A model predictive control framework for constrained uncertain positive systems

ABSTRACT

In this paper, a new model predictive control framework is proposed for positive systems subject to input/state constraints and interval/polytopic uncertainty. Instead of traditional quadratic performance index, simple linear performance index, linear Lyapunov function, cone invariant set with linear form and linear computation tool are first adopted. Then, a control law that can handle the constraints and robustly stabilise the systems is proposed. The advantages of the new framework lie in the following facts: (1) an equivalent linear problem is formulated that can be easily solved than other problems including the quadratic ones, (2) simple linear index and linear tool can be used based on the essential property of positive systems to achieve the desired control performance and (3) a general model predictive control law without sign restriction is designed. Finally, an attempt of application on mitigating viral escape is provided to verify the effectiveness of the proposed approach.

KEYWORDS:

• Positive systems
• model predictive control
• interval/polytopic uncertainties

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported partly by the National Natural Science Foundation of the People's Republic of China [grant number 61503107], [grant number 61673146], [grant number 61703132], [grant number U1509203]; Zhejiang Provincial Natural Science Foundation of China [grant number LY16F030005].

Notes on contributors

Junfeng Zhang

Junfeng Zhang received his M.S. and Ph.D. degrees in the College of Mathematics and Information Science from Henan Normal University in 2008 and in the School of Electronic Information and Electrical Engineering from Shanghai Jiao Tong University in 2014, respectively. He is an associate professor in the School of Automation in Hangzhou Dianzi University (HDU). He was a recipient of Outstanding Master Degree Thesis Award from Henan Province, China, in 2011 and a recipient of Outstanding Ph.D. Graduate Award from Shanghai, China, in 2014, respectively. He is the co-chair of Program Committee in The 6th International Conference on Positive Systems (POSTA2018). His research interests include positive systems, switched systems, model predictive control, and differential inclusions.

Xianglei Jia

Xianglei Jia received his Ph.D. degree from Nanjing University of Science and Technology, Nanjing, China, in 2017. From November 2015 to May 2016, he was a visiting scholar in the Department of Electronic and Information Systems, Shibaura Institute of Technology, Japan. He joined the School of Automation at Hangzhou Dianzi University as an associate professor in January 2017. His current research interests include robust adaptive control, observer design of nonlinear systems and control of time-delay systems.

Ridong Zhang

Ridong Zhang received the Ph.D. degree in control science and engineering from Zhejiang University, Hangzhou, China, in 2007. He is currently a visiting scholar at the Chemical and Biomolecular Engineering Department, The Hong Kong University of Science and Technology, Hong Kong. His research interests include process modeling, process control and nonlinear systems.

Yan Zuo

Yan Zuo received the B.S. degree in control theory and application from North China Electric Power University in 2003 and the Ph.D. degree in control science and engineering from Shanghai Jiao Tong University in 2007. From August 2016 to August 2017, she was a visiting professor at the School Electrical Computer Engineering, McMaster University, Canada. She is an associate professor in the School of Automation in Hangzhou Dianzi University. Her research interests include sensor resource management, optimal scheduling and predictive control etc.