4rd Iranian conference of applied mathematics , 2010-04-12

Title : ( Measure theory approach in sliding mode control for nonlinear systems )

Authors: Mohammad Reza Zarrabi , Mohammad Hadi Farahi , Sohrab Effati , A.J. Koshkouei ,

Citation: BibTeX | EndNote

Abstract A new sliding mode control (SMC) design approach using measure theory and Lyapunov functional candidate is presented for nonlinear control problems. A 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 into a given point on a sliding surface in the minimum time, and then tends to the origin (equilibrium point) along the sliding surface. A 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 Lyapunove function, and using measure theoty, an embedding is constructed to solve a time optimal control problem such that the system trajectory reaches a 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. A numerical example is presented to illustrate the effectiveness of the proposed method.

Keywords

, Keywords: Sliding surface design, Lyapunov function, Time optimal control, Measure theory, Sliding mode
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@inproceedings{paperid:1015225,
author = {Zarrabi, Mohammad Reza and Farahi, Mohammad Hadi and Effati, Sohrab and A.J. Koshkouei},
title = {Measure theory approach in sliding mode control for nonlinear systems},
booktitle = {4rd Iranian conference of applied mathematics},
year = {2010},
location = {Zahedan, IRAN},
keywords = {Keywords: Sliding surface design; Lyapunov function; Time optimal control; Measure theory; Sliding mode control},
}

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%0 Conference Proceedings
%T Measure theory approach in sliding mode control for nonlinear systems
%A Zarrabi, Mohammad Reza
%A Farahi, Mohammad Hadi
%A Effati, Sohrab
%A A.J. Koshkouei
%J 4rd Iranian conference of applied mathematics
%D 2010

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