饱和离散随机非线性系统的H_∞模型预测控制

H_∞ Model Predictive Control for Nonlinear Discrete Stochastic Systems with Actuator Saturation

针对饱和离散随机非线性系统,研究状态反馈H∞模型预测控制问题.该系统同时考虑了执行器饱和、随机发生非线性和外部扰.利用扇形有界条件将非线性饱和函数分解为线性部分和非线性部分,并且采用概率统计的方法刻画系统的随机非线性.基于Lyapunov稳定性定理和线性矩阵不等式(LMI)技术给出了保证H∞性能和闭环系统随机稳定的充分条件.最后通过仿真算例验证所提H∞模型预测控制方法的可行性和有效性.

In this paper, the H~ model predictive control is investigated for nonlinear discrete stochastic systems with actuator saturation. The actuator saturation, random nonlinearity and external disturbances simultaneously are included in this controlled systems. The saturation function is decomposed into a linear and a nonlinear part by u- sing the sector conditions, and the stochastic nonlinearity is described by statistical means. Based on the Lyapunov stability theorem and linear matrix inequality （LMI） technique, sufficient conditions are given to guarantee the H performance and the stochastic stability of closed-loop system. Finally, a simulation example is employed to show the feasibility and effectiveness of the H~ model oredietive control method.