- Email: [email protected]
Report
REPORT
B. N. PETROV Chairman of the Theoretical Committee of I.F.A.C. I have the pleasant but difficult task of summarizing the main results of the work of the sections of the First International I.F.A.C. Congress on the problems of the theory of automatic control. On these problems, 139 papers have been read in nine sections, with a large number of questions and discussions contributed by over 330 participants at the Congress. The very intense activity which manifested itself in discussing the problems of automatic control characterizes the general state of the theory of automatic control. Recent years, and particularly the last decade, have been characterized by rapid developments in this new field of science. It is not by accident that a larger number of papers were presented than could be included in the programme of the Congress, neither is it because they were of low quality, the reason is that the number of good papers presented was very large. Discussion, at the Congress, of the more important problems of automatic control is a clear manifestation of the high standard of development of the theory of automatic control and of the wide application of strict mathematical methods for solving the basic problems of analysis and synthesis of control systems. During recent years some very general and effective methods of solving complex problems have been developed. The theory of automatic control has become an accurate technical science which possesses effective means for investigating and designing automatic systems. Statistical methods have penetrated into practically all the fields of the theory of automatic control. The principle of the maximum, and the methods of dynamic programming, provided a basis for the theory of optimum systems. The apparatus of mathematical logic is being applied for evolving a structural theory of automatic systems. The theory of invariance, methods of designing multiple connected and non-interacting control (regulation) systems and other new theoretical trends have been developed to a considerable extent. A general theory of automatic control is in the process of formation. Finally, in the field of automatic control there is still a large number of unsolved problems which will require further development of mathematical methods. In addition to developing new methods, earlier applied methods are being further developed, particularly approximate methods of calculation of automatic systems of regulation and control, for instance, the method of harmonic equilibrium, frequency methods, etc. These methods have been developed in a form which is convenient for use in practical engineering. . The slogan of the Congress, 'Theory-widest application. technical means-maximum reliability, automation systemshigh effectiveness', characterizes very aptly the trend of work in progress in various countries during recent years. In addition to discussions on the important problems of the theory and on developed methods of calculation of automatic regulation and control systems, much attention has been paid by the participants of the Congress to new principles of designing automatic systems and, particularly, self-adjusting systems, self-adapting and self-learning systems, combined systems,
control systems using computers and logical elements, and other new types of automatic systems. I will now review briefly the scientific problems considered in the individual sections. I should like to ask the forgiveness of the authors of papers and of the participants in the discussions of the Congress for not including their names, due to lack of time, when discussing the problems which were dealt with in the papers and discussions, the majority of which were relevant and interesting. In the section on continuous linear systems, the problem of the invariance theory and of designing multiply-connected systems and non-interacting regulation proved of the greatest interest and produced the largest number of discussion contributions. This is obviously due to the fact that developments in engineering lead to more complex automatic systems, to the necessity of analysis of systems with numerous regulated variables and to applying systems in which the action is based on deviations and on disturbance (load), etc. Even now the theory provides the main trends in designing highly perfected systems which are not too sensitive to harmful disturbances and which follow very accurately the control actions. Of considerable interest in this section was the problem of analysis of multiple connected regulation systems, general methods of synthesis of the structures of multiply-connected regulation systems, methods and means of improving the dynamic properties of systems of automatic regulation with one or several regulated quantities, and also problems of the theory of systems containing delay elements. Of interest also were the papers which dealt with perfecting the criteria of stability and of evolving more general methods of evaluating the quality of control systems, which represent the sum total of various methods developed earlier for solving this problem. In this section 23 papers were read and over 40 people participated in the discussions. The work of the section on the theory of continuous nonlinear systems, in which 14 papers were read and 30 people contributed to the discussion, encompassed a wide range of problems of analysis and synthesis of non-linear, continuous systems of automatic regulation and control. A review was given of the methods of investigation of such systems, both accurate and approximate methods. A large number of papers were devoted to the development of the method of harmonic equilibrium. This method, which is used extensively in engineering practice, was extended in the matrix form to the case of multi-periodic oscillations, to the study of phenomena of subharmonic and upper-harmonic resonance, synchronization of oscillations, parametric amplification, etc. Forced oscillations in non-linear systems were considered. By means of the method of harmonic equilibrium, combined with the method of statistical Iinearization, an approach was found to the solution of certain problems of synthesis of systems in the case of random inputs. By applying various variants of the method of harmonic linearization it became possible to study the influence of limiting the power of the supply sources on regulation processes
1088
1098
REPORT
