Stability Analysis of Fuzzy Control for Nonlinear Systems

In this study, we propose a method of stability analysis for a GA-Based reference ANNC capable of handling these types of problems for a nonlinear system. The initial values of the consequent parameter vector are decided via a genetic algorithm (GA) after which a modified adaptive law is derived based on Lyapunov stability theory to control the nonlinear system for tracking a user-defined reference model. The requirement of Kalman-Yacubovich lemma is fulfilling. A boundary-layer function is introduced into these updating laws to cover parameter and modeling errors, and to guarantee that the state errors converge into a specified error bound. After this, an adaptive neural network controller (ANNC) is derived to simultaneously stabilize and control the system.