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Fractional Stochastic Modeling for Random Dynamic Delays in Computer Control System

Shantanu Das

Abstract


A new extension of a fractality concept and fractional calculus for random delay dynamics in computer control system is described. We have introduced a new fractional Langevin type stochastic differential equation that differs from standard integer order Langevin equation, to get the insight of random delay dynamics. The excitation to the fractional Langevin equation is a stochastic force ‘shot noise’, which has pulse of random amplitude with stable Levy distribution. This method is developed as the observed delays of computer control system vary with time in random fashion similar to ‘Brownian motion’. There are large spikes in delay and the delay of the computer control system varies. Perhaps this is one way to express the dynamics of random delay in computer control systems. This will help in study of computer based control systems, where the random delay is important part of control loop.

Keywords


Levy alfa-stable process, Shot-noise, Langevin Equation, Fractional Differential equation, Fractal, Stochastic Process, Fourier Integral, Brownian motion, Random delay.

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