and systems, to determine the conditions for suppressing self-generated oscillations by means of external periodic effects and the methods of suppressing self-generated oscillations in systems containing play. Furthermore, the variant of the method of harmonic linearization was considered which is based on applying logarithmic frequency characteristics. In the discussion of these papers two points of view were expressed, one was that the method of harmonic equilibrium, although extremely effective, has to be used with care, since, due to the absence of points of intersection of the described functions, they do not provide a sufficient condition of stability. Particularly, in the absence of intersection points, complex self-generated oscillations may exist in the system. The second point of view was that the method of harmonic equilibrium is a very effective and simple method and its use can be extended for obtaining subharmonic solutions and, in the cases which occur in practice, this method provides correct results. At the meetings of this section problems of the influence of programmed changes of the amplification coefficient on the quality of the process, problems of using semi-proportional elements in regulators, methods of computing static characteristics of complicated non-linear systems and a new method of calculating the integral quadratic estimation of non-linear regulation systems were also considered. One of the new and rapidly developing branches of the theory of automatic control is the theory of discrete systems. The basic problems in this field are the problem of analysis and synthesis of ordinary discrete automatic systems including relay systems, pulse and digital systems and also the development of methods of designing optimum and self-adjusting discrete systems. In the field of the theory of relay systems, main attention was paid in the papers presented to the Congress to accurate and approximate methods of analysis of subharmonic oscillations. The problems of optimizing from the point of view of speed of response during random actions were also considered. The theory of pulse systems has been elucidated to the greatest extent during this Congress. A review was presented of the mathematical methods of investigation of such systems, considerable attention was paid to methods of calculating multiple and multiply-connected systems, systems with variable parameters and methods of statistical calculation of pulse systems. In the presented papers the difficult problems relating to non-linear pulse systems were also considered. For these the method of the difference phase-plane was applied, by means of which methods were developed for investigating amplitude pulse systems. In the field of optimum pulse systems, problems of selecting the structure of such systems without imposing any limitations, and for the case of imposing limitations as regards saturation and energy, were dealt with. Methods of designing self-adjusting systems with feedback based on a quality criterion have also been considered. In the field of the theory of relay pulse (digital) systems, the simplest systems of such a type were dealt with on the basis of the phase-plane method and introduction of a random delay time. Elements of the theory of digital automatic systems have been developed. The effect of quantizing was evaluated, a method of investigating periodic regimes was developed and also a method of synthesis from the conditions of compensation of the delay time and materialization of optimal processes. At this section 64 people spoke and altogether 23 papers were read, a part of which contained new ideas and methods which have not been dealt with hitherto in literature. The idea of
designing self-adjusting pulse systems based on using feedback of a quality criterion and the idea of designing optimum digital systems on the basis of the method of dynamic programming are considered as being the most interesting ideas in the field of the theory of discrete automatic systems. In this section there was an extensive and useful oiscussion which was most lively on problems of application of digital computing equipment in pulse control systems, investigation of non-linear pulse systems by means of the phase space methods, and application of operator methods for analysis of pulse regulation systems. The necessity of developing methods of analysis and synthesis of non-linear pulse systems and systems subjected to random effects was emphasized. In the section relating to stochastic problems of automation, several scientific trends were dealt with. One of the main problems of the modern statistical theory of control systems is the problem of statistical analysis and synthesis of non-linear systems. In papers dealing with this problem, and during the discussion of these papers, three differing trends emerged: development and generalization of the method of statistical linearization and its applications; working out of an accurate theory for a certain class of nonlinear system on the basis of the Markov theory of random processes; development of methods of synthesis of systems reduced to linear ones. During the discussion it appeared that scientists of various countries expressed great interest in the method of statistical linearization which in its basic idea is near to the method of harmonic linearization in the deterministic theory of non-linear systems. In the field of application of the theory of Markov random processes to the analysis of automatic systems, in addition to the people who presented papers, Soviet scientists who participated "in the discussions presented a number of interesting results which hitherto have not been known outside the Soviet Union. In the field of the statistical theory of non-linear systems which are reduced to linear ones, a number of interesting results emerged during the discussion which have promising applications in the design of selfadjusting and self-optimizing systems. A second interesting trend which created a lively discussion was the theory of statistical synthesis of linear systems. In this field, which has been well developed in the works of American and Soviet scientists, the discussion has shown that there are two new competing trends in the U.S.A. The first trend is the application of methods of dynamic programming for determining the optimum programme of the controlling part, the second trend is the development of methods of direct determination of differential or difference equations of optimum systems. The problem of finding algorithms of optimal systems also created much interest. It was shown that in this field the major part of the problem of detecting and optimal processing of information in presence of random noise and disturbances can be considered from a single point of view and solved by a single general theoretical method. In addition to the papers and discussions on the above enumerated three basic trends, the section of stochastic problems also considered the problem of experimental determination of the characteristics of systems and of objects of control and the statistical characteristics of random processes, statistical calculation of linear systems, investigation of errors of transformation of continuous information into discrete (digital) information and also the problem of applications of methods of the information theory to evaluating the throughput capacity of automatic systems and its elements. Altogether there were 17 papers and 40 discussion contributions in this section.
