单输入多时滞离散系统的线性二次调节问题

The Problem of Linear Quadratic Regulation for Discrete-time Systems with Single Input and Multiple Delays

研究了单输入多时滞的离散时间系统的线性二次调节问题(LQR问题),给出了求解最优控制输入序列的一种简单有效而又新颖的方法.将该动态的离散时滞系统的LQR最优控制问题最终转化成了一个静态的、不带时滞的数学规划模型——带等式线性约束的严格凸二次规划问题,并利用两种方法解这个二次规划问题,均成功地导出了系统的最优控制输入序列.仿真结果验证了我们的方法的正确有效性.

This paper presents and analyzes the optimal control problem of linear quadratic regulation（the LQR problem） for linear discrete-time systems with single input and multiple input delays.A simple and new approach to derive the optimal control input sequences is given.The problem is finally converted to a strictly convex quadratic programming problem subject to an equal constraint.Thus the delayed control inputs are converted into control inputs delay-free,and a dynamic LQR optimal control problem for the linear discrete-time delayed systems is converted into a static mathematical programming model without delays.Solving this strictly convex quadratic programming problem with two methods successfully derives the optimal control input sequences.The simulated results show that the approach is right and very effective.