Stochastic Networked Control Systems

Networked control systems are increasingly ubiquitous today, with applications ranging from vehicle communication and adaptive power grids to space exploration and economics. The optimal design of such systems presents major challenges, requiring tools from various disciplines within applied mathematics such as decentralized control, stochastic control, information theory, and quantization.

 

A thorough, self-contained book, Stochastic Networked Control Systems: Stabilization and Optimization under Information Constraints aims to connect these diverse disciplines with precision and rigor, while conveying design guidelines to controller architects. Unique in the literature, it lays a comprehensive theoretical foundation for the study of networked control systems, and introduces an array of concrete tools for work in the field.  Salient features included:

 

·         Characterization, comparison and optimal design of information structures in static and dynamic teams. Operational, structural and topological properties of information structures in optimal decision making, with a systematic program for generating optimal encoding and control policies. The notion of signaling, and its utilization in stabilization and optimization of decentralized control systems.

 

·         Presentation of mathematical methods for stochastic stability of networked control systems using random-time, state-dependent drift conditions and martingale methods.

 

·         Characterization and study of information channels leading to various forms of stochastic stability such as stationarity, ergodicity, and quadratic stability; and connections with information and quantization theories. Analysis of various classes of centralized and decentralized control systems.

 

·         Jointly optimal design of encoding and control policies over various information channels and under general optimization criteria, including a detailed coverage of linear-quadratic-Gaussian models.

 

·         Decentralized agreement and dynamic optimization under information constraints.

 

This monograph is geared toward a broad audience of academic and industrial researchers interested in control theory, information theory, optimization, economics, and applied mathematics. It could likewise serve as a supplemental graduate text. The reader is expected to have some familiarity with linear systems, stochastic processes, and Markov chains, but the necessary background can also be acquired in part through the four appendices included at the end.

 

·         Characterization, comparison and optimal design of information structures in static and dynamic teams. Operational, structural and topological properties of informationstructures in optimal decision making, with a systematic program for generating optimal encoding and control policies. The notion of signaling, and its utilization in stabilization and optimization of decentralized control systems.

 

·         Presentation of mathematical methods for stochastic stability of networked control systems using random-time, state-dependent drift conditions and martingale methods.

 

·         Characterization and study of information channels leading to various forms of stochastic stability such as stationarity, ergodicity, and quadratic stability; and connections with information and quantization theories. Analysis of various classes of centralized and decentralized control systems.

 

·         Jointly optimal design of encoding and control policies over various information channels and under general optimization criteria, including a detailed coverage of linear-quadratic-Gaussian models.

 

·         Decentralized agreement and dynamic optimization under information constraints.

 

This monograph is geared toward a broad audience of academic and industrial researchers interested in control theory, information theory, optimization, economics, and applied mathematics. It could likewiseserve as a supplemental graduate text. The reader is expected to have some familiarity with linear systems, stochastic processes, and Markov chains, but the necessary background can also be acquired in part through the four appendices included at the end.

From the reviews:

“Explains the mathematics useful for the description of those systems, when imbedded in a mathematical framework of discrete time, and elements which take their values either in discrete or in Euclidean spaces … . The reviewer sees two uses for the book. It could be a valuable information source for someone interested in an overall picture of the subject … . other use would be for a reading course by a courageous student willing to reconstruct part of the material.” (A. F. Gualtierotti, Mathematical Reviews, March, 2014)