Time-optimal hands-off control for linear time-invariant systems
Time-optimal hands-off control for linear time-invariant systems
复制标题
线性时不变系统的时间最优放手控制
DOI：
10.1016/j.automatica.2018.10.004
复制
发表时间：
2019
期刊：
影响因子：
6.4
通讯作者：
Nagahara Masaaki
中科院分区：
文献类型：
--
作者：
Ikeda Takuya;Nagahara Masaaki
在本文中，我们研究了线性时不变系统的时间最优不干涉控制的理论性质。控制的目的是最大化控制值为零的持续时间（最大的不干涉控制），并且最小化响应时间以实现给定的状态转换（时间最优控制）。为此，我们引入一个由l0测量和控制器响应时间的线性组合描述的代价函数。由于l0测度是非凸和不连续的，我们采用l1松弛技术进行最优控制的分析。利用这一松弛，我们证明了时间最优不干涉控制的存在性，以及在正态性假设下l0和l1最优控制之间的等价性。
In this article, we investigate theoretical properties of the time-optimal hands-off control for linear time-invariant systems. The purpose of the control is to maximize the time duration on which the control value is exactly zero (maximum hands-off control) and also to minimize the response time to achieve a given state transition (time-optimal control). For this, we introduce a cost function described by a linear combination of the L 0 measure and the response time of the control. Since the L 0 measure is non-convex and discontinuous, we adopt the L 1 relaxation technique for the analysis of the optimal control. By using this relaxation, we show the existence of the time-optimal hands-off control, and the equivalence between L 0 and L 1 optimal controls under the normality assumption.