Communication-protocol-based filtering and control of networked systems (Q2122123)

The focus of this research monograph is on filtering and control of systems when one or more communication channels are included in the loop, bringing in special constraints such as rate constraints, constraints arising out of multiple access, etc. This creates a need for protocols for channel allocation among competing users. The objective here is to revisit the classical issues in control and filtering in the light of such protocols, for some standard protocols and control problems. The first chapter describes the broader issues and then narrows down to the special classes of problems treated in the book. The rest of the book is a medley of a succession of problems that fit the broad framework, with some common ideas running through them, particularly the models, protocols, criteria and techniques of analysis. Each of the subsequent chapters deals with one such problem. Chapter 2 considers a problem of filtering under a round robin scheme for channel access and gives sufficient conditions for the mean square error to remain bounded. This is further specialized to make stronger claims in specific situations. Chapter 3 considers a finite horizon control problem with a robust (\(H_\infty\)) filter, with a random access protocol. The system has time delays and a time-varying filter is developed that meets the stated inequality constraint. A related development follows in Chapter 4 for the problem of fault diagnosis in a linear control system. Chapter 5 also gives an analogous development for a linear system with delays when the noise is prescribed in terms of set membership, under resp., round robin and `try once and discard' protocols. Chapter 6 derives a recursive predictor-corrector type filter and gives upper and lower bounds for the error covariance under random access protocol. Chapter 7 considers the filtering problem for a specific train control system with CSMA protocol. Chapter 8 extends the robust filter ideas to an observer based control. Chapter 10 extends these ideas to a multi-agent consensus control problem. A concluding chapter discusses the results with pointers to future directions. The monograph is largely based on research publications of the authors and their colleagues. The techniques are mainly linear algebraic. Illustrative numerical experiments supporting the theory are included everywhere.