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Decentralized control of complex systems
570
Book Reviews
aspect, in my opinion, was not the main intention of authors in presenting the algorithms. The methods for analysis and design of linear systems are rather sophisticated and therefore, the development of robust software implementations is a task for numerical analysis experts. Many algorithmic details, not mentioned in the book can further improve the efficiency of algorithms and the accuracy of results. For almost all of presented methods and for many other algorithms only referred to, robust implementations are available either in Fortran libraries or in MATLAB Toolboxes.
References H. and C. F. Van Loan (1983). Matrix Computations. The John Hopkins Univ. Press, Baltimore.
Golub, G.
Varga, A. (1981). On stabilization algorithms for linear time-invariant systems. Rev. Roum. Sci. Techn.-Electrotechn. & Energ., 26, 115-124. Varga, A. and V. Sima (1993). Algorithms and Commented
Fortran Subprograms for Computer Aided Control Systems Engineering. Technical Press, Bucharest. (In print). About the reviewer Andras Varga was born in 1950 in Baraolt, Romania. He obtained the diploma in control engineering in 1974 and the
Ph.D. degree in electrical engineering in 1981, both from the Polytechnic Institute of Bucharest. In 1974, Dr Varga joined the Institute of Informatics in Bucharest where he worked first as a research and development engineer, and beginning with 1982 as a senior research engineer. In 1990 he was promoted as first degree senior research engineer, a research position equivalent with the academic position of full professor. In 1987, Dr Varga was awarded with an Alexander von Humbold Research Fellowship. Since September 1990, he has been working at the Department of Mechanical Engineering of the Ruhr University of Bochum in the framework of this fellowship. Dr Varga's interests are in numerical methods for control systems, with emphasis on model reduction, robust control and descriptor systems, as well as in the area of developing software tools (libraries, interactive packages) for the computer aided design of control systems (CADCS). He has authored or coauthored more than 50 papers and three books (two of them being in print). He is the author or coauthor of several professional level CADCS packages and of a H~-synthesis MATLAB Toolbox. Dr Varga is member of the Benelux Working Group on Software and an active contributor to the SLICOT Control Library developed by this group.
Decentralized Control of Complex Systems* D. D. Siljak
Reviewer: RENHOU LI Xian Jiatong University, Xian, P.R. China. MANY REAL ENGINEERING and non-engineering problems facing researchers of the world are highly complex and stochastic in nature. Modelling and controlling of most complex systems must deal with 'high' dimension, uncertainty, and information structure constraints. One way for solving these problems is to use the strategy called decentralized control in which system inputs are assigned to a given set of local controllers (stations) which observe only local system outputs. This approach can avoid difficulties in data gathering, storage requirements, computer program debugging and geographical separation of system components. A great number of papers and books (Jamshidi (1983); Siljak (1978); Singh (1981), etc.) have been published to indicate concepts and methodologies of decentralized control of complex system since the 1970s. Decentralized control has been successfully applied to many industrial systems, for example, power systems, traffic systems and communication systems, and has become one of the most important branches of modern systems theory. Following the book Large Scale Dynamic Systems: Stability and Structure which presented some ideas about decentralized control, published in 1978, Professor Siljak has written another book Decentralized Control of Complex Systems which is mainly concerned with the characteristics of complex systems: dimensionality, uncertainty, and information structure constraints, and provides a series of novel concepts and methods to handle the problems of decentralized control of interconnected subsystems. The book summarizes the research achievements developed by the author and his colleagues in the decentralized control field in the last two decades. Throughout the book great care is taken to differentiate between centralized and
* Decentralized Control of Complex Systems, Math. en Science and Eng., Vol. 184 by D. D. Siljak. Academic Press, New York (1991). $75.00.
