Geodesic
Dependence on the parameters of the set of trajectories of the control system described by a nonlinear Volterra integral equation
Applications of Mathematics, Tome 59 (2014) no. 3, pp. 303-317

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In this paper the control system with limited control resources is studied, where the behavior of the system is described by a nonlinear Volterra integral equation. The admissible control functions are chosen from the closed ball centered at the origin with radius $\mu $ in $L_p$ $(p>1)$. It is proved that the set of trajectories generated by all admissible control functions is Lipschitz continuous with respect to $\mu $ for each fixed $p$, and is continuous with respect to $p$ for each fixed $\mu $. An upper estimate for the diameter of the set of trajectories is given.
DOI : 10.1007/s10492-014-0056-4
Classification : 45D05, 93B03, 93C23
Keywords: nonlinear Volterra integral equation; control system; integral constraint 
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Huseyin, Anar; Huseyin, Nesir. Dependence on the parameters of the set of trajectories of the control system described by a nonlinear Volterra integral equation. Applications of Mathematics, Tome 59 (2014) no. 3, pp. 303-317. doi: 10.1007/s10492-014-0056-4

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