基于观测器的不确定非线性系统的自适应鲁棒模糊控制

Observer-based adaptive robust fuzzy control for uncertain nonlinear systems

针对单输入单输出不确定非线性系统提出了一种自适应鲁棒模糊控制算法.该算法通过设计观测器来估计系统的状态向量,因此不要求假设系统的状态向量是可测的.在这个算法中,主要的假设为最优逼近参数向量与标称参数向量之差的范数和逼近误差的界限是未知的.通过只对未知界限估计的调节,该算法减轻了在线计算量并且提高了系统的鲁棒性.所设计的自适应鲁棒模糊控制算法保证了闭环系统的所有信号是一致有界的并且跟踪误差估计收敛到一个小的零邻域内.仿真例子证实了所提方法的可行性.

An adaptive robust fuzzy control algorithm is proposed for SISO uncertain nonlinear systems in this paper. The system state vector is estimated by an observer. The system state vector is not necessarily fully observable. The key assumptions are that the norm of the difference （between optimal approximation parameter vector and nominal parameter vector） and the approximation errors are bounded and the bounds are unknown. The proposed algorithm reduces the online computation burden and improves robustness of the systems by tuning only estimations of the unknown bounds. It is also proved that the proposed adaptive robust fuzzy control algorithm can guarantee uniform boundedness of all the signals in the closed-loop system and the estimation of the tracking error is proved to be convergent to a small neighborhood of the origin. A simulation example demonstrates the feasibility of the proposed approach.