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Continuity of $L_p$ Balls and an Application to Input-Output Systems
(Pleiades Publishing, 24.02.2022)
In this paper, the continuity of the set-valued map $p\rightarrow B_{\Omega, \mathcal{X},p}$, $p\in (1,+\infty)$, is proved where $B_{\Omega, \mathcal{X},p}$ is the closed ball of radius $r$ in the space $L_p(\Omega, ...
On the p-integrable trajectories of the nonlinear control system described by Urysohn type integral equation
(Walter de Gruyter GmbH, 11.10.2022)
The control systems described by the Urysohn-type integral equations and integral constraints on the control functions are considered. The functions from the closed ball of the space $L_p$, $p>1$, with radius $r$, are ...
Approximations of the set of trajectories and integral funnel of the nonlinear control systems with $L_p$ norm constraints on the control functions
(Oxford University Press, 29.11.2022)
In this paper, approximations of the set of trajectories and integral funnel of the control system described by non-linear ordinary differential equation with integral constraint on the control functions are considered. ...
Approximations of the images and integral funnels of the $L_p$ balls under a Urysohn-type integral operator.
(Springer New York, 25.12.2022)
Approximations of the image and integral funnel of a closed ball of the space $L_p$, $p>1$, under a Urysohn-type integral operator are considered. A closed ball of the space $L_p$, $p>1$, is replaced by a set consisting ...
On the robustness of the integrable trajectories of the control systems with limited control resources
(Polish Academy of Sciences, 14.09.2023)
The control system described by Urysohn type integral equation is considered where the system is nonlinear with respect to the phase vector and is affine with respect to the control vector. The control functions are chosen ...
On the Vietoris semicontinuity property of the $L_p$ balls at $p=1$ and an application
(Birkhauser Verlag, 19.07.2023)
In this paper the Vietoris right lower semicontinuity at $p=1$ of the set valued map $p\rightarrow B_{\Omega,\mathcal{X},p}(r)$, $p\in [1,\infty]$, is discussed where $B_{\Omega,\mathcal{X},p}(r)$ is the closed ball of ...
On the properties of the set of trajectories of the nonlinear control system with quadratic integral constraint on the control functions.
(Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences, 30.06.2023)
In this paper the control system described by a nonlinear differential equation is studied. It is assumed that the control functions have a quadratic integral constraint, more precisely, the admissible control functions ...
On the robustness of continuous trajectories of the control system described by an integral equation
(KOREAN SOC MATHEMATICAL EDUCATION, 30.05.2023)
In this paper the control system described by Urysohn type integral equation is studied. It is assumed that control functions are integrally constrained. The trajectory of the system is defined as multivariable continuous ...
On the continuity properties of the L_p balls.
(Walter de Gruyter GmbH, 11.04.2023)
In this paper the right upper semicontinuity at p = 1 and continuity at p = ∞ of the set-valued map p → B_{Ω,X,p}(r), p ∈ [1, ∞], are studied where B_{Ω,X,p}(r) is the closed ball of the space L_p(Ω, Σ, μ; X) centered at ...
On the Continuity Properties of the Set of Trajectories of the Control System with Limited Control Resources
(Celal Bayar University, 30.06.2023)
In this paper the control system with integral constraint on the control functions is studied where the behavior of the system by the Urysohn type integral equation is described. The admissible control functions are chosen ...