线性二次型最优控制器的设计

The Design of Linear Quadratic Optimal Controller

摘要: 最优控制中目标函数是一个泛函数，最优控制的求解可以归结为求泛函极值问题。线性二次型泛函的最优解可以用统一解析式表示，且可得到一个简单的线性状态反馈控制律而构成闭环最优控制。本文给出了线性二次型系统最优解的求解算法及线性二次型最优控制系统的组成框图，由于在实际系统中状态变量不一定都是能测量的，本文给出了带有状态观测器的线性二次型最优控制系统的实现方法。

Abstract: The aim of optimal control is a functional extreme. An optimal solution is equivalent to a functional extreme. The optimal solution to the linear quadratic regulator can be expressed by a uniform formula. In addition, closed-loop optimal control can be achieved by simple linear feedback of state. This paper gives the procedures of calculating the optimal solution to the linear quadratic system and gives the diagram of the controller. As all states of a practical system can’t be measured, this paper gives the diagram of a linear quadratic controller with a state observer.