decentralized control. In this book, a great deal of attention is paid to the explanation of the substantial problems involved in decentralized control systems, such as interconnected subsystems modelling, decomposition, stability, optimization and robustness of decentralized controllers. In the first chapter of the book the important concept of graph-theoretic framework is presented starting from the view point of structural modelling for complex systems. Because the decentralized control problems are essentially structural, the graph-theoretic framework provides a very good environment for the computation of system structural fixed modes with arbitrary feedback structure constraints, reachability, controllability and observability. It also can be used to identify the minimal set of lines in directed graphs which are essential for preserving input reachability and structural controllability of a given system. The graphtheoretic algorithm is computationally attractive because one can use the Boolean operations instead of algebraic manipulation to get results needed. I think that the graph-theoretic framework and its algorithms which are used repeatedly, almost in each chapter, can be considered as the cream of the book, it is an excellent part, which is superior to other books on the same topic. In the second chapter of the book, an effort is made to deal with the important problem of the connective stability of complex systems under structural perturbations. The book provides an M-matrix condition based on Vector Lyapunov Function for testing the connective stability of decentralized control systems. Having this result, the control strategy may become very simple: stabilize each subsystem when decoupled, and then check stability of the connective closed-loop subsystems using M-matrix conditions. The condition is further modified in the successive chapters and frequently applied to study inherent properties of decentralized control systems, such as robustness, suboptimization and decentralized stabilizability of interconnected subsystems. The entire second chapter should be considered as the theoretical fundamentals of the later chapters. The third part of the book is concerned with the optimization of decentralized control systems. Due to the
Book Reviews nonclassical information structure constraints, the standard optimization concepts and methods cannot be extended to formulate decentralized control strategies. The most important factor to be considered is the interconnection between the subsystems. In this context, the book regards interconnections as perturbations of subsystems that are controlled by decentralized LQ feedback and introduces a new idea of suboptimality index to measure the cost of robustness to structural perturbations. The book constructs and solves the inverse optimal problem of decentralized control which leads to an interesting result that the global optimality can be recovered from local optimal LQ control subsystems (even with nonlinear interconnections) if the performance index is modified. This is a very useful conclusion for the design of decentralized control laws, and also is an important contribution to the theory and application of decentralized control. Based on the graph-theoretic framework, interpreting the interconnections as perturbations of subsystems and using M-matrix test techniques the book extend the main results made in Chapters 1-3 to Chapters 4 and 5, in which stochastic control, dynamic feedback control, and adaptive control of complex systems are analysed and discussed. In these parts an effort is made to derive many important theorems which establish the basis of arguments, such as the sufficient conditions for the existence of decentralized asymptotic observers, suboptimal estimator, and optimal decentralized control laws for a given system. The book provides several methods for designing decentralized observers, estimators and controllers which can be carried out by using a parallel processing scheme. In order to control a complex system decentrally, the prerequisite is that the system can and must be decomposed into several subsystems. But how is this done? The book gives sufficient space (three chapters) to introduce three decomposition approaches: LBT (Low Block Triangular) decomposition, nested Epsilon decomposition and overlapping decomposition, which can be easily achieved using the algorithms listed in the Appendix demonstrating the inherent efficiency of these algorithms and their easy implementation in a structural language, such as PASCAL and C. The last part of the book is concerned with the reliability of control which is the basic requirement in design of complex systems. So far as reliability is concerned, it has been discussed from different view points in relevant
571
disciplines and there exist various techniques to increase the reliability of control systems from both hardware and software. In the book, the emphasis is placed on the control structure and multiple control systems. Using the Inclusion Principle and overlapping decomposition made in the preceding chapter it gives an example to illustrate the design of reliable control. The contents discussed in the last chapter are not detailed and may be regarded as a brief introduction to the reliable control of complex systems. Finally it is worthy to point out that at end of each chapter the book includes a section of notes and references, which not only provide readers with a large amount of relevant literature, but also introduce the evolution of some novel concepts and methodology obviously beneficial to those who wish further to pursue studies in some subjects of decentralized control of complex systems. Another merit of the book is that each chapter contains many examples of both analysis and design which makes the content of the book to be understood easily and well-readable. In my opinion the book is tailored to the needs of the readers who have acquired a degree of proficiency in modern control systems theory.
References Jamshidi, M. (1983). Large-scale Systems: Modelling and Control. North-Holland, New York. Siljak, D. D. (1978). Large-scale Dynamic Systems: Stability and Structure. North-HoUand, New York. Singh, M. G. (1981). Decentralized Control. North-Holland, New York.
About the reviewer Renhou Li graduated from Jiaotong University, Shanghai, China, in 1957, he began working in Xian Jiaotong University as a teaching assistant, lecturer, associate professor and now as a professor. He was the vice chairman of the Department of Radio Engineering from 1978 to 1984. Since then he has been the Dean of ICE department. His main research interests are in Large Scale Systems Theory and Its Applications, Distributed Computer Control Systems, The Application of Expert Methodology to Industrial Process and Intelligent Control. He has more than 60 papers published and is the author and coauthor of six books.
