Comparative Study of Model-Free Predictive Control and Its Database Maintenance for Unstable Systems

This study provides a comparison of three methods, i.e., standard locally weighted averaging (LWA), least-norm solutions, and l1-minimization, for model-free predictive control based on Just-In-Time modeling and database maintenance for an unstable system. In contrast to conventional model predictive control, the model-free predictive control method does not use any mathematical model; rather, it uses the past input/output data stored in a database. Although conventional stabilizing feedback is used to obtain the input/output data of an unstable system, model-free predictive control is assumed to be used without it. Three methods based on standard LWA, least-norm solutions, and l1-minimization are statistically compared using a simple model. The results show that the methods of least-norm solutions and l1-minimization are superior to that of LWA. The method by l1-minimization yields tracking errors smaller than that by least-norm solutions; however, the method by l1-minimization requires a long computational time. In addition, the effectiveness of a method of database maintenance is illustrated by numerical simulations.