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The Inverse Optimal Control (IOC) problem is a structured systemidentification problem that aims to identify the underlying objective functionbased on observed optimal trajectories. This provides a data-driven way tomodel experts' behavior. In this paper, we consider the case of discrete-timefinite-horizon linear-quadratic problems where: the quadratic cost term in theobjective is not necessarily positive semi-definite; the planning horizon is arandom variable; we have both process noise and observation noise; the dynamicscan have a drift term; and where we can have a linear cost term in theobjective. In this setting, we first formulate the necessary and sufficientconditions for when the forward optimal control problem is solvable. Next, weshow that the corresponding IOC problem is identifiable. Using the optimalityconditions of the forward problem, we then formulate an estimator for theparameters in the objective function of the forward problem as the globallyoptimal solution to a convex optimization problem, and prove that the estimatoris statistical consistent. Finally, the performance of the algorithm isdemonstrated on a numerical example.

Statistically consistent inverse optimal control for discrete-time indefinite linear-quadratic systems