  The choice of objective is critical for the performance of an optimal
controller. When control requirements vary during operation, e.g. due to
changes in the environment with which the system is interacting, these
variations should be reflected in the cost function. In this paper we consider
the problem of identifying a time dependent cost function from given
trajectories. We propose a strategy for explicitly representing time dependency
in the cost function, i.e. decomposing it into the product of an unknown time
dependent parameter vector and a known state and input dependent vector,
modelling the former via a linear combination of trigonometric basis functions.
These are incorporated within an inverse optimal control framework that uses
the Karush-Kuhn-Tucker (KKT) conditions for ensuring optimality, and allows for
formulating an optimization problem with respect to a finite set of basis
function hyperparameters. Results are shown for two systems in simulation and
evaluated against state-of-the-art approaches.
