×

The quadratic control for linear discrete-time systems with independent random perturbations in Hilbert spaces connected with uniform observability. (English) Zbl 1107.49026

Summary: The optimal control problem for linear discrete-time, time varying systems with state dependent noise and quadratic control is considered. The asymptotic behaviour of the solution of the related discrete-time Riccati equation is investigated. The existence of an optimal control, under stabilizability and uniform observability (respectively detectability) conditions, for the given quadratic cost function is proved.

MSC:

49N10 Linear-quadratic optimal control problems
39A11 Stability of difference equations (MSC2000)
93E20 Optimal stochastic control
PDF BibTeX XML Cite
Full Text: EuDML