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Robust and adaptive Higher Order Sliding mode controllers

In this paper, we present Lyapunov-based robust and adaptive Higher Order Sliding Mode (HOSM) controllers for nonlinear SISO systems with bounded uncertainty. The proposed controllers can be designed for any arbitrary sliding mode order. The uncertainty bounds are known in the robust control problem whereas they are partially known in the adaptive control problem. Both these problems are formulated as the finite time stabilization of a chain of integrators with bounded uncertainty. Saturation functions are used for gain adaptation, which do not let the states exit the neighborhood after convergence. The effectiveness of these controllers is illustrated through simulations.