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.

Original languageEnglish
Pages (from-to)54-59
Number of pages6
JournalIFAC-PapersOnLine
Volume52
Issue number16
DOIs
StatePublished - Sep 2019
Event11th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2019 - Vienna, Austria
Duration: 4 Sep 20196 Sep 2019

    Research areas

  • Boundary control, Distributed-parameter system, Energy control, Klein-Gordon equation, Semilinear wave equation, Speed-gradient

    Scopus subject areas

  • Control and Systems Engineering
  • Mathematics(all)
  • Computer Science(all)

ID: 75995338