Two-Point Output Feedback Boundary Control for Semilinear Hyperbolic Systems

Maksim Dolgopolik1, Alexander L. Fradkov2, Boris Andrievsky3

  • 1Institute for Problems in Mechanical Engineering of the RAS
  • 2Russian Academy of Sciences
  • 3Inst. for Problems of Mechanical Engineering of the RAS

Details

11:00 - 11:20 | Wed 4 Sep | Room FH 2 | WeB2.4

Session: Control of Nonlinear PDEs I

Abstract

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.