Under a known proportional terminal cost, finite-horizon gain variation makes the open-loop dynamics and quadratic cost jointly identifiable in continuous time, and the CR-IOC algorithm recovers them consistently from noisy samples.
Statistically consistent inverse optimal control for linear-quadratic tracking with random time horizon,
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Joint Identifiability and Conditioning in Finite-Horizon Continuous-Time Inverse LQR with Unknown Dynamics
Under a known proportional terminal cost, finite-horizon gain variation makes the open-loop dynamics and quadratic cost jointly identifiable in continuous time, and the CR-IOC algorithm recovers them consistently from noisy samples.