Indirect fuzzy adaptive control of a class of SISO nonlinear systems

This paper presents an adaptive fuzzy control scheme for a class of continuous-time single-input single-output nonlinear systems with unknown dynamics and disturbance. Within this scheme, the fuzzy systems are employed to approximate the unknown system's dynamics. The proposed controller is composed of a well-defined adaptive fuzzy control term that uses the adaptive fuzzy approximators; and a robustifying control term that is used to accommodate the approximation errors and disturbance. Based on a Lyapunov synthesis method, it is shown that the proposed adaptive control scheme guarantees the convergence of the tracking error to zero and the global boundedness of all signals in the closed-loop system. Moreover, The proposed controller allows initialization by zero of all adjusted parameters in the fuzzy approximators, and does not require the knowledge of the lower bound of the control gain and the upper bounds of approximation errors and disturbance. Simulation results performed on an inverted pendulum system are given to point out the good performances of the developed adaptive controller.