Optimal control of linear fractional differential equations in the Caputo sense

Abstract

In this work, we study a time-optimal control problem involving bounded controls to regulate the dynamics of a linear fractional differential equation in the Caputo sense. We prove that the equation governing the dynamics admits optimal controls, which are of the bang–bang type. Additionally, we establish the validity of a maximum principle for determining the optimal control. The paper includes two application examples. The first example demonstrates that the optimal time can be achieved by appropriately selecting the fractional index. The second example illustrates that the choice between the classical and the fractional model may depend on the initial state of the dynamics.