On the Uniqueness of Solution to the Inverse Optimal Control Problem for the Hard-Constrained Minimum Principle-Based Method

In this letter, the hard-constrained minimum principle based method for solving the inverse optimal control (IOC) problem has been considered. Specifically, this letter investigates the kinds of closed-loop system trajectories, initial conditions and system dynamics for which a unique solution to the IOC problem can be obtained for this method. For this purpose, a matrix associated with the optimization problem involved in this IOC approach is tested for full rankness. It was found that for this method, in addition to initial conditions and types of closed-loop system trajectories, the open-loop system dynamics has an important role in determining if a unique solution to the IOC problem can be obtained. Rigorous mathematical and numerical analysis for different types of trajectories, initial conditions and system dynamics have been presented.