Fixed-time HOSM controller design for constrained sliding mode systems with mismatched terms

Abstract

The current study has systematically presented a strategy of designing the fixed-time high-order sliding mode (HOSM) controller with asymmetric output constraints. This constructive method is accomplished by three crucial mechanisms. First of all, some nonlinear terms satisfying homogeneous growth conditions are implanted into the mismatched channels of the traditional HOSM system. Based on this, a HOSM system with mismatched terms is built to weaken the uncertainties in control input channels. Secondly, a barrier Lyapunov function (BLF) is developed to resolve the constraints. Thirdly, by integrating the BLF with a backstepping-like method, a fixed-time HOSM controller is explicitly proposed to handle the HOSM dynamics with mismatched terms and asymmetric output constraints. It is shown via the strict Lyapunov analysis that under the constructed controller, the closed-loop system is fixed-time stabilized and the realization of prescribed constraints is insured. The investigations of two cases are provided to validate the established theoretical results.