Distributed Geometric Control of Wave Equation

An approach for the geometric control of a one-dimensional non-autonomous linear wave equation is presented. The idea consists in reducing the wave equation to a set of first-order linear hyperbolic equations. Then based on geometric control concepts, a distributed control law that enforces stability and output tracking in the closed-loop system is designed. The presented control approach is applied to obtain a distributed control law that brings a stretched uniform string, modeled by a wave equation with Dirichlet boundary conditions, to rest in infinite time by considering the displacement of the middle point of the string as the controlled output. The controller performances have been evaluated in simulation.