Optimal fuzzy control of exponential synchronisation via genetic algorithm

In this study, a novel approach via GA-based fuzzy control is proposed to realize the exponential optimal H^∞ synchronisation of MTDC systems. A robustness design of model-based fuzzy control is first presented to overcome the effect of modelling errors between the MTDC systems and T-S fuzzy models. Next, a delay-dependent exponential stability criterion is derived in terms of Lyapunov's direct method to guarantee that the trajectories of the slave system can approach those of the master system. Subsequently, the stability conditions of this criterion are reformulated into LMIs. According to the LMIs, a fuzzy controller is then synthesised to exponentially stabilise the error systems. Moreover, the capability of GA in random search for near-optimal solutions, the lower and upper bounds of the search space based on the feedback gains via LMI approach can be set so that the GA will seek better feedback gains of fuzzy controllers to speed up the synchronisation. Additionally, an IGA was proposed to overcome both the shortcomings of premature convergence of GA and local search. According to the IGA, a fuzzy controller is synthesised not only to realise the exponential synchronisation but also to achieve the optimal H^∞ performance by minimising the disturbance attenuation level.