Optimal Control on Disconnected Sets Using Extreme Point Relaxations and Normality Approximations
Optimal Control on Disconnected Sets Using Extreme Point Relaxations and Normality Approximations
复制标题
使用极值点松弛和正态近似对不连通集进行最优控制
DOI：
10.1109/tac.2021.3059682
复制
发表时间：
2021
影响因子：
6.8
通讯作者：
M. Harris
中科院分区：
文献类型：
--
作者：
M. Harris
本文给出了定义在不连通控制集上的非凸最优控制问题的精确松弛和近似松弛的新的数学结果。精确的松弛基于极值点松弛，其中松弛控制集被构造为使其极值点属于原始集合。精确度所需的系统属性是正态。在没有正态分布的情况下，引入了控制集近似和系统动态摄动，使得正态分布成立。结果对线性动力系统和仿射在控制中的非线性系统都成立。结果表明，凸松弛能够有效地解决航天工程、稀疏性促进优化、过驱动系统和多路系统中的问题。与凸优化相关的计算保证使松弛技术适合于实时控制。
This article presents new mathematical results for exact and approximate relaxations of nonconvex optimal control problems defined on disconnected control sets. The exact relaxations are based upon extreme point relaxations wherein the relaxed control set is constructed so that its extreme points belong to the original set. A system property required for exactness is normality. In the absence of normality, control set approximations and system dynamic perturbations are introduced so that normality holds. The results hold for linear dynamical systems and nonlinear systems affine in the control. It is shown that the convex relaxations enable the efficient solution of problems in aerospace engineering, sparsity-promoting optimization, overactuated systems, and multiplexing systems. The computational guarantees associated with convex optimization make the relaxation techniques suitable for real-time control.