关于一类球约束下的LQ奇异最优控制问题

Solution to constrained LQ singular optimal control

摘要:

研究一类有约束的LQ奇异最优控制问题。有别于传统方法，这里避免引入小摄动量进行逼近，而是利用Pontryagin极值原理和倒向微分流的方法，通过伴随变量直接给出最优控制的解析表达式。

关键词:球约束LQ奇异最优控制;Pontryagin极值原理;canonical倒向微分流

Abstract:

This paper is devoted to solving a constrained linear-quadratic (LQ) singular optimal control problem. Differing from the traditional way, it avoids adding a small perturbation for an approximation process. The optimal control of this problem is given explicitly with the co-state variable by the Pontryagin maximum principle and the canonical backward differential flow.

Key words:LQ singular optimal control problem; Pontryagin maximum principle; canonical backward differential flows