Introducing System Identification Strategy into Model Predictive Control

• Published in: Journal of systems science and complexity Vol. 33; no. 5; pp. 1402 - 1421
• Main Authors: Wang, Jianhong, Ricardo, A. Ramirez-Mendoza, Jorge, de J Lozoya Santos
• Format: Journal Article
• Language: English
• Published: Beijing Academy of Mathematics and Systems Science, Chinese Academy of Sciences 01.10.2020; Springer Nature B.V
• Subjects: Algorithms; Bayesian analysis; Complex Systems; Control; Control systems; Cost function; Fields (mathematics); Mathematics; Mathematics and Statistics; Mathematics of Computing; Nonlinear systems; Nonparametric statistics; Operations Research/Decision Theory; Optimization; Predictive control; Quadratic programming; Statistics; System identification; Systems Theory; model predictive control; Equivalence; system identification; nonparametric estimation
• ISSN: 1009-6124; 1559-7067
• DOI: 10.1007/s11424-020-9058-3

As system identification theory and model predictive control are belonged to two different research fields separately, so one gap exists between these two subjects. To alleviate this gap between them, one new idea proposed in this paper is to introduce system identification theory into model predictive control. As the most important element in model predictive control is the prediction of the output value for a nonlinear system, then the problem of deriving the prediction of the output value can be achieved by system identification theory. More specifically, a Bayesian approach is applied for the nonparametric estimation by modeling the prediction as realizations of zero mean random fields. Through comparing this kind of prediction corresponding to this Bayesian approach and the former direct weight optimization identification for nonlinear system, the authors see that if the unknown weights are chosen appropriately, these two approaches are equivalent to each other. Based on the obtained prediction of the output value, the authors substitute this prediction of the output value into one cost function of model predictive control, and then a quadratic programming problem with inequality constraints is formulated. When to solve this quadratic programming problem, a detailed process about how to derive its dual form is given. As the dual problem has a simple constraint set, it is amenable to the use of the common Gauss-Seidel algorithm, whose convergence can be shown easily. Finally, one simulation example confirms the proposed theoretical results.