A Fokker-Planck model for a non-linear switched system

Abstract

Switched electrical networks are formalized as vector ordinary differential equations utilizing the notion of the Lagrangian in the general theory of dynamical systems and control. After accounting the noise influence, the switched electrical networks assume the structure of stochastic differential equations. This paper analyses a stochastically influenced boost converter, a non-linear stochastic switched system using the Fokker-Planck technique. From the systemtheoretic viewpoint, the non-linear switched system of the paper assumes the structure of a vector bilinear stochastic differential equation.The Fokker-Planck equation has a central importance in the theory of random processes that has found its applications in stochastic stability, estimation and stochastic control as well.More notably, in this paper, we develop the Fokker-Planck model and subsequently, we accomplish the noise analysis of the non-linear stochastic switched system of this paper by deriving the conditional mean and variance evolutions. It is imperative to know the estimated states before designing a dynamic controller for the systems involving switched electrical networks.Index Terms-Bilinear stochastic differential equations, Euler-Lagrangian equations, the Fokker-Planck equation, randomly switched electrical systems.