A Kalman–Koopman LQR Control Approach to Robotic Systems

This article presents a Kalman–Koopman linear quadratic regulator (KKLQR) control approach to robotic systems. In the proposed approach, an optimal Koopman modeling method based on neural networks, in which continuous Koopman eigenfunctions are constructed without requiring any predefined dictionary, is proposed to obtain approximated linear models with high precision for robotic systems. Specifically, the linear model is constructed through a multistep prediction error minimization, which enables a long-term prediction capability. Furthermore, the Kalman filter is employed to alleviate the effects of disturbances in the KKLQR control approach. Experimental results show that the proposed KKLQR control approach achieves better prediction and control performance than other existing representative methods.