- Email: [email protected]
Adaptive control design and analysis
Automatica 42 (2006) 509 – 511 www.elsevier.com/locate/automatica
Book review
Adaptive control design and analysis, Gang Tao, Copyright 2003 by John Wiley & Sons, Inc., Hoboken, New Jersey, 640pp., ISBN: 0-471-27452-6. Developed in the second half of the last century, the field of adaptive control is still interesting, challenging, and exciting with a variety of applications in modern control systems. There are several classical books/schools in adaptive control (Astrom & Wittenmark, 1995; Goodwin & Sin, 1984; Krstic, Kanellakopoulos, & Kokotovic, 1995; Narendra & Annaswamy, 1989, and others). The book has some similarities with those, particularly of Kokotovic’s school (they co-authored another book on adaptive control of systems with hard nonlinearities, Sastry & Bodson, 1989; Tao & Kokotovic, 1996). Overall, Tao’s book is a very comprehensive and detailed book on adaptive control theory. It covers almost all aspects of adaptive control including continuous and discrete-time adaptive control systems, single-input, single-output (SISO) and multiinput, multi-output (MIMO) systems, state feedback and output feedback, model reference adaptive control and indirect adaptive control. Compared with the above-mentioned classics in adaptive control, the book includes extensions such as an adaptive backstepping approach and a whole chapter on adaptive control of systems with nonlinearities. The book does not deal with adaptive control design methods for stochastic systems. The chapter on multivariable adaptive control is the best I have seen in the literature. The book does not cover applications of adaptive control to systems that are not linearly parametrizable and to intelligent control—a technique that is closely related to adaptive control. The level of presentation is mostly intended for graduate students. The author does a nice job by including many examples, and in particular, a large number of problems at the end of each chapter. At the same time there are not many simulation examples, computer code examples, or algorithm realizations that can help engineers and researchers who work on implementation of those techniques. However, at the end of every chapter, there are many problems requiring simulations. The introductory part of the book includes an overview of basic feedback control methods including optimal control, robust control, and nonlinear control. It also discusses, in a simple form, direct and indirect adaptive control concepts and backstepping nonlinear design. The book includes a detailed
doi:10.1016/j.automatica.2005.11.002
overview of system theories covering both linear and nonlinear systems, vector and matrix norms. The stability is discussed through the Lyapunov stability and input–output stability for both linear and nonlinear systems. Results from system theory are accompanied with mathematical proofs and numerous examples. Chapter 3 deals with the adaptive parameter estimation for a linear parametric model in both continuous and discrete time cases. Gradient and least squares algorithms were given with their parameter convergence analyses. Robustness due to the modeling disturbance is analyzed and standard modifications such as deadzone, -mod, parameter projection, and -mod are given. The same style is seen throughout the book and particularly obvious in this chapter—one of the most complete parameter estimation sections I have seen but without illustrative simulation examples or any illustration. It is nice and inspiring to see suggestions for advanced topics at the end of sections for further study and research. This chapter is related to several applications of robust adaptive control including intelligent control such as neural net control and fuzzy logic control. I wish there was at least one example or subsection dedicated to those areas that are a driving force of applied adaptive control research in recent years. The reader is then introduced to a simple model reference adaptive control in state-feedback control and output feedback control cases. A full-order and a reduced-order state observers for parametrization of the state feedback are given. Adaptive disturbance rejection is analyzed which has an application to an actuator failure compensation (Tao’s recent book on adaptive control of systems with actuator failures, Tao, Chen, Tang, & Joshi, 2004). Chapter 5 is the “heart” of the book with Model Reference Adaptive Control (MRAC) for continuous time systems. First, matching conditions for ideal controller parameters are discussed when the plant parameters are assumed known. In a case of unknown plant parameters, MRAC provides an adaptation law for estimated controller parameters. Besides standard MRAC design, the author presents a modified adaptive law that leads to a reduced tracking error. This result comes with a proof and a novel Lyapunov function. Even though the book does not have many simulation examples, it has a lot of examples—actually many more than comparable books on adaptive control. Some examples are hidden in the text, immediately following the proofs. As a reader, I prefer
510
Book review / Automatica 42 (2006) 509 – 511
