具有饱和执行器跳变系统的鲁棒模型预测控制

Robust model predictive control for Markov jump systems subject to actuator saturation

针对一类具有饱和执行器的不确定离散Markov跳变系统,提出鲁棒模型预测控制器设计方法。为便于工程应用,考虑被控跳变系统各模态下的动态系统参数以及各模态间的跳变转移模态均存在不确定性的情形,这些不确定性均以凸多面体的形式给出。预测控制器的求解通过在每一个采样时刻优化无穷时域的最坏二次性能指标实现,该预测控制序列在每个采样时刻表现为具有饱和特性的状态反馈控制律,从而使得所形成的闭环系统鲁棒均方稳定。为方便求解,将控制器的求解转化为以线性矩阵不等式形式给出的正半定规划(SDP)问题。数值示例验证了所提方法的有效性。

A robust model predictive controller design method is proposed for a class of uncertain discretetime Markov jump systems subject to actuator saturation. In terms of the engineering application, the uncertainties are considered to exist in system parameters and jumping transition probabilities, both of which are assumed to belong to some convex sets. The predictive controller is obtained by minimizing a worst case infinite horizon objective function at each sampling time and the predictive control sequence is presented as a saturated state feedback control law at each step. The resulting closed loop system is mean square stable and the proposed controller is obtained using semidefinite programming （SDP） which can be easily solved by means of linear matrix inequalities. The simulation results of a numerical example are given to verify the effectiveness of this method.