1089
1099
B. N. PETROV
In the section on the theory of optimal systems, 12 papers were discussed, to which about 40 people contributed. In this section problems of the theory of optimal systems were considered which encompass general methods of investigation of optimization problems, as well as the results of a similar study of individual concrete problems. The general complex of problems of the theory of optimal systems is linked principally with the development of methods of solution of non-classical variational problems. In this respect a paper devoted to the maximum principle in the theory of optimal systems of automatic control was of major interest. The speaker and the contributors to the discussion mentioned that this principle provides an effective method of investigation of non-linear problems of optimization, with very general limitations imposed on the controlling function. The maximum principle is one of the general principles and is applicable to a very wide class of problem. In this section much attention was paid to the problems of synthesis of optimal systems. In this respect methods of inverse time and methods of constructing isosurfaces in the phase-space of systems, based on applying the maximum principle, were considered. During the discussion examples of synthesis of concrete systems on the basis of applying these methods were mentioned. An example of synthesis of a system of the third order which is optimal from the point of view of fast response (action) was also considered. In the discussion, the relation between the maximum principle and the method of dynamic programming was dealt with. Applied to problems of optimal control the method of dynamic programming yields functional equations which are closely. linked with the equations of the maximum principle. It was shown that considerable computation difficulties are involved in applying the method of dynamic programming. The formulation and solution of certain problems of optimal control for systems with distributed parameters, which can be described by equations with partial derivatives, were also received with interest. At the section on the theory of self-adjusting systems 20 papers were presented. Systems of biological and mechanical nature were considered, which have the capacity of adapting themselves to changing conditions for the purpose of ensuring such an interaction between the controlled object and the ambient medium which will provide the best state of the controlled object in a certain sense. In this section systems were considered which ensure adaptation by automatic probing as well as by changing the state of the system along an open or closed cycle without automatic probing. Problems of the statistical theory of systems of automatic optimizing, of the dynamics of self-adjusting systems, of bioelectrical control, of certain properties of physiological systems of regulation, and also problems of the theory of selfadjusting autopilots were dealt with. The discussion in the section on self-adjusting systems was one of the liveliest and the audience was very large. Usually there were more than 200 people at this section. In the discussion over 70 people participated and more than 200 questions were asked. This confirms the particular attention of the scientific community to this very important and promising trend in the theory of automatic control. Interesting papers were presented on the theory and application of computing equipment intended for approximate determination of the characteristics of objects of automatic control systems and of self-adjusting systems. There was a lively discussion on papers relating to problems of biological cybernetics. Soviet, Yugoslav and American scientists have
made a considerable contribution to the development of the theory of designing systems which are similar in many respects to living organisms. The papers in this section were devoted to problems relating to the study of self-adapting systems of a biological nature. The results obtained by a group of scientists on the problem of bio-electric control has attracted deserved attention. There is a real possibility of utilizing biocurrents generated in the organism for controlling artificial organs which substitute for lost ones. Investigation of biological systems by the methods of the theory of automatic regulation and control is being used on an increasing scale. Similarly, cybernetics begin to yield interesting results which were reflected in the papers presented at the Congress. In a number of papers, and in the discussions, the necessity was pointed out of investigating and developing self-adjusting systems which are capable of operating in the case of fast drifting of the characteristics and the parameters of the controlled object. These problems are closely linked with the problems of the stability of the process of self-adjusting. Therefore, the importance of accurate mathematical formulation of the conditions of stability of self-adjusting systems during various regimes of their operation was underlined repeatedly. The structural theory of relay equipment is at present one of the important trends in the theory of automatic control. It originated as a result of application to problems of analysis and synthesis of relay circuits of automatic equipment, but the methods resulting from it are now applied for solving a wide range of automatic control problems. On the basis of this method, a number of trends emerged in the modern general theory of automatic computing and control equipment: the theory of logical and nerve networks, and the theory of finite