A robust fuzzy adaptive law for evolving control systems

In this paper an adaptive law with leakage is presented. This law can be used in the consequent part of Takagi–Sugeno-based control. The approach enables easy implementation in the control systems with evolving antecedent part. This combination results in a high-performance and robust control of nonlinear and slowly varying systems. It is shown in the paper that the proposed adaptive law is a natural way to cope with the parasitic dynamics. The boundedness of estimated parameters, the tracking error and all the signals in the system is guaranteed if the leakage parameter σ′ is large enough. This means that the proposed adaptive law ensures the global stability of the system. A simulation example is given that illustrates the proposed approach.