Geodesic
On the Uniform Convergence of Solutions of Volterra-Type Controlled Systems of Integral Equations Linear in the Control
Matematičeskie zametki, Tome 96 (2014) no. 3, pp. 333-342.

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For systems of integral equations with properties cited in the title, we propose a constraint on the convergence of the controls guaranteeing the uniform convergence of the solutions of such systems. This requirement is weaker than weak convergence. Relevant examples are given.
Keywords: Volterra-type controlled system, weak convergence, Lipschitz operator, modulus of continuity.
Mots-clés : uniform convergence 
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Yu. I. Beloglazov; A. V. Dmitruk. On the Uniform Convergence of Solutions of Volterra-Type Controlled Systems of Integral Equations Linear in the Control. Matematičeskie zametki, Tome 96 (2014) no. 3, pp. 333-342. http://geodesic.mathdoc.fr/item/MZM_2014_96_3_a2/

[1] W. Liu, H. J. Sussmann, “Continuous dependence with respect to the input of trajectories of control-affine systems”, SIAM J. Control Optim., 37:3 (1999), 777–803 | DOI | MR | Zbl

[2] W. Liu, H. J. Sussmann, “Limits of highly oscillatory controls and the approximation of general paths by admissible trajectories”, Proceedings of the 30th IEEE Conference on Decision and Control, Vol. 1 (11–13 Dec 1991, Brighton), 1991, 437–442 | DOI

[3] Z. Artstein, “Continuous dependence of solutions of Volterra integral equations”, SIAM J. Math. Anal., 6:3 (1975), 446–456 | DOI | MR | Zbl

[4] J. Kurzweil, J. Jarník, “Limit processes in ordinary differential equations”, Z. Angew. Math. Phys., 38:2 (1987), 241–256 | DOI | MR | Zbl

[5] G. Buttazzo, G. Dal Maso, “$\Gamma$-convergence and optimal control problems”, J. Optim. Theory Appl., 38:3 (1982), 385–407 | DOI | MR | Zbl

[6] A. V. Dmitruk, A. A. Milyutin, N. P. Osmolovskii, “Teorema Lyusternika i teoriya ekstremuma”, UMN, 35:6 (1980), 11–46 | MR | Zbl