Hybrid adaptive fuzzy identification and control of nonlinear systems

In this paper, we present a combined direct and indirect adaptive control scheme for adjusting an adaptive fuzzy controller, and an adaptive fuzzy identification model parameters. First, using adaptive fuzzy building blocks, with a common set of parameters, we design and study an adaptive controller and an adaptive identification model that have been proposed for a general class of the uncertain structure nonlinear dynamic systems. We then propose a hybrid adaptive (HA) law for adjusting the parameters. The HA law utilizes two types of errors in the adaptive system, the tracking error and the modeling error. Performance analysis using a Lyapunov synthesis approach proves the superiority of the HA law over the direct adaptive (DA) method in terms of faster and improved tracking and parameter convergence. Furthermore, this is achieved at a negligible increasing in the implementation cost and the computational complexity. We prove a theorem that shows the properties of this hybrid adaptive fuzzy control system, i.e., bounds for the integral of the squared errors, and the conditions under which these errors converge asymptotically to zero are obtained. Finally, we apply the hybrid adaptive fuzzy controller to control a chaotic system, and the inverted pendulum system. The simulation results demonstrate and confirm the theoretical results.