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Minimax Theory and its Applications 05 (2020), No. 2, 327--346
Copyright Heldermann Verlag 2020

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

Anar Huseyin
Dept. of Statistics and Computer Sciences, Faculty of Science, Cumhuriyet University, 58140 Sivas, Turkey

Nesir Huseyin
Dept. of Mathematics and Science Education, Faculty of Education, Cumhuriyet University, 58140 Sivas, Turkey

Khalik G. Guseinov
Dept. of Mathematics, Faculty of Science, Eskisehir Technical University, 26470 Eskisehir, Turkey

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 Lp, 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.

Keywords: Control system, integral constraint, Urysohn integral equation, integral funnel, approximation.

MSC: 93C10, 49M25, 45G15.

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