<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</abstract>

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.

Time–Optimal Control of Linear Fractional Systems with Variable Coefficients

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Linear systems described by fractional differential equations (FDEs) with variable coefficients involving Riemann–Liouville and Caputo derivatives are examined...

Time–Optimal Control of Linear Fractional Systems with Variable Coefficients

Publié en ligne: 27 sept. 2021

Pages: 375 - 386

Reçu: 25 nov. 2020

Accepté: 26 avr. 2021

DOI: https://doi.org/10.34768/amcs-2021-0025

Mots clés
fractional calculus, Riemann–Liouville derivative, variable coefficients, optimal control

© 2021 Ivan Matychyn et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Time–Optimal Control of Linear Fractional Systems with Variable Coefficients

Publié en ligne: 27 sept. 2021

Pages: 375 - 386

Reçu: 25 nov. 2020

Accepté: 26 avr. 2021

DOI: https://doi.org/10.34768/amcs-2021-0025

Mots clésfractional calculus, Riemann–Liouville derivative, variable coefficients, optimal control

© 2021 Ivan Matychyn et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
fractional calculus, Riemann–Liouville derivative, variable coefficients, optimal control