Constrained approximate null controllability of coupled heat equation with periodic impulse controls

2020/05/15 by Lijuan Wang, Wang, Lijuan, Qishu Yan +3 · 1 citation
Computer Science · Engineering · Mathematics · #35K40 #93B05 #93C20 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2005.07386

openalex publication_date 2020/05/15 · openalex created_date 2020/05/21 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the constrained approximate null controllability of heat equation coupled by a real matrix P, where the controls are impulsive and periodically acted into the system through a series of real matrices \Q_k\_k=1^ℏ. The conclusions are given in two cases. In the case that the controls act globally into the system, we prove that the system is global constrained approximate null controllable under a spectral condition of P together with a rank condition of P and \Q_k\_k=1^ℏ; While in the case that the controls act locally into the system, we prove the global constrained approximate null controllability under a stronger condition for P and the same rank condition as the above case. Moreover, we prove that the above mentioned spectral condition of P is necessary for global constrained approximate null controllability of the control problem considered in this paper.

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