Recovery-Matrix Inverse Optimal Control for Deterministic Feedforward-Feedback Controllers

This paper presents an optimisation approach to solve the inverse optimal control problem when the controller is in the feedforward-feedback form. The goal of inverse optimal control is to recover the cost function from the observed trajectory. We consider the problem of direct and inverse optimal control for both linear and nonlinear systems, assuming a quadratic cost function structure. We adapt the recovery matrix inverse optimal control approach, originally developed for recovering the cost matrices from trajectories observed under feedforward control, and apply it to trajectories observed from systems controlled in the feedback form plus the additional feedforward term for nonlinear systems, and the feedback form for linear systems. Accurate cost function recovery is demonstrated via simulation examples with both linear and nonlinear systems.