A new approach to lineary perturbed Riccati equations arising in stochastic control
type: Item
instance of: scholarly article
title: A new approach to lineary perturbed Riccati equations arising in stochastic control
zbMATH Open document ID: 0895.93042
published in: Applied Mathematics and Optimization
publication date: 1998-09-21T00:00:00Z
review text: A linearly perturbed version of the well-known Riccati equations, which arise in certain stochastic optimal control problems, is studied. Using the concepts of mean square stabilizability and mean square detectability, previous results concerning both convergence properties of the linearly perturbed Riccati differential equation and the solutions of the linearly perturbed algebraic Riccati equation are improved. The proposed approach unifies, in some way, the study of this class of Riccati equations with that one arising from the classical theory, by eliminating certain inconvenient assumptions used in other papers. Thus, for example, the existence of a strong solution is subjected only to the mean square stabilizability assumption.
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 93C73
Mathematics Subject Classification ID: 93C99
zbMATH DE Number: 1129437
zbMATH Keywords: perturbation
zbMATH Keywords: Riccati equations
zbMATH Keywords: mean square stabilizability
author: Marcelo Dutra Fragoso
author: Oswaldo Luiz V. Costa
author: Carlos E. de Souza
reviewed by: Ryszard Gessing
MaRDI profile type: Publication
full work available at URL: s002459900070
OpenAlex ID: W2067573516
DOI: 10.1007/S002459900070
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description: scientific article; zbMATH DE number 1129437