Fragility of Polyhedral Partition for PWA Control Laws Designed for Constrained Discrete-Time Systems

• 成果类型: Article
• 署名作者: Yang, Songlin; Olaru, Sorin; Rodriguez-Ayerbe, Pedro; Dorea, Carlos E. T.
• 署名单位: Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Universidade Federal do Rio Grande do Norte
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3570214
• 发表日期: 2025
• 关键词: model-predictive control; PIECEWISE AFFINE CONTROL; Robustness

摘要

This article deals with the fragility margins of discrete-time piecewise affine (PWA) closed-loop dynamics. The chosen framework is one of the nominal linear systems in closed-loop with a PWA controller implemented using a binary search tree mechanism for effective gain selection. Our objective is to preserve the properties of nominal dynamics, particularly the positive invariance under perturbations in the control law representation. The main contribution revolves around defining and constructing two distinct types of fragility margins: the single hyperplane fragility margin (sHFM) and the multiple hyperplane fragility margin (mHFM). The sHFM specifically examines the admissible perturbations for a single hyperplane defining the nominal PWA controller's partition. In contrast, the mHFM explores the admissible perturbations for multiple hyperplanes simultaneously, and the perturbed multiple hyperplanes need to adapt special operations to decouple the influence between each hyperplane. This margin exhibits the extent of freedom for perturbations across multiple hyperplanes simultaneously.