Bellman functions in the optimization of dynamic systems under uncertainty
type: Item
instance of: scholarly article
title: Bellman functions in the optimization of dynamic systems under uncertainty
zbMATH Open document ID: 0609.49020
published in: Automation and Remote Control
publication date: 1986-01-01T00:00:00Z
review text: The author discusses a specific optimization problem of dynamic systems under uncertainty namely, the ''game of two cars'' of \textit{R. Isaacs} [Differential games (1965; Zbl 0125.380)]. It is shown that the well known sufficient optimality conditions expressed in terms of the solution to Bellman's equation (Bellman's function) for a deterministic system do not hold here. However, assuming that no allowed disturbances can move the path of the system out of the domain of definition of the obtained Bellman function before this path reaches the terminal set of the system, then sufficient optimality conditions for the deterministic case hold even for the nondeterministic system.
reviewed by: R. N. Kaul
Mathematics Subject Classification ID: 49L20
Mathematics Subject Classification ID: 91A24
Mathematics Subject Classification ID: 49K15
Mathematics Subject Classification ID: 91A99
Mathematics Subject Classification ID: 91A23
zbMATH DE Number: 3986040
zbMATH Keywords: dynamic systems under uncertainty
zbMATH Keywords: Bellman's equation
zbMATH Keywords: Bellman's function
zbMATH Keywords: sufficient optimality conditions
author: È. N. Simakova
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3986040