Approximation of the Integral Funnel of a Nonlinear Control System with Limited Control Resources

Abstract

Approximation of the integral funnel of the control system described by Urysohn type integral equation is studied. It is assumed that the control resource of the system is limited. The closed ball of the space L-p , p>1, with radius r and centered at the origin is chosen as the set of admissible control functions. The integral funnel of the system is defined as the set of graphs of the system's trajectories generated by all admissible control functions. The approximation of the integral funnel by the set consisting of a finite number of points is presented and convergence of the approximation procedure is proved.