automats, etc. The theory of producing signals is closely associated with the structural theory of relay equipment. Work in these fields is carried out in a number of countries and every year 150 to 200 scientific papers on these subjects are published throughout the world. In the section on the theory of structures and on producing signals seven papers were presented and 36 people participated in the discussion. A number of important problems of the theory of relay equipment and of the theory of producing signals were broached, including the following: the problem of evolving methods of synthesis of relay equipment; designing relay structures with a given reliability; application of a new logical language for describing discrete sequences; mechanization of processes of analysis and synthesis of relay equipment; stability against interference and effectiveness of transmission of information in telemetering systems. In view of the limited number of papers in this section, and particularly in view of the absence of papers of outstanding scientists from the U.S.A. and a number of other countries working in this field, there was no possibility in this section of elucidating numerous problems of the modern theory of structures and of producing signals. This gap was partly filled by the contributions of Soviet and foreign scientists during the discussions which followed the papers presented in this section. It was proposed to organize, in the future, a special symposium on the theory of relay equipment and the associated scientific fields. In the section on special mathematical problems 13 papers were read and 25 people participated in the discussion; several scientific problems were discussed. The first problem was that of unifying the problem of
1090
1100
REPORT
finding and investigating steady-state regimes in automatic regulation systems which can be described by differential equations with continuous right-hand parts. A number of important aspects of this problem were elucidated in the papers. The ideas were expressed more precisely and a stricter mathematical definition was given of the stable steady-state regime. Furthermore, the results of investigations of the dependence of periodic solutions of systems of differential equations on the parameters were summarized. A second problem dealt with in this section was that of investigating non-linear systems with discrete characteristics. In this field the problems were considered of determining steady-state regimes in analogous systems. There was a lively discussion. A third problem discussed in this section was that of the stability of regulated systems. The main problems dealt with in the papers and in the interesting discussion related to the further development of methods of determination of the stability by utilizing the second method of Lyapunov. In the section on simulation and experimental methods of investigation, I1 papers were read and 12 people participated in the discussions. The problem of application of methods of simulation and of experimental methods for investigating and designing complex control systems attracted the deserved attention of the Congress participants. The methods of simulation used recently include analogue equipment and also digital and combined equipment, and these methods permit mechanization of individual aspects of human mental effort and to a large extent permit increasing its effectiveness. The experimental technique is improving in accuracy and conditions are being created for a major economy of means involved in carrying out full-scale ('natural') investigations. In the papers and in the discussion a picture of the develop-
mcnt of m~ans and methods of digital simulation emerged. ]\icw meth ods of reproducing second-order curves by means of digital equ;pment were presented which are applicable to programme control systems. Combined digital-analogue eqUipment was considered, particularly equipment for simulating the kinetics of a nuclear reactor. In addition to increasing the accuracy, the application of digital methods results in a considerable widening of the permissible range of variation in the values of the variables. A method of solving differential equations with partial derivatives on electronic models, based on the relation between these equations and random processes occurring in electrical circuits subjected to random disturbances, created such interest. In one of the papers original modelling equipment was described which operates on alternating current of an increased frequency, and consists of passive circuits in combination with multiple servo-system. This equipment ensures a relatively high accuracy and has the feature of reversibility (including the non-linear elements), which extends considerably its potentialities. New ideas in the field of optimization of the work of systems for controlling production processes, and applying electronic models, opens up wide prospects both in designing optimum systems and also for improving the accuracy of the mathematical description of processes to be controlled. I believe I express the general opinion of the participants of the Congress if I say that evaluation of the papers, the fruitful discussions which followed, and the extensive exchange of opinions between the scientists of various countries, which took place in a cordial atmosphere, will have a great influence on the further development of the theory of automatic control and will contribute to still more effective development of this new branch of science and engineering. A new brilliant page in the history of science has been written.
