Supervisory adaptive dynamic RBF-based neural-fuzzy control system design for unknown nonlinear systems

Many published papers show that a TSK-type fuzzy system provides more powerful representation than a Mamdani-type fuzzy system. Radial basis function (RBF) network has a similar feature to the fuzzy system. As this result, this article proposes a dynamic TSK-type RBF-based neural-fuzzy (DTRN) system, in which the learning algorithm not only online generates and prunes the fuzzy rules but also online adjusts the parameters. Then, a supervisory adaptive dynamic RBF-based neural-fuzzy control (SADRNC) system which is composed of a DTRN controller and a supervisory compensator is proposed. The DTRN controller is designed to online estimate an ideal controller based on the gradient descent method, and the supervisory compensator is designed to eliminate the effect of the approximation error introduced by the DTRN controller upon the system stability in the Lyapunov sense. Finally, the proposed SADRNC system is applied to control a chaotic system and an inverted pendulum to illustrate its effectiveness. The stability of the proposed SADRNC scheme is proved analytically and its effectiveness has been shown through some simulations.

Supervisory adaptive dynamic RBF-based neural-fuzzy control.Figure optionsDownload as PowerPoint slideHighlights
► We propose a dynamic TSK-type RBF-based neural-fuzzy system.
► The learning algorithm not only online generates and prunes the fuzzy rules but also online adjusts the parameters.
► The proposed control system is applied to control a chaotic system and an inverted pendulum.
► The simulation results verify that a favorable control performance can be achieved.