examples that are very visible such as the ones in Chapter 5 and accompanied with illustrations. Lyapunov and gradient designs for adaptive laws were presented here. There is also a detailed discussion about modified adaptation laws to ensure robustness of the MRAC algorithms in the presence of an unmodeled dynamics and an external disturbance. In order to develop an MRAC controller, there is an assumption that the sign of the high frequency gain is known. To the authors’ credit, he devoted a significant part of this section to a Nussbaum gain concept which relaxes this assumption, more than comparable textbooks in adaptive control. Similarly, discrete-time MRAC for linear systems is discussed in Chapter 6. It is a much shorter version of the continuous time case that includes adaptive control schemes and robustness analysis. As opposed to direct adaptive control methods, an indirect adaptive control consists of adaptive estimation of the plant parameters which are then used for calculation of controller parameters. The section on indirect adaptive control also includes indirect adaptive pole placement design method that can even be applied to nonminimum phase systems (MRAC requires minimum phase assumption). The author also provides equivalent indirect adaptive control design for a discrete-time case that also includes indirect adaptive pole placement design. Chapter 8 presents comparative design of five adaptivecontrollers for a two-body system with joint flexibility and damping. Included controllers are state-feedback direct adaptive controller, output feedback direct adaptive controller, indirect and direct–indirect adaptive controllers, and backsteppingbased controller. The chapter does a good job in presenting these designs, but does not show simulation examples except in one case. I would expect to see how these controllers compare to each other, how they differ in performance, complexity, implementation issues, etc. If a student needs to choose one of those five controllers, how can he/she select it? This section does not provide insight and intuition to answer that. While Chapter 5 is the “heart” of the book, Chapter 9 on adaptive control of multi-input, multi-output (MIMO) systems is the most comprehensive, complete, and detailed part of the book. The chapter first analyzes adaptive state feedback control for MIMO systems. The MRAC design and analysis are given for both continuous and discrete time MIMO systems along with the parametrizations of plant and the controller. Rigorous stability and robustness analyses are given for a MIMO case. This chapter also contains adaptive control designs for MIMO systems with input and output delays and adaptive backstepping control method. As an example of MIMO adaptive control, the author presents an adaptive control design for robot manipulators (2-link robot arm). A detailed simulation is definitely missing in this illustrative example. Also, this would be a good place to include intelligent control as an applied adaptive control field. More than a half of the results in intelligent robot manipulator control apply one of the adaptive control
techniques described in this book. The chapter closes with the pole placement design for MIMO systems. The author certainly did an excellent job on adaptive control design for MIMO systems. It is the best and most comprehensive and detailed analysis I have seen in similar adaptive control books with a large number of problems at the end of the chapter. Chapter 10 discusses adaptive control of systems with hard nonlinearities such as deadzone, backlash, hysteresis, and other. This chapter is for a more advanced study and is closely related to Tao’s book Sastry & Bodson, 1989; Tao & Kokotovic, 1996). The adaptive inverse method is presented for canceling hard nonlinearities for both linear and nonlinear systems. Even though the book mostly deals with adaptive control design for linear systems, it is refreshing to see some extensions for feedback linearizable nonlinear systems. State feedback and output feedback controls are presented for SISO and MIMO systems. This chapter is closely related to some current research problems where adaptive control can be applied. In summary, Tao’s book is an excellent addition to the adaptive control references, one of the most comprehensive, detailed, and mathematically rigorous books in adaptive control. The strength of the book is unparalleled breadth and depth of presentation of the methods used in adaptive control. It is very theoretical and mathematically rigorous. The book is weak in illustrative examples, simulation examples, and graphical illustrations (there are just a few figures in the whole book). I will probably adopt this book for my course but will use it with additional references that have more simulations and reallife examples. However, the book has a large number of problems after every chapter—more than any other book in adaptive control field. References Astrom, K. J., & Wittenmark, B. (1995). Adaptive control. (2nd ed.), Reading, MA: Addison-Wesley. Goodwin, G. C., & Sin, K. S. (1984). Adaptive filtering prediction and control. Englewood Cliffs, NJ: Prentice-Hall. Krstic, M., Kanellakopoulos, I., & Kokotovic, P. V. (1995). Nonlinear and adaptive control design. New York: Wiley. Narendra, K. S., & Annaswamy, A. M. (1989). Stable adaptive systems. Englewood Cliffs, NJ: Prentice-Hall. Sastry, S., & Bodson, M. (1989). Adaptive control: Stability, convergence, and robustness. Englewood Cliffs, NJ: Prentice-Hall. Tao, G., Chen, S., Tang, X., & Joshi, S. M. (2004). Adaptive control of systems with actuator failures. London: Springer. Tao, G., & Kokotovic, P. V. (1996). Adaptive control of systems with actuator and sensor nonlinearities. New York: Wiley.
