混沌系统的一种新型模糊控制方法

基于T-S模糊动态模型,针对气象学中的Lorenz混沌系统设计出一种新型的模糊控制器和模糊观测器,均采用分段Lyapunov函数法进行设计,即对每一个子系统选一个Lyapunov函数,系统总的Lyapunov函数为各个子系统的加权和。避免了并行分配补偿法(PDC)中求解公共正定矩阵P的困难,进一步减少了设计中的保守性,扩大了解的范围。并就其稳定性问题进行了研究。得出了系统全局渐近稳定的条件。模糊观测器的设计解决了系统状态不能直接测量的问题。通过对Lorenz混沌系统的仿真,证明了该方法的有效性。该方案也适合其他类型的非线性系统,有实际应用价值。

New Kind of fuzzy control method for a chaos system

Based on T-S fuzzy dynamical model, the design of new and fuzzy controller and fuzzy observer is addressed for the Lorenz chaos system in atmosphere, and the stability of a closed system is discussed using piecewise Lyapunov function. The total Lyapunov function is the weight sum of the Lyapunov functions of all sub-systems. The difficulty in solving common positive matrix P is avoided by using parallel-distributed compensation (PDC) , the conservatism is decreased further, and the scope of solution is enlarged. The problem that the state of the system is unable to be measured is solved by using the fuzzy observer. The efiectiveness is tested by the Lorenz chaos system. The scheme is also suited to other nonlinear systems, and is worth being applied practically.