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Time-optimal control of linear fractional systems with variable coefficients

Matychyn Ivan, Onyshchenko Viktoriia

International Journal of Applied Mathematics and Computer Science

2021

Vol. 31, no. 3

375--386

Linear systems described by fractional differential equations (FDEs) with variable coefficients involving Riemann–Liouville and Caputo derivatives are examined in the paper. For these systems, a solution of the initial-value problem is derived in terms of the generalized Peano–Baker series and a time-optimal control problem is formulated. The optimal control problem is treated from the convex-analytical viewpoint. Necessary and sufficient conditions for time-optimal control similar to that of Pontryagin’s maximum principle are obtained. Theoretical results are supported by examples.