Variance and Entropy Assignment for Continuous-Time Stochastic Nonlinear Systems

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

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.

Citation

Tang, X., Zhou, Y., Zou, Y., & Zhang, Q. (2022). Variance and Entropy Assignment for Continuous-Time Stochastic Nonlinear Systems. Entropy, 24(1), Article 25. https://doi.org/10.3390/e24010025

• 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
• DOI: https://doi.org/10.3390/e24010025
• Keywords: stochastic differential equation; Fokker–Planck–Kolmogorov equation; variance and entropy assignment
• Public URL: http://researchrepository.napier.ac.uk/Output/2844787