\091
1101
B. N. PETROV Chairman of the Theoretical Committee of I.F.A.C. I have the pleasant but difficult task of summarizing the main results of the work of the sections of the First International I.F.A.C. Congress on the problems of the theory of automatic control. On these problems, 139 papers have been read in nine sections, with a large number of questions and discussions contributed by over 330 participants at the Congress. The very intense activity which manifested itself in discussing the problems of automatic control characterizes the general state of the theory of automatic control. Recent years, and particularly the last decade, have been characterized by rapid developments in this new field of science. It is not by accident that a larger number of papers were presented than could be included in the programme of the Congress, neither is it because they were of low quality, the reason is that the number of good papers presented was very large. Discussion, at the Congress, of the more important problems of automatic control is a clear manifestation of the high standard of development of the theory of automatic control and of the wide application of strict mathematical methods for solving the basic problems of analysis and synthesis of control systems. During recent years some very general and effective methods of solving complex problems have been developed. The theory of automatic control has become an accurate technical science which possesses effective means for investigating and designing automatic systems. Statistical methods have penetrated into practically all the fields of the theory of automatic control. The principle of the maximum, and the methods of dynamic programming, provided a basis for the theory of optimum systems. The apparatus of mathematical logic is being applied for evolving a structural theory of automatic systems. The theory of invariance, methods of designing multiple connected and non-interacting control (regulation) systems and other new theoretical trends have been developed to a considerable extent. A general theory of automatic control is in the process of formation. Finally, in the field of automatic control there is still a large number of unsolved problems which will require further development of mathematical methods. In addition to developing new methods, earlier applied methods are being further developed, particularly approximate methods of calculation of automatic systems of regulation and control, for instance, the method of harmonic equilibrium, frequency methods, etc. These methods have been developed in a form which is convenient for use in practical engineering. . The slogan of the Congress, 'Theory-widest application. technical means-maximum reliability, automation systemshigh effectiveness', characterizes very aptly the trend of work in progress in various countries during recent years. In addition to discussions on the important problems of the theory and on developed methods of calculation of automatic regulation and control systems, much attention has been paid by the participants of the Congress to new principles of designing automatic systems and, particularly, self-adjusting systems, self-adapting and self-learning systems, combined systems,
control systems using computers and logical elements, and other new types of automatic systems. I will now review briefly the scientific problems considered in the individual sections. I should like to ask the forgiveness of the authors of papers and of the participants in the discussions of the Congress for not including their names, due to lack of time, when discussing the problems which were dealt with in the papers and discussions, the majority of which were relevant and interesting. In the section on continuous linear systems, the problem of the invariance theory and of designing multiply-connected systems and non-interacting regulation proved of the greatest interest and produced the largest number of discussion contributions. This is obviously due to the fact that developments in engineering lead to more complex automatic systems, to the necessity of analysis of systems with numerous regulated variables and to applying systems in which the action is based on deviations and on disturbance (load), etc. Even now the theory provides the main trends in designing highly perfected systems which are not too sensitive to harmful disturbances and which follow very accurately the control actions. Of considerable interest in this section was the problem of analysis of multiple connected regulation systems, general methods of synthesis of the structures of multiply-connected regulation systems, methods and means of improving the dynamic properties of systems of automatic regulation with one or several regulated quantities, and also problems of the theory of systems containing delay elements. Of interest also were the papers which dealt with perfecting the criteria of stability and of evolving more general methods of evaluating the quality of control systems, which represent the sum total of various methods developed earlier for solving this problem. In this section 23 papers were read and over 40 people participated in the discussions. The work of the section on the theory of continuous nonlinear systems, in which 14 papers were read and 30 people contributed to the discussion, encompassed a wide range of problems of analysis and synthesis of non-linear, continuous systems of automatic regulation and control. A review was given of the methods of investigation of such systems, both accurate and approximate methods. A large number of papers were devoted to the development of the method of harmonic equilibrium. This method, which is used extensively in engineering practice, was extended in the matrix form to the case of multi-periodic oscillations, to the study of phenomena of subharmonic and upper-harmonic resonance, synchronization of oscillations, parametric amplification, etc. Forced oscillations in non-linear systems were considered. By means of the method of harmonic equilibrium, combined with the method of statistical Iinearization, an approach was found to the solution of certain problems of synthesis of systems in the case of random inputs. By applying various variants of the method of harmonic linearization it became possible to study the influence of limiting the power of the supply sources on regulation processes
1088
1098
REPORT
