Nonlinear hybrid adaptive fuzzy identification and control

A combined direct and indirect adaptive control scheme for adjusting an adaptive fuzzy controller parameters is presented in this paper. First, using adaptive fuzzy building blocks, with a common set of parameters, we design an adaptive controller and an adaptive identification model for a general class of the uncertain structure nonlinear dynamic systems. We then propose a hybrid adaptive (HA) law for adjusting the parameters, which utilizes a combination of the tracking error and the modeling error. Performance analysis using a Lyapunov synthesis approach proves the superiority (fast tracking error convergence, fast and improved parameter convergence) of the HA law. Furthermore, these advantages are achieved at a negligible increasing in the implementation cost and the computational complexity, over the conventional method [the direct adaptive (DA) law], We also prove a theorem that shows the properties of this hybrid adaptive fuzzy control system.