Randomized algorithms for analysis and control of uncertain systems. With a foreword by M. Vidyasagar
The central theme of the present work is the application of randomized algorithms to various problems in control system analysis and synthesis. The major developments in robustness analysis and robust controller synthesis are reviewed. When the idea of randomization is applied to control-theoretic problems, some complicated problems become tractable, provided a somewhat diluted notation of the concept of a ``solution'' is accepted. The content of the book is organized as follows: After an overview, some elements of probability theory are reviewed in Chap. 2. Classical results regarding robustness analysis are given in Chap. 3, and synthesis problems can be found in Chap. 4. Limitations of the classical robustness paradigm are discussed in Chap. 5. Especially, complexity issues, conservatism and discontinuity problems are studied here. A probabilistic approach for robustness is suggested next. Monte Carlo methods for point estimation, integration and optimization are reviewed in Chap. 7. A meta-algorithm for analysis and design of uncertain systems is described in Chap. 8. Then probability inequalities and their applications to the reliability of estimates are reviewed, and some elements of statistical learning theory are given in Chaps. 9 and 10. Sequential algorithms, as e.g. stochastic approximation methods, for robust controller design including output feedback design problems are described in Chaps. 11 and 12. The generation of random samples and radial random vectors are studied in Chaps. 14 and 15. Vector and matrix randomization methods are presented in Chap. 16 and 18, while radial random vectors can be found in Chap. 17. In the final Chap. 19 applications to congestion control of highspeed communication networks, robustness of flexible structures and iterative algorithms for quadratic stability of sampled-data quantized systems are given. This well-written book can be recommended to readers in control systems analysis and synthesis, especially in robustness analysis and robust controller synthesis.
scientific article; zbMATH DE number 2133312