Model reference type-2 fuzzy sliding mode control for a novel uncertain hyperchaotic system

Abstract

Hyperchaotic systems have more complex dynamics than the low-dimensional chaotic system. Since hyperchaotic systems have many applications, controlling these systems for engineering applications is a new and attractive field. This paper investigates a design scheme for a class of nonlinear systems with uncertainties and unknown disturbances. In this regard, the idea of classical model reference control, feedback linearization, sliding mode control technique and interval type-2 fuzzy systems (IT2FLS) are combined to suggest a novel hybrid control scheme to resolve the model reference control problem and address the tracking problem for the novel uncertain hyperchaotic Lü system. The IT2FLS is used to approximate the unknown nonlinear terms in control law. The interval type-2 fuzzy adaptation law adjusts the consequent parameters of the rules based on a Lyapunov synthesis approach. It is further equipped with a novel PI type switching structure to attenuate the chattering of the switching law resulting from the fast and large bounded unknown disturbances. There are three major contributions worthy of emphasis. Firstly, the dynamics of the system need not to be known and just the relative degree should be known in advance, which is more flexible in the real implementations. Secondly, it can be applied to a wide range of chaotic or hyperchaotic systems, which is its unique feature. Finally, having applied the proposed approach, both the transient and steady state behavior are improved. Using the Lyapunov theory, the stability of the proposed controller is proved. Compared to conventional sliding mode control and type-1 fuzzy controller, simulation results illustrate that although the proposed approach is highly effective in providing a good tracking performance even in the face of external disturbance and uncertainty; however, it is more computational compared to other mentioned methods, as expected.