A fast, fully distributed nonlinear model predictive control algorithm with parametric sensitivity through Jacobi iteration. (February 2022) - Yu, Tianyu; Xu, Zuhua; Zhao, Jun; Chen, Xi; Biegler, Lorenz T.
Abstract: Centralized model predictive control is impractical for many complex systems due to communication burden and robustness issues. For these systems, distributed model predictive control (DMPC) is an alternative control strategy. In DMPC, the use of nonlinear first-principle model improves the prediction accuracy. However, it also brings about computational delay due to time-consuming optimization of large, non-convex nonlinear programs, which can then degrade the control performance. In this work, a fully distributed nonlinear model predictive control (DNMPC) algorithm is developed to accelerate control feedback. The input computation procedure contains background and online stages, in which prediction–correction mode is applied. In the background stage, the future state is predicted one step forward based on the nominal plant model. Each controller optimizes its own local input and exchanges latest information with other controllers to improve decision making. After distributed optimization, the local controllers collect optimality information to prepare for future computation. When the true state is available, the state prediction error can be calculated. Each controller formulates its local sensitivity equation based on parametric sensitivity. All the sensitivity equations are solved in parallel with application of the Jacobi iterative method. After solution, the nominal optimum is updated with the correction vector and then implemented to the plant. The theoretical analysis of the proposed method is presented. Four case studies are given to demonstrate the effectiveness of the proposed algorithm. Highlights: A fast, fully distributed model predictive control algorithm is proposed for nonlinear systems. Prediction–correction mode is applied in the proposed method. The future inputs are computed in background with advanced-step distributed optimization. The local sensitivity equations are solved in parallel through Jacobi iteration. computation. The closed-loop system is proved to be input-to-state practical stable.