7R10. Applied Linear Optimal Control: Examples and Algorithms. - AE Bryson (Dept of Aeronaut and Astronaut, Stanford Univ, Stanford CA). Cambridge UP, Cambridge, UK. 2002. 362 pp. Softcover, CD-Rom incl. ISBN 0-521-01231-7. $45.00. (Also available in Hardcover ISBN 0-521-81285-2, $120.00.)

Reviewed by M Reyhanoglu (Dept of Phys Sci, Embry-Riddle Aeronaut Univ, 600 S. Clyde Morris Blvd, Daytona Beach FL 32114).

This book updates and extends part of the material in Applied Optimal Control by Bryson and Ho 1. In particular, it focuses on linear optimal control in the presence of uncertainties, including random inputs, measurement errors and model uncertainties. It completes the picture that has begun with the author’s book Dynamic Optimization2, a successor of the first part of 1, which deals with the deterministic (nonrandom) case.

The book commences in Chapter 1 with an overview of random variables and static estimation. In Chapter 2, discrete and continuous linear Gauss-Markov processes are introduced. Chapter 3 treats discrete and continuous filtering. Both time-invariant and time-varying Kalman and Kalman-Bucy filters are discussed and new software codes are presented. Chapter 4 covers smoothing without control inputs and discusses both batch and recursive algorithms. Chapter 5 is devoted to the synthesis of time-varying linear quadratic followers and terminal controllers for deterministic systems using state feedback. Chapter 6 treats linear-quadratic-Gaussian (LQG) controllers, which use output measurements instead of full state feedback. Chapter 7 extends the ideas in Chapter 4 to include smoothing of data from runs of controlled plants. Both batch and recursive algorithms are presented and demonstrated on examples. Chapter 8 presents discrete and continuous time-invariant filters. Chapters 9 and 10 treat time-invariant linear-quadratic (LQ) state feedback controllers and LQG controllers, respectively. Chapter 11 presents discrete and continuous linear-quadratic worst-case (LQW) controllers and estimators. Chapter 12 develops a parameter-robust LQG controller design method based on minimizing the maximum quadratic performance index at the corners of a specified plant parameter space. The resulting controllers are shown to achieve best performance for a specified plant-parameter robustness. The book concludes with two appendices: one appendix covers filters and controllers with colored measurement noise, and the other appendix contains mathematical models of plants used in the examples and problems.

The book is written as a theoretical and practical tool for anyone involved in optimal control. The author has carefully collected many realistic examples drawn from diverse engineering fields. The examples are very helpful in explaining new concepts and ideas behind theories. Intriguing problems are available within each chapter. In an effort to close the gap between theory and practice, computational algorithms are included for solving practical optimization problems. The algorithms are coded in MATLAB. Students are asked to write simple MATLAB programs as they progress through the book, to convince themselves that they have confidence in the theory and understand its practical implications.

The author stated the goal at the beginning of the book as “to aid readers in utilizing the theory of optimal control to solve practical problems in the face of uncertainty.” It appears this goal has been achieved. Applied Linear Optimal Control: Examples and Algorithms should be a good addition to the optimal control community. It makes an excellent text for engineering and applied mathematics students who already have some optimal control background. It is strongly recommended as a helpful guide for anyone who desires to learn and apply many of the current state of the art results in optimal control.

Bryson AE and Ho YC, 1975, Applied Optimal Control, Hemisphere, New York.
Bryson AE, 1999, Dynamic Optimization, Addison Wesley Longman, Menlo Park CA.