A Primal decomposition algorithm for distributed multistage scenario model predictive control

• Published in: Journal of process control Vol. 81; pp. 162 - 171
• Main Authors: Krishnamoorthy, Dinesh, Foss, Bjarne, Skogestad, Sigurd
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-09-2019
• Subjects: Distributed optimization; Model predictive control; Primal decomposition; Uncertainty; Model predictive control; Distributed optimization; Uncertainty; Primal decomposition
• ISSN: 0959-1524; 1873-2771
• DOI: 10.1016/j.jprocont.2019.02.003

•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.
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.