Geometric Properties of Time-Optimal Controls With State Constraints Using Strong Observability
Geometric Properties of Time-Optimal Controls With State Constraints Using Strong Observability
复制标题
使用强可观测性的具有状态约束的时间最优控制的几何特性
DOI：
10.1109/tac.2021.3134627
复制
发表时间：
2022
影响因子：
6.8
通讯作者：
M. Harris
中科院分区：
文献类型：
--
作者：
Nathaniel T. Woodford;M. Harris
本文考虑了线性动态系统在状态等式约束和控制不等式约束下的最小时间最优控制问题。在不存在状态约束的情况下，存在众所周知的充分条件来保证最优控制处于控制集的边界或极值点。强可观性作为关键工具，类似的条件推导出的问题受到外在和内在的状态约束。理解这些几何性质可以实现精确的凸松弛。利用松弛技术将非凸二次规划转化为二阶锥规划，将混合整数线性规划转化为线性规划。松弛加速数值解时间的因素，分别为18000和150。因此，定理和松弛被视为实时优化控制的重要工具。
This article considers minimum time optimal control problems with linear dynamics subject to state equality constraints and control inequality constraints. In the absence of state constraints, there are well-known sufficient conditions to guarantee that optimal controls are at the boundary or extreme points of the control set. With strong observability as the key tool, analogous conditions are derived for problems subject to both extrinsic and intrinsic state constraints. Understanding these geometric properties enables exact convex relaxations. The relaxation technique is used to convert a nonconvex quadratic program to a second-order cone program and a mixed integer linear program to a linear program. The relaxations accelerate numerical solution times by factors of 18 000 and 150, respectively. As such, the theorems and relaxations are seen as important tools for real-time optimization-based control.