Occurrence of big bang bifurcations in discretized sliding-mode control systems

Enric  Fossas; Albert Granados

doi:10.1007/s12591-012-0121-y

Occurrence of big bang bifurcations in discretized sliding-mode control systems

Enric Fossas, Albert Granados

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

In this work we describe the bifurcation scenario found in a general first order system when a relay based proportional control (sliding-mode control) is considered. Based on the results given in the literature, we show the occurrence of a big bang bifurcation causing the existence of an infinite number of periodic orbits near a co-dimension two bifurcation point. We also extend in a natural way the applied theoretical result for second order systems involving 2D piecewise-defined maps.

Original language	English
Journal	Differential Equations and Dynamical Systems
Volume	21
Issue number	1-2
Pages (from-to)	35-43
ISSN	0971-3514
DOIs	https://doi.org/10.1007/s12591-012-0121-y
Publication status	Published - 2012
Externally published	Yes

Keywords

Big bang bifurcations
Two-dimensional piecewise-defined maps
Period adding
Sliding-mode control
Relays

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10.1007/s12591-012-0121-y

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AU - Granados, Albert

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AB - In this work we describe the bifurcation scenario found in a general first order system when a relay based proportional control (sliding-mode control) is considered. Based on the results given in the literature, we show the occurrence of a big bang bifurcation causing the existence of an infinite number of periodic orbits near a co-dimension two bifurcation point. We also extend in a natural way the applied theoretical result for second order systems involving 2D piecewise-defined maps.

KW - Big bang bifurcations

KW - Two-dimensional piecewise-defined maps

KW - Period adding

KW - Sliding-mode control

KW - Relays

U2 - 10.1007/s12591-012-0121-y

DO - 10.1007/s12591-012-0121-y

M3 - Journal article

SN - 0971-3514

VL - 21

SP - 35

EP - 43

JO - Differential Equations and Dynamical Systems

JF - Differential Equations and Dynamical Systems

IS - 1-2

ER -

Occurrence of big bang bifurcations in discretized sliding-mode control systems

Abstract

Keywords

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