Hybrid adaptive fuzzy identification and control of nonlinear systems

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, 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.

I. Introduction

Adaptive control [1] is a model-free approach for controlling uncertain dynamic systems. The basic idea in adaptive control is to estimate the uncertainties in the plant (or equivalently, in the corresponding controller) on-line based on the measured signals. In principle, the system under control can be uncertain in terms of its dynamic structure (nonparametric uncertainty), or its parameters (parametric uncertainty). Generally, the basic objective of adaptive control is to maintain consistent performance of the control system in the presence of these uncertainties. However, conventional adaptive control theory can only deal with the systems with known dynamic structure, but unknown (constant or slowly-varying) parameters [20], [17]. Furthermore, conventional adaptive controllers cannot make use of human operators' experience, which is usually expressed in linguistic terms.