Multiple-objective risk-sensitive control and its small noise limit
type: Item
instance of: scholarly article
title: Multiple-objective risk-sensitive control and its small noise limit
zbMATH Open document ID: 1030.93054
DOI: 10.1016/S0005-1098(02)00270-4
author: Andrew Lim
author: Xun Yu Zhou
author: John Moore
published in: Automatica
publication date: 2003-04-27T00:00:00Z
review text: This paper deals with a multiple-objective, risk-sensitive control problem. The authors study asymptotic properties of the value function, as the noise approaches \(0\), and introduce a new class of two-player, zero-sum, deterministic differential games whose cost functional is multiple-objective, being composed of the risk-neutral integral costs associated with the original risk-sensitive control. In this game, the opposing player seeks to maximize the most vulnerable member of a given set of cost functionals, while the original controller seeks to minimize the worst damage that the opponent can do over this set. Using the dynamic programming approach and the viscosity solution, they show the connection between the original risk-sensitive control and the differential game. In particular, they prove that the differential game is independent of the weights on the different objective in the original risk-sensitive control and moreover an efficient risk-sensitive controller can be determined asymptotically by solving the differential game. Applying their results to the single-objective case, they generalize some known results.
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 91A05
Mathematics Subject Classification ID: 49L25
Mathematics Subject Classification ID: 49L20
zbMATH DE Number: 1900994
zbMATH Keywords: risk-sensitive control
zbMATH Keywords: multiple-objective optimization differential games
zbMATH Keywords: Hamilton-Jacobi-Bellman equations
zbMATH Keywords: upper/lower Isaacs equations
zbMATH Keywords: viscosity solutions
zbMATH Keywords: two-player differential games
zbMATH Keywords: dynamic programming
reviewed by: Makiko Nisio
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1900994