On Sparse Optimal Control for General Linear Systems
On Sparse Optimal Control for General Linear Systems
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DOI：
10.1109/tac.2018.2863220
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发表时间：
2019-05
影响因子：
6.8
通讯作者：
Takuya Ikeda;K. Kashima
中科院分区：
文献类型：
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作者：
Takuya Ikeda;K. Kashima
本文研究了一个以沃尔泰拉积分方程和L^{\infty }$范数为约束的L^0 $优化问题.特别地，我们得到了$L^p$优化之间的等价性定理，它提供了现有结果的以下两个方面的推广：首先，这些理论结果使我们能够解决稀疏最优控制问题，而不需要强加被控系统的有限维，这是现有结果推导的关键假设。其次，部分状态约束问题和输出可控性之间的关系是新的特点。
In this paper, we investigate an $L^0$ optimization problem with constraints in a form of Volterra integral equation and the $L^{\infty }$ norm. In particular, the equivalence theorem among the $L^p$ optimizations with $p\in [0, 1]$ is derived, which provides the following twofold extension of the existing results: First, these theoretical results enable us to solve sparse optimal control problems without imposing the finite dimensionality of the system to be controlled, which was the crucial assumption for the derivation of the existing results. Second, the relationship between the partial state constrained problem and output controllability is newly characterized.