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IMA Journal of Mathematical Control and Information 1997 14(4):385-399; doi:10.1093/imamci/14.4.385
© 1997 by Institute of Mathematics and its Applications
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Quadratic optimal control for discrete-time infinite-dimensional stochastic bilinear systems

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

Department of Electronic Engineering, University of São Paulo 05508 900 São Paulo SP, Brazil
Catholic University PUC/RJ, and National Laboratory for Scientific Computation (LNCC) 22290 160 Rio de Janeiro RJ, Brazil

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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