TWO-TERM LARGE-TIME ASYMPTOTIC EXPANSION OF THE VALUE FUNCTION FOR DISSIPATIVE NONLINEAR OPTIMAL CONTROL PROBLEMS

被引：0

作者：

Askovic, Veljko ^{[1
]}

Trelat, Emmanuel ^{[2
]}

Zidani, Hasnaa ^{[3
]}

机构：

[1] MBDA, Le Plessis Robinson, France

[2] Sorbonne Univ, Univ Paris Cite, CNRS, Inria,Lab JacquesLouis Lions LJLL, F-75005 Paris, France

[3] Normandie Univ, INSA Rouen Normandie, Lab Mathe, Matiques LMI 3226,UR 3226, F-76000 Rouen, France

来源：

MATHEMATICAL CONTROL AND RELATED FIELDS | 2024年 / 14卷 / 04期

关键词：

Value function; ergodicity; strict dissipativity; static optimization prob- lem; turnpike; QUADRATIC OPTIMAL-CONTROL; STRICT DISSIPATIVITY; TURNPIKE PROPERTY; LOCAL REGULARITY; STEADY-STATE;

D O I：

10.3934/mcrf.2024041

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Considering a general nonlinear dissipative finite dimensional optimal control problem in fixed time horizon T , we establish a two-term asymptotic expansion of the value function as T -> infinity . The dominating term is T times the optimal value obtained from the optimal static problem within the classical turnpike theory. The second term, of order unity, is interpreted as the sum of two values associated with optimal stabilization problems related to the turnpike.

引用

页码：1501 / 1516

页数：16

共 4 条

[1] On the asymptotic behavior of the value function in large time optimal control problems
Askovic, Veljko
Trelat, Emmanuel
Zidani, Hasnaa
IFAC PAPERSONLINE, 2022, 55 (16): : 38 - 43
[2] Linear quadratic optimal control turnpike in finite and infinite dimension: Two-term expansion of the value function
Askovic, Veljko
Trelat, Emmanuel
Zidani, Hasnaa
SYSTEMS & CONTROL LETTERS, 2024, 188
[3] Continuous Differentiability of the Value Function of Semilinear Parabolic Infinite Time Horizon Optimal Control Problems on L2(Ω) Under Control Constraints
Kunisch, Karl
Priyasad, Buddhika
APPLIED MATHEMATICS AND OPTIMIZATION, 2022, 85 (02)
[4] Continuous Differentiability of the Value Function of Semilinear Parabolic Infinite Time Horizon Optimal Control Problems on L2(Ω)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2(\Omega )$$\end{document} Under Control Constraints
Karl Kunisch
Buddhika Priyasad
Applied Mathematics & Optimization, 2022, 85 (2)

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