Derivative-orthogonal wavelets for discretizing constrained optimal control problems

Ashpazzadeh E., Han B., Lakestanı M., Razzaghi M.

International Journal of Systems Science, cilt.51, sa.5, ss.786-810, 2020 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 51 Sayı: 5
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1080/00207721.2020.1739356
  • Dergi Adı: International Journal of Systems Science
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.786-810
  • Anahtar Kelimeler: Derivative-orthogonal wavelets, Hermite cubic splines, inequality constraints, optimal control problem, Riesz wavelets on the unit interval
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this article, a pair of wavelets for Hermite cubic spline bases are presented. These wavelets are in (Formula presented.) and supported on (Formula presented.). These spline wavelets are then adapted to the interval (Formula presented.) and we prove that they form a Riesz wavelet in (Formula presented.). The wavelet bases are used to solve the linear optimal control problems. The operational matrices of integration and product are then utilised to reduce the given optimisation problems to the system of algebraic equations. Because of the sparsity nature of these matrices, this method is computationally very attractive and reduces CPU time and computer memory. In order to save the memory requirement and computation time, a threshold procedure is applied to obtain algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.