Error-Free Approximation of Explicit Linear MPC Through Lattice Piecewise Affine Expression

Journal Article (2025)
Author(s)

Jun Xu (Harbin Institute of Technology)

Yunjiang Lou (Harbin Institute of Technology)

Bart de de Schutter (TU Delft - Delft Center for Systems and Control)

Zhenhua Xiong (Shanghai Jiao Tong University)

Department
Delft Center for Systems and Control
DOI related publication
https://doi.org/10.1109/TAC.2024.3466869
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Publication Year
2025
Language
English
Department
Delft Center for Systems and Control
Bibliographical Note
Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.@en
Issue number
3
Volume number
70
Pages (from-to)
1745-1760
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Abstract

In this paper, the disjunctive and conjunctive lattice piecewise affine (PWA) approximations of explicit linear model predictive control (MPC) are proposed. Training data consisting of states and corresponding affine control laws are generated in a control invariant set, and redundant sample points are removed to simplify the construction of lattice PWA approximations. Resampling is proposed to guarantee the equivalence of lattice PWA approximations and optimal MPC control law at the sample points. Under certain conditions, the disjunctive lattice PWA approximation constitutes a lower bound, while the conjunctive version formulates an upper bound of the original optimal control law. The equivalence of the two lattice PWA approximations then guarantees error-free approximations in the domain of interest, which is tested through a statistical guarantee. The performance of the proposed approximation strategy is tested through two simulation examples, and the results show that error-free lattice PWA approximations can be obtained with low offline complexity and small storage requirements. Besides, the online complexity is less compared with the state-of-the-art method.

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