Problem of time-optimal control of linear systems with fractional Caputo derivatives is examined using technique of attainability sets and their support functions. A method to construct a control function that brings trajectory of the system to a strictly convex terminal set in the shortest time is elaborated. The proposed method uses technique of set-valued maps and represents a fractional version of Pontryagin’s maximum principle. A special emphasis is placed upon the problem of computing of the matrix Mittag-Leffler function, which plays a key role in the proposed methods. A technique for computing matrix Mittag-Leffler function using Jordan canonical form is discussed, which is implemented in the form of a MATLAB routine. Theoretical results are supported by examples, in which the optimal control functions, in particular of the “bang-bang” type, are obtained.

Problem of time-optimal control of linear systems with fractional dynamics is treated in the paper from the convex-analytic standpoint. A linear system of fractional differential equations involving Riemann-Liouville derivatives is considered. A method to construct a control function that brings trajectory of the system to the terminal state in the shortest time is proposed in terms of attainability sets and their support functions.

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Optimal control problem for linear systems of arbitrary fractional order in the sense of Riemann–Liouville is treated in the paper. The technique of attainability sets and their support functions is used to obtain sufficient conditions for time-optimal control similar to that of Pontryagin’s maximum principle. Theoretical results are supported by example.

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