Global exact controllability of bilinear quantum systems on compact graphs and energetic controllability

2018/09/17 by Alessandro Duca, Duca, Alessandro · 1 citation
Engineering · Mathematics · #35Q41 #81Q15 #93B05 #93C20 #Advanced Mathematical Physics Problems #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1809.06249

openalex publication_date 2018/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this work is to study the controllability of the bilinear Schrödinger equation on compact graphs. In particular, we consider the equation (BSE) i∂_tψ=-Δψ+u(t)Bψ in the Hilbert space L²(\mathscrG,ℂ), with \mathscrG being a compact graph. The Laplacian -Δ is equipped with self-adjoint boundary conditions, B is a bounded symmetric operator and u∈ L²((0,T),ℝ) with T>0. We provide a new technique leading to the global exact controllability of the (BSE) in D(|Δ|^s/2) with s≥ 3. Afterwards, we introduce the "energetic controllability", a weaker notion of controllability useful when the global exact controllability fails. In conclusion, we develop some applications of the main results involving for instance star graphs.

Cited by

• Hamilton--Jacobi--Bellman equation for optimal control of stochastic Wasserstein--Hamiltonian system on graphs

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