Optimal stabilization of stochastic systems
type: Item
instance of: scholarly article
title: Optimal stabilization of stochastic systems
zbMATH Open document ID: 0537.93068
DOI: 10.1016/0022-247X(83)90077-X
author: Yannis A. Phillis
published in: Journal of Mathematical Analysis and Applications
publication date: 1983-01-01T00:00:00Z
review text: The paper deals with optimal stabilization of stochastic systems which are solutions of Ito-equations using performance criteria of the type \(E(\int^{\infty}_{t_ 0}g(x,u,t,)\quad dt).\) Assume that the state vector is known for all t, and the system is completely controllable. Then a Lyapunov function that ensures stochastic (asymptotic) stability (in the large) and fulfills the steady state Bellman equation yields optimal stability (in one of the senses above). This result is specialized for systems that are linear in the control with performance criterion quadratic in the control. For linear systems, i.e. linear in state and control with quadratic performance criterion in x and u, the Lyapunov function can be made specific, which for time-invariant systems under the condition of complete controllability entails optimal stability in the sense of stochastic asymptotic stability in the large.
Mathematics Subject Classification ID: 93E15
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 49J55
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93C99
Mathematics Subject Classification ID: 93E03
zbMATH DE Number: 3854944
zbMATH Keywords: optimal stabilization
zbMATH Keywords: Lyapunov function
zbMATH Keywords: stochastic asymptotic stability in the large
reviewed by: Wolfgang Kliemann
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3854944