and systems, to determine the conditions for suppressing self-generated oscillations by means of external periodic effects and the methods of suppressing self-generated oscillations in systems containing play. Furthermore, the variant of the method of harmonic linearization was considered which is based on applying logarithmic frequency characteristics. In the discussion of these papers two points of view were expressed, one was that the method of harmonic equilibrium, although extremely effective, has to be used with care, since, due to the absence of points of intersection of the described functions, they do not provide a sufficient condition of stability. Particularly, in the absence of intersection points, complex self-generated oscillations may exist in the system. The second point of view was that the method of harmonic equilibrium is a very effective and simple method and its use can be extended for obtaining subharmonic solutions and, in the cases which occur in practice, this method provides correct results. At the meetings of this section problems of the influence of programmed changes of the amplification coefficient on the quality of the process, problems of using semi-proportional elements in regulators, methods of computing static characteristics of complicated non-linear systems and a new method of calculating the integral quadratic estimation of non-linear regulation systems were also considered. One of the new and rapidly developing branches of the theory of automatic control is the theory of discrete systems. The basic problems in this field are the problem of analysis and synthesis of ordinary discrete automatic systems including relay systems, pulse and digital systems and also the development of methods of designing optimum and self-adjusting discrete systems. In the field of the theory of relay systems, main attention was paid in the papers presented to the Congress to accurate and approximate methods of analysis of subharmonic oscillations. The problems of optimizing from the point of view of speed of response during random actions were also considered. The theory of pulse systems has been elucidated to the greatest extent during this Congress. A review was presented of the mathematical methods of investigation of such systems, considerable attention was paid to methods of calculating multiple and multiply-connected systems, systems with variable parameters and methods of statistical calculation of pulse systems. In the presented papers the difficult problems relating to non-linear pulse systems were also considered. For these the method of the difference phase-plane was applied, by means of which methods were developed for investigating amplitude pulse systems. In the field of optimum pulse systems, problems of selecting the structure of such systems without imposing any limitations, and for the case of imposing limitations as regards saturation and energy, were dealt with. Methods of designing self-adjusting systems with feedback based on a quality criterion have also been considered. In the field of the theory of relay pulse (digital) systems, the simplest systems of such a type were dealt with on the basis of the phase-plane method and introduction of a random delay time. Elements of the theory of digital automatic systems have been developed. The effect of quantizing was evaluated, a method of investigating periodic regimes was developed and also a method of synthesis from the conditions of compensation of the delay time and materialization of optimal processes. At this section 64 people spoke and altogether 23 papers were read, a part of which contained new ideas and methods which have not been dealt with hitherto in literature. The idea of
designing self-adjusting pulse systems based on using feedback of a quality criterion and the idea of designing optimum digital systems on the basis of the method of dynamic programming are considered as being the most interesting ideas in the field of the theory of discrete automatic systems. In this section there was an extensive and useful oiscussion which was most lively on problems of application of digital computing equipment in pulse control systems, investigation of non-linear pulse systems by means of the phase space methods, and application of operator methods for analysis of pulse regulation systems. The necessity of developing methods of analysis and synthesis of non-linear pulse systems and systems subjected to random effects was emphasized. In the section relating to stochastic problems of automation, several scientific trends were dealt with. One of the main problems of the modern statistical theory of control systems is the problem of statistical analysis and synthesis of non-linear systems. In papers dealing with this problem, and during the discussion of these papers, three differing trends emerged: development and generalization of the method of statistical linearization and its applications; working out of an accurate theory for a certain class of nonlinear system on the basis of the Markov theory of random processes; development of methods of synthesis of systems reduced to linear ones. During the discussion it appeared that scientists of various countries expressed great interest in the method of statistical linearization which in its basic idea is near to the method of harmonic linearization in the deterministic theory of non-linear systems. In the field of application of the theory of Markov random processes to the analysis of automatic systems, in addition to the people who presented papers, Soviet scientists who participated "in the discussions presented a number of interesting results which hitherto have not been known outside the Soviet Union. In the field of the statistical theory of non-linear systems which are reduced to linear ones, a number of interesting results emerged during the discussion which have promising applications in the design of selfadjusting and self-optimizing systems. A second interesting trend which created a lively discussion was the theory of statistical synthesis of linear systems. In this field, which has been well developed in the works of American and Soviet scientists, the discussion has shown that there are two new competing trends in the U.S.A. The first trend is the application of methods of dynamic programming for determining the optimum programme of the controlling part, the second trend is the development of methods of direct determination of differential or difference equations of optimum systems. The problem of finding algorithms of optimal systems also created much interest. It was shown that in this field the major part of the problem of detecting and optimal processing of information in presence of random noise and disturbances can be considered from a single point of view and solved by a single general theoretical method. In addition to the papers and discussions on the above enumerated three basic trends, the section of stochastic problems also considered the problem of experimental determination of the characteristics of systems and of objects of control and the statistical characteristics of random processes, statistical calculation of linear systems, investigation of errors of transformation of continuous information into discrete (digital) information and also the problem of applications of methods of the information theory to evaluating the throughput capacity of automatic systems and its elements. Altogether there were 17 papers and 40 discussion contributions in this section.
