Estimation and control for linear, partially observable systems with non-gaussian initial distribution,
The nonlinear filtering problem of estimating the state of a linear stochastic system from noisy observations is solved for a broad class of probability distributions of the initial state. It is shown that the conditional density of the present state, given the past observations, is a mixture of Gaussian distributions, and is parametrically determined by two sets of sufficient statistics which satisfy stochastic DEs; this result leads to a generalization of the Kalman-Bucy filter to a structure with a conditional mean vector, and additional sufficient statistics that obey nonlinear equations, and determine a generalized (random) Kalman gain. The theory is used to solve explicitly a control problem with quadratic running and terminal costs, and bounded controls.
Year of publication: |
1983
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Authors: | Benes, Václav E. ; Karatzas, Ioannis |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 14.1983, 3, p. 233-248
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Publisher: |
Elsevier |
Keywords: | Stochastic control Kalman-Bucy filter Zakai equation |
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