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

Abstract

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 L_p, 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.

Keywords:

• nonlinear Volterra integral equation
• control system
• integral constraint
• set of trajectories
• approximation method

AMS Subject Classification:

• 93C23
• 45D05