Output Feedback Second-Order Sliding Mode Control for a Class of Nonlinear Systems With Non-Matched Uncertainties

Abstract

The problem of the design of an output feedback second-order sliding mode control for a class of nonlinear systems affine in the control law with non-matched uncertainties is considered in this paper. An observer-based backstepping design procedure is followed to construct a suitable sliding manifold that guarantees the attainment of a tracking control objective. The construction of the sliding manifold is performed so that the problem of steering the sliding quantity to zero in finite time turns out to be solvable locally through a second-order sliding mode control approach, as in the conventional matched uncertainty case, and the associated zero dynamics is minimum phase. On the other hand, the observer operates in first-order sliding mode, also fed by the control signal generated by the backstepping-second-order sliding mode algorithm. This signal presents the advantage of being continuous by virtue of the second-order sliding mode nature of the controller, enabling the fast convergence to zero of the observation error.