Predefined-time fractional-order time-varying sliding mode control for arbitrary order systems with uncertain disturbances.

This paper proposes a fractional-order time-varying sliding mode control method with predefined-time convergence for a class of arbitrary-order nonlinear control systems with compound disturbances. The method has global robustness and strongly predefined-time stability. All state errors of the system can converge to zero at a desired time, which can be set arbitrarily with a simple parameter. The strongly predefined-time convergence of the system is clearly demonstrated by the analytic expression of state error, which is obtained by solving fractional-order differential equations corresponding to the sliding mode function. The simulation results show that the proposed method still has good control performance in the presence of input saturation and external interference. • The main contributions of this paper are summarized as follows: • A predefined-time fractional-order time-varying sliding mode control scheme is proposed for a class of arbitrary order nonlinear control systems with complex disturbances. All state errors are simultaneously converged to zero by the scheme at a time, which can be presented by a simple parameter. • Different from most of the existing methods, this paper obtains the analytical expression of the state errors by solving the fractional-order differential equation to prove the predefined-time convergence of the system. • The fractional-order term and time-varying term are introduced into the proposed control scheme, which improves the control performance and makes the system have global robustness. The simulation results show that the proposed controller has strong robustness and resistance to input saturation. [ABSTRACT FROM AUTHOR]