Time-optimal control of linear fractional systems with variable coefficients

Matychyn, Ivan ; Onyshchenko, Viktoriia

International Journal of Applied Mathematics and Computer Science, Tome 31 (2021) no. 3, pp. 375-386.

Résumé

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.

Détail

Keywords: fractional calculus, Riemann-Liouville derivative, variable coefficients, optimal control
Mots-clés : rachunek ułamkowy, pochodna ułamkowa Riemanna-Liouville'a, współczynnik zmienny, sterowanie optymalne

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