This book helps students, researchers, and practicing engineers to understand the theoretical framework of control and system theory for discrete-time stochastic systems so that they can then apply its principles to their own stochastic control systems and to the solution of control, filtering, and realization problems for such systems. Applications of the theory in the book include the control of ships, shock absorbers, traffic and communications networks, and power systems with fluctuating power flows. The focus of the book is a stochastic control system defined for a spectrum of probability distributions including Bernoulli, finite, Poisson, beta, gamma, and Gaussian distributions. The concepts of observability and controllability of a stochastic control system are defined and characterized. Each output process considered is, with respect to conditions, represented by a stochastic system called a stochastic realization. The existence of a control law is related to stochastic controllability while the existence of a filter system is related to stochastic observability. Stochastic control with partial observations is based on the existence of a stochastic realization of the filtration of the observed process.

Motivates detailed theoretical work with relevant real-world problems Broadens reader understanding of control and system theory Provides comprehensive definitions of multiple related concepts Offers in-depth treatment of stochastic control with partial observation Equips readers with uniform treatment of various system probability distributions

Autorentext
Professor Jan H. van Schuppen gained his PhD from the Department of Electrical Engineering and Computer Science of the University of California at Berkeley in 1973. His research contributions are primarily in control and system theory, in particular in the subareas of stochastic control, filtering, stochastic realization, control of discrete-event systems and of hybrid systems, and control and system theory of rational systems. He has teaching experience at Washington University, University of Illinois, the VU University Amsterdam and University of Technology in Delft. He has acted as research advisor of 12 post-doctoral researchers and of 19 Ph.D. students.  His organizational activities include being Co-Editor of the journal Mathematics of Control, Signals, and Systems, Co-Editor-at-Large of the journal IEEE Transactions on Automatic Control, co-editor of two conference proceedings, co-editor of two edited books, coordinator of four projects which were financially supported by the European Commission, and being director of the Dutch Network Systems and Control for the organization of a course program of systems and control for Ph.D. students.

Zusammenfassung
"The book is written for students in applied mathematics and engineering with an interest in control theory and its application in various contexts ... . All chapters offer numerous examples ... all contain hints to further reading and end with a specific list of references. The way the book is organized and written, it is suited as textbook for university courses and seminars at master and Ph.D. level, as well as for self-instruction." (Heinrich Hering, zbMATH 1478.93005, 2022)

Inhalt
Introduction.- Chapter 1. Stochastic Processes Introduction.- Chapter 2. Stochastic Systems.- Chapter 3. Stochastic Realization Gaussian Systems.- Chapter 4. Stochastic Realization General Framework.- Chapter 5. Stochastic Control Systems.- Chapter 6. Stochastic Control Problems.- Chapter 7. Stochastic Control Complete Observations Finite Horizon.- Chapter 8. Stochastic Control - Complete Observations Infinite Horizon.- Chapter 9. Stochastic Control - General Theory.- Chapter 10. Filtering Kalman Filters.- Chapter 11. Filtering General Stochastic Systems.- Chapter 12. Stochastic Control Partial Observations Finite Horizon.- Chapter 13. Stochastic Control Partial Observations Infinite Horizon.- Chapter 14. The Communication of Information.- Chapter 15. Mathematics Notation, Concepts, and Results.- Chapter 16. Probability Further Theory.- Chapter 17. Stochastic Processes - Specialized Topics.- Chapter 18. Deterministic Dynamic Systems.- Chapter 19. The Lyapunov and the Riccati Systems and Their Equations.- Chapter 20. Dissipative Systems.- Chapter 21. The Dissipation Matrix Inequality. <p