Inverse Optimal Control with System Output

This paper presents an incremental approach for addressing inverse optimal control (IOC) with only system output trajectory available. The unknown objective function is expressed as a weighted combination of features, where the weights are unknown. The proposed approach utilizes the optimality conditions for optimal state trajectory and the system output equation to iteratively solve the IOC problem with the initial optimal state available. In the case when the initial optimal state is unavailable, by utilizing the observed system output segments, we proposed a method to incrementally estimate the optimal initial state. Combining the aforementioned methods, we proposed an incremental algorithm to estimate the unknown weights. The method’s effectiveness is demonstrated through simulations on a 2-link robot arm and a 6-DoF maneuvering quadrotor system. In both cases, only limited system output segments are available.