Dual layer barrier functions based adaptive higher order sliding mode control

This article presents an adaptive discontinuous higher order sliding mode control (HOSMC) strategy for a disturbed chain of integrators of order n. This strategy employs a barrier function-based dual layer adaptation and it ensures the convergence of the sliding variable and its (n - 1) first derivatives to zero without requiring any information on the bounds of the disturbances or their derivatives. It consists in applying a barrier function-based adaptive super-twisting methodology compensating Lipschitz disturbances with some error, and a growing gain-based adaptive HOSMC which just needs to counteract this error. Real-time simulation platform is used to test the efficacy of the proposed strategy to control a linear induction motor considering dynamic end effects.