Fractional-Order Dynamics in Large Scale Control Systems

Fractional-order differential equations are increasingly used to model systems in engineering for purposes such as control and health-monitoring. Because of the nature of a fractional derivative, mechanistically fractional-order dynamics will most naturally arise when there are non-local features in the dynamics. Even if there are no non-local effects, however, when searching for an approximate model for a very high order system, it is worth considering whether a fractional-order model is better than an integer-order model. This work is motivated by the challenges presented by very large scale systems, which will be increasingly common as integration of the control of formerly decoupled systems occurs such as in cyber-physical systems. Because fractional-order differential equations are more difficult to numerically compute, justifying the use of a fractional-order model is a balance between accuracy of the approximation and ease of computation. This paper constructs large, random networks and compares the accuracy of integerorder and fractional-order models for their dynamics. Over the range of parameter values considered, fractional-order models generally provide a more accurate approximation to the response of the system than integer order models. To ensure a fair comparison, both the fractional-order and integer-order models considered had two parameters.