A novel stability condition and its application to GA-based fuzzy control for nonlinear systems with uncertainty

Abstract

In this study, we strive to combine the advantages of fuzzy logic control (FLC), genetic algorithms (GA), H∞ tracking control schemes, smooth control and adaptive laws to design an adaptive fuzzy sliding model controller for the rapid and efficient stabilization of complex and nonlinear systems. First, we utilize a reference model and a fuzzy model (both nvolv-ing FLC rules) to describe and well-approximate an uncertain, nonlinear plant. The FLC rules and the consequent parameter are decided on via GA. A boundary-layer function is intro-duced into these updated laws to cover modeling errors and to guarantee that the state errors converge into a specified error bound. After this, a H∞ tracking problem is characterized. We solve an eigenvalue problem (EVP), and derive a modified adaptive neural network controller (MANNC) to simultane-ously stabilize and control the system and achieve H∞ control performance. Furthermore, a stability criterion is derived utilizing Lyapunov's direct method to ensure the stability of the nonlinear system. Finally, the control methodology is dem-onstrated via a numerical simulation.