An Inverse Optimal Control Approach for Learning and Reproducing Under Uncertainties

This letter presents a novel inverse optimal control (IOC) approach that can account for uncertainties in measurements and system models. The proposed IOC approach aims to recover an objective function including a time-varying term, called variability, from a given demonstration. All uncertainties of the demonstration and the system model can be lumped into the variability such that the optimality condition violation is further reduced. The inferred objective function including the variability has two advantages over the objective function inferred by existing IOC approaches: first, the variability can enhance the capability of describing the given demonstration since it represents how the uncertainties of the system affect the objective function; and second, the proposed IOC approach can reproduce the trajectories such that we can predict the behavior of the system even with system modeling errors. We show that the variability exists and is unique under attainable assumptions. Illustrative numerical examples are presented to demonstrate the proposed method.