Biorthogonal multiwavelets on the interval for solving multidimensional fractional optimal control problems with inequality constraint

Ashpazzadeh E., Lakestanı M., YILDIRIM A.

Optimal Control Applications and Methods, cilt.41, sa.5, ss.1477-1494, 2020 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 5
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1002/oca.2615
  • Dergi Adı: Optimal Control Applications and Methods
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1477-1494
  • Anahtar Kelimeler: biorthogonal Hermite cubic spline multiwavelets, Caputo fractional derivative, fractional order optimal control, Riemann-Liouville fractional integration
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

This article proposes a new numerical approach for solving fractional optimal control problems including state and control inequality constraints using new biorthogonal multiwavelets. The properties of biorthogonal multiwavelets are first given. The Riemann-Liouville fractional integral operator for biorthogonal multiwavelets is utilized to reduce the solution of optimal control problems to a nonlinear programming one, to which existing, well-developed algorithms may be applied. In order to save the memory requirement and computation time, a threshold procedure is applied to obtain algebraic equations. The method is computationally very attractive and gives very accurate results.