Data-Driven Minimum Entropy Control for Stochastic Nonlinear Systems Using the Cumulant-Generating Function

• 成果类型: Article
• 署名作者: Zhang, Qichun; Zhang, Jianhua; Wang, Hong
• 署名单位: University of Bradford; North China Electric Power University; United States Department of Energy (DOE); Oak Ridge National Laboratory
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3208170
• 发表日期: 2023
• 页码: 4912-4918
• 关键词: Cumulant-generating function; data-driven design; kernel density estimation (KDE); non-Gaussian stochastic systems; stabilization

摘要

This article presents a novel minimum entropy control algorithm for a class of stochastic nonlinear systems subjected to non-Gaussian noises. The entropy control can be considered as an optimization problem for the system randomness attenuation, but the mean value has to be considered separately. To overcome this disadvantage, a new representation of the system stochastic properties was given using the cumulant-generating function based on the moment-generating function, in which the mean value and the entropy was reflected by the shape of the cumulant-generating function. Based on the samples of the system output and control input, a time-variant linear model was identified, and the minimum entropy optimization was transformed to system stabilization. Then, an optimal control strategy was developed to achieve the randomness attenuation, and the boundedness of the controlled system output was analyzed. The effectiveness of the presented control algorithm was demonstrated by a numerical example. In this article, a data-driven minimum entropy design is presented without preknowledge of the system model; entropy optimization is achieved by the system stabilization approach in which the stochastic distribution control and minimum entropy are unified using the same identified structure; and a potential framework is obtained since all the existing system stabilization methods can be adopted to achieve the minimum entropy objective.