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.
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.
