基于T-S模型的一类时滞非线性系统模型预测控制

摘要

Aiming at a class of nonlinear discrete systems with time-delay,model predictive control problem based on state feedback is addressed by using linear matrix inequality and Lyapunov stability theory.The target system is described by the T-S fuzzy model,and the"min-max"type of model predictive control algorithm is given.The model predictive control is combined with fuzzy model,and the principle of parallel distributed compensation is used.At each sampling time,the performance of the infinite time domain is optimized,and the design problem of the predictive controller in the case of the norm bounded is dis-cussed.The solvability of the problem is analyzed and the stability of the system is guaranteed,and the state feedback control-ler design algorithm based on linear matrix inequality is given.Finally,a simulation example is given to prove the effectiveness of the proposed method and the stability of the systems.This method can be well applied in the model predictive control process in fields of chemistry,metallurgy,and machinery.%针对具有状态时滞特性的非线性离散系统,利用线性矩阵不等式的方法和 Lyapunov 稳定性理论,研究了基于状态反馈的非线性系统模型预测控制问题.基于 T-S模糊模型对非线性离散系统进行描述并给出一种"min-max"预测控制算法,采用模型预测控制与模糊理论相结合的方法,利用平行分布补偿的原理,通过在每一个采样时刻优化无穷时域的性能指标,来求解在范数有界条件下相应的状态反馈控制律,讨论了预测控制器的设计问题,分析了此设计问题的可解性,给出了状态反馈控制器基于线性矩阵不等式的设计算法,保证了系统的稳定性,通过仿真实例证明了所提控制算法的有效性及系统的稳定性.该方法能够在化工、冶金、机械等具有时滞特性的工业生产过程中得到很好的应用.