LIE-POISSON REDUCTION FOR OPTIMAL CONTROL OF LEFT-INVARIANT CONTROL SYSTEMS WITH SUBGROUP SYMMETRY
We study the reduction by symmetries for optimality conditions in optimal control problems of left-invariant affine control systems with partial symmetry breaking cost functions. We recast the optimal control problem as a constrained problem with a partial symmetry breaking Hamiltonian and we obtain...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/369223 |
| Acceso en línea: | http://hdl.handle.net/10261/369223 |
| Access Level: | acceso abierto |
| Palabra clave: | obstacle avoidance symmetry reduction Lie–Poisson equations optimal control Lie group actions Lie- Poisson equations |
| Sumario: | We study the reduction by symmetries for optimality conditions in optimal control problems of left-invariant affine control systems with partial symmetry breaking cost functions. We recast the optimal control problem as a constrained problem with a partial symmetry breaking Hamiltonian and we obtain the reduced optimality conditions for normal extrema from Pontryagin's Maximum Principle and a Lie–Poisson bracket on the reduced state space. We apply the results to an energy-minimum obstacle avoidance problems. |
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