Geethu Joseph

This volume provides a comprehensive overview of recent research advances in the upcoming field of sparse control and state estimation of linear dynamical systems. The contents offer a detailed introduction to the subject by combining classical control theory and compressed sensing. It covers conceptual foundations, including the formulation, theory, and algorithms, and outlines numerous remaining research challenges. Specifically, the book provides a detailed discussion on observability, controllability, and stabilizability under sparsity constraints. It also presents efficient, systematic, and rigorous approaches to estimating the sparse initial states and designing sparse control inputs. It also gives background materials from real analysis and probability theory and includes applications in network control, wireless communication, and image processing. It serves as a compendious source for graduate students and researchers in signal processing and control systems to acquire a thorough understanding of the underlying unified themes. The academic and industrial professionals working on the design and optimization of sparsity-constrained systems also benefit from the exposure to the array of recent works on linear dynamical systems and related mathematical machinery.

This monograph presents new results on the analysis and design of control of discrete-time linear dynamical systems using sparse actuator control. Sparsity constraints on control inputs arise naturally in the inputs of several linear systems due to limited resources such as computational power, energy, and communication bandwidth, or the underlying physics. The monograph deals with two types of sparsity constraints: time-varying and time-invariant supported sparse control inputs. It first provides a detailed theoretical discussion on controllability under sparsity constraints, including algebraic necessary and sufficient conditions for ensuring controllability. Several related formulations, covering stabilizability, output controllability, and nonnegative controllability under sparsity constraints, are also presented. Further, for sparsely controllable systems, the monograph describes two efficient, systematic, and rigorous approaches to designing sparse control inputs: compressed sensing algorithms and spare actuator scheduling algorithms. Overall, the concepts covered in the monograph provide various sparsity models, algorithms, and analysis tools that are readily accessible to systems and control, signal processing, and applied mathematics readers.