ON OPTIMAL CONTROL OF THE INITIAL VELOCITY OF AN EULER-BERNOULLI BEAM SYSTEM

Engin A., Sarac Y., Celik E.

THERMAL SCIENCE, cilt.26, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 26
  • Basım Tarihi: 2022
  • Doi Numarası: 10.2298/tsci22s2735e
  • Dergi Adı: THERMAL SCIENCE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Directory of Open Access Journals
  • Anahtar Kelimeler: hyperbolic system, beam equation, frechet derivative, optimal control, BOUNDARY CONTROL, PARABOLIC EQUATIONS, STABILIZATION, VIBRATIONS
  • Atatürk Üniversitesi Adresli: Evet

Özet

In this study, we consider an optimal control problem for an Euler-Bernoulli beam equation. The initial velocity of the system is given by the control function. We give sufficient conditions for the existence of a unique solution of the hyperbolic system and prove that the optimal solution for the considered optimal control problem is exists and unique. After obtaining the Frechet derivative of the cost functional via an adjoint problem, we also give an iteration algorithm for the numerical solution of the problem by using the Gradient method. Finally, we furnish some numerical examples to demonstrate the effectiveness of the result obtained.