From Relaxed Constraint Satisfaction to p-Invariance of Sets

• 成果类型: Article
• 署名作者: Olaru, Sorin; Soyer, Martin; Zhao, Zhixin; Dorea, Carlos E. T.; Kofman, Ernesto; Girard, Antoine
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Universidade Federal do Rio Grande do Norte; National University of Rosario
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3394544
• 发表日期: 2024
• 页码: 7036-7042
• 关键词: trajectory; dynamical systems; Electron tubes; Lyapunov methods; indexes; Finite element analysis; Complexity theory; Constrained systems; set invariance

摘要

The present article proposes a general framework for the analysis of constraints satisfaction with respect to the trajectories of a dynamical system. The results are presented in a discrete-time framework and pertain to the class of set-theoretic methods. The main objective is to go beyond the state of the art by characterizing the intermittent constraint satisfaction along the evolution of the trajectories of a dynamical system. Two relaxed notions are introduced in this sense, one characterizing the validation of constraints within a given finite window and the other imposing the validation after a fixed number of time-steps following a violation. The constraint satisfaction with respect to a controlled trajectory will then be extended to a set of constraints and then to tubes of trajectories. It is shown that all these notions can be accordingly anchored to the well-known controlled positive set invariance, thus offering a generalized framework for the analysis of dynamical systems in a set-theoretic framework. This technical note is completed with illustrations of the constructions on both linear and nonlinear case.