Data-driven Minimum Entropy Control for Stochastic Nonlinear Systems using the Cumulant-Generating Function

Journal Article · Tue Sep 20 00:00:00 EDT 2022 · IEEE Transactions on Automatic Control

DOI:https://doi.org/10.1109/TAC.2022.3208170· OSTI ID:1890284

Zhang, Qichun ^[1]; Zhang, Jianhua ^[2]; Wang, Hong ^[3]

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1. University of Bradford (United Kingdom)
2. North China Electric Power University, Beijing (China)
3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Here, we present 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 paper, a data-driven minimum entropy design is presented without pre-knowledge 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.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 1890284
• Journal Information: IEEE Transactions on Automatic Control, Vol. 68, Issue 8; Related Information: https://ieeexplore.ieee.org/document/9896147; ISSN 0018-9286
• Publisher: IEEE
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
Entropy
Stochastic processes
Optimization
Probability density function
Stochastic systems
Random variables
Nonlinear systems
Cumulant-generating function
Data-driven design
Kernel Density Estimation (KDE)
Non-Gaussian stochastic systems
Stabilization