On the modelling and exact controllability of networks of vibrating strings

Using Hamilton's principle a nonlinear system of partial differential equations describing the dynamics of a network of vibrating strings is derived. An equilibrium is linearized to obtain a linear system of "wave equations." The equations are complemented by "coupling conditions" at the "multiple nodes" where several elements meet and by "boundary conditions" at the "simple nodes." Existence of solutions to the linear system is proved. Finally, multiplier techniques are used to prove exact controllability for certain specific networks.