  We formulate the discrete-time inverse optimal control problem of inferring
unknown parameters in the objective function of an optimal control problem from
measurements of optimal states and controls as a nonlinear filtering problem.
This formulation enables us to propose a novel extended Kalman filter (EKF) for
solving inverse optimal control problems in a computationally efficient
recursive online manner that requires only a single pass through the
measurement data. Importantly, we show that the Jacobians required to implement
our EKF can be computed efficiently by exploiting recent Pontryagin
differentiable programming results, and that our consideration of an EKF
enables the development of first-of-their-kind theoretical error guarantees for
online inverse optimal control with noisy incomplete measurements. Our proposed
EKF is shown to be significantly faster than an alternative unscented Kalman
filter-based approach.
