Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems

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