Bringing order to chaos: Hybrid modelling of a discontinuous chaotic system

Eva M. Navarro-López; Juan G. Barajas-Ramírez

doi:10.1109/VSS.2010.5544705

Bringing order to chaos: Hybrid modelling of a discontinuous chaotic system

Eva M. Navarro-López, Juan G. Barajas-Ramírez

Research output: Chapter in Book/Conference proceeding › Conference contribution › peer-review

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Abstract

We propose a computational-oriented perspective within the study of discontinuous chaotic systems, and provide insights into the modelling, control and simulation of chaotic systems with switching dynamics. In particular, the Lorenz system in its piecewise-linear version is studied. This system is reinterpreted within the hybrid-automaton framework, and what is referred to as the Lorenz hybrid automaton is established. Furthermore, a discontinuous control which eliminates the chaotic behaviour and steers the trajectories to a desired equilibrium is proposed. An integral characteristic of the modelling framework is that the controlled system, exhibiting three discontinuity surfaces, is reduced to the composition of several Lorenz hybrid automata. The approach proposed here is especially useful in order to specify the transitions between the different system operation modes, which becomes a crucial problem due to the existence of multiple switching surfaces. © 2010 IEEE.

Original language	English
Title of host publication	Proceedings of the 2010 11th International Workshop on Variable Structure Systems, VSS 2010\|Proc. Int. Workshop Var. Struct. Syst., VSS
Publisher	IEEE
Pages	325-330
Number of pages	5
ISBN (Print)	9781424458318
DOIs	https://doi.org/10.1109/VSS.2010.5544705
Publication status	Published - 2010
Event	2010 11th International Workshop on Variable Structure Systems, VSS 2010 - Mexico City Duration: 1 Jul 2010 → …

Conference

Conference	2010 11th International Workshop on Variable Structure Systems, VSS 2010
City	Mexico City
Period	1/07/10 → …

Keywords

Hybrid automata
Chaotic systems
Sliding-mode-based control
Discontinuous systems
Switched control

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title = "Bringing order to chaos: Hybrid modelling of a discontinuous chaotic system",

abstract = "We propose a computational-oriented perspective within the study of discontinuous chaotic systems, and provide insights into the modelling, control and simulation of chaotic systems with switching dynamics. In particular, the Lorenz system in its piecewise-linear version is studied. This system is reinterpreted within the hybrid-automaton framework, and what is referred to as the Lorenz hybrid automaton is established. Furthermore, a discontinuous control which eliminates the chaotic behaviour and steers the trajectories to a desired equilibrium is proposed. An integral characteristic of the modelling framework is that the controlled system, exhibiting three discontinuity surfaces, is reduced to the composition of several Lorenz hybrid automata. The approach proposed here is especially useful in order to specify the transitions between the different system operation modes, which becomes a crucial problem due to the existence of multiple switching surfaces. {\textcopyright} 2010 IEEE.",

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author = "Navarro-L{\'o}pez, {Eva M.} and Barajas-Ram{\'i}rez, {Juan G.}",

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language = "English",

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Navarro-López, EM & Barajas-Ramírez, JG 2010, Bringing order to chaos: Hybrid modelling of a discontinuous chaotic system. in Proceedings of the 2010 11th International Workshop on Variable Structure Systems, VSS 2010|Proc. Int. Workshop Var. Struct. Syst., VSS. IEEE, pp. 325-330, 2010 11th International Workshop on Variable Structure Systems, VSS 2010, Mexico City, 1/07/10. https://doi.org/10.1109/VSS.2010.5544705

Bringing order to chaos: Hybrid modelling of a discontinuous chaotic system. / Navarro-López, Eva M.; Barajas-Ramírez, Juan G.
Proceedings of the 2010 11th International Workshop on Variable Structure Systems, VSS 2010|Proc. Int. Workshop Var. Struct. Syst., VSS. IEEE, 2010. p. 325-330.

Research output: Chapter in Book/Conference proceeding › Conference contribution › peer-review

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AU - Barajas-Ramírez, Juan G.

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AB - We propose a computational-oriented perspective within the study of discontinuous chaotic systems, and provide insights into the modelling, control and simulation of chaotic systems with switching dynamics. In particular, the Lorenz system in its piecewise-linear version is studied. This system is reinterpreted within the hybrid-automaton framework, and what is referred to as the Lorenz hybrid automaton is established. Furthermore, a discontinuous control which eliminates the chaotic behaviour and steers the trajectories to a desired equilibrium is proposed. An integral characteristic of the modelling framework is that the controlled system, exhibiting three discontinuity surfaces, is reduced to the composition of several Lorenz hybrid automata. The approach proposed here is especially useful in order to specify the transitions between the different system operation modes, which becomes a crucial problem due to the existence of multiple switching surfaces. © 2010 IEEE.

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Bringing order to chaos: Hybrid modelling of a discontinuous chaotic system

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