离散不确定系统的鲁棒预测控制

Robust Model Predictive Control for Uncertain Discrete-time Systems

对预测控制中模型不确定性的处理一直是预测控制算法亟待解决的问题。考虑一类包含模型不确定性的控制对象模型,提出一种极大极小预测控制器设计方法。在滚动优化的每一步,考虑了状态变量不完全可测的情况,引入动态输出反馈的思想得到一个最坏条件下的性能指标的最优解,以最坏条件下的性能指标为求解优化问题的上界,通过线性矩阵不等式的方法求解凸优化问题。并从理论上证明了所设计的鲁棒预测控制器对不确定模型是稳定的。通过仿真算例的分析,证明了极大极小鲁棒预测控制器设计的有效性。

The model uncertainty problem in model predictive control is discussed. A uncertain discrete-time model that allows explicit incorporation of the description of model uncertainty is considered. A max-min model predictive controller is presented. In the case that not all states are available, a dynamic output feedback law is introduced at each iteration, which minimizes a ＇worst-case＇ infinite horizon objective function. And the problem of minimizing an upper bound on the ＇worst-case＇ objective function is reduced to a convex optimization involving linear matrix inequalities. The stability of the closed-loop system is proved. The simulation results show the effectiveness of max-min model predictive controller.