Adaptive sliding mode control for 2D nonlinear Fornasini–Marchesini model subject to quantisation and packet dropouts

Abstract

This paper aims to solve the sliding mode control issue for the discrete nonlinear two-dimensional (2D) Fornasini–Marchesini second (FMII) model under the influence of quantisation error and stochastic packet loss. Firstly, an innovative stochastic 2D FMII sliding mode control model is constructed by considering quantisation error and Bernoulli packet loss process. And then we study the stability issue and formulate the corresponding stability criterion by virtue of the 2D sliding mode surface and a 2D sliding mode control law with data compensation. Subsequently, the reachability for the 2D sliding surface is verified by a innovative and executable 2D sliding mode control law. Besides, the article also formulates the adaptive intelligent iterative algorithms for the sliding mode surface gain and 2D sliding mode control algorithm, respectively. To conclude the paper, an example is provided to analyse its SMC problem under quantisation and stochastic packet loss. This example also shows the effectiveness of the theorems and algorithms proposed in this paper.

Keywords:

• Fornasini–Marchesini second model
• 2D sliding mode control
• Bernoulli packet dropout
• quantisation error
• sliding mode control algorithm design

Acknowledgments

This work was supported by General project of Natural Science Foundation of Ningxia Hui Autonomous Region (No. 2020AAC03234) and National Natural Science Foundation of China (No. 62073001; 61673001).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Ningxia Natural Science Foundation [grant number 2020AAC03234] and National Natural Science Foundation of China [grant numbers 61673001, 62073001].

Notes on contributors

Guangchen Zhang

Guangchen Zhang received his Ph.D degree from Nanjing University of Technology in 2017. He is now a lecturer of mathematics and information science in Northern Minzu University. His research interests include multi-dimensional system stability and control, networked control system stability and optimal control theory, finite time stability and control, etc.

Xufei Li

Xufei Li received the B.S. degree in Mathematic and applied mathematics from lvliang university, lvliang, China in 2017. He is currently pur-suing the M.S. degree at North Minzu University, Yinchuan, china. His research interests intelligent optimization algorithm, networked control system, sliding mode control.

Yuanqing Xia

Yuanqing Xia received the Ph.D. degree in control theory and control engineer- ing from the Beijing University of Aeronautics and Astronautics, Beijing, China, in 2001. From 2002 to 2003, he was a Postdoctoral Research Associate with the Instituteof Systems Science, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing. From 2003 to 2004, he was a Research Fellow with the National University of Singapore,Singapore, where he researched variable structurecontrol. From 2004 to 2006, he was a Research Fellow with the University of Glamorgan, Pontypridd, U.K. From 2007 to2008, he was a Guest Professor with Innsbruck Medical University, Innsbruck, Austria. Since 2004, he has been with the School of Automation, BeijingInstitute of Technology, Beijing, first as an Associate Professor, and then a Professor since 2008. His current research interests include networked control systems, robust control and signal processing, and active disturbancerejection control.

Shuping He

Shuping He received the B.S.degree in automation and Ph.D degree in control theory and control engineering in Jiangnan University, Wuxi, China respectively in 2005 and 2011. From2010 to 2011, he was a visiting scholar with the Control Systems Centre, School of Electrical and Electronic Engineering, The University of Manch-ester, UK. He is a Professor with School of Electri-cal Engineering and Automation, Anhui University, Hefei, China. His current research interests include stochastic systems and stochastic control, finite-timecontrol theory, reinforcement learning and adaptive optimal control, system modeling methods and applications, signal processing and artificial intelligence methods. He has authored or co-authored more than 90 papers inprofessional journals, conference proceedings and technical reports in theserelated areas and co-authored a book about stochastic systems.