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The Essentials of Model Predictive Control Read chapter Read first chapter

2019 | OriginalPaper | Chapter

Efficient Convex Optimization for Linear MPC

Author : Stephen J. Wright

Published in: Handbook of Model Predictive Control

Publisher: Springer International Publishing

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Abstract

MPC formulations with linear dynamics and quadratic objectives can be solved efficiently by using a primal-dual interior-point framework, with complexity proportional to the length of the horizon. An alternative, which is more able to exploit the similarity of the problems that are solved at each decision point of linear MPC, is to use an active-set approach, in which the MPC problem is viewed as a convex quadratic program that is parametrized by the initial state \(x_{0}\). Another alternative is to identify explicitly polyhedral regions of the space occupied by \(x_{0}\) within which the set of active constraints remains constant, and to pre-calculate solution operators on each of these regions. All these approaches are discussed here.

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previous chapter Scalable MPC Design
next chapter Implicit Non-convex Model Predictive Control
Footnotes
1
The LU factorization does not exploit the fact that the coefficient matrix is symmetric. The \(LDL^{T}\) factorization is commonly used for such matrices, but unfortunately the permutations required in this factorization tend to destroy the band structure, so it is not appropriate here.
 
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Metadata
Title
Efficient Convex Optimization for Linear MPC
Author
Stephen J. Wright
Copyright Year
2019
Book
Handbook of Model Predictive Control

Print ISBN: 978-3-319-77488-6

Electronic ISBN: 978-3-319-77489-3

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-319-77489-3_13