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, 2024. To appear.
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.
Bibtex entry:
@article{XuLu:24-028,