Optimal control of linear stochastic evolution equations in Hilbert spaces and uniform observability

Title:

Optimal control of linear stochastic evolution equations in Hilbert spaces and uniform observability

Creator:

Ungureanu, Viorica Mariela

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:eadd592c-b503-4056-8321-070f1ee082a9
uuid:eadd592c-b503-4056-8321-070f1ee082a9

Subject:

Riccati equation, stochastic uniform observability, stabilizability, quadratic control, and tracking problem

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this paper we study the existence of the optimal (minimizing) control for a tracking problem, as well as a quadratic cost problem subject to linear stochastic evolution equations with unbounded coefficients in the drift. The backward differential Riccati equation (BDRE) associated with these problems (see \cite {chen}, for finite dimensional stochastic equations or \cite {UC}, for infinite dimensional equations with bounded coefficients) is in general different from the conventional BDRE (see \cite {1990}, \cite {ukl}). Under stabilizability and uniform observability conditions and assuming that the control weight-costs are uniformly positive, we establish that BDRE has a unique, uniformly positive, bounded on ${\mathbf R}_{+}$ and stabilizing solution. Using this result we find the optimal control and the optimal cost. It is known \cite {ukl} that uniform observability does not imply detectability and consequently our results are different from those obtained under detectability conditions (see \cite {1990}).

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

317-342

Source:

Czechoslovak Mathematical Journal | 2009 Volume:59 | Number:2

Harvested from:

CDK

Metadata only:

false