On the Hamilton-Jacobi-Bellman equations in Banach spaces

H. Mete Soner

doi:10.1007/BF02346162

On the Hamilton-Jacobi-Bellman equations in Banach spaces

H. Mete Soner

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

38 Scopus citations

Abstract

This paper is concerned with a certain class of distributed parameter control problems. The value function of these problems is shown to be the unique viscosity solution of the corresponding Hamiltonian-Jacobi-Bellman equation. The main assumption is the existence of an increasing sequence of compact invariant subsets of the state space. In particular, this assumption is satisfied by a class of controlled delay equations.

Original language	English (US)
Pages (from-to)	429-437
Number of pages	9
Journal	Journal of Optimization Theory and Applications
Volume	57
Issue number	3
DOIs	https://doi.org/10.1007/BF02346162
State	Published - Jun 1988
Externally published	Yes

All Science Journal Classification (ASJC) codes

Control and Optimization
Management Science and Operations Research
Applied Mathematics

Keywords

Distributed control problems
controlled delay equations
viscosity solutions

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10.1007/BF02346162

Cite this

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title = "On the Hamilton-Jacobi-Bellman equations in Banach spaces",

abstract = "This paper is concerned with a certain class of distributed parameter control problems. The value function of these problems is shown to be the unique viscosity solution of the corresponding Hamiltonian-Jacobi-Bellman equation. The main assumption is the existence of an increasing sequence of compact invariant subsets of the state space. In particular, this assumption is satisfied by a class of controlled delay equations.",

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year = "1988",

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AU - Mete Soner, H.

PY - 1988/6

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N2 - This paper is concerned with a certain class of distributed parameter control problems. The value function of these problems is shown to be the unique viscosity solution of the corresponding Hamiltonian-Jacobi-Bellman equation. The main assumption is the existence of an increasing sequence of compact invariant subsets of the state space. In particular, this assumption is satisfied by a class of controlled delay equations.

AB - This paper is concerned with a certain class of distributed parameter control problems. The value function of these problems is shown to be the unique viscosity solution of the corresponding Hamiltonian-Jacobi-Bellman equation. The main assumption is the existence of an increasing sequence of compact invariant subsets of the state space. In particular, this assumption is satisfied by a class of controlled delay equations.

KW - Distributed control problems

KW - controlled delay equations

KW - viscosity solutions

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U2 - 10.1007/BF02346162

DO - 10.1007/BF02346162

M3 - Article

AN - SCOPUS:0024017910

SN - 0022-3239

VL - 57

SP - 429

EP - 437

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 3

ER -

On the Hamilton-Jacobi-Bellman equations in Banach spaces

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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