On the asymptotic behavior of the value function in large time optimal control problems

Veljko Aškovic; Emmanuel Trélat; Hasnaa Zidani

doi:10.1016/j.ifacol.2022.08.078

On the asymptotic behavior of the value function in large time optimal control problems

Veljko Aškovic
, Emmanuel Trélat
, Hasnaa Zidani

Sorbonne Université
INSA Rouen Normandie

Résultats de recherche: Contribution à un journal › Article de conférence › Revue par des pairs

1 Citation (Scopus)

Résumé

We investigate the large time behavior of the value function associated to an optimal control problem in the finite dimensional case. We first establish the large time asymptotic expansion in the linear quadratic (LQ) case using the Hamiltonian structure of the Pontryagin Maximum Principle (PMP) extremal equations and some basic results of LQ theory. We then state, without proof, a general result for dissipative nonlinear systems.

langue originale	Anglais
Pages (de - à)	38-43
Nombre de pages	6
journal	IFAC-PapersOnLine
Volume	55
Numéro de publication	16
Les DOIs	https://doi.org/10.1016/j.ifacol.2022.08.078
état	Publié - 1 juil. 2022
Modification externe	Oui
Evénement	18th IFAC Workshop on Control Applications of Optimization, CAO 2022 - Gif sur Yvette, France Durée: 18 juil. 2022 → 22 juil. 2022

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title = "On the asymptotic behavior of the value function in large time optimal control problems",

abstract = "We investigate the large time behavior of the value function associated to an optimal control problem in the finite dimensional case. We first establish the large time asymptotic expansion in the linear quadratic (LQ) case using the Hamiltonian structure of the Pontryagin Maximum Principle (PMP) extremal equations and some basic results of LQ theory. We then state, without proof, a general result for dissipative nonlinear systems.",

keywords = "dissipativity, hyperbolicity, optimal control, turnpike, value function",

author = "Veljko A{\v s}kovic and Emmanuel Tr{\'e}lat and Hasnaa Zidani",

note = "Publisher Copyright: Copyright {\textcopyright} 2022 The Authors.; 18th IFAC Workshop on Control Applications of Optimization, CAO 2022 ; Conference date: 18-07-2022 Through 22-07-2022",

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doi = "10.1016/j.ifacol.2022.08.078",

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T1 - On the asymptotic behavior of the value function in large time optimal control problems

AU - Aškovic, Veljko

AU - Trélat, Emmanuel

AU - Zidani, Hasnaa

PY - 2022/7/1

Y1 - 2022/7/1

N2 - We investigate the large time behavior of the value function associated to an optimal control problem in the finite dimensional case. We first establish the large time asymptotic expansion in the linear quadratic (LQ) case using the Hamiltonian structure of the Pontryagin Maximum Principle (PMP) extremal equations and some basic results of LQ theory. We then state, without proof, a general result for dissipative nonlinear systems.

AB - We investigate the large time behavior of the value function associated to an optimal control problem in the finite dimensional case. We first establish the large time asymptotic expansion in the linear quadratic (LQ) case using the Hamiltonian structure of the Pontryagin Maximum Principle (PMP) extremal equations and some basic results of LQ theory. We then state, without proof, a general result for dissipative nonlinear systems.

KW - dissipativity

KW - hyperbolicity

KW - optimal control

KW - turnpike

KW - value function

UR - https://www.scopus.com/pages/publications/85142222945

U2 - 10.1016/j.ifacol.2022.08.078

DO - 10.1016/j.ifacol.2022.08.078

M3 - Conference article

AN - SCOPUS:85142222945

SN - 2405-8963

VL - 55

SP - 38

EP - 43

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 16

T2 - 18th IFAC Workshop on Control Applications of Optimization, CAO 2022

Y2 - 18 July 2022 through 22 July 2022

ER -

On the asymptotic behavior of the value function in large time optimal control problems

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