Matychyn I. Control of processes with fractional dynamics under uncertainty conditions

Analytical representations of solutions to linear systems with fractional derivatives of Riemann - Liouville, Caputo, Miller - Ross, and Hilfer are derived and corresponding game-theoretical problems of approaching terminal set are formulated. Using the resolving functions technique, control strategies are developed and sufficient conditions are obtained guaranteeing bringing of the system's trajectory to the terminal set. The developed methods are applied to game-theoretical problems for processes with fractional dynamics including fractional oscillation and relaxation processes. Modifications of the Method of Resolving Functions are developed for conflict-controlled processes with impulse impact, in particular, with impulse control of players. Sufficient conditions for capture in problem of group pursuit with impulse controls of the pursuers are derived. In an example with "simple motions" these conditions are also necessary and coincident with the well-known "encirclement" condition. The resolving functions apparatus is used to study conflict-controlled processes described by fractional differential equations involving impulses.