# Approximate solutions of the bellman equation of deterministic control theory

I. Capuzzo Dolcetta, H. Ishii

Research output: Contribution to journalArticle

91 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 161-181 21 Applied Mathematics & Optimization 11 1 https://doi.org/10.1007/BF01442176 Published - 1984 Feb Yes

### Fingerprint

Bellman Equation
Control theory
Control Theory
Approximate Solution
Relaxed Controls
Infinite Horizon
Value Function
Optimal Control Problem
Optimal Control
Rate of Convergence
Discretization
Tend
Zero
Approximation
Framework

### ASJC Scopus subject areas

• Applied Mathematics
• Mathematics(all)

### Cite this

Approximate solutions of the bellman equation of deterministic control theory. / Dolcetta, I. Capuzzo; Ishii, H.

In: Applied Mathematics & Optimization, Vol. 11, No. 1, 02.1984, p. 161-181.

Research output: Contribution to journalArticle

Dolcetta, I. Capuzzo ; Ishii, H. / Approximate solutions of the bellman equation of deterministic control theory. In: Applied Mathematics & Optimization. 1984 ; Vol. 11, No. 1. pp. 161-181.
title = "Approximate solutions of the bellman equation of deterministic control theory",
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.",
author = "Dolcetta, {I. Capuzzo} and H. Ishii",
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