  In this paper, the problem of finite horizon inverse optimal control (IOC) is
investigated, where the quadratic cost function of a dynamic process is
required to be recovered based on the observation of optimal control sequences.
We propose the first complete result of the necessary and sufficient condition
for the existence of corresponding LQ cost functions. Under feasible cases, the
analytic expression of the whole solution space is derived and the equivalence
of weighting matrices in LQ problems is discussed. For infeasible problems, an
infinite dimensional convex problem is formulated to obtain a best-fit
approximate solution with minimal control residual. And the optimality
condition is solved under a static quadratic programming framework to
facilitate the computation. Finally, numerical simulations are used to
demonstrate the effectiveness and feasibility of the proposed methods.
