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

• 成果类型: Article
• 署名作者: Xu, Jun; Lou, Yunjiang; De Schutter, Bart; Xiong, Zhenhua
• 署名单位: Harbin Institute of Technology; Delft University of Technology; Shanghai Jiao Tong University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3466869
• 发表日期: 2025
• 页码: 1745-1760
• 关键词: lattices; optimization; Complexity theory; optimal control; indexes; Upper bound; training; Error-free approximation; lattice piecewise affine (PWA); linear model predictive control (MPC)

摘要

In this article, 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, whereas 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.