Approximation of the Sections of the Set of Trajectories of the Control System Described by a Nonlinear Volterra Integral Equation

• Main Authors: Anar Huseyin, Nesir Huseyin, Khalik G. Guseinov
• Format: Article
• Language: English
• Published: Vilnius Gediminas Technical University 2015-07-01
• Series: Mathematical Modelling and Analysis
• Subjects: nonlinear Volterra integral equation; control system; integral constraint; set of trajectories; approximation method
• Online Access: https://journals.vgtu.lt/index.php/MMA/article/view/1016

Approximation of the sections of the set of trajectories of the control system described by a nonlinear Volterra integral equation is studied. The admissible control functions are chosen from the closed ball of the space Lp, p > 1, with radius µ and centered at the origin. The set of admissible control functions is replaced by the set of control functions, which includes a finite number of control functions and generates a finite number of trajectories. It is proved that the sections of the set of trajectories can be approximated by the sections of the set of trajectories, generated by a finite number of control functions.