Optimal control for linear discrete-time systems with Markov perturbations in Hilbert spaces |
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Authors: | Ungureanu Viorica Mariela |
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Affiliation: | "Constantin Brancusi" University of Tirgu-Jiu, Bulevardul Republicii nr.1, Tg-Jiu, Gorj, Romania |
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Abstract: | Email: vio{at}utgjiu.roReceived on September 12, 2007; Accepted on December 26, 2008 In this article, we discuss a quadratic control problem forlinear discrete-time systems with Markov perturbations in Hilbertspaces, which is linked to a discrete-time Riccati equationdefined on certain infinite-dimensional ordered Banach space.We prove that under stabilizability and stochastic uniform observabilityconditions, the Riccati equation has a unique, uniformly positive,bounded on N and stabilizing solution. Based on this result,we solve the proposed optimal control problem. An example illustratesthe theory. |
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Keywords: | discrete-time stochastic systems stochastic observability Riccati equation optimal control. |
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