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...

Descripción completa

Detalles Bibliográficos
Autores: Colombo, Leonardo, Stratoglou, Efstratios
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
Descripción
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.