Robust model predictive control based on recurrent multi-dimensional Taylor network for discrete-time non-linear time-delay systems

This study is concerned with the robust model predictive control (MPC) based on recurrent multi-dimensional Taylor network (RMTN) for the discrete-time non-linear time-delay systems. Regarding the MPC algorithm for the discrete-time time-delay systems, the existing literature only considers the linear case. In this study, by designing the suitable terminal cost and terminal region, the MPC scheme is firstly investigated for the non-linear case. Meanwhile, to reduce the computational burden of MPC using the existing model types (e.g. recurrent neural network) as the identified model, an RMTN possessing the concise structure and high computational efficiency is constructed to approximate the state-space model of the system. After trained by the backpropagation through time algorithm, the RMTN obtaining the high accuracy of prediction over a long-range horizon is capable of serving as the prediction model in the MPC scheme. Furthermore, aiming at alleviating the adverse effect of the inevitable identification error, the tube-based MPC is proposed via leveraging dual-mode MPC to guarantee that actual trajectory is contained within a robust tube. The stability of the considered system is proved theoretically, and numerical simulation is employed to validate the effectiveness of the proposed method.