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Variance and Entropy Assignment for Continuous-Time Stochastic Nonlinear Systems

Tang, Xiafei; Zhou, Yuyang; Zou, Yiqun; Zhang, Qichun


Xiafei Tang

Yiqun Zou

Qichun Zhang


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.

Journal Article Type Article
Acceptance Date Dec 17, 2021
Online Publication Date Dec 24, 2021
Publication Date 2022-01
Deposit Date Feb 11, 2022
Publicly Available Date Feb 11, 2022
Journal Entropy
Publisher MDPI
Peer Reviewed Peer Reviewed
Volume 24
Issue 1
Article Number 25
Keywords stochastic differential equation; Fokker–Planck–Kolmogorov equation; variance and entropy assignment
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