Linear, stationary, optimal feedback control systems

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Based upon Kalman's theory of controllability and observability, the author extends the relation between optimal regulator and optimal filter and amplifies the meaning of those optimalities. It is shown that, in case of a single input and a single output, (1) two optimal feedback systems (one is the optimal regulator, the other is the optimal filter) are algebraically equivalent if they have originally the same dynamical structure and (2) the optimality of the regulator includes that in minimizing a certain kind of noise disturbance effect, in addition to original one.

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