Some mathematical characteristics in sparse control for linear time‐varying systems

Abstract

SummaryThe existence, solution structure, and equivalence of sparse control for linear time‐varying systems are investigated. We proved the existence of the optimal solution of sparse control for the linear time‐varying systems. By using the non‐smooth maximum principle, we are given the necessary conditions for the sparse control optimality for linear time‐varying systems. We proved that the optimal solution of sparse control taking values of and 0. Under the normality of the linear time‐varying systems, we proved an equivalence theorem between the sparse control and optimal control. Numerical examples are included to illustrate the effectiveness of the sparse control for linear time‐varying systems.