{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:39:24Z","timestamp":1760236764835,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,12,24]],"date-time":"2021-12-24T00:00:00Z","timestamp":1640304000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51807010"],"award-info":[{"award-number":["51807010"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Hunan Province","award":["2020JJ5585; 2020JJ5777"],"award-info":[{"award-number":["2020JJ5585; 2020JJ5777"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2013Planck\u2013Kolmogorov 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.<\/jats:p>","DOI":"10.3390\/e24010025","type":"journal-article","created":{"date-parts":[[2021,12,24]],"date-time":"2021-12-24T08:38:46Z","timestamp":1640335126000},"page":"25","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Variance and Entropy Assignment for Continuous-Time Stochastic Nonlinear Systems"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5781-9867","authenticated-orcid":false,"given":"Xiafei","family":"Tang","sequence":"first","affiliation":[{"name":"Engineering Research Center of the Ministry of Education (Power Grid Security Monitoring and Control Technology), Changsha University of Science and Technology, Changsha 410114, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2188-2781","authenticated-orcid":false,"given":"Yuyang","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Engineering and The Built Environment, Edinburgh Napier University, Edinburgh EH11 4BN, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9208-0340","authenticated-orcid":false,"given":"Yiqun","family":"Zou","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2479-8195","authenticated-orcid":false,"given":"Qichun","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Bradford, Bradford BD7 1DP, UK"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Kumar, P.R., and Varaiya, P. 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