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 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.

On the existence of ε-optimal trajectories of the control systems with constrained control resources

“…In [7] the approximation of 76 ANAR HUSEYIN the sets of trajectories of the aforementioned systems is discussed. A similar problem for the systems described by the ordinary di¤erential equations is considered in [5].…”

Approximation of the Set of Trajectories of the Nonlinear Control System with Limited Control Resources

“…In [14], [16], [15], [17] approximation and topological properties of the set of trajectories of the control systems described by nonlinear integral equations with integral constraints on the control functions are considered. In this paper the control system described by a Urysohn type integral equation with integral constraint on the control functions is studied, where the trajectory of the system is multivariable continuous function.…”