A Mixed Integer Dual Quadratic Programming Algorithm Tailored for MPC

• Published in: Proceedings of the 45th IEEE Conference on Decision and Control pp. 5693 - 5698
• Main Authors: Axehill, D., Hansson, A.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.12.2006
• Subjects: Binary search tree; Binary search trees; Branch and bound method; Computational complexity; Computational modeling; Integer programming; Iterative methods; KKT system; Linear systems; Mixed integer dual quadratic programming algorithm; Model predictive control; Prediction horizon; Predictive control; Predictive models; QP iterations; QP relaxations; Quadratic programming; Riccati equations; Riccati recursion; TECHNOLOGY; TEKNIKVETENSKAP; Tin; Tree searching; USA Councils
• ISBN: 9781424401710; 1424401712
• ISSN: 0191-2216
• DOI: 10.1109/CDC.2006.377215

The objective of this work is to derive an MIQP solver tailored for MPC. The MIQP solver is built on the branch and bound method, where QP relaxations of the original problem are solved in the nodes of a binary search tree. The difference between the subproblems is often small and therefore it is interesting to be able to use a previous solution as a starting point in a new subproblem. This is referred to as a warm start of the solver. Because of its good warm start properties, a dual active set QP method was chosen. The method is tailored for MPC by solving a part of the KKT system using a Riccati recursion, which makes the computational complexity of the QP iterations grow linearly with the prediction horizon. Simulation results are presented both for the QP solver itself and when it is incorporated as a part of the MIQP solver. In both cases the computational complexity is significantly reduced compared to if a primal active set solver not utilizing structure is used