Tang Xiafei, Zhou Yuyang, Zou Yiqun, Zhang Qichun
Engineering Research Center of the Ministry of Education (Power Grid Security Monitoring and Control Technology), Changsha University of Science and Technology, Changsha 410114, China.
School of Engineering and The Built Environment, Edinburgh Napier University, Edinburgh EH11 4BN, UK.
Entropy (Basel). 2021 Dec 24;24(1):25. doi: 10.3390/e24010025.
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.
本文研究了一类连续时间随机非线性系统的随机性分配问题，其中采用方差和熵来描述所研究的系统。具体而言，系统模型由一个随机微分方程来表述。由于系统的非线性特性，即使系统受到布朗运动的影响，系统状态和系统输出的概率密度函数也不能表征为高斯分布。为了处理非高斯随机性，我们提出了一种基于反步法的新颖设计方法，将随机非线性系统转换为线性随机过程，从而可以通过求解福克-普朗克-柯尔莫哥洛夫方程来解析地表述系统变量的方差和熵。通过这种方式，进而可以获得反步过程的设计参数以实现方差和熵的分配。此外，可以保证所提出设计方案的稳定性，并且还讨论了多变量情况。为了验证该设计方法，提供了仿真结果以表明所提算法的有效性。
