Optimal control of linear stochastic evolution equations in Hilbert spaces and uniform observability |
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Authors: | Viorica Mariela Ungureanu |
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Institution: | (1) Department of Mathematics, “Constantin Brancusi” University, Tg. Jiu, B-dul Republicii, nr. 1, jud., Gorj, Romania |
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Abstract: | 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 2], for finite dimensional stochastic equations or 21], for
infinite dimensional equations with bounded coefficients) is in general different from the conventional BDRE (see 10], 18]).
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 ℝ + and stabilizing solution. Using this result we find the optimal control and the optimal cost. It is known 18] that uniform
observability does not imply detectability and consequently our results are different from those obtained under detectability
conditions (see 10]).
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Keywords: | Riccati equation stochastic uniform observability stabilizability quadratic control tracking problem |
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