ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. LXXIV, 1 (2005)
p. 107 - 126
The quadratic control for linear discrete-time systems with independent random
perturbations in Hilbert spaces connected with uniform observability
V. M. Ungureanu
Abstract.
The optimal control problem for linear
discrete-time, time-varying systems with state dependent noise and quadratic
control is considered. The asymptotic behavior 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.
Keywords:
Quadratic control, Riccati equation, uniform observability.
AMS Subject classification: 93E20, 49N10, 39A11.
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