Rastko R. Selmic Department of Electrical Engineering Louisiana Tech University Ruston, LA 71270, USA E-mail address: [email protected]
Book review / Automatica 42 (2006) 509 – 511 About the reviewer Rastko R. Selmic received his B.S. degree in 1994 in Electrical Engineering from the University of Belgrade, Serbia. He received his M.S. degree in 1997 and Ph.D. degree in 2000 in Electrical Engineering from the University of Texas at Arlington, USA. From 2000 to 2002 he was a senior Digital Signal Processing systems engineer at Signalogic, Dallas, Texas. Since 2002, he has been assistant professor at Department of Electrical Engineering and Institute for Micromanufacturing at Louisiana Tech University, USA.
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His research interests are in wireless sensor networks, adaptive control, intelligent control, nonlinear systems, and neural networks. He is the author/coauthor of 2 book chapters, 35 journal and conference papers, including a textbook Neuro-Fuzzy Control of Industrial Systems with Actuator Nonlinearities, and has a US patent in intelligent actuator compensation. He currently serves as an Associate Editor for IEEE Transactions on Neural Networks.
Book review
Adaptive control design and analysis, Gang Tao, Copyright 2003 by John Wiley & Sons, Inc., Hoboken, New Jersey, 640pp., ISBN: 0-471-27452-6. Developed in the second half of the last century, the field of adaptive control is still interesting, challenging, and exciting with a variety of applications in modern control systems. There are several classical books/schools in adaptive control (Astrom & Wittenmark, 1995; Goodwin & Sin, 1984; Krstic, Kanellakopoulos, & Kokotovic, 1995; Narendra & Annaswamy, 1989, and others). The book has some similarities with those, particularly of Kokotovic’s school (they co-authored another book on adaptive control of systems with hard nonlinearities, Sastry & Bodson, 1989; Tao & Kokotovic, 1996). Overall, Tao’s book is a very comprehensive and detailed book on adaptive control theory. It covers almost all aspects of adaptive control including continuous and discrete-time adaptive control systems, single-input, single-output (SISO) and multiinput, multi-output (MIMO) systems, state feedback and output feedback, model reference adaptive control and indirect adaptive control. Compared with the above-mentioned classics in adaptive control, the book includes extensions such as an adaptive backstepping approach and a whole chapter on adaptive control of systems with nonlinearities. The book does not deal with adaptive control design methods for stochastic systems. The chapter on multivariable adaptive control is the best I have seen in the literature. The book does not cover applications of adaptive control to systems that are not linearly parametrizable and to intelligent control—a technique that is closely related to adaptive control. The level of presentation is mostly intended for graduate students. The author does a nice job by including many examples, and in particular, a large number of problems at the end of each chapter. At the same time there are not many simulation examples, computer code examples, or algorithm realizations that can help engineers and researchers who work on implementation of those techniques. However, at the end of every chapter, there are many problems requiring simulations. The introductory part of the book includes an overview of basic feedback control methods including optimal control, robust control, and nonlinear control. It also discusses, in a simple form, direct and indirect adaptive control concepts and backstepping nonlinear design. The book includes a detailed
doi:10.1016/j.automatica.2005.11.002
overview of system theories covering both linear and nonlinear systems, vector and matrix norms. The stability is discussed through the Lyapunov stability and input–output stability for both linear and nonlinear systems. Results from system theory are accompanied with mathematical proofs and numerous examples. Chapter 3 deals with the adaptive parameter estimation for a linear parametric model in both continuous and discrete time cases. Gradient and least squares algorithms were given with their parameter convergence analyses. Robustness due to the modeling disturbance is analyzed and standard modifications such as deadzone, -mod, parameter projection, and -mod are given. The same