一类不确定离散时间非线性系统保性能控制

Guaranteed Cost Control of Discrete-time Nonlinear System with Parametric Uncertainties

针对状态不完全可测的一类不确定离散时间非线性系统,基于状态观测器研究其保性能控制问题。采用T-S模型对非线性系统进行建模,根据李雅普诺夫稳定性理论,基于线性矩阵不等式(LMI),利用分散化并行分布补偿(PDC)的方法设计了基于观测器的控制器,给出了实现该非线性系统保性能控制的充分条件。并通过数值仿真对提出的方法进行了验证,仿真结果表明了该方法的正确性。

Against the guaranteed cost control problem of a discrete-time nonlinear system in the presence of parametric uncertainties, the problem on designing an guaranteed cost controller based on state observer was considered. The Takagi-Sugeno（T-S） fuzzy model was adopted for fuzzy modeling of the system. According to Lyapunov stability theory, the scheme of decentralized PDC（Parallel Distributed Compensation） fuzzy control was used to have designed controller via LMI method, and apart from the above, the sufficient condition that ensures guaranteed cost control of nonlinear system was derived. The conclusion was tested by numerical simulation, which illustrated the correctness of the conclusion.