Controllability and stabilization of a conservation law modeling a highly re-entrant manufacturing system. (December 2019)

• Record Type: Journal Article
• Authors: Chu, Jixun; Shang, Peipei; Wang, Zhiqiang
• Is Part Of: Nonlinear analysis. Volume 189(2019)
• Publication Date: 2019-12
• Subjects: 35Q65 -- 93B05 -- 93D15 -- 93C20; Controllability -- Stabilization -- Conservation law -- Nonlocal velocity -- Re-entrant manufacturing system; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111577
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study the controllability and stabilization for a scalar conservation law modeling a highly re-entrant manufacturing system with local and nonlocal velocity. We prove a local state controllability result, i.e., there exists a control that drives the solution from any given initial condition to any desired final condition in a certain time period, provided that the initial and final data are both close to the origin. A local result on nodal profile controllability is also given, i.e., for any initial data and any given out-flux in a neighborhood of the origin, there exists a control under which the solution starts from any initial data reaches exactly any desired out-flux over a fixed time period. Besides, using a Lyapunov function approach, we can stabilize the system to the origin exponentially by output feedback control.