished - and so on . PROBLEMS OF HIGH LEVEL CONTROL During the past decade physiologists and bioengineers were trying more and more to trace at least the qua l itative functional structure of the main physiological systems as circulation and respiration and their i nterdependences. As an examp 1e a scheme of the control of the body temperature and its connections to other systems is presented in detail by WERNER . The contro l task of pooling main body functions for an integra ted performance is at the order of multi level-multi-goal systems . But the difficulties arising from the attempt to analyse such a system can imagined by recall ing the complicated structure of the rather small control system for the eye tracking movement. Moreover the question arises wether the criteria appl ied so far to the pattern of ana lysis are sufficient . This is at least doubtful. As already mentioned above the fuzziness with which the measurements are taken is often neglected. (For large receptor arrays like the retina or the cochlea this aspect is especially analysed.) The continuous computation of the measurement vector significant for the system and the implementation of the reference system are achievements especially to be taken into accou nt. At the higher levels of control the formation of the reference is of another order than in the example of the saccadic eyemove ment. A high diver performing a triple so mersault and diving almost splashless into the water has to ha ve a complete i nterna 1 image of the diving pool and the dynamic diving path of his own body to execute the
dive correctly . On the other side normally the movements are conducted at 1east partially in a prograrrrned - predicted - manner. For fast movements the continuous control including the eye would be too slow because of delay times of the system. For instance while performing a tennis stroke it is a 1most i mposs i b1e to change the pattern of the stroke successfully . Only small correcti ons with the hand may be made . The prograrrrned execution of the movements has yet another cause. Playing tennis with a firm grip, arm and hand have still about 10 degrees of freedom left. A unique system measuring the position of the arm does not exist. The receptors are distributed all over the muscels and the joints. Therefore the complete observability is not given. On the motori c side the same is true for the controllability. This might be illustrated again for a tennis player . Without a trainer the player has a good chance to develop wrong patterns of movement severely limi ting his ability of playing. But he will be unable to recognize this fact . The trainer (and the videorecorder) circumvents the gap by correcting the false movement in an external loop while the internal one is missing . The nervous centers of motor control close the gap by building up a model, which has to be updated constantly through daily training. The limited to incomplete observability is not only a problem while executing the actual control task, but is as much a hurdle for the identification, the development of the internal models, the prediction, and the build-up of the reference . Therefore the training of the system of motor control as well as the one of basic physiological functions needs so much time . Despite this deficiency the control in and by man might be conducted in an optimal way . For instance CHOW and JACOBSON or HASTE showed that man is able to perform his movements in an energy or time optimal manner . Other valuable properties of biological sy stems as robustness or insensitivity to pa rameter changes and the stabi 1ity have not been given much attention so far. Physiological systems for instance must be stable, otherwise life would be impossible . But this stabi 1ity is not neccessari ly granted .
Problems of High Level Control in Man
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gai n factor. The blood pressure starts to oscillate with increasing amplitudes causing the patient finally to collaps. The 1i vi ng organism is a status referred to
G. Vossius
3608
by BERTALANFFY as an equi 1 i brium of exchange. The state of the living organism is, accordi ng to BERTALANFFY, an equ i 1 i bri urn of flowing exchange. This equilibrium is like the one of a pyramid balancing on its tip. Additionally the pyramid is not solid but consists of billions of parts more or less tightly interconnected with certain mainlines of a systemic structure. To keep the pyramid on its tip the equilibrium has to be controlled. But the observability is fuzzy and 1 i mi ted, as is the cont ro 11 abi 1 ity. In addition the partitions and the environments are always changing their states. To match these condit ions the control principles appl ied grew more and more sophisticated to keep the pyramid in line for the sake of the equi 1 i brium. The development of modern cont ro 1 theori es is now at a point, at which we corrrnence to gain an idea about the order of magni tude the core of biological control has achieved. But unless we know the functional principal of the core our role in solving the problems of biological control is like the one of man in PLATO'S parable of the cave.
REFERENCES
Allgemeine Neurophysiologie, ed . Gauer, Kramer, Jung (1980). Urban und Schwarzenberg, Miinchen. Bertalanffy, L.v. :(1942). Theoretische Biologie. Bd.II, Gebr. Borntraeger, Berlin. Bouis D., Vossius G.:(1978). Interpendence betvleen the Saccadi c and the cont i nous Eye Movement Control Systems. IFAC, Pergamon Press, S 489 - 493. Chow C.K ., Jacobson D.H.: (1971) Studies of human locomotion via optimal programming . Math . Biosciences, lQ 239 -306. Drischel H. :(1972). Einfiihrung in die Biokybernetik. Akademie -V erlag, Berlin . Haken H.:(1978).Synergetics. Springer, Berl in. Haste H. :(1976) The Complete Optimiza tion of a Human Motion . Math Biosciences, 28 . Kalman R. E. :(1961) On the General Theory of Cont ro 1 Systems. Auto mat i c and Remote Cont ro 1. Bd. I, S. 481 -492, Butterworth, London. Oldenbourg Verlag Miinchen . Lerner A. Y. : (1975) Fundamenta 1s of Cyberne tics. Plenum Press, London.
Mechelke K., Christian P.: (1958) Formen und Bedeutu ng a bnormer Rege 1ungs vorgange im Kreislauf. Kreislaufforschung, 47, 246 -2 60. Mesarovic M.D. :(1960) The Control of Multivariable Systems. New York. Mesarovic M.D.:(1968) System Theory and Biology. Springer Berlin. McRuer 0 . :(1978) Human Dynamics in Man-Machine Systems. IFAC, Pergamon Press,New York. Robinson D.A.:(1975) Oculomotor Control Signals. In: Basic Mechanisms of Ocular Motility pp. 373 -374, Pergamon Press Rosen R.:(1976) Optimality Principles in Biology. Butterworth, London. Stark L.: (1968) Neurological Control Systems. Plenum Press, New York. Thoma M.:(1973) Theorie linearer Regelungssysteme. Vieweg, Braunschweig. Vossius G.:(1974) Die Augen- und Kopfbewegungen als Verarbeitungsergebnis hoher organis. Systemstrukturen. Proc. of the 5th Congr. of the Dtsch.Ges.f.Kyb. Oldenbourg. Werner J. Vossius G.:(1972) Die Identifizierung der effektiven Riickkopplung der sakkadischen Augenbewegung durch das ZNS. Kybernetik,10, 98 -102. Werner J.: (1981) Control Aspects of Human Temperature Regulation. Automatica, in Press. Zypkin J.S.:(1970). Adaption und Lernen in kybernetischen Systemen . Oldenbourg Verl ag MUnchen.