Fractional calculus, delay dynamics and networked control systems

Abstract

In networked control systems (NCS), the spiky nature of the random delays makes us wonder about the benefits we can expect if the spikiness, or what we call delay dynamics can be considered in the NCS controller design. It turns out that the spikiness of the network induced random delays can be better characterized by the so-called α-stable processes, or processes with fractional lower-order statistics (FLOS) which are linked to fractional calculus. Many real dynamic systems are better characterized using a noninteger order dynamic model based on fractional calculus or, differentiation or integration of non-integer order. Traditional calculus is based on integer order differentiation and integration. The concept of fractional calculus has tremendous potential to change the way we see, model, and control the nature around us. Denying fractional derivatives is like saying that zero, fractional, or irrational numbers do not exist. This article proposes a transformative research idea to link fractional calculus, delay dynamics and NCSs. Specifically, fractional order modeling of delay dynamics will be used to better characterize the dynamic delay behavior. Then, a fractional order controller will be designed based on the fractional order delay dynamic model. Initial evidence confirmed that, incorporating delay dynamics in the controller design offers improved NCS control performance.