A dual Newton strategy for scenario decomposition in robust multi-stage MPC

This paper considers the solution of tree-structured Quadratic Programs (QPs) as they may arise in multi-stage Model Predictive Control (MPC). In this context, sampling the uncertainty on prescribed decision points gives rise to different scenarios that are linked to each other via the so-called nonanticipativity constraints. Previous work suggests to dualize these constraints and apply Newton’s method on the dual problem in order to achieve a parallelizable scheme. However, it has been observed that the globalization strategy in such an approach can be expensive. To alleviate this problem, we propose to dualize both the non-anticipativity constraints and the dynamics to obtain a computationally cheap globalization. The dual Newton system is then reformulated into small, highly structured linear systems that can be solved in parallel to a large extent. The algorithm is complemented by an open-source software implementation that targets embedded optimal control applications.