Extended Kalman filter -- Koopman operator for tractable stochastic optimal control

It has been more than seven decades since the introduction of the theory of dual control \cite{feldbaum1960dual}. Although it has provided rich insights to the fields of control, estimation, and system identification, dual control is generally computationally prohibitive. In recent years, however, the use of Koopman operator theory for control applications has been emerging. The paper presents a new reformulation of the stochastic optimal control problem that, employing the Koopman operator, yields a standard LQR problem with the dual control as its solution. We conclude the paper with a numerical example that demonstrates the effectiveness of the proposed approach, compared to certainty equivalence control, when applied to systems with varying observability.