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

Veljko Ašković; Emmanuel Trélat; Hasnaa Zidani

doi:10.3934/mcrf.2024041

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

Veljko Ašković
, Emmanuel Trélat
, Hasnaa Zidani

MBDA France
Sorbonne Université
INSA Rouen Normandie

Research output: Contribution to journal › Article › peer-review

Abstract

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 Ñ `8. 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.

Original language	English
Pages (from-to)	1501-1516
Number of pages	16
Journal	Mathematical Control and Related Fields
Volume	14
Issue number	4
DOIs	https://doi.org/10.3934/mcrf.2024041
Publication status	Published - 1 Dec 2024
Externally published	Yes

Keywords

Value function
ergodicity
static optimization problem
strict dissipativity
turnpike

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10.3934/mcrf.2024041

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

abstract = "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 {\~N} `8. 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.",

keywords = "Value function, ergodicity, static optimization problem, strict dissipativity, turnpike",

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

year = "2024",

month = dec,

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doi = "10.3934/mcrf.2024041",

language = "English",

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AU - Ašković, Veljko

AU - Trélat, Emmanuel

AU - Zidani, Hasnaa

PY - 2024/12/1

Y1 - 2024/12/1

N2 - 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 Ñ `8. 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.

AB - 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 Ñ `8. 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.

KW - Value function

KW - ergodicity

KW - static optimization problem

KW - strict dissipativity

KW - turnpike

UR - https://www.scopus.com/pages/publications/85213396442

U2 - 10.3934/mcrf.2024041

DO - 10.3934/mcrf.2024041

M3 - Article

AN - SCOPUS:85213396442

SN - 2156-8472

VL - 14

SP - 1501

EP - 1516

JO - Mathematical Control and Related Fields

JF - Mathematical Control and Related Fields

IS - 4

ER -

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

Abstract

Keywords

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