Linear quadratic optimal control turnpike in finite and infinite dimension: Two-term expansion of the value function

被引：0
|
作者：
Askovic, Veljko [1 ]
Trelat, Emmanuel [1 ]
Zidani, Hasnaa [2 ]
机构：
[1] Univ Paris Cite, Sorbonne Univ, CNRS, Inria,Lab Jacques Louis LJLL, F-75005 Paris, France
[2] Normandie Univ, Lab Math LMI, INSA Rouen Normandie, UR 3226, F-76000 Rouen, France
来源：
SYSTEMS & CONTROL LETTERS | 2024年 / 188卷
关键词：
LQ optimal control problems; Turnpike property; Value function; PONTRYAGINS PRINCIPLE; EXISTENCE; STATE; CONTROLLABILITY; STABILIZATION; DISSIPATIVITY; EQUATIONS; PROPERTY;
D O I：
10.1016/j.sysconle.2024.105803
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we consider a linear quadratic (LQ) optimal control problem in both finite and infinite dimensions. We derive an asymptotic expansion of the value function as the fixed time horizon T tends to infinity. The leading term in this expansion, proportional to T, corresponds to the optimal value attained through the classical turnpike theory in the associated static problem. The remaining terms are associated with optimal stabilization problems towards the turnpike.
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页数：8
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