饱和非线性时滞系统约束预测控制

Constrained model predictive control for nonlinear system subject to actuator saturation

针对一类具有执行器饱和与输出约束的离散非线性时滞系统,提出新的模糊预测控制方法。首先,采用T-S模糊模型来逼近实际非线性系统,运用平行分步补偿(PDC)原理将该系统转化为一系列线性系统的凸组合。其次,通过每个采样时刻优化无穷时域的"min-max"性能指标来求解状态反馈预测控制器,得到系统满足Lyapunov渐近稳定的充分条件,并进一步将该条件转化为基于线性矩阵不等式(LMI)技术的半正定规划(SDP)问题。最后,通过数值仿真验证该方法的有效性。

Aiming at a class of discrete-time nonlinear systems subject to actuator saturation and output constraint,a novel fuzzy predictive control method is proposed in this paper.Firstly,the approximation of a practical nonlinear system is realized by utilizing the T-S fuzzy model.Then,the above system is further converted into convex combinations of a series of linear subsystems by Parallel Distributed Compensation（PDC） scheme.Secondly,a state feedback predictive controller is obtained by optimizing an infinite time＂min-max＂performance index at each sampling instant.A sufficient condition for the Lyapunov asymptotical stability is obtained and it is further transformed into positive Semi-definite Programming（SDP）which can be easily solved by means of Linear Matrix Inequality（LMI）.Finally,the availability and feasibility of the proposed method are both verified by specific numerical examples,respectively.