  The goal of Inverse Optimal Control (IOC) is to identify the underlying
objective function based on observed optimal trajectories. It provides a
powerful framework to model expert's behavior, and a data-driven way to design
an objective function so that the induced optimal control is adapted to a
contextual environment. In this paper, we design an IOC algorithm for
linear-quadratic tracking problems with random time horizon, and prove the
statistical consistency of the algorithm. More specifically, the proposed
estimator is the solution to a convex optimization problem, which means that
the estimator does not suffer from local minima. This enables the proven
statistical consistency to actually be achieved in practice. The algorithm is
also verified on simulated data as well as data from a real world experiment,
both in the setting of identifying the objective function of human tracking
locomotion. The statistical consistency is illustrated on the synthetic data
set, and the experimental results on the real data shows that we can get a good
prediction on human tracking locomotion based on estimating the objective
function. It shows that the theory and the model have a good performance in
real practice. Moreover, the identified model can be used as a control target
in personalized rehabilitation robot controller design, since the identified
objective function describes personal habit and preferences.
