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

Research output: Contribution to journal › Conference article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	38-43
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	55
Issue number	16
DOIs	https://doi.org/10.1016/j.ifacol.2022.08.078
Publication status	Published - 1 Jul 2022
Externally published	Yes
Event	18th IFAC Workshop on Control Applications of Optimization, CAO 2022 - Gif sur Yvette, France Duration: 18 Jul 2022 → 22 Jul 2022

Keywords

dissipativity
hyperbolicity
optimal control
turnpike
value function

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10.1016/j.ifacol.2022.08.078

Cite this

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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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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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Keywords

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