Book Reviews
aspect, in my opinion, was not the main intention of authors in presenting the algorithms. The methods for analysis and design of linear systems are rather sophisticated and therefore, the development of robust software implementations is a task for numerical analysis experts. Many algorithmic details, not mentioned in the book can further improve the efficiency of algorithms and the accuracy of results. For almost all of presented methods and for many other algorithms only referred to, robust implementations are available either in Fortran libraries or in MATLAB Toolboxes.
References H. and C. F. Van Loan (1983). Matrix Computations. The John Hopkins Univ. Press, Baltimore.
Golub, G.
Varga, A. (1981). On stabilization algorithms for linear time-invariant systems. Rev. Roum. Sci. Techn.-Electrotechn. & Energ., 26, 115-124. Varga, A. and V. Sima (1993). Algorithms and Commented
Fortran Subprograms for Computer Aided Control Systems Engineering. Technical Press, Bucharest. (In print). About the reviewer Andras Varga was born in 1950 in Baraolt, Romania. He obtained the diploma in control engineering in 1974 and the
Ph.D. degree in electrical engineering in 1981, both from the Polytechnic Institute of Bucharest. In 1974, Dr Varga joined the Institute of Informatics in Bucharest where he worked first as a research and development engineer, and beginning with 1982 as a senior research engineer. In 1990 he was promoted as first degree senior research engineer, a research position equivalent with the academic position of full professor. In 1987, Dr Varga was awarded with an Alexander von Humbold Research Fellowship. Since September 1990, he has been working at the Department of Mechanical Engineering of the Ruhr University of Bochum in the framework of this fellowship. Dr Varga's interests are in numerical methods for control systems, with emphasis on model reduction, robust control and descriptor systems, as well as in the area of developing software tools (libraries, interactive packages) for the computer aided design of control systems (CADCS). He has authored or coauthored more than 50 papers and three books (two of them being in print). He is the author or coauthor of several professional level CADCS packages and of a H~-synthesis MATLAB Toolbox. Dr Varga is member of the Benelux Working Group on Software and an active contributor to the SLICOT Control Library developed by this group.
Decentralized Control of Complex Systems* D. D. Siljak
Reviewer: RENHOU LI Xian Jiatong University, Xian, P.R. China. MANY REAL ENGINEERING and non-engineering problems facing researchers of the world are highly complex and stochastic in nature. Modelling and controlling of most complex systems must deal with 'high' dimension, uncertainty, and information structure constraints. One way for solving these problems is to use the strategy called decentralized control in which system inputs are assigned to a given set of local controllers (stations) which observe only local system outputs. This approach can avoid difficulties in data gathering, storage requirements, computer program debugging and geographical separation of system components. A great number of papers and books (Jamshidi (1983); Siljak (1978); Singh (1981), etc.) have been published to indicate concepts and methodologies of decentralized control of complex system since the 1970s. Decentralized control has been successfully applied to many industrial systems, for example, power systems, traffic systems and communication systems, and has become one of the most important branches of modern systems theory. Following the book Large Scale Dynamic Systems: Stability and Structure which presented some ideas about decentralized control, published in 1978, Professor Siljak has written another book Decentralized Control of Complex Systems which is mainly concerned with the characteristics of complex systems: dimensionality, uncertainty, and information structure constraints, and provides a series of novel concepts and methods to handle the problems of decentralized control of interconnected subsystems. The book summarizes the research achievements developed by the author and his colleagues in the decentralized control field in the last two decades. Throughout the book great care is taken to differentiate between centralized and
* Decentralized Control of Complex Systems, Math. en Science and Eng., Vol. 184 by D. D. Siljak. Academic Press, New York (1991). $75.00.
