Shape, Velocity, and Exact Controllability for the Wave Equation on a Graph with Cycle
Optimization and Control
2022-10-10 v1 Analysis of PDEs
Abstract
Exact controllability is proven on a graph with cycle. The controls can be a mix of controls applied at the boundary and interior vertices. The method of proof first uses a dynamical argument to prove shape controllability and velocity controllability, thereby solving their associated moment problems. This enables one to solve the moment problem associated to exact controllability. In the case of a single control, either boundary or interior, it is shown that exact controllability fails.
Cite
@article{arxiv.2210.03344,
title = {Shape, Velocity, and Exact Controllability for the Wave Equation on a Graph with Cycle},
author = {Sergei Avdonin and Julian Edward and Yuanyuan Zhao},
journal= {arXiv preprint arXiv:2210.03344},
year = {2022}
}