style is seen throughout the book and particularly obvious in this chapter—one of the most complete parameter estimation sections I have seen but without illustrative simulation examples or any illustration. It is nice and inspiring to see suggestions for advanced topics at the end of sections for further study and research. This chapter is related to several applications of robust adaptive control including intelligent control such as neural net control and fuzzy logic control. I wish there was at least one example or subsection dedicated to those areas that are a driving force of applied adaptive control research in recent years. The reader is then introduced to a simple model reference adaptive control in state-feedback control and output feedback control cases. A full-order and a reduced-order state observers for parametrization of the state feedback are given. Adaptive disturbance rejection is analyzed which has an application to an actuator failure compensation (Tao’s recent book on adaptive control of systems with actuator failures, Tao, Chen, Tang, & Joshi, 2004). Chapter 5 is the “heart” of the book with Model Reference Adaptive Control (MRAC) for continuous time systems. First, matching conditions for ideal controller parameters are discussed when the plant parameters are assumed known. In a case of unknown plant parameters, MRAC provides an adaptation law for estimated controller parameters. Besides standard MRAC design, the author presents a modified adaptive law that leads to a reduced tracking error. This result comes with a proof and a novel Lyapunov function. Even though the book does not have many simulation examples, it has a lot of examples—actually many more than comparable books on adaptive control. Some examples are hidden in the text, immediately following the proofs. As a reader, I prefer
510
Book review / Automatica 42 (2006) 509 – 511
examples that are very visible such as the ones in Chapter 5 and accompanied with illustrations. Lyapunov and gradient designs for adaptive laws were presented here. There is also a detailed discussion about modified adaptation laws to ensure robustness of the MRAC algorithms in the presence of an unmodeled dynamics and an external disturbance. In order to develop an MRAC controller, there is an assumption that the sign of the high frequency gain is known. To the authors’ credit, he devoted a significant part of this section to a Nussbaum gain concept which relaxes this assumption, more than comparable textbooks in adaptive control. Similarly, discrete-time MRAC for linear systems is discussed in Chapter 6. It is a much shorter version of the continuous time case that includes adaptive control schemes and robustness analysis. As opposed to direct adaptive control methods, an indirect adaptive control consists of adaptive estimation of the plant parameters which are then used for calculation of controller parameters. The section on indirect adaptive control also includes indirect adaptive pole placement design method that can even be applied to nonminimum phase systems (MRAC requires minimum phase assumption). The author also provides equivalent indirect adaptive control design for a discrete-time case that also includes indirect adaptive pole placement design. Chapter 8 presents comparative design of five adaptivecontrollers for a two-body system with joint flexibility and damping. Included controllers are state-feedback direct adaptive controller, output feedback direct adaptive controller, indirect and direct–indirect adaptive controllers, and backsteppingbased controller. The chapter does a good job in presenting these designs, but does not show simulation examples except in one case. I would expect to see how these controllers compare to each other, how they differ in performance, complexity, implementation issues, etc. If a student needs to choose one of those five controllers, how can he/she select it? This section does not provide insight and intuition to answer that. While Chapter 5 is the “heart” of the book, Chapter 9 on adaptive control of multi-input, multi-output (MIMO) systems is the most comprehensive, complete, and detailed part of the book. The chapter first analyzes adaptive state feedback control for MIMO systems. The MRAC design and analysis are given for both continuous and discrete time MIMO systems along with the parametrizations of plant and the controller. Rigorous stability and robustness analyses are given for a MIMO case. This chapter also contains adaptive control designs for MIMO systems with input and output delays and adaptive backstepping control method. As an example of MIMO adaptive control, the author presents an adaptive control design for robot manipulators (2-link robot arm). A detailed simulation is definitely missing in this illustrative example. Also, this would be a good place to include intelligent control as an applied adaptive control field. More than a half of the results in intelligent robot manipulator control apply one of the adaptive control
