Fractional Optimal Control Problems with Several State and Control Variables

Abstract

In many applications, fractional derivatives provide better descriptions of the behavior of dynamic systems than other techniques. For this reason, fractional calculus has been used to analyze systems having noninteger order dynamics and to solve fractional optimal control problems. In this study, we describe a formulation for fractional optimal control problems defined in multi-dimensions. We consider the case where the dimensions of the state and control variables are different from each other. Riemann—Liouville fractional derivatives are used to formulate the problem. The fractional differential equations involving the state and control variables are solved using Grünwald—Letnikov approximation. The performance of the formulation is shown using an example.