Abstract:
In this paper a control system described by an Urysohn type integral equation with an integral constraint on the control functions is studied. It is assumed that the system is nonlinear with respect to the state vector and is affine with respect to the control vector. The control functions are chosen from a closed ball of the space Lp(p>1) with radius r. It is proved that the set of trajectories of the control system generated by all admissible control functions is Lipschitz continuous with respect to r and is continuous with respect to p as a set valued map. It is shown that the system's trajectory is robust with respect to the full consumption of the remaining control resource and every trajectory can be approximated by a trajectory generated by the control function with full control resource consumption.
Keywords:
integral equation, control system, integral constraint, set of trajectories, robustness.
Citation:
N. Huseyin, A. Huseyin, Kh. G. Guseinov, “On the Robustness Property of a Control System Described by an Urysohn Type Integral Equation”, Trudy Inst. Mat. i Mekh. UrO RAN, 27, no. 3, 2021, 263–270
\Bibitem{HusHusGus21}
\by N.~Huseyin, A.~Huseyin, Kh.~G.~Guseinov
\paper On the Robustness Property of a Control System Described by an Urysohn Type Integral Equation
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2021
\vol 27
\issue 3
\pages 263--270
\mathnet{http://mi.mathnet.ru/timm1855}
\crossref{https://doi.org/10.21538/0134-4889-2021-27-3-263-270}
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Linking options:
https://www.mathnet.ru/eng/timm1855
https://www.mathnet.ru/eng/timm/v27/i3/p263
This publication is cited in the following 3 articles:
M. I. Gusev, “O nekotorykh svoistvakh mnozhestv dostizhimosti nelineinykh sistem s ogranicheniyami na upravlenie v Lp”, Tr. IMM UrO RAN, 30, no. 3, 2024, 99–112
M. I. Gusev, “On Some Properties of Reachable Sets for Nonlinear Systems with Control Constraints in Lp”, Proc. Steklov Inst. Math., 327:S1 (2024), S124
N. Huseyin, A. Huseyin, Kh. G. Guseinov, “On the properties of the set of trajectories of nonlinear control systems with integral constraints on the control functions”, Tr. IMM UrO RAN, 28, no. 3, 2022, 274–284
Citation in format AMSBIB
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