1089
1099
B. N. PETROV
In the section on the theory of optimal systems, 12 papers were discussed, to which about 40 people contributed. In this section problems of the theory of optimal systems were considered which encompass general methods of investigation of optimization problems, as well as the results of a similar study of individual concrete problems. The general complex of problems of the theory of optimal systems is linked principally with the development of methods of solution of non-classical variational problems. In this respect a paper devoted to the maximum principle in the theory of optimal systems of automatic control was of major interest. The speaker and the contributors to the discussion mentioned that this principle provides an effective method of investigation of non-linear problems of optimization, with very general limitations imposed on the controlling function. The maximum principle is one of the general principles and is applicable to a very wide class of problem. In this section much attention was paid to the problems of synthesis of optimal systems. In this respect methods of inverse time and methods of constructing isosurfaces in the phase-space of systems, based on applying the maximum principle, were considered. During the discussion examples of synthesis of concrete systems on the basis of applying these methods were mentioned. An example of synthesis of a system of the third order which is optimal from the point of view of fast response (action) was also considered. In the discussion, the relation between the maximum principle and the method of dynamic programming was dealt with. Applied to problems of optimal control the method of dynamic programming yields functional equations which are closely. linked with the equations of the maximum principle. It was shown that considerable computation difficulties are involved in applying the method of dynamic programming. The formulation and solution of certain problems of optimal control for systems with distributed parameters, which can be described by equations with partial derivatives, were also received with interest. At the section on the theory of self-adjusting systems 20 papers were presented. Systems of biological and mechanical nature were considered, which have the capacity of adapting themselves to changing conditions for the purpose of ensuring such an interaction between the controlled object and the ambient medium which will provide the best state of the controlled object in a certain sense. In this section systems were considered which ensure adaptation by automatic probing as well as by changing the state of the system along an open or closed cycle without automatic probing. Problems of the statistical theory of systems of automatic optimizing, of the dynamics of self-adjusting systems, of bioelectrical control, of certain properties of physiological systems of regulation, and also problems of the theory of selfadjusting autopilots were dealt with. The discussion in the section on self-adjusting systems was one of the liveliest and the audience was very large. Usually there were more than 200 people at this section. In the discussion over 70 people participated and more than 200 questions were asked. This confirms the particular attention of the scientific community to this very important and promising trend in the theory of automatic control. Interesting papers were presented on the theory and application of computing equipment intended for approximate determination of the characteristics of objects of automatic control systems and of self-adjusting systems. There was a lively discussion on papers relating to problems of biological cybernetics. Soviet, Yugoslav and American scientists have
made a considerable contribution to the development of the theory of designing systems which are similar in many respects to living organisms. The papers in this section were devoted to problems relating to the study of self-adapting systems of a biological nature. The results obtained by a group of scientists on the problem of bio-electric control has attracted deserved attention. There is a real possibility of utilizing biocurrents generated in the organism for controlling artificial organs which substitute for lost ones. Investigation of biological systems by the methods of the theory of automatic regulation and control is being used on an increasing scale. Similarly, cybernetics begin to yield interesting results which were reflected in the papers presented at the Congress. In a number of papers, and in the discussions, the necessity was pointed out of investigating and developing self-adjusting systems which are capable of operating in the case of fast drifting of the characteristics and the parameters of the controlled object. These problems are closely linked with the problems of the stability of the process of self-adjusting. Therefore, the importance of accurate mathematical formulation of the conditions of stability of self-adjusting systems during various regimes of their operation was underlined repeatedly. The structural theory of relay equipment is at present one of the important trends in the theory of automatic control. It originated as a result of application to problems of analysis and synthesis of relay circuits of automatic equipment, but the methods resulting from it are now applied for solving a wide range of automatic control problems. On the basis of this method, a number of trends emerged in the modern general theory of automatic computing and control equipment: the theory of logical and nerve networks, and the theory of finite