APPROXIMATIONS OF THE SET OF TRAJECTORIES, ATTAINABLE SETS, AND INTEGRAL FUNNEL OF A CONTROL SYSTEM WITH INTEGRAL AND GEOMETRIC CONSTRAINTS ON THE CONTROL FUNCTIONS

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

Electronic Journal of Differential Equations, cilt.2026, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2026
  • Basım Tarihi: 2026
  • Doi Numarası: 10.58997/ejde.2026.27
  • Dergi Adı: Electronic Journal of Differential Equations
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: approximation, attainable set, Control system, geometric constraint, integral constraint, integral funnel, trajectories
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Sivas Cumhuriyet Üniversitesi Adresli: Evet

Özet

This article studies approximations to the set of trajectories, attainable sets and integral funnel of a control system described by an ordinary differential equation. It is assumed that the equation is nonlinear with respect to the phase state vector and affine with respect to the control vector. The system includes control functions, some of which satisfy the Lp (p ∈ (1, ∞)) norm constraint, while the others satisfy the L∞ norm constraint. Step by step, the set of admissible control functions is replaced by a set consisting of a finite number of piecewise-constant control functions that generate a finite number of trajectories. Error evaluations are provided for the Hausdorff distances between the set of trajectories, attainable sets, integral funnel, and their approximations, which depend on discretization parameters.