Abstract
In this letter, we provide a deterministic characterization of optimality of the steady-state behavior of the Kalman–Bucy filter, via an inverse optimal control argument. The result is achieved in two steps, both interesting per se . First, a singular linear-quadratic (LQ) optimal control problem is formulated and solved with respect to the innovation term of a classic Luenberger observer, hence yielding a LQ optimal observer. Then, such a construction is employed to interpret the optimality of the steady-state behavior of the celebrated Kalman–Bucy filter in a purely deterministic sense.
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