Inverse Optimal Control for Deterministic Continuous-time Nonlinear Systems

Inverse optimal control is the problem of computing a cost function with respect to which observed state and input trajectories are optimal. We present a new method of inverse optimal control based on minimizing the extent to which observed trajectories violate first-order necessary conditions for optimality. We consider continuous-time deterministic optimal control systems with a cost function that is a linear combination of known basis functions. We compare our approach with three prior methods of inverse optimal control. We demonstrate the performance of these methods by performing simulation experiments using a collection of nominal system models. We compare the robustness of these methods by analysing how they perform under perturbations to the system. To this purpose, we consider two scenarios: one in which we exactly know the set of basis functions in the cost function, and another in which the true cost function contains an unknown perturbation. Results from simulation experiments show that our new method is more computationally efficient than prior methods, performs similarly to prior approaches under large perturbations to the system, and better learns the true cost function under small perturbations.