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The choice of objective is critical for the performance of an optimalcontroller. When control requirements vary during operation, e.g. due tochanges in the environment with which the system is interacting, thesevariations should be reflected in the cost function. In this paper we considerthe problem of identifying a time dependent cost function from giventrajectories. We propose a strategy for explicitly representing time dependencyin the cost function, i.e. decomposing it into the product of an unknown timedependent 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 usesthe Karush-Kuhn-Tucker (KKT) conditions for ensuring optimality, and allows forformulating an optimization problem with respect to a finite set of basisfunction hyperparameters. Results are shown for two systems in simulation andevaluated against state-of-the-art approaches.

Time Dependent Inverse Optimal Control using Trigonometric Basis Functions