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

页码：131 / 141

页数：11

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