2023/01/24 by Sergei Avdonin, Avdonin, Sergei A., Julian Edward +1
Mathematics · Physics and Astronomy · #35L05 #35Q93 #93B05 #93C20 #Advanced Mathematical Physics Problems #FOS: Mathematics #Optimization and Control (math.OC) #Quantum chaos and dynamical systems #Quantum optics and atomic interactions
paper · pdf · doi:10.48550/arxiv.2301.10269
openalex publication_date 2023/01/24 · openalex created_date 2023/01/27 · openalex updated_date 2026/07/28
In this paper we study the exact controllability problem for the wave equation on a finite metric graph with the Kirchhoff-Neumann matching conditions. Among all vertices and edges we choose certain active vertices and edges, and give a constructive proof that the wave equation on the graph is exactly controllable if H1(0,T)' Neumann controllers are placed at the active vertices and L2(0,T) Dirichlet controllers are placed at the active edges. The proofs for the shape and velocity controllability are purely dynamical, while the proof for the exact controllability utilizes both dynamical and moment method approaches. The control time for this construction is determined by the chosen orientation and path decomposition of the graph.