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Tracking problem for linear discrete-time stochastic systems in Hilbert spaces and the uniform observability. (English) Zbl 1164.93013

The tracking problem for linear discrete-time systems with independent random perturbations in Hilbert spaces is studied for both periodic and unperiodic cases. Here, a certain quadratic cost criterion is minimized under stabilizability and uniform observability (or detectability) conditions. Introducing a certain Riccati difference equation, the optimal costs and an optimal control is determined.

MSC:

93E20 Optimal stochastic control
93C55 Discrete-time control/observation systems
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