Solution of optimal control problems with payoff term and fixed state endpoint by using bezier polynomials

Yari A., Mirnia M., Lakestanı M., Heydari A.

Boletim da Sociedade Paranaense de Matematica, cilt.35, sa.1, ss.247-267, 2017 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 35 Sayı: 1
  • Basım Tarihi: 2017
  • Doi Numarası: 10.5269/bspm.v35i1.28534
  • Dergi Adı: Boletim da Sociedade Paranaense de Matematica
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.247-267
  • Anahtar Kelimeler: Best approximating, Bezier and bernstein polynomial family, Fixed state endpiont, Operational matrices of derivative and integration, Optimal control, Payoff term
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this paper, a new numerical method for solving the optimal con-Trol problems with payoff term or fixed state endpiont by quadratic performance index is presented. The method is based on Bezier polynomial. The properties of Bezier polynomials in any intervel as [a, b] are presented. The operational matri- ces of integration and derivative are utilized to reduce the solution of the optimal control problems to a nonlinear programming one to which existing well-developed algorithms may be applied. Illustrative examples are included to demonstrate the validity and applicability of the technique.