Sparse Actuator Control of Discrete-Time Linear Dynamical Systems

<p class=ql-align-justify>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.</p><p class=ql-align-justify><br></p><p class=ql-align-justify>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.</p>