Randomly perturbed switching dynamics of a DC/DC converter

2016/01/05 by Chetan D. Pahlajani, Pahlajani, Chetan D.
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1601.00843

Submitted

arxiv created 2016/01/05 · arxiv updated 2016/01/06

Abstract

In this paper, we study the effect of small Brownian noise on a switching dynamical system which models a first-order DC/DC buck converter. The state vector of this system comprises a continuous component whose dynamics switch, based on the ON/OFF configuration of the circuit, between two ordinary differential equations (ODE), and a discrete component which keeps track of the ON/OFF configurations. Assuming that the parameters and initial conditions of the unperturbed system have been tuned to yield a stable periodic orbit, we study the stochastic dynamics of this system when the forcing input in the ON state is subject to small white noise fluctuations of size ε, 0<ε ≪ 1. For the ensuing stochastic system whose dynamics switch at random times between a small noise stochastic differential equation (SDE) and an ODE, we prove a functional law of large numbers which states that in the limit of vanishing noise, the stochastic system converges to the underlying deterministic one on time horizons of order \mathscrO(1/ε^ν), 0 ≤ ν< 2/3.

Related

• Phase-shifts in stochastic resonance in a Chua circuit
• The Dynamics of Bistable Switching Behavior in Limit Cycle Systems with Additive Noise
• Stochastic Response, Cascading and Control of Colored Noise in Dynamical System
• Explicit formulas for the Variance of the State of a Linearized Power System driven by Gaussian stochastic disturbances
• TOWARD AN UNDERSTANDING OF STOCHASTIC HOPF BIFURCATION