Small-time global approximate controllability of bilinear wave equations

2023/05/19 by Eugenio Pozzoli, Pozzoli, Eugenio · 5 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Quantum chaos and dynamical systems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2305.11794

openalex publication_date 2023/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a bilinear control problem for the wave equation on a torus of arbitrary dimension. We show that the system is globally approximately controllable in arbitrarily small times from a dense family of initial states. The control strategy is explicit, and based on a small-time limit of conjugated dynamics to move along non-directly accessible directions (a.k.a. Lie brackets of the generators).

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