带有持续扰动的线性系统的前馈-反馈最优控制

Feedforward and feedback optimal control for linear systems with persistent disturbances

研究具有已知动态特性但未知初始条件的持续外界扰动作用下线性系统的前馈-反馈最优控制问题。利用求解Riccati方程和矩阵方程推导出前馈-反馈最优控制律。给出了前馈-反馈最优控制律的存在唯一性条件,并提出了最优控制律的实现算法。仿真结果表明,该方法易于实现且抑制外部持续扰动的鲁棒性优于经典反馈最优控制。

We consider an optimal control problem linear systems affected by external persistent disturbances with known dynamic characteristics but unknown initial conditions. A feedforward and feedback optimal control law is derived from a Riccati equation and a Matrix equation. We give the existence and uniqueness conditions of the feedforward and feedback optimal control law, and present an actualizing algorithm of solving the optimal control law. It is shown that the feedforward and feedback optimal control law is easily realized and is more robust with respect to additive persistent disturbances than the classical feedback optimal control law through simulation results.