A Primal decomposition algorithm for distributed multistage scenario model predictive control. (September 2019)

• Record Type: Journal Article
• Authors: Krishnamoorthy, Dinesh; Foss, Bjarne; Skogestad, Sigurd
• Is Part Of: Journal of process control. Volume 81(2019)
• Page Start: 162
• Page End: 171
• Publication Date: 2019-09
• Subjects: Model predictive control -- Primal decomposition -- Distributed optimization -- Uncertainty; Process control -- Periodicals; Fabrication -- Contrôle -- Périodiques; Process control; Periodicals; Electronic journals; 660.281
• DOI: 10.1016/j.jprocont.2019.02.003
• Languages: English
• ISSNs: 0959-1524

Abstract

Highlights: Computationally efficient solution of multistage model predictive control using scenario decomposition. A primal decomposition framework for scenario decomposition. Primal decomposition always ensures feasibility of non-anticipativity constraints, hence enabling closed-loop implementation. A novel backtracking algorithm to determine suitable step length in the master problem to ensure feasibility of nonlinear constraints. Abstract: This paper proposes a primal decomposition algorithm for efficient computation of multistage scenario model predictive control, where the future evolution of uncertainty is represented by a scenario tree. This often results in large-scale optimization problems. Since the different scenarios are only coupled via the so-called non-anticipativity constraints, which ensures that the first control input is the same for all the scenarios, the different scenarios can be decomposed into smaller subproblems, and solved iteratively using a master problem to co-ordinate the subproblems. We review the most common scenario decomposition methods, and argue in favour of primal decomposition algorithms, since it ensures feasibility of the non-anticipativity constraints throughout the iterations, which is crucial for closed-loop implementation. We also propose a novel backtracking algorithm to determine a suitable step length in the master problem that ensures feasibility of the nonlinear constraints. The performance of the proposed approach, and the backtracking algorithm is demonstrated using a CSTR case study.