Stabilising control for a class of chaotic systems based on adaptive fuzzy logic systems

Abstract

For a class of chaotic systems with unknown functions and disturbances, asymptotic stabilisation of the chaotic systems is achieved by designing a stability controller based on the adaptive fuzzy logic systems. At first, based on the universal approximation property of fuzzy logic systems, the Mamdani-type fuzzy logic systems with the parameter adaptive laws are designed utilising the data information sampled from the inputs and outputs of unknown functions in the chaotic systems, then the fuzzy logic systems are used to design the stability controller with three parameter adaptive laws, but the three parameters have no relationship with the number of fuzzy rules, so the stability controller is not only able to achieve asymptotic stabilisation for the chaotic system’s states, but also to reduce the number of fuzzy rules and the no-line computational burden significantly. Finally, simulations are used to show the validity of the stabilisation method.