Reachable set estimation for switched positive systems

ABSTRACT

This paper focuses on the problem of reachable set estimation for discrete-time switched positive systems under two possible classes of exogenous disturbance. The multiple linear copositive Lyapunov function approach is applied to determine the bounding hyper-pyramids for the reachable set. Based on some Lyapunov-based inequalities and the linear version of the S-procedure technique, the bounding hyper-pyramids for the reachable set can be determined by solving a set of inequalities. Two optimisation methods are adopted to make the bounding hyper-pyramids as small as possible. Genetic Algorithm (GA) is utilised to search for the optimal value of the decision variables in the obtained inequalities. Finally, numerical examples are given to illustrate the effectiveness of the theoretical findings.

KEYWORDS:

• Discrete-time systems
• hyper-pyramid
• Lyapunov methods
• reachable set estimation
• switched positive systems

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

James Lam   http://orcid.org/0000-0002-0294-0640

Panshuo Li   http://orcid.org/0000-0003-3682-1698

Additional information

Funding

The work was partially supported by the National Natural Science Foundation of China [61603180], the Natural Science Foundation of Jiangsu Province [BK20160810] and GRF HKU [7137/13E].

Notes on contributors

Yong Chen

Yong Chen was born in Changsha, Hunan province, China, in 1988. He received his B.Eng. degree and M.Eng. degree from Harbin Institute of Technology (HIT), Harbin, China, in 2010 and 2012, respectively, and Ph.D. degree from The University of Hong Kong (HKU), Hong Kong, in 2016. His current research interests include switched systems, stochastic systems, periodic systems, fuzzy systems, positive systems in control theory, micro quadrotor in control engineering and empirical study of financial market.

James Lam

Professor James Lam received a BSc (1st Hons.) degree in Mechanical Engineering from the University of Manchester, and was awarded the Ashbury Scholarship, the A.H. Gibson Prize, and the H. Wright Baker Prize for his academic performance. He obtained the MPhil and PhD degrees from the University of Cambridge. He is a Croucher Scholar, Croucher Fellow, and Distinguished Visiting Fellow of the Royal Academy of Engineering. Prior to joining the University of Hong Kong in 1993 where he is now Chair Professor of Control Engineering, he was a lecturer at the City University of Hong Kong and the University of Melbourne. Professor Lam is a Chartered Mathematician, Chartered Scientist, Chartered Engineer, Fellow of Institute of Electrical and Electronic Engineers, Fellow of Institution of Engineering and Technology, Fellow of Institute of Mathematics and Its Applications, Fellow of Institution of Mechanical Engineers, and Fellow of Hong Kong Institution of Engineers. He is Editor-in-Chief of IET Control Theory and Applications and Journal of The Franklin Institute, Subject Editor of Journal of Sound and Vibration, Editor of Asian Journal of Control, Senior Editor of Cogent Engineering, Associate Editor of Automatica, International Journal of Systems Science, Multidimensional Systems and Signal Processing, and Proc. IMechE Part I: Journal of Systems and Control Engineering. He is a member of the Engineering Panel (Joint Research Scheme), Research Grant Council, HKSAR. His research interests include model reduction, robust synthesis, delay, singular systems, stochastic systems, multidimensional systems, positive systems, networked control systems and vibration control. He is a Highly Cited Researcher in Engineering (2014, 2015, 2016, 2017) and Computer Science (2015).

Jun Shen

Jun Shen received the B.Sc. and M.Sc. degrees from Southeast University, Nanjing, China, in 2008 and 2011, respectively, and the Ph.D. degree from the Department of Mechanical Engineering, the University of Hong Kong, Hong Kong, in 2015. Since 2016, he is an Associate Professor in the College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China. His current research interests include positive systems, monotone systems, fractional order systems, model reduction, and robust control and filtering.

Baozhu Du

Baozhu Du received the B.S. in Information and Computing Science, and M.S. degree in Operational Research and Cybernetics from Northeastern University, Shenyang, Liaoning Province, China, in 2003 and 2006, respectively. She obtained the Ph.D. degree in Mechanical Engineering from the University of Hong Kong in 2010. She joined Nanjing University of Science and Technology in April 2011, taking a lectureship in School of Automation. Her current research interests include stability analysis and robust control/filter theory of time-delay systems, positive systems, Markovian jump systems, and networked control systems.

Panshuo Li

Panshuo Li received her B.S. and M.S. degrees in Mechanical Engineering from Dong Hua University and Shanghai Jiao Tong University, Shanghai, China, in 2009 and 2012, respectively. She obtained the PhD degree in Mechanical Engineering from the University of Hong Kong in 2016. Since 2016, she is an Associate Professor in the School of Automation, Guangdong University of Technology, Guangzhou, China. Her current research interests include switched systems, periodic systems, intelligent vehicle control, and power systems.