techniques described in this book. The chapter closes with the pole placement design for MIMO systems. The author certainly did an excellent job on adaptive control design for MIMO systems. It is the best and most comprehensive and detailed analysis I have seen in similar adaptive control books with a large number of problems at the end of the chapter. Chapter 10 discusses adaptive control of systems with hard nonlinearities such as deadzone, backlash, hysteresis, and other. This chapter is for a more advanced study and is closely related to Tao’s book Sastry & Bodson, 1989; Tao & Kokotovic, 1996). The adaptive inverse method is presented for canceling hard nonlinearities for both linear and nonlinear systems. Even though the book mostly deals with adaptive control design for linear systems, it is refreshing to see some extensions for feedback linearizable nonlinear systems. State feedback and output feedback controls are presented for SISO and MIMO systems. This chapter is closely related to some current research problems where adaptive control can be applied. In summary, Tao’s book is an excellent addition to the adaptive control references, one of the most comprehensive, detailed, and mathematically rigorous books in adaptive control. The strength of the book is unparalleled breadth and depth of presentation of the methods used in adaptive control. It is very theoretical and mathematically rigorous. The book is weak in illustrative examples, simulation examples, and graphical illustrations (there are just a few figures in the whole book). I will probably adopt this book for my course but will use it with additional references that have more simulations and reallife examples. However, the book has a large number of problems after every chapter—more than any other book in adaptive control field. References Astrom, K. J., & Wittenmark, B. (1995). Adaptive control. (2nd ed.), Reading, MA: Addison-Wesley. Goodwin, G. C., & Sin, K. S. (1984). Adaptive filtering prediction and control. Englewood Cliffs, NJ: Prentice-Hall. Krstic, M., Kanellakopoulos, I., & Kokotovic, P. V. (1995). Nonlinear and adaptive control design. New York: Wiley. Narendra, K. S., & Annaswamy, A. M. (1989). Stable adaptive systems. Englewood Cliffs, NJ: Prentice-Hall. Sastry, S., & Bodson, M. (1989). Adaptive control: Stability, convergence, and robustness. Englewood Cliffs, NJ: Prentice-Hall. Tao, G., Chen, S., Tang, X., & Joshi, S. M. (2004). Adaptive control of systems with actuator failures. London: Springer. Tao, G., & Kokotovic, P. V. (1996). Adaptive control of systems with actuator and sensor nonlinearities. New York: Wiley.
Rastko R. Selmic Department of Electrical Engineering Louisiana Tech University Ruston, LA 71270, USA E-mail address: [email protected]
Book review / Automatica 42 (2006) 509 – 511 About the reviewer Rastko R. Selmic received his B.S. degree in 1994 in Electrical Engineering from the University of Belgrade, Serbia. He received his M.S. degree in 1997 and Ph.D. degree in 2000 in Electrical Engineering from the University of Texas at Arlington, USA. From 2000 to 2002 he was a senior Digital Signal Processing systems engineer at Signalogic, Dallas, Texas. Since 2002, he has been assistant professor at Department of Electrical Engineering and Institute for Micromanufacturing at Louisiana Tech University, USA.
511
His research interests are in wireless sensor networks, adaptive control, intelligent control, nonlinear systems, and neural networks. He is the author/coauthor of 2 book chapters, 35 journal and conference papers, including a textbook Neuro-Fuzzy Control of Industrial Systems with Actuator Nonlinearities, and has a US patent in intelligent actuator compensation. He currently serves as an Associate Editor for IEEE Transactions on Neural Networks.