Title: Measure theory approach in sliding mode control for nonlinear systems with disturbances

Authors: Mohammad Reza Zarrabi; Mohammad Hadi Farahi; Sohrab Effati; Ali J. Koshkouei

Addresses: Department of Applied Mathematics, School of Mathematics and Computer Science, Damghan University, Damghan, Iran ' Department of Applied Mathematics, Ferdowsi University of Mashhad, Iran ' Department of Applied Mathematics, Ferdowsi University of Mashhad, Iran ' Control Theory and Applications Centre, Coventry University, UK

Abstract: A new sliding mode control (SMC) design approach using measure theory and Lyapunov functional candidate is presented for nonlinear control problems with disturbances. Lyapunov function is supposed for designing a sliding surface (SS). In fact, the problem that is considered is as follows. A state trajectory from a given initial point reaches a given point on a sliding surface in a short time, and then tends to the origin (equilibrium point) along the sliding surface. Measure theory approach with embedding process is used to solve such a problem in two phases. In the first phase, after designing an appropriate SS by a suggested Lyapunov function, an embedding is constructed to solve a time optimal control problem such that the system trajectory reaches the SS in minimum time, then in the second phase, using SS, a control is designed such that the system trajectory tends to the origin along the SS.

Keywords: Lyapunov function; measure theory; sliding mode control; SMC; sliding surface design; time optimal control; nonlinear systems; disturbances; nonlinear control.

DOI: 10.1504/IJMIC.2015.071888

International Journal of Modelling, Identification and Control, 2015 Vol.24 No.2, pp.120 - 126

Received: 30 Sep 2014
Accepted: 02 Mar 2015

Published online: 22 Sep 2015 *

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