Control strategies for systems with information bottlenecks often follow an estimate-then-control paradigm. This paper presents a \u201cnon-coherent\u201d system where this strategy cannot work and provides an alternative. The paper considers the estimation and control of a discrete time linear system with continuous random observation gain, i.e. through a non-coherent channel. It is shown that such an unstable system is not mean-squared observable regardless of the density of the random observation gain: the mean-squared estimation error for any estimator must go to infinity. This is surprising in the context of threshold results for rate-limited estimation. In contrast to other results with rate-limited feedback, the paper shows that the system can be closed-loop mean-square stabilized in a certain parameter regime even though its open-loop counterpart is not mean-square observable. Finally, carry-free models (generalized deterministic models) provide an intuitive interpretation for the results.<\/p>\n","protected":false},"excerpt":{"rendered":"
Control strategies for systems with information bottlenecks often follow an estimate-then-control paradigm. This paper presents a \u201cnon-coherent\u201d system where this strategy cannot work and provides an alternative. The paper considers the estimation and control of a discrete time linear system with continuous random observation gain, i.e. through a non-coherent channel. It is shown that such 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