Two-point Output Feedback Boundary Control for Semilinear Hyperbolic Systems

A new control problem is posed and solved: regulation problem for the one-dimensional Klein-Gordon and semilinear wave equations with Neumann boundary conditions in the case when the control acts at both ends of the space interval ("two-point control"). A control algorithm based on the speed-gradient method is proposed. The global exponential stability of the closed loop system for the case of the Klein-Gordon equation is established by means of a new Lyapunov functional. This results is extended to the case of the semilinear wave equation by means of linearization. The two-point energy control problem for the sine-Gordon and semilinear wave equations is analyzed by simulation. It is demonstrated that the proposed two-point control algorithm may provide 30% faster transients. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.