Chattering-free quasi-sliding mode control for fractional-order chaotic systems with unmatched uncertainties

Abstract

Traditional sliding mode control (SMC) provides good robustness in chaotic systems with matched uncertainties. However, it uses a discontinuous sign function, which causes chattering and degrades control performance. Many methods in the literature have been proposed to reduce chattering, but they are ineffective for fractional-order systems with unmatched disturbances and input nonlinearities. To address this issue, this paper proposes a new quasi-sliding mode control (QSMC) method for controlling generalized fractional-order chaotic systems with unmatched disturbances and input nonlinearities. Based on Lyapunov stability theory, the proposed method replaces the discontinuous function in traditional SMC with a continuous one. This modification not only eliminates chattering but also enables the system state to suppress chaotic behaviour. In addition, by incorporating the rippling design concept, the method reduces the dimension of the control input. This results in a simpler control strategy, thus lowering the complexity and improving the efficiency of the control system. Even in the presence of input nonlinearities and disturbances, the controller can maintain the system state within the desired bound using only a single input. Numerical results demonstrate that the proposed method stabilizes the system, effectively suppresses chaotic behaviour, and verifies its feasibility and effectiveness.