Indirect Adaptive Fuzzy Control with Approximation Error Estimator for Nonlinear Systems

For a class of single-input single-output (SISO)nonlinear systems with unknown bound functions and unknown function control gain, a novel approach of indirect adaptive fuzzy controller (AFC) without supervisory controller is proposed by Lyapunov synthesis. Firstly, it is presented a novel indirect AFC with adaptive laws using improved projection operator. Then an adaptive compensator with approximation error estimator is developed, which is used for estimating optimal approximation error (OAE) dynamically and reducing the influence of approximation error on system performance.In closed-loop system analysis, it does not require that the OAE is square-integrable or the OAE supremum is known. It is proved that the overall controller guarantees the global asymptotical stability of the closed-loop system in sense that all variables are bounded. Control simulation results of inverted pendulum system demonstrate that this approach achieves favorable performance with smooth controller output, small tracking error and strong robustness.