Optimal H^∞ fuzzy control for nonlinear interconnected systems via genetic algorithm

This paper presents an effective approach for stabilizing nonlinear multiple time-delay (NMTD) interconnected systems via a composite of genetic algorithm (GA) and fuzzy controllers. First, a neural-network (NN) model is employed to approximate each subsystem with multiple time delays. Then, the dynamics of the NN model is converted into a linear differential inclusion (LDI) state-space representation. Next, in terms of Lyapunov's direct method, a delay-dependent stability criterion is derived to guarantee the exponential stability of the NMTD interconnected system. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). Due to the capability of GA in a random search for global optimization, the lower and upper bounds of the search space can be set so that the GA will seek better feedback gains of fuzzy controllers in order to stabilize more quickly the NMTD interconnected system based on the feedback gains via LMI-based approach. According to the Improved genetic algorithm (IGA), which is demonstrated to have better performance than that of a traditional GA, a robustness design of fuzzy control is synthesized not only to stabilize the NMTD interconnected system but also to achieve optimal H^∞ performance by minimizing the disturbance attenuation level.