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

Dimitris Kouzoupis (dimitris.kouzoupis***at***imtek.uni-freiburg.de)
Emil Klintberg (kemil***at***chalmers.se)
Moritz Diehl (moritz.diehl***at***imtek.uni-freiburg.de)
Sebastien Gros (grosse***at***chalmers.se)

Abstract: 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 non-anticipativity 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.

Keywords: Robust control; Multi-stage MPC; Quadratic Programming; Dual decomposition

Category 1: Applications -- Science and Engineering (Control Applications )

Citation:

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Entry Submitted: 02/14/2017
Entry Accepted: 02/14/2017
Entry Last Modified: 07/25/2017

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