decentralized control. In this book, a great deal of attention is paid to the explanation of the substantial problems involved in decentralized control systems, such as interconnected subsystems modelling, decomposition, stability, optimization and robustness of decentralized controllers. In the first chapter of the book the important concept of graph-theoretic framework is presented starting from the view point of structural modelling for complex systems. Because the decentralized control problems are essentially structural, the graph-theoretic framework provides a very good environment for the computation of system structural fixed modes with arbitrary feedback structure constraints, reachability, controllability and observability. It also can be used to identify the minimal set of lines in directed graphs which are essential for preserving input reachability and structural controllability of a given system. The graphtheoretic algorithm is computationally attractive because one can use the Boolean operations instead of algebraic manipulation to get results needed. I think that the graph-theoretic framework and its algorithms which are used repeatedly, almost in each chapter, can be considered as the cream of the book, it is an excellent part, which is superior to other books on the same topic. In the second chapter of the book, an effort is made to deal with the important problem of the connective stability of complex systems under structural perturbations. The book provides an M-matrix condition based on Vector Lyapunov Function for testing the connective stability of decentralized control systems. Having this result, the control strategy may become very simple: stabilize each subsystem when decoupled, and then check stability of the connective closed-loop subsystems using M-matrix conditions. The condition is further modified in the successive chapters and frequently applied to study inherent properties of decentralized control systems, such as robustness, suboptimization and decentralized stabilizability of interconnected subsystems. The entire second chapter should be considered as the theoretical fundamentals of the later chapters. The third part of the book is concerned with the optimization of decentralized control systems. Due to the
Book Reviews nonclassical information structure constraints, the standard optimization concepts and methods cannot be extended to formulate decentralized control strategies. The most important factor to be considered is the interconnection between the subsystems. In this context, the book regards interconnections as perturbations of subsystems that are controlled by decentralized LQ feedback and introduces a new idea of suboptimality index to measure the cost of robustness to structural perturbations. The book constructs and solves the inverse optimal problem of decentralized control which leads to an interesting result that the global optimality can be recovered from local optimal LQ control subsystems (even with nonlinear interconnections) if the performance index is modified. This is a very useful conclusion for the design of decentralized control laws, and also is an important contribution to the theory and application of decentralized control. Based on the graph-theoretic framework, interpreting the interconnections as perturbations of subsystems and using M-matrix test techniques the book extend the main results made in Chapters 1-3 to Chapters 4 and 5, in which stochastic control, dynamic feedback control, and adaptive control of complex systems are analysed and discussed. In these parts an effort is made to derive many important theorems which establish the basis of arguments, such as the sufficient conditions for the existence of decentralized asymptotic observers, suboptimal estimator, and optimal decentralized control laws for a given system. The book provides several methods for designing decentralized observers, estimators and controllers which can be carried out by using a parallel processing scheme. In order to control a complex system decentrally, the prerequisite is that the system can and must be decomposed into several subsystems. But how is this done? The book gives sufficient space (three chapters) to introduce three decomposition approaches: LBT (Low Block Triangular) decomposition, nested Epsilon decomposition and overlapping decomposition, which can be easily achieved using the algorithms listed in the Appendix demonstrating the inherent efficiency of these algorithms and their easy implementation in a structural language, such as PASCAL and C. The last part of the book is concerned with the reliability of control which is the basic requirement in design of complex systems. So far as reliability is concerned, it has been discussed from different view points in relevant
571
disciplines and there exist various techniques to increase the reliability of control systems from both hardware and software. In the book, the emphasis is placed on the control structure and multiple control systems. Using the Inclusion Principle and overlapping decomposition made in the preceding chapter it gives an example to illustrate the design of reliable control. The contents discussed in the last chapter are not detailed and may be regarded as a brief introduction to the reliable control of complex systems. Finally it is worthy to point out that at end of each chapter the book includes a section of notes and references, which not only provide readers with a large amount of relevant literature, but also introduce the evolution of some novel concepts and methodology obviously beneficial to those who wish further to pursue studies in some subjects of decentralized control of complex systems. Another merit of the book is that each chapter contains many examples of both analysis and design which makes the content of the book to be understood easily and well-readable. In my opinion the book is tailored to the needs of the readers who have acquired a degree of proficiency in modern control systems theory.
References Jamshidi, M. (1983). Large-scale Systems: Modelling and Control. North-Holland, New York. Siljak, D. D. (1978). Large-scale Dynamic Systems: Stability and Structure. North-HoUand, New York. Singh, M. G. (1981). Decentralized Control. North-Holland, New York.
About the reviewer Renhou Li graduated from Jiaotong University, Shanghai, China, in 1957, he began working in Xian Jiaotong University as a teaching assistant, lecturer, associate professor and now as a professor. He was the vice chairman of the Department of Radio Engineering from 1978 to 1984. Since then he has been the Dean of ICE department. His main research interests are in Large Scale Systems Theory and Its Applications, Distributed Computer Control Systems, The Application of Expert Methodology to Industrial Process and Intelligent Control. He has more than 60 papers published and is the author and coauthor of six books.