Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems

Faïçal Ndaïrou and Delfim F. M. Torres ()
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Faïçal Ndaïrou: Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
Delfim F. M. Torres: Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

Mathematics, 2023, vol. 11, issue 19, 1-12

Abstract: We introduce a new optimal control problem where the controlled dynamical system depends on multi-order (incommensurate) fractional differential equations. The cost functional to be maximized is of Bolza type and depends on incommensurate Caputo fractional-orders derivatives. We establish continuity and differentiability of the state solutions with respect to perturbed trajectories. Then, we state and prove a Pontryagin maximum principle for incommensurate Caputo fractional optimal control problems. Finally, we give an example, illustrating the applicability of our Pontryagin maximum principle.

Keywords: incommensurate fractional-orders derivatives; fractional optimal control; continuity and differentiability of state trajectories; needle-like variations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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