The value function of singularly perturbed control systems

Z. Artstein; V. Gaitsgory

doi:10.1007/s002459911022

The value function of singularly perturbed control systems

Z. Artstein^*, V. Gaitsgory

^*Corresponding author for this work

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

59 Citations (Scopus)

Abstract

The limit as ε → 0 of the value function of a singularly perturbed optimal control problem is characterized. Under general conditions it is shown that limit value functions exist and solve in a viscosity sense a Hamilton-Jacobi equation. The Hamiltonian of this equation is generated by an infinite horizon optimization on the fast time scale. In particular, the limit Hamiltonian and the limit Hamilton-Jacobi equation are applicable in cases where the reduction of order, namely setting ε = 0, does not yield an optimal behavior.

Original language	English
Pages (from-to)	425-445
Number of pages	21
Journal	Applied Mathematics and Optimization
Volume	41
Issue number	3
DOIs	https://doi.org/10.1007/s002459911022
Publication status	Published - May 2000
Externally published	Yes

Keywords

Hamilton-jacobi equation
Limit hamiltonian
Optimal control
Singular perturbation

Access to Document

10.1007/s002459911022

Cite this

@article{4f8b9ca2145b480a8cfd44512a0af72b,

title = "The value function of singularly perturbed control systems",

abstract = "The limit as ε → 0 of the value function of a singularly perturbed optimal control problem is characterized. Under general conditions it is shown that limit value functions exist and solve in a viscosity sense a Hamilton-Jacobi equation. The Hamiltonian of this equation is generated by an infinite horizon optimization on the fast time scale. In particular, the limit Hamiltonian and the limit Hamilton-Jacobi equation are applicable in cases where the reduction of order, namely setting ε = 0, does not yield an optimal behavior.",

keywords = "Hamilton-jacobi equation, Limit hamiltonian, Optimal control, Singular perturbation",

author = "Z. Artstein and V. Gaitsgory",

year = "2000",

month = may,

doi = "10.1007/s002459911022",

language = "English",

volume = "41",

pages = "425--445",

journal = "Applied Mathematics and Optimization",

issn = "0095-4616",

publisher = "Springer, Springer Nature",

number = "3",

}

TY - JOUR

T1 - The value function of singularly perturbed control systems

AU - Artstein, Z.

AU - Gaitsgory, V.

PY - 2000/5

Y1 - 2000/5

N2 - The limit as ε → 0 of the value function of a singularly perturbed optimal control problem is characterized. Under general conditions it is shown that limit value functions exist and solve in a viscosity sense a Hamilton-Jacobi equation. The Hamiltonian of this equation is generated by an infinite horizon optimization on the fast time scale. In particular, the limit Hamiltonian and the limit Hamilton-Jacobi equation are applicable in cases where the reduction of order, namely setting ε = 0, does not yield an optimal behavior.

AB - The limit as ε → 0 of the value function of a singularly perturbed optimal control problem is characterized. Under general conditions it is shown that limit value functions exist and solve in a viscosity sense a Hamilton-Jacobi equation. The Hamiltonian of this equation is generated by an infinite horizon optimization on the fast time scale. In particular, the limit Hamiltonian and the limit Hamilton-Jacobi equation are applicable in cases where the reduction of order, namely setting ε = 0, does not yield an optimal behavior.

KW - Hamilton-jacobi equation

KW - Limit hamiltonian

KW - Optimal control

KW - Singular perturbation

UR - http://www.scopus.com/inward/record.url?scp=0033885874&partnerID=8YFLogxK

U2 - 10.1007/s002459911022

DO - 10.1007/s002459911022

M3 - Article

AN - SCOPUS:0033885874

SN - 0095-4616

VL - 41

SP - 425

EP - 445

JO - Applied Mathematics and Optimization

JF - Applied Mathematics and Optimization

IS - 3

ER -

The value function of singularly perturbed control systems

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this