Structure exploiting optimization methods for model predictive control
Doktorsavhandling, 2017

This thesis considers optimization methods for Model Predictive Control (MPC). MPC is the preferred control technique in a growing set of applications due to its flexibility and to the natural way in which constraints can be incorporated in the control policy. Its applicability is, however, limited by the high computational burden associated with the solution of the underlying optimization problems. To alleviate this drawback we study structures in the MPC problems, which can enhance their solution. The first topic of the thesis is numerical structures in matrices arising in gradient-based optimization methods for MPC. The idea is that due to the nu-merical structures, dense matrices can be approximated by sparse matrices to reduce the computational cost per iteration, and also for the overall solution of the MPC problem. The second topic of the thesis is parallelizable optimization methods for multi-stage MPC. Multi-stage MPC is a popular framework used to increase the robustness of MPC schemes. One major drawback, however, is that the under-lying optimization problems become very large. In this context, we consider parallel implementations of two different classes of optimization methods. First, we propose a parallelizable linear algebra for a primal-dual interior point method for two-stage MPC problems, i.e. for multi-stage MPC problems where the sce-nario tree is restricted to only branch in its root node. Secondly, we consider Newton’s method to solve the Lagrange dual problem of multi-stage MPC prob-lems. We show that the Hessian of the dual function is permutation similar to a block-tridiagonal matrix, propose a strategy for reducing the need for regularization, and reduce the cost of globalization strategies for problems with simple constraints and a diagonal cost. The third topic of the thesis is optimization methods for solving distributed MPC problems in a distributed fashion using dual decomposition. Dual decomposition is commonly used with gradient-based methods to achieve a completely distributed method. In this thesis, however, we use dual decomposition together with Newton’s method to achieve semi-distributed methods with a fast practical convergence. We study the occurence of a singular dual Hessian and pro-pose a constraint relaxation to prevent it. Additionally, we propose a distributed dual Newton strategy which can be viewed as a distributed primal-dual interior point method, and study the numerical structure of the dual Hessian for problems stemming from MPC deployed on multi-agent systems that are interacting via non-delayed couplings.

Multi-stage robust MPC

Optimization methods.

Model Predictive Control

Distributed optimization

HA4, EDIT building, Hörsalsvägen 4, Campus Johanneberg
Opponent: Professor Anders Hansson, Linköping University


Emil Klintberg

Signaler och system, System- och reglerteknik, Reglerteknik

A Parallelizable Interior Point Method for Two-Stage Robust MPC

IEEE Transactions on Control Systems Technology,; Vol. 25(2017)p. 2087-2097

Artikel i vetenskaplig tidskrift

A Primal-Dual Newton Method for Distributed Quadratic Programming

Proceedings of the 53rd IEEE Annual Conference on Decision and Control, CDC 2014, Los Angeles, United States, 15-17 December 2014,; (2015)p. 5843-5848

Paper i proceeding

Numerical Structure of the Hessian of the Lagrange Dual Function for a Class of Convex Problems

SIAM Journal on Control and Optimization,; Vol. 55(2017)p. 574-593

Artikel i vetenskaplig tidskrift

An improved distributed dual newton-CG method for convex quadratic programming problems

American Control Conference,; (2014)p. 2324-2329

Paper i proceeding

Approximate inverses in preconditioned fast dual gradient methods for MPC

IFAC-PapersOnLine,; Vol. 50(2017)p. 5901-5906

Artikel i vetenskaplig tidskrift

An improved dual Newton strategy for scenario-tree MPC

Proceedings of the 55th IEEE Conference on Decision and Control (CDC 2016); Las Vegas; United States; 12-14 December 2016,; (2016)p. Art no 7798822, Pages 3675-3681

Paper i proceeding

E. Klintberg, D. Kouzoupis, M. Diehl, S. Gros. A dual Newton strategy with fixed iteration complexity for multi-stage MPC




Datavetenskap (datalogi)





Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4248


Chalmers tekniska högskola

HA4, EDIT building, Hörsalsvägen 4, Campus Johanneberg

Opponent: Professor Anders Hansson, Linköping University