Approximation of the set of integrable trajectories of the control system with $ L_2 $ norm constraints on control functions

Nesir Huseyin; Anar Huseyin; Khalik G. Guseinov

doi:10.3934/eect.2024023

Article Contents

2024, Volume 13, Issue 4: 1212-1228. Doi: 10.3934/eect.2024023

This issue Previous Article On the internal and boundary stabilization of a nonlinear suspension bridge system: Exponential and polynomial decay rates Next Article Painlevé-Kuratowski convergences of solutions to nonlinear multiobjective optimal control problems

Approximation of the set of integrable trajectories of the control system with $ L_2 $ norm constraints on control functions

1.
Department of Mathematics and Science Education, Sivas Cumhuriyet University, 58140, Sivas, Turkey
2.
Department of Statistics and Computer Sciences, Sivas Cumhuriyet University, 58140, Sivas, Turkey
3.
School of Engineering, Karabakh University, AZ 2600, Khankendi, Azerbaijan

^*Corresponding author: Anar Huseyin
^*Corresponding author: Anar Huseyin

Received: August 2023

Revised: February 2024

Early access: April 17, 2024

Published online: April 17, 2024

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Abstract

In this paper an approximation of the set of multivariable and $ L_2 $ integrable trajectories of the control system described by Urysohn type integral equation is considered. It is assumed that the system is affine with respect to the control vector. The admissible control functions are chosen from the closed ball of the space $ L_2 $, centered at the origin with radius $ \rho $. The set of admissible control functions is replaced, step by step, by the set of controls consisting of a finite number of piecewise-constant control functions. It is proved that under appropriate choosing of the discretization parameters, the set of trajectories generated by a finite number of piecewise-constant control functions is an internal approximation of the set of trajectories.

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Mathematics Subject Classification: Primary: 93C23, 93C35; Secondary: 45G15.

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References

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