Optimal control of a stochastic system with an exponential-of-integral performance criterion
type: Item
instance of: scholarly article
title: Optimal control of a stochastic system with an exponential-of-integral performance criterion
zbMATH Open document ID: 0815.93084
DOI: 10.1016/0167-6911(94)90089-2
author: Thordur Runolfsson
published in: Systems \& Control Letters
publication date: 1994-01-01T00:00:00Z
review text: The author considers the nonlinear system described by the Itô stochastic differential equation: \[ dx(t)= h(x,u)dt+ \sigma(x) dw(t) \tag{1} \] where \(x\in \mathbb{R}^ n\) is the state, \(u\in \mathbb{R}^ m\) is the control and \(w(t)\) is an \(r\)-dimensional standard Wiener process. The cost functional (to be minimized) is the infinite-horizon or long-run average exponential-of-integral performance criterion: \[ J(u)= {1\over\theta} \lim_{T\to \infty} {1\over T}\ln E_ x^ u \Biggl[ \exp \biggl\{ \theta \int_ 0^ T c(x,u) dt \biggr\} \Biggr], \tag{2} \] where \(c(x,u)\) is a nonnegative continuous function and \(\theta\) is a scalar; \(E_ x^ u [\cdot ]\) denotes the expectation associated with the closed-loop system with control \(u\in U\) (admissible control). The author derives existence conditions for the state-feedback admissible controllers and optimality conditions. He discusses connections between the exponential-of-integral optimal control problem and stochastic differential games. The obtained results are illustrated by examples.
reviewed by: L. Socha
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 91A60
zbMATH DE Number: 612406
zbMATH Keywords: optimal stochastic control
zbMATH Keywords: continuous-time control systems
zbMATH Keywords: stochastic differential games
zbMATH Keywords: continuous-time
MaRDI profile type: Publication
full work available at URL: 0167-6911(94)90089-2
OpenAlex ID: W2021135967
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description: scientific article; zbMATH DE number 612406