The genetic algorithm approach in stability analysis of fuzzy control systems

摘要

For a given control system, stability is usually the most important thing to be determined. In control engineering problems, a desirable feature is asymptotic stability in the large. If the equilibrium state is not asymptotically stable in the large, then the problem becomes that of determining the largest region of asymptotic stability that is called the domain of attraction. Several methods based on the second method of Lyapunov are used in this paper for testing the stability of fuzzy control system, namely: linear matrix inequalities (LMIs) algorithm, variable gradient method, and genetic algorithms (GAs). Lyapunov function does not affect the dynamics of the system under consideration, it is only used to test the stability and detect the domain of attraction. The choice of a Lyapunov function to test the stability may not be optimum so that the real (actual) domain of attraction is determined. The goal of this research is to detect the actual domain of attraction by selecting the proper Lyapunov function. The three analysis methods are illustrated with an example. The GAs method determined the most proper Lyapunov function.