子群对称左变量控制系统最优控制的LIE-POISSON约简

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2023-02-01 DOI:10.1016/S0034-4877(23)00015-0

Leonardo Colombo, Efstratios Stratoglou

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引用次数: 1

摘要

研究了具有部分对称性破缺代价函数的左不变仿射控制系统最优控制问题的最优性条件的对称约简。我们将最优控制问题转化为一个具有部分对称破缺哈密顿量的约束问题，并利用简化状态空间上的庞特里亚金极大值原理和Lie—Poisson托架，得到了正规极值的简化最优性条件。我们将结果应用于能量最小的避障问题。

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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 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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来源期刊

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.