Optimal stabilization of unstable periodic orbits embedded in chaotic systems
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| Format: | Artículo científico |
| Language: | en |
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Sociedad Mexicana de Física A.C.
2007
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| _version_ | 1876436109227982848 |
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| author | C.A. Cruz-Villar |
| author_facet | C.A. Cruz-Villar |
| contents | Optimal stabilization of unstable periodic orbits embedded in chaotic systems C.A. Cruz-Villar Física, Astronomía y Matemáticas gradient flow sensitivity theory Optimal stabilization unstable periodic orbits A gradient-flow-based approach is proposed in this paper for stabilizing unstable periodic orbits (UPO) embedded in chaotic systems. Inorder to obtain an on-line stabilizing solution, the stabilization problem is considered to be an optimal control problem, and system statesensitivities with respect to the control input are introduced. The resulting feedback controller is able to stabilize UPO embedded in bothkind of systems, with or without an odd Floquet number. Moreover, the proposed approach is easily extended to identifying the period of theUPO to be stabilized when it is unknown. Simulation experiments of the proposed controller are carried out on the R¨ossler and the Lorenzsystems. 2007 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57053513 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.5 Vol.53 |
| format | Artículo científico |
| id | redalyc_57053513 |
| institution | Redalyc |
| language | en |
| publishDate | 2007 |
| publisher | Sociedad Mexicana de Física A.C. |
| spellingShingle | Optimal stabilization of unstable periodic orbits embedded in chaotic systems C.A. Cruz-Villar Física, Astronomía y Matemáticas gradient flow sensitivity theory Optimal stabilization unstable periodic orbits Optimal stabilization of unstable periodic orbits embedded in chaotic systems C.A. Cruz-Villar Física, Astronomía y Matemáticas gradient flow sensitivity theory Optimal stabilization unstable periodic orbits A gradient-flow-based approach is proposed in this paper for stabilizing unstable periodic orbits (UPO) embedded in chaotic systems. Inorder to obtain an on-line stabilizing solution, the stabilization problem is considered to be an optimal control problem, and system statesensitivities with respect to the control input are introduced. The resulting feedback controller is able to stabilize UPO embedded in bothkind of systems, with or without an odd Floquet number. Moreover, the proposed approach is easily extended to identifying the period of theUPO to be stabilized when it is unknown. Simulation experiments of the proposed controller are carried out on the R¨ossler and the Lorenzsystems. 2007 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57053513 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.5 Vol.53 |
| title | Optimal stabilization of unstable periodic orbits embedded in chaotic systems |
| topic | Física, Astronomía y Matemáticas gradient flow sensitivity theory Optimal stabilization unstable periodic orbits |
| url | https://www.redalyc.org/articulo.oa?id=57053513 |