INVESTIGATION OF OPTIMAL CONTROL PROBLEMS AND SOLVING THEM USING BEZIER POLYNOMIALS

Yari A. A., Mirnia M. K., Lakestanı M.

Applied and Computational Mathematics, cilt.16, sa.2, ss.133-147, 2017 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 2
  • Basım Tarihi: 2017
  • Dergi Adı: Applied and Computational Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.133-147
  • Anahtar Kelimeler: Best Approximating, Bezier and Bernstein Polynomial Family, Operational Matrix of Derivative, Operational Matrix of Integration, Optimal Control
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this paper, a new numerical method for solving the optimal control problems with quadratic performance index is presented. The method is based on Bezier polynomial. The properties of Bezier polynomials are presented. The operational matrices of integration and derivative are introduced. These matrices are then utilized to reduce the solution of the optimal control problems to a nonlinear programming problem to which existing well-developed algorithms may be applied. Illustrative examples are included to demonstrate the validity and applicability of the technique.