Control Law Learning Based on LQR Reconstruction With Inverse Optimal Control

Designing controllers to generate various trajectories has been studied for years, while recently, recovering an optimal controller from trajectories receives increasing attention. In this article, we reveal that the inherent linear quadratic regulator (LQR) problem of a moving agent can be reconstructed based on its trajectory observations only, which enables one to learn the control law of the target agent autonomously. Specifically, we propose a novel inverse optimal control method to identify the weighting matrices of a discrete-time finite horizon LQR, and we also provide the corresponding identifiability conditions. Then, we obtain the optimal estimate of the control horizon using binary search, and finally, reconstruct the LQR problem with aforementioned estimates. The strength of the learning control law with optimization problem recovery lies in less computation consumption and strong generalization ability. We apply our algorithm to the future control input prediction and the discrepancy loss is further derived. Simulations and hardware experiments on a self-designed robot platform illustrate the effectiveness of our work.