Minimum energy exact null-controllability problem for linear time-delay equations

2020/04/21 by Pavel Barkhayev, Barkhayev, Pavel
Engineering · Mathematics · #49N10 #FOS: Mathematics #Nonlinear Differential Equations Analysis #Numerical methods for differential equations #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #math.OC #msc:49N10

paper · pdf · doi:10.48550/arxiv.2004.10149

arxiv created 2020/04/21 · openalex publication_date 2020/04/21 · arxiv updated 2020/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the minimum energy null-controllability problem for differential equations with point-wise delays. For the equations of both neutral and retarded type we reduce the problem of finding the optimal control to a Volterra integral equation and solve it explicitly. We prove that for any initial state and any controllability time the corresponding optimal control belongs to the characteristic space generated by the equation's exponentials. Besides, we show that the proposed approach can be applied to the systems of retarded equations with one delay term.

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