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.

中文翻译：

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线性时变系统稀疏控制的一些数学特性

摘要 研究了线性时变系统稀疏控制的存在性、解结构和等价性。我们证明了线性时变系统稀疏控制最优解的存在性。利用非光滑极大值原理，给出了线性时变系统稀疏控制最优性的必要条件。证明了稀疏控制的最优解取值为0和0。在线性时变系统的正态性下，证明了稀疏控制与最优控制的等价定理。数值例子说明了线性时变系统稀疏控制的有效性。