NDLI: Relaxations applicable to mixed integer predictive control comparisons and efficient computations

Content Provider	IEEE Xplore Digital Library
Author	Axehill, D. Hansson, A. Vandenberghe, L.
Copyright Year	2007
Description	Author affiliation: Linkopings Univ., Linkoping (Axehill, D.; Hansson, A.)
Abstract	In this work, different relaxations applicable to an MPC problem with a mix of real valued and binary valued control signals are compared. In the problem description considered, there are linear inequality constraints on states and control signals. The relaxations are related theoretically and both the tightness of the bounds and the computational complexities are compared in numerical experiments. The relaxations considered are the quadratic programming (QP) relaxation, the standard semidefinite programming (SDP) relaxation and an equality constrained SDP relaxation. The result is that the standard SDP relaxation is the one that usually gives the best bound and is most computationally demanding, while the QP relaxation is the one that gives the worst bound and is least computationally demanding. The equality constrained relaxation presented in this paper often gives a better bound than the QP relaxation and is less computationally demanding compared to the standard SDP relaxation. Furthermore, it is also shown how the equality constrained SDP relaxation can be efficiently computed by solving the Newton system in an Interior Point algorithm using a Riccati recursion. This makes it possible to compute the equality constrained relaxation with approximately linear computational complexity in the prediction horizon.
Starting Page	4103
Ending Page	4109
File Size	263849
Page Count	7
File Format	PDF
ISBN	9781424414970
ISSN	01912216
DOI	10.1109/CDC.2007.4434608
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-12-12
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Predictive control Quadratic programming Computational complexity Riccati equations Control systems Tin USA Councils Linear approximation Predictive models Linear systems
Content Type	Text
Resource Type	Article

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