Journal Article

Quadratic optimal control for discrete-time infinite-dimensional stochastic bilinear systems

O. L. V. COSTA and C. S. KUBRUSLY

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 14, issue 4, pages 385-399
Published in print December 1997 | ISSN: 0265-0754
Published online December 1997 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/14.4.385
Quadratic optimal control for discrete-time infinite-dimensional stochastic bilinear systems

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In this paper, we consider the class of infinite-dimensional discrete-time linear systems with multiplicative random disturbances (i.e. with the state multiplied by a random sequence), also known as stochastic bilinear systems. We formulate and solve the quadratic optimal-control problem for this class of systems subject to an arbitrary additive stochastic l2 input disturbance. Under assumptions that guarantee the existence of a solution to an algebraic Riccati-like operator equation (derived previously by the authors), we characterize a bounded linear operator that takes the additive stochastic l2 input disturbance and the inital condition into the optimal control law. Such a result generalizes, to the infinite-dimensional bilinear stochastic case, some known result for the deterministic linear case.

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Subjects: Mathematics

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