Reference
J. Xu, Y. Lou, B. De Schutter, and Z. Xiong, "Error-free approximation of
explicit linear MPC through lattice piecewise affine expression,"
IEEE Transactions on Automatic Control, vol. 70, no. 3, pp.
1745-1760, Mar. 2025.
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.
Publisher page
BibTeX
@article{XuLu:24-028,
author = {Xu, Jun and Lou, Yunjiang and De Schutter, Bart and Xiong,
Zhenhua},
title = {Error-free Approximation of Explicit Linear {MPC} through Lattice
Piecewise Affine Expression},
journal = {IEEE Transactions on Automatic Control},
volume = {70},
number = {3},
pages = {1745--1760},
month = mar,
year = {2025}
}