01.01.02; 01.01.09 (Differential equations; Discrete mathematics and mathematical cybernetics)
Birth date:
13.09.1962
E-mail:
Keywords:
control problems; differential inclusions; quasidifferential equations; differential games; avereging method.
Subject:
The notion of the differential inclusion with Hukuhara derivative is introdused, different definitions of the solution are given and some theorems of theirs existence are proved. The properties of the bunches trajectories of control differential inclusions and some control problems of bunches trajectories are reseached. The necessary and sufficient conditions of optimality their solutions are proved. Some schemes of the averaging conrol differential inclusions, control quasidifferential equations, differential equations and inclusions with Hukuhara derivative are justified.
Biography
Graduated from Faculty of Mathematics and Mechanics of Odessa State University in 1984 (department of optimal control). Ph. D. thesis was defended in 1988. D. Sci. thesis was defended in 1995. A list of my works contains more than 120 titles.
Main publications:
Plotnikov V. A., Plotnikov A. V., Vityuk A. N. Differentsialnye uravneniya s mnogoznachnoi pravoi chastyu. Asimptoticheskie metody. - Monografiya – Odessa: AstroPrint, 1999. - 356 s.
Plotnikov A. V., Skripnik N. V. Differentsialnye uravneniya s «chetkoi» i nechetkoi mnogoznachnoi pravoi chastyu. Asimptoticheskie metody. - Monografiya – Odessa: AstroPrint, 2009. - 192 s.
Plotnikov A. V., Skripnik N. V. The generalized solutions of the fuzzy differential inclusions // International J. of Pure and Appl. Math., 2009. – Vol. 56, (2). – P. 165-172.
Plotnikov A. V., Komleva T. A. Linear Problems of Optimal Control of Fuzzy Maps // Intelligent Information Management (Scientific Research Publishing, Inc., USA), 2009. - Vol. 1, N3. – P. 139-144.
Plotnikov A. V., Komleva T. A., Arsiry A. V. Necessary and Sufficient Optimality Conditions for a Control Fuzzy Linear Problem // Int. J. Industrial Mathematics, 2009. – Vol. 1, N 3. – P. 197-207.
A. V. Plotnikov, “Some Properties of Solutions of Integro-Differential Inclusions”, Differ. Uravn., 38:9 (2002), 1214–1217; Differ. Equ., 38:9 (2002), 1293–1297
2000
2.
A. V. Plotnikov, “Some properties of integro-differential inclusions”, Differ. Uravn., 36:10 (2000), 1410–1414; Differ. Equ., 36:10 (2000), 1556–1561
1998
3.
A. V. Plotnikov, “Controlled quasi-differential equations and some of their properties”, Differ. Uravn., 34:10 (1998), 1332–1336; Differ. Equ., 34:10 (1998), 1332–1336
1993
4.
A. V. Plotnikov, “A property of the set of attainability of a controlled differential inclusion”, Izv. Vyssh. Uchebn. Zaved. Mat., 1993, no. 11, 35–39; Russian Math. (Iz. VUZ), 37:11 (1993), 33–37
1992
5.
A. V. Plotnikov, “A problem on the control of pencils of trajectories”, Sibirsk. Mat. Zh., 33:2 (1992), 196–199; Siberian Math. J., 33:2 (1992), 351–354
A. V. Plotnikov, “Compactness of the attainability set of a controllable differential inclusion in partial derivatives”, Differ. Uravn., 27:3 (1991), 526–530; Differ. Equ., 27:3 (1991), 379–382
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