Adaptive fuzzy control systems with dynamic structure

This article proposes a novel fuzzy system, referred to as a dynamic structure fuzzy system, to address tracking control problems for unknown nonlinear dynamical systems. The fuzzy system is employed to reconstruct the unknown nonlinearities of dynamic systems. In the dynamic structure fuzzy system, the number of fuzzy rules can be either increased or decreased over time based on the required approximation accuracy. The advantage of the dynamic structure fuzzy system is that a suitable-sized fuzzy system can be found to avoid overfitting or underfitting data sets. By using Gaussian radial basis function (GRBF) as a membership function, adaptation laws are presented for tuning all parameters of the parameterized fuzzy system, including the output weights, the widths and the centers of the GRBF's. Global boundedness of the overall control scheme is guaranteed in the sense of Lyapunov. The tracking error converges to the required precision through the adaptive control scheme derived by the Lyapunov synthesis approach. Simulations performed on an underwater vehicle system demonstrate the effectiveness of our scheme.