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Sliding Mode Control Design via Piecewise Smooth Lipschitz Surfaces based on Contingent Cone Criteria

Xin Huo*, Kai Zheng, and Kemao Ma
International Journal of Control, Automation, and Systems, vol. 12, no. 4, pp.733-741, 2014

Abstract : In order to improve flexibility of sliding mode control (SMC) for a class of nonlinear systems, a new control design method is proposed in this paper. The sliding surface is extended to be a generic Lipschitz continuous surface instead of a smooth one, with which different characteristics of sliding motion may be realized. Due to the nonsmoothness of the sliding surface, the control design problem is discussed in the framework of Filippov’s differential inclusion, by analyzing the geometric properties of the nonsmooth surface. Discontinuous control laws are presented based on new contingent cone criteria, which steer all of the trajectories of the closed-loop system to reach the piecewise smooth sliding surface in finite time.

Keyword : Contingent cone, Filippov’s solution, piecewise smooth Lipschitz surface, sliding mode control.

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