Title: Control design with Lipschitz switching surfaces based on new contingent cone criteria

Authors: Xin Huo; Yu Yao; Kai Zheng

Addresses: Control and Simulation Center, Harbin Institute of Technology, Building-E1, Science Park, Harbin, 150080, China. ' Control and Simulation Center, Harbin Institute of Technology, Building-E1, Science Park, Harbin, 150080, China. ' Information Science and Technology College, Dalian Maritime University, Xishan Campus, Dalian, 116026, China

Abstract: In this paper, a control design method for a class of non-linear uncertain systems is proposed based on the new contingent cone criteria, which are used to estimate the relation between the phase trajectories and an arbitrary Lipschitz continuous surface. A series of Lipschitz domains are constructed recursively, each of which contains two Lipschitz switching surfaces that may be non-smooth. Filippov|s differential inclusion is adopted to describe the dynamics of the closed-loop system. Based on the constructed Lipschitz domains, a feedback controller is designed to drive the trajectories of the closed-loop system to the origin asymptotically. Finally, the validity of the method is illuminated by some numerical examples.

Keywords: Lipschitz switching surfaces; Filippov solution; contingent cone; non-smooth analysis; control design; uncertain systems; nonlinear systems; phase trajectories; feedback control.

DOI: 10.1504/IJMIC.2011.042656

International Journal of Modelling, Identification and Control, 2011 Vol.14 No.3, pp.205 - 215

Published online: 21 Mar 2015 *

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