Recent Advances in Non-Gaussian Stochastic Systems Control Theory and Its Applications

Abstract

Survey/review study Recent Advances in Non-Gaussian Stochastic Systems Control Theory and Its Applications Qichun Zhang 1, and Yuyang Zhou 2,* 1 Department of Computer Science, University of Bradford, Bradford BD7 1DP, United Kingdom 2 School of Computing, Engineering and the Built Environment, Edinburgh Napier University, Edinburgh EH10 5DT, United Kingdom * Correspondence: y.zhou@napier.ac.uk     Received: 24 October 2022 Accepted: 18 November 2022 Published: 22 December 2022   Abstract: Non-Gaussian randomness widely exists in complex dynamical systems, in which the traditional mean-variance index cannot fully reflect the systematic characteristics. To improve the performance of control design subjected to non-Gaussian noises, stochastic distribution control (SDC) theory was proposed in the 1990s, where the output probability density function (PDF) has been investigated as an additional system variable. Following this framework, SDC has been extended to other research subjects in control systems such as filter design, fault diagnosis, and so on. It shows that SDC supplies an important solution to enhance the accuracy of system design, which is further beneficial to almost all the topics subject to non-Gaussian randomness. Meanwhile, the theoretical results of the SDC have been applied to several practical industrial applications. As data science raises based on the development of industrial artificial intelligence, SDC has been further developed recently focusing on data-driven design and multi-agent systems. To explore the new challenges with the evolution of SDC, e.g. unknown system models, unknown noise distributions, strong non-stationary transient dynamics, stability analysis and industrial applications, this survey summarises the most recent published results in the last 5 years of SDC work in terms of modelling, control, filtering, fault diagnosis, and industrial applications. Based on the technical analysis, potential future work is discussed in the end.