Discrete-time Inverse Optimal Control with Partial-State Information: A Soft-Optimality Approach with Constrained State Estimation

In this paper, we consider the problem of estimating the parameters of an optimal control objective function based on measurements of the closed loop system. In contrast to previous work on inverse optimal control, we consider measurements that are noise-corrupted and contain only partial-state information. We propose an inverse optimal control method based on a new soft-optimality constrained methodology of state estimation. We establish a sufficient condition for recovery of the unknown objective function parameters given complete-state information, and develop results characterising the performance of our method for linear systems. We illustrate our proposed soft-optimality approach through simulations of a nonlinear and fully-actuated mechanical system.