Stochastic networked control systems. Stabilization and optimization under information constraints
This is a book that encompasses a large area of problems extending from vehicle communication to space exploration, and economics. Due to the variety of treated problems, this new domain is based on some subdomains which are themselves studied separately in most of cases, such as applied mathematics, decentralized stochastic control, information theory and quantization. The book represents a self-contained theoretical foundation endowed with mathematical rigor of a general structure where the various components interact due the exchange of mutual information in order to realize the stochastic stability according to some optimization criteria established by the local leaders. In order the reader have a general idea of the scientific content and included items, we look at the table of contents: 1) Introduction; Part I Information Structures in Networked Control containing the chapters: 2) Networked Control Systems as Stochastic Team Decision Problems: A General Introduction; 3) Characterization and Comparison of Information Structures; 4) Topological Properties of Information Structures: Comparison, Convergence, and Optimization; Part II Stabilization of Networked Control Systems containing the chapters: 5) Coding for Control and Connections with Information Theory; 6) Stochastic Stability and Drift Criteria for Markov Chains in Networked Control; 7) Stochastic Stabilization over Noiseless Channels; 8) Stochastic Stabilization over Noisy Channels; 9) Stabilization of Decentralized Systems over Communication Channels; Part III: Optimization in Networked Control; Design of Optimal Policies under Information Constraints 10) Optimization of Real-Time Coding and Control Policies: Structural and Existence Results 11) Optimal Coding and Control for Linear Gaussian Systems over Gaussian Channels under Quadratic Cost; 12) Agreement in Teams and the Dynamic Programming Approach under Information Constraints. Appendices: A Topological Notions and Optimization; B Probability Theory and Stochastic Processes; C Markov Chains, Martingales, and Ergodic Processes; D Markov Decision Theory and Optimality of Markov Policies; References; Index. Conceived as a theoretical introduction and foundation to the domain, the book does not contain problems and exercises. But, in exchange, it has an excellent organization: each chapter contains Introduction, Exposition, Appendix and Proofs, Concluding Remarks, and Bibliographical Notes. The references are very rich, up-to-date (447 positions) and shows clearly the significant contributions of the authors in the domain. The Index is rather poor and it represents an alphabetically ordered contents. The volume is geared toward a broad academic and industrials audience, researchers working in control theory, information theory, information and optimization, applied mathematics. It is expected from the readers to be familiar with linear analysis, probability, stochastic processes and Markov chains. Minimal mathematical notions are given in the four appendices. Finally, we think that the present book is an excellent foundation of the domain whose lecture needs some effort from the reader.
scientific article; zbMATH DE number 6151693