Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems

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.

Automated summary

This paper introduces a new optimal control problem involving a controlled dynamical system with multi-order fractional differential equations. The continuity and differentiability of the state solutions are established with respect to perturbed trajectories. A Pontryagin maximum principle for incommensurate Caputo fractional optimal control problems is stated and proven. An example is provided to illustrate the applicability of the Pontryagin maximum principle.