Tracking for a Wave Equation Using Homogeneous Boundary Control

In this paper, a wave equation with control input in one of its boundaries is considered. Using a Lyapunov approach, the control is designed as a homogeneous algorithm to drive the states to a vicinity of a reference signal, achieving exponential Input to State Stability of the closed-loop system. This homogeneity-based tracking control strategy is evaluated in a simplified earthquake model, allowing a controlled dissipation of its energy. In addition, simulations are conducted to support the robustness and the smoothness of the control signal depending on the homogeneous control parameter selection.