Approximate solutions of the bellman equation of deterministic control theory

I. Capuzzo Dolcetta; H. Ishii

doi:10.1007/BF01442176

Approximate solutions of the bellman equation of deterministic control theory

I. Capuzzo Dolcetta^*, H. Ishii

^*Corresponding author for this work

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

109 Citations (Scopus)

Abstract

We consider an infinite horizon discounted optimal control problem and its time discretized approximation, and study the rate of convergence of the approximate solutions to the value function of the original problem. In particular we prove the rate is of order 1 as the discretization step tends to zero, provided a semiconcavity assumption is satisfied. We also characterize the limit of the optimal controls for the approximate problems within the framework of the theory of relaxed controls.

Original language	English
Pages (from-to)	161-181
Number of pages	21
Journal	Applied Mathematics & Optimization
Volume	11
Issue number	1
DOIs	https://doi.org/10.1007/BF01442176
Publication status	Published - 1984 Feb
Externally published	Yes

ASJC Scopus subject areas

Applied Mathematics
Mathematics(all)

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10.1007/BF01442176

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AB - We consider an infinite horizon discounted optimal control problem and its time discretized approximation, and study the rate of convergence of the approximate solutions to the value function of the original problem. In particular we prove the rate is of order 1 as the discretization step tends to zero, provided a semiconcavity assumption is satisfied. We also characterize the limit of the optimal controls for the approximate problems within the framework of the theory of relaxed controls.

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Approximate solutions of the bellman equation of deterministic control theory

Abstract

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