二次多阶段不确定系统的Bang-Bang最优控制（英文）

Uncertain Bang-Bangoptimal control for multi-stage uncertain linear quadratic systems

在多阶段系统中,当系统转移方程受到不确定变量的干扰,该问题就称为多阶段不确定控制问题.本文把目标函数的期望值的最小值作为最优解,在贝尔曼最优性原理的基础上提出递推公式,采用动态规划方法,对问题进行求解,最终得出Bang-Bang最优控制和相应的最优解.

In a multi-stage system,when the state of the system at a stage is derived from the state of the former stage and disturbed by an uncertain variable,a multi-stage uncertain optimal control problem is proposed.The idea of considering optimizing the expected value of an uncertain objective is adopted in this paper.Based on Bellman’s principle of optimality,the Bang-Bang optimal controls for the uncertain optimal control problem with a quadratic objective function subject to an uncertain linear system can be obtained.At every stage,the boundary of the optimal objective values can only be gotten,so the upper limit value is taken as the approximation of the optimal objective values.