Stages and main tasks of the century-long control theory and system identification development. Part VIII. Data-driven terminal predictive control

In 2005, the journal Systems & Control Letters published an article by Willems et al. devoted to the behavioral theory of dynamic systems with a permanently exciting input. This was followed in 2019 by an article by van Waarde et al., which described how the results of the first article can be applied to the control of dynamic systems within the framework of a direction that has been developing very intensively in recent years, called «Model Predictive Control». This relatively new direction of research and development has come to the forefront in control theory and practice. Thanks to the publication of these two articles, it became possible to abandon the mathematical model of dynamic systems in predictive control and instead use trajectory data presented as a matrix equation linking both measured and predicted data. The predicted data are to be found by solving synthesis problems. This article describes some of the developed methods for finding optimal predictive control based on trajectory data, provided that they are permanently exciting. The main attention is paid to the problems of terminal control, which seems to be promising in solving many applied problems. Optimal predictive control is found by solving minimization problems with constraints. The use of sliding intervals with discrete trajectory data allows implementing the feedback mode in predictive control. The presence of errors in the measured data leads to the need to find a robust control. The article considers methods for constructing robust predictive control for two cases of error interpretation. In both of them, errors are considered arbitrary, but limited in magnitude or power. Depending on the levels of input signals and noise, optimization problems with constraints can become ill-posed, i.e. their solutions become sensitive to errors. Therefore, regularization procedures are used to determine stable solutions. Considerable attention in the article is paid to the issues of solvability of optimization problems and satisfying of existing constraints. A number of issues related to the adaptation of the developed methods to applied problems are not ignored. A number of modifications of the problem statements are proposed, in which the conditions of their solvability and the fulfillment of constraints are quite simply considered.