Emerging methodologies in stability and optimization problems of learning‐based nonlinear model predictive control: A survey

Since last 40 years, the theory and technology of model predictive control (MPC) have been developed rapidly. However, nonlinear MPC still faces difficulties such as high online computational complexity and inability to accurately model the system. In order to improve or solve the problems mentioned above of MPC, recent researches have deepened the learning‐based control. The learned method can model unknown or highly uncertain nonlinearities. And the emergence of efficient algorithms has greatly improved the feasibility of computing. Stability is at the heart of control design. Learning‐based nonlinear model predictive control (LB‐NMPC) has achieved systematic research results in the past 10 years. But the stability of LB‐NMPC is still an open question that has not been fully addressed in the literature. This review mainly summarizes the latest research progress of LB‐NMPC. More specifically, the uncertainty and online optimization problems of the considered systems are investigated mainly focusing on the use of learning techniques. At the same time, the research hotspots such as the control stability and constraint satisfaction of LB‐NMPC are briefly discussed. Finally, the application of LB‐NMPC technology in integrated circuits, path tracking control, and other fields is reviewed, which provides a reference for the research and application of LB‐NMPC.