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Prediction, filtering, smoothing and deconvolution in a discrete \(H^\infty\) setting: A game theory approach. (English) Zbl 0945.93025

For a linear finite-dimensional discrete-time input-output dynamical system with additively disturbed outputs, an optimal estimator of states is sought. The latter minimizes the maximum of a performance index \( J \) defined as a quadratic distance between the trajectory of state estimates and the system’s trajectory minus the sum of quadratic norms of the system’s input and observation disturbance; \( J \) is maximized over arbitary inputs and observation disturbances. Optimal estimators that estimate the system’s states at every next instant (a prediction problem), at every current instant (a filtering problem), and at the instants preceding the current ones (a smoothing problem) are described. In the latter case an estimator of inputs (a deconvolution problem) is presented. A technique of quadratic games is used.

MSC:

93E11 Filtering in stochastic control theory
93E14 Data smoothing in stochastic control theory
93C55 Discrete-time control/observation systems
93B36 \(H^\infty\)-control
91A80 Applications of game theory
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