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.
Possieri, C., Sassano, M. (2019). Deterministic Optimality of the Steady-State Behavior of the Kalman-Bucy Filter. IEEE CONTROL SYSTEMS LETTERS, 3(4), 793-798 [10.1109/LCSYS.2019.2918488].
Deterministic Optimality of the Steady-State Behavior of the Kalman-Bucy Filter
Possieri C.;Sassano M.
2019-05-01
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.File | Dimensione | Formato | |
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