Stability Properties of the Value Function in an Infinite Horizon Optimal Control Problem

Properties of the value function are examined in an infinite horizon optimal control problem with an integrand index appearing in the quality functional with a discount factor. The properties are analyzed in the case when the payoff functional of the control system includes a quality index represent...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the Steklov Institute of Mathematics 2018-07, Vol.301 (Suppl 1), p.1-14
Main Authors: Bagno, A. L., Tarasyev, A. M.
Format: Article
Language:English
Subjects:
Approximation
Asymptotic properties
Control stability
Economic development
Economic models
Functionals
Horizon
Mathematics
Mathematics and Statistics
Minimax technique
Modelling
Optimal control
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Properties of the value function are examined in an infinite horizon optimal control problem with an integrand index appearing in the quality functional with a discount factor. The properties are analyzed in the case when the payoff functional of the control system includes a quality index represented by an unbounded function. An upper estimate is given for the growth rate of the value function. Necessary and sufficient conditions are obtained to ensure that the value function satisfies the infinitesimal stability properties. The question of coincidence of the value function with the generalized minimax solution of the Hamilton–Jacobi–Bellman–Isaacs equation is discussed. The uniqueness of the corresponding minimax solution is shown. The growth asymptotic behavior of the value function is described for the logarithmic, power, and exponential quality functionals, which arise in economic and financial modeling. The obtained results can be used to construct grid approximation methods for the value function as the generalized minimax solution of the Hamilton–Jacobi–Bellman–Isaacs equation. These methods are effective tools in the modeling of economic growth processes.
ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543818050012