Output feedback stabilization for heat equations with sampled-data controls

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Lin, Ping¹  Liu, Hanbing²  Wang, Gengsheng³ 

[1] Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

[2] China Univ Geosci, Sch Math & Phys, Wuhan 430074, Peoples R China

[3] Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China

关键词: Sampled-data control;    Output feedback stabilization;    Partial null approximate controllability;    Minimal norm control;    Heat equation;   

DOI  :  10.1016/j.jde.2019.11.019

来源: Elsevier

【 摘 要 】

In this paper, we build up an output feedback law to stabilize a sampled-data controlled heat equation (with a potential) in a bounded domain Omega. The feedback law abides the following rules: First, we divide equally the time interval [0, +infinity) into infinitely many disjoint time periods, and divide each time period into three disjoint subintervals. Second, for each time period, we observe a solution over an open subset of Omega in the first subinterval; take sample from outputs at one time point of the first subinterval; add a time-invariant output feedback control over another open subset of Omega in the second subinterval; let the equation evolve free in the last subinterval. Thus, the corresponding feedback control is of sampled-data. Our feedback law has the following advantages: the sampling period (which is the length of the above time period) can be arbitrarily taken; the feedback law has an explicit expression in terms of the sampling period; the behaviors of the norm of the feedback law, when the sampling period goes to zero or infinity, are clear. The construction of the feedback law is based on two kinds of approximate null-controllability for heat equations. One has time-invariant controls, while another has impulse controls. The studies of the aforementioned controllability with time-invariant controls need a new observability inequality for heat equations built up in the current work. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free