Optimal stabilization of unstable periodic orbits embedded in chaotic systems
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...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2007 |
| País: | México |
| Institución: | Centro de Investigación y de Estudios Avanzados del IPN |
| Repositorio: | Redalyc-CINVESTAV |
| OAI Identifier: | oai:redalyc.org:57053513 |
| Acceso en línea: | https://www.redalyc.org/articulo.oa?id=57053513 |
| Access Level: | acceso abierto |
| Palabra clave: | Física, Astronomía y Matemáticas gradient flow sensitivity theory Optimal stabilization unstable periodic orbits |
| Sumario: | 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. |
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