Optimal control problems with symmetry breaking cost functions
We investigate symmetry reduction of optimal control problems for left-invariant control affine systems on Lie groups, with partial symmetry breaking cost functions. Our approach emphasizes the role of variational principles and considers a discrete-time setting as well as the standard continuoustim...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/378446 |
| Acceso en línea: | http://hdl.handle.net/10261/378446 |
| Access Level: | acceso abierto |
| Palabra clave: | Euler–Poincar´e equations Lie–Poisson equations Optimal control symmetry reduction |
| Sumario: | We investigate symmetry reduction of optimal control problems for left-invariant control affine systems on Lie groups, with partial symmetry breaking cost functions. Our approach emphasizes the role of variational principles and considers a discrete-time setting as well as the standard continuoustime formulation. Specifically, we recast the optimal control problem as a constrained variational problem with a partial symmetry breaking Lagrangian and obtain the Euler–Poincar´e equations from a variational principle. By using a Legendre transformation, we recover the Lie–Poisson equations obtained by Borum and Bretl [IEEE Trans. Automat. Control, 62 (2017), pp. 3209–3224] in the same context. We also discretize the variational principle in time and obtain the discrete-time Lie–Poisson equations. We illustrate the theory with some practical examples including a motion planning problem in the presence of an obstacle. |
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