The article deals with linear controlled objects described by linear integro-differential equations. The main object of the study is the attainable sets of such controlled objects and some of their properties. In particular, the continuous dependence in the Hausdorff metric of the attainable sets for small deviations in special norms of matrix functions that determine the dynamics of the controlled object under consideration.
Keywords: linear integro-differential equations, controlled objects, attainable sets, Hausdorff metric
Received January 16, 2026
Revised February 10, 2026
Accepted February 16, 2026
Mikhail Sergeevich Nikol’skii, Dr. Phys.-Math. Sci., Prof., Leading Researcher, Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia, e-mail: mni@mi-ras.ru
Moussa Aboubacar, Cand. Sci., Maitre de Conférences, Department of Mathematics and Computer Science Abdou Moumouni University of Niamey, Niamey, Niger, e-mail: msaboubacar@yahoo.fr
REFERENCES
1. Volterra V. Leçons sur la théorie mathématique de la lutte pour la vie. Paris: Gauthier-Villars & Cie, 1931. 214 p.
2. Vasil’eva A.B., Tikhonov N.A. Integral’nie uravneniya [Integral equations]. Moscow, Moscow Univ. Publ., 1989. 160 p.
3. Lakshmikantham V., Rao M.R.M. Theory of integro-differential equations. Amsterdam: Gordon & Breach, Science Publ., 1995. 384 p.
4. Matvienko V.A. Elektrotekhnika: uchebnoe posobie dlya studentov [Electrical engineering: A Textbook for students]. Yekaterinburg, UGTU-UPI Publ., 2009. 114 p.
5. Lee E.B., Markus L. Foundations of optimal control theory. NY, London, Sydney: John Wiley & Sons, 1967, 576 p. Translated to Russian under the title Osnovy teorii optimal’nogo upravleniya, Moscow, Nauka Publ., 1972, 576 p. ISBN: 0471522635 .
6. Blagodatskikh V.I. Vvedenie v optimal’noe upravlenie (lineinaya teoriya) [Introduction to optimal control (linear theory)]. Moscow, Vysshaya Shkola Publ., 2001, 240 p. ISBN: 5-06-00398-8.
7. Krasnov M.L. Integral’nye uravneniya. Vvedenie v teoriyu [Integral equations. Introduction to theory]. Moscow: Nauka, 1975, 303 p.
8. Vasil’ev F.P. Metody optimizatsii [Optimization methods], in 2 books, Moscow: MTsNMO Publ., 2011, book 1, 620 p.
Cite this article as: M.S. Nikol’skii, Moussa Aboubacar. Linear controlled integro-differential equations. Attainable sets. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2026, vol. 32, no. 2, pp. 165–173.
