LIE-POISSON REDUCTION FOR OPTIMAL CONTROL OF LEFT-INVARIANT CONTROL SYSTEMS WITH SUBGROUP SYMMETRY

被引：0
作者：
Colombo, Leonardo [1 ]
Stratoglou, Efstratios [2 ]
机构：
[1] CSIC UPM, Ctr Automat & Robot, Ctra M300 Campo Real,Km 0,200 Arganda Rey, Madrid 28500, Spain
[2] Univ Politecn Madrid UPM, Calle de Jose Gutierrez Abascal 2, Madrid 28006, Spain
来源：
REPORTS ON MATHEMATICAL PHYSICS | 2023年 / 91卷 / 01期
关键词：
symmetry reduction; optimal control; obstacle avoidance; Lie group actions; Lie- Poisson equations; SEMIDIRECT PRODUCTS;
D O I：
10.1016/S0034-4877(23)00015-0
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
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.
引用
收藏
页码：131 / 141
页数：11
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