A new approach to lineary perturbed Riccati equations arising in stochastic control
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.
scientific article; zbMATH DE number 1129437
scientific article