  In this paper, we consider the inverse optimal control problem for the
discrete-time linear quadratic regulator, over finite-time horizons. Given
observations of the optimal trajectories, and optimal control inputs, to a
linear time-invariant system, the goal is to infer the parameters that define
the quadratic cost function. The well-posedness of the inverse optimal control
problem is first justified. In the noiseless case, when these observations are
exact, we analyze the identifiability of the problem and provide sufficient
conditions for uniqueness of the solution. In the noisy case, when the
observations are corrupted by additive zero-mean noise, we formulate the
problem as an optimization problem and prove the statistical consistency of the
problem later. The performance of the proposed method is illustrated through
numerical examples.
