Combined switched/time-based adaptation in second order sliding mode control

Controlling highly uncertain nonlinear systems is in general a quite difficult task, for which Sliding Mode (SM) control has proved to be an effective option. However, if only very conservative upper bounds on the uncertainties are known, SM control succeeds in stabilising the closed-loop system at the price of a large control authority, which may cause performance degradation. To address this issue, this paper proposes a novel SM control strategy which combines a switched policy with a time-based adaptation of the control gain. By doing so, the conservatism in the selection of the control magnitude is eliminated, and better performance are achieved. In the paper, the convergence properties of the proposed control law are discussed, and its performance illustrated by means of a numerical example.