Variance and Entropy Assignment for Continuous-Time Stochastic Nonlinear Systems

Abstract

This paper investigates the randomness assignment problem for a class of continuous-time stochastic nonlinear systems, where variance and entropy are employed to describe the investigated systems. In particular, the system model is formulated by a stochastic differential equation. Due to the nonlinearities of the systems, the probability density functions of the system state and system output cannot be characterised as Gaussian even if the system is subjected to Brownian motion. To deal with the non-Gaussian randomness, we present a novel backstepping-based design approach to convert the stochastic nonlinear system to a linear stochastic process, thus the variance and entropy of the system variables can be formulated analytically by the solving Fokker–Planck–Kolmogorov equation. In this way, the design parameter of the backstepping procedure can be then obtained to achieve the variance and entropy assignment. In addition, the stability of the proposed design scheme can be guaranteed and the multi-variate case is also discussed. In order to validate the design approach, the simulation results are provided to show the effectiveness of the proposed algorithm.

Recent Advances in Non-Gaussian Stochastic Systems Control Theory and Its Applications

“…So far, only a few results have been developed. For example, [23] presented an output feedback stabilisation problem with entropy optimisation for the Ito process model while the entropy assignment problem has been solved analytically for a class of nonlinear continuous-time stochastic systems in [24]. So far, it is still an open question for solving the general continuous-time stochastic differential equation and only some special types of equations have been investigated.…”