Approximation of the Set of Integrable Trajectories of the Control Systems with Limited Control Resources

Nesir Huseyin; Anar Huseyin; Khalik G. Guseinov

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arXiv · 2110.06994

Approximation of the Set of Integrable Trajectories of the Control Systems with Limited Control Resources

Nesir Huseyin·Anar Huseyin·Khalik G. Guseinov

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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 $\rho$. Step by step way, the set of admissible control functions is replaced 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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Nesir Huseyin, Anar Huseyin, Khalik G. Guseinov. 2021-10-13. Approximation of the Set of Integrable Trajectories of the Control Systems with Limited Control Resources. https://arxiv.org/abs/2110.06994

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