Adaptive-Sliding Mode Control of Lorenz Hyperchaotic System Considering Uncertainties, External Disturbances, Nonlinear Inputs and Unknown Parameters

In this paper, the dynamical model of the Lorenz hyperchaotic system is briefly introduced. An adaptive-sliding mode control scheme is proposed to stabilize the Lorenz hyperchaotic system in the presence of uncertainties, external disturbances, nonlinearity in the control inputs while parameters of the Lorenz system and the bounds of uncertainties and external disturbances are unknown. The mentioned control scheme is composed of two adaptive sliding surfaces and adaptation laws for unknown parameters. The Lyapunov stability theorem is used to prove the stability of sliding mode dynamics and guarantee the reaching condition. High frequency switching of control inputs is removed by substituting the sign function with a continuous sign-like function. Numerical simulations based on MATLAB software are used to verify the feasibility and effectiveness of the proposed controllers.