Hybrid adaptive fuzzy identification and control of nonlinear systems

TLDR: 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, and this is achieved at negligible increased implementation cost or computational complexity.

Abstract: We present a combined direct and indirect adaptive control scheme for adjusting an adaptive fuzzy controller, and 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 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 negligible increased implementation cost or computational complexity We prove a theorem that shows the properties of this hybrid adaptive fuzzy control system, ie, 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