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Extracting state information from a quantized output record. (English) Zbl 0697.93012

Summary: We consider the problem of manipulating the input to a discrete-time state space linear system with the goal of obtaining information at each time about the system’s current state from a record of past quantized measurements of the system’s output. We find that if the system is not excessively unstable, there exist feedback control strategies that allow one to make an asymptotically perfect determination of the current stage based on the output records that result.
Even if the system is too unstable to apply such strategies, there are feedback control laws that make the system’s output record more informative about the system’s state evolution than one might expect. In deriving these control laws, we regard quantized measurements of real numbers more as partial observations than as strict approximations, and employ techniques from information theory and the theory of Markov chains with countable state spaces.

MSC:

93B07 Observability
94A15 Information theory (general)
93C05 Linear systems in control theory
93C55 Discrete-time control/observation systems
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References:

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