Exact Boundary Controllability on a Planar Tree-Like Network of Vibrating Strings with Dynamical Boundary Conditions

Abstract

This paper concerns a planar tree-like network of vibrating strings with point masses at the nodes. We use a constructive method with modular structure to get the ‘one-sided’ exact boundary controllability for this system with dynamical boundary conditions. Moreover, by constructing the ‘longest’ chain-like subnetwork and its ‘midpoint’, we divide the whole tree-like network into two tree-like sub-networks, and prove the ‘two-sided’ exact boundary controllability.