automats, etc. The theory of producing signals is closely associated with the structural theory of relay equipment. Work in these fields is carried out in a number of countries and every year 150 to 200 scientific papers on these subjects are published throughout the world. In the section on the theory of structures and on producing signals seven papers were presented and 36 people participated in the discussion. A number of important problems of the theory of relay equipment and of the theory of producing signals were broached, including the following: the problem of evolving methods of synthesis of relay equipment; designing relay structures with a given reliability; application of a new logical language for describing discrete sequences; mechanization of processes of analysis and synthesis of relay equipment; stability against interference and effectiveness of transmission of information in telemetering systems. In view of the limited number of papers in this section, and particularly in view of the absence of papers of outstanding scientists from the U.S.A. and a number of other countries working in this field, there was no possibility in this section of elucidating numerous problems of the modern theory of structures and of producing signals. This gap was partly filled by the contributions of Soviet and foreign scientists during the discussions which followed the papers presented in this section. It was proposed to organize, in the future, a special symposium on the theory of relay equipment and the associated scientific fields. In the section on special mathematical problems 13 papers were read and 25 people participated in the discussion; several scientific problems were discussed. The first problem was that of unifying the problem of
1090
1100
REPORT
finding and investigating steady-state regimes in automatic regulation systems which can be described by differential equations with continuous right-hand parts. A number of important aspects of this problem were elucidated in the papers. The ideas were expressed more precisely and a stricter mathematical definition was given of the stable steady-state regime. Furthermore, the results of investigations of the dependence of periodic solutions of systems of differential equations on the parameters were summarized. A second problem dealt with in this section was that of investigating non-linear systems with discrete characteristics. In this field the problems were considered of determining steady-state regimes in analogous systems. There was a lively discussion. A third problem discussed in this section was that of the stability of regulated systems. The main problems dealt with in the papers and in the interesting discussion related to the further development of methods of determination of the stability by utilizing the second method of Lyapunov. In the section on simulation and experimental methods of investigation, I1 papers were read and 12 people participated in the discussions. The problem of application of methods of simulation and of experimental methods for investigating and designing complex control systems attracted the deserved attention of the Congress participants. The methods of simulation used recently include analogue equipment and also digital and combined equipment, and these methods permit mechanization of individual aspects of human mental effort and to a large extent permit increasing its effectiveness. The experimental technique is improving in accuracy and conditions are being created for a major economy of means involved in carrying out full-scale ('natural') investigations. In the papers and in the discussion a picture of the develop-
mcnt of m~ans and methods of digital simulation emerged. ]\icw meth ods of reproducing second-order curves by means of digital equ;pment were presented which are applicable to programme control systems. Combined digital-analogue eqUipment was considered, particularly equipment for simulating the kinetics of a nuclear reactor. In addition to increasing the accuracy, the application of digital methods results in a considerable widening of the permissible range of variation in the values of the variables. A method of solving differential equations with partial derivatives on electronic models, based on the relation between these equations and random processes occurring in electrical circuits subjected to random disturbances, created such interest. In one of the papers original modelling equipment was described which operates on alternating current of an increased frequency, and consists of passive circuits in combination with multiple servo-system. This equipment ensures a relatively high accuracy and has the feature of reversibility (including the non-linear elements), which extends considerably its potentialities. New ideas in the field of optimization of the work of systems for controlling production processes, and applying electronic models, opens up wide prospects both in designing optimum systems and also for improving the accuracy of the mathematical description of processes to be controlled. I believe I express the general opinion of the participants of the Congress if I say that evaluation of the papers, the fruitful discussions which followed, and the extensive exchange of opinions between the scientists of various countries, which took place in a cordial atmosphere, will have a great influence on the further development of the theory of automatic control and will contribute to still more effective development of this new branch of science and engineering. A new brilliant page in the history of science has been written.
\091
1101