Abstract
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.
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Matychyn, I., Onyshchenko, V. Optimal control of linear systems with fractional derivatives. FCAA 21, 134–150 (2018). https://doi.org/10.1515/fca-2018-0009
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DOI: https://doi.org/10.1515/fca-2018-0009