A Distributed Algorithm for Scenario-based Model Predictive Control using Primal Decomposition

Abstract

In this paper, we consider the decomposition of scenario-based model predictive control problem. Scenario MPC explicitly considers the concept of recourse by representing the evolution of uncertainty by a discrete scenario tree, which can result in large optimization problems. Due to the inherent nature of the scenario tree, the problem can be decomposed into each scenario. The different subproblems are only coupled via the non-anticipativity constraints which ensures that the first control input is the same for all the scenarios. This constraint is relaxed in the dual decomposition approaches, which may lead to infeasibility of the non-anticipativity constraints if the master problem does not converge within the required time. In this paper, we present an alternative approach using primal decomposition which ensures feasibility of the non-anticipativity constraints throughout the iterations. The proposed method is demonstrated using gas-lift optimization as case study.