Data-driven inverse optimal control for linear quadratic tracking with unknown target states

This paper studies the inverse optimal control for discrete-time finite-horizon linear quadratic tracking with unknown target states. Due to the time-varying feedback policies caused by the finite-horizon setting and the unknown system dynamics, the concerned inverse optimal control becomes challenging. To deal with it, a novel data driven inverse identification approach is developed, for which the corresponding identifiability conditions are provided and the statistical consistency is analyzed in the presence of observation noise. Compared to the existing solutions, the proposed approach requires only optimal trajectories, possibly corrupted by additive observation noise with zero mean and bounded covariance, and achieves consistent results without knowledge of the noise covariance. Finally, simulation examples are presented to show the effectiveness of the proposed approach.