On the testing for alpha-stable distributions of network traffic
Computer Communications
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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" are 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. Using a real world networked control system platform called the CSOIS Smart Wheel, the effect of modeling the network delay dynamics using non-Gaussian distributions, and compensating for such a delay in closed-loop systems using a FO-PI (fractional order proportional and integral) controller has been experimentally studied. The cases studied include the case when the delay compensated is exactly the same as the actual delay. Other scenarios are the ones when the nature of the estimated delay is similar to the actual delay, but the magnitude is slightly smaller. The effect of phase shifting between the estimated and the original delay is also considered. Finally the order of the fractional order proportional integral controller which gives least ITAE, ISE for a particular distribution of the delay is presented. The conclusion is strikingly stimulating: in NCS, when the random delay is spiky, we should consider to model the delay dynamics using α-stable distributions and using fractional order controller whose best fractional order has shown to be related to the FLOS parameter α as evidenced by our extensive experimental results on a real NCS platform.