Contact Geometry in Optimal Control of Thermodynamic Processes for Gases

被引：0
作者：
Kushner, A. G. [1 ,2 ]
Lychagin, V. V. [3 ]
Roop, M. D. [1 ,3 ]
机构：
[1] Lomonosov Moscow State Univ, Fac Phys, Moscow 119991, Russia
[2] Moscow State Pedag Univ, Moscow 119435, Russia
[3] Russian Acad Sci, Trapeznikov Inst Control Sci, Moscow 117997, Russia
来源：
DOKLADY MATHEMATICS | 2020年 / 102卷 / 01期
基金：
俄罗斯基础研究基金会;
关键词：
contact geometry; thermodynamics; optimal control; Hamiltonian systems; integrability;
D O I：
10.1134/S1064562420040109
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We solve an optimal control problem for thermodynamic processes in an ideal gas. The thermodynamic state is given by a Legendrian manifold in a contact space. Pontryagin's maximum principle is used to find an optimal trajectory (thermodynamic process) on this manifold that maximizes the work of the gas. In the case of ideal gases, it is shown that the corresponding Hamiltonian system is completely integrable and its quadrature-based solution is given. Keywords :contact geometry, thermodynamics, optimal control, Hamiltonian systems, integrability
引用
收藏
页码：346 / 349
页数：4
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