Approximation of the set of integrable trajectories of the control system with limited control resources

Guseinov K. G., HÜSEYİN A., HÜSEYİN N., Ushakov V. N.

International Journal of Control, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1080/00207179.2025.2487638
  • Dergi Adı: International Journal of Control
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, zbMATH
  • Anahtar Kelimeler: approximation, control system, integrable trajectory, integral constraint, Urysohn integral equation
  • Sivas Cumhuriyet Üniversitesi Adresli: Evet

Özet

Approximation of the set of trajectories of a control system described by Urysohn type integral equation is studied. It is assumed that the system is affine with respect to the control vector and is nonlinear with respect to the state vector. As the set of admissible control functions, the closed ball centred at the origin with radius r of the space (Formula presented.), (Formula presented.) is chosen, where (Formula presented.) is a compact set. The trajectory of the system is defined as a multivariable integrable function from the space (Formula presented.) satisfying the system's equation almost everywhere, where (Formula presented.). An approximation of the set of trajectories by a set, consisting of a finite number of trajectories and generated by piecewise constant control functions, is presented. Convergence of the approximating sets of trajectories is proved.