Properties of the Set of L∞ Trajectories of the Control Systems With Limited Control Resources

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

Mathematical Methods in the Applied Sciences, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1002/mma.70213
  • Dergi Adı: Mathematical Methods in the Applied Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: L∞-trajectory, control system, integral constraint, optimal process, robustness, Urysohn integral equation
  • Sivas Cumhuriyet Üniversitesi Adresli: Evet

Özet

In this paper, the set of trajectories of the control system described by Urysohn type integral equation is considered. It is assumed that the system is nonlinear with respect to the state vector and affine with respect to the control vector. The closed ball of the space (Formula presented.), is chosen as the set of admissible control functions. The trajectory of the system is defined as multivariable Lebesgue measurable function from the space (Formula presented.) that satisfies the system's equation almost everywhere. Boundedness of the set of trajectories is shown, and it is proved that every sequence of trajectories has a subsequence that converges almost everywhere to a system's trajectory. Existence of the optimal process in the optimal control problem with linear quality functional is presented. It is shown that every trajectory is robust with respect to the fast consumption of the remaining control resource and the set of trajectories as a set valued map depending on (Formula presented.) is continuous with respect to (Formula presented.) in the Hausdorff pseudometric generated by the norm of the space (Formula presented.).