Journal Article

Optimal control for linear discrete-time systems with Markov perturbations in Hilbert spaces

Viorica Mariela Ungureanu

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 26, issue 1, pages 105-127
Published in print March 2009 | ISSN: 0265-0754
Published online March 2009 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dnp001
Optimal control for linear discrete-time systems with Markov perturbations in Hilbert spaces

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In this article, we discuss a quadratic control problem for linear discrete-time systems with Markov perturbations in Hilbert spaces, which is linked to a discrete-time Riccati equation defined on certain infinite-dimensional ordered Banach space. We prove that under stabilizability and stochastic uniform observability conditions, 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 illustrates the theory.

Keywords: discrete-time stochastic systems; stochastic observability; Riccati equation; optimal control

Journal Article.  0 words. 

Subjects: Mathematics

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