Output feedback tracking control by additive state decomposition for a class of uncertain systems

Abstract

Besides parametric uncertainties and disturbances, unmodelled dynamics and time delay at the input are often present in practical systems, and cannot always be ignored. This paper aims to solve the problem of output feedback tracking control for a class of non-linear uncertain systems subject to unmodelled high-frequency gains and time delay in the input. By additive state decomposition, the uncertain system is transformed to an uncertainty-free system, in which the uncertainties, disturbances and effects of unmodelled dynamics along with time delay are lumped into a new disturbance at the output. Subsequently, additive state decomposition is used to decompose the transformed system to simplify the tracking controller design. The proposed control scheme is applied to three benchmark examples to demonstrate its effectiveness.

Keywords:

• additive state decomposition
• tracking
• input delay
• unmodelled dynamics
• output feedback
• non-linear systems

Acknowledgements

This work was supported by the National Natural Science Foundation of China (61104012), the 973 Program (2010CB327904) and the Ph.D. Programs Foundation of Ministry of Education of China (20111102120008).

Notes

In this paper, we have replaced the term ‘additive decomposition’ in Quan and Cai (2009) with the more descriptive term ‘additive state decomposition’.

Refer to (Khalil 2002, p. 144) for the definition.

Since the initial values are both assigned by the designer, they are all determinate. So, we have

the notation means ‖x(t) − y‖ → 0;

Additional information

Notes on contributors

Quan Quan

Quan Quan is an Assistant Professor at the School of Automation Science and Electrical Engineering, Beihang University (Beijing University of Aeronautics and Astronautics) since 2010. He received his BS degree in 2004 and PhD degree in 2010, all from Beihang University. He was a research fellow at National University of Singapore from 7/2011– 9/2011. His research interests cover flight control and vision-based navigation and control. Web: http://quanquan.buaa.edu.cn/.

Hai Lin

Hai Lin obtained his PhD degree from the University of Notre Dame in 2005. Dr Lin is currently an Assistant Professor at the Department of Electrical Engineering, University of Notre Dame. Before returning to his alma mater, Hai has been working as an Assistant Professor in the National University of Singapore from 2006 to 2011. Dr Lin’s research interests are in the multidisciplinary study of the problems at the intersections of control, communication, computation and life sciences. His current research thrust is on cyber-physical systems, multi-robot cooperative tasking, and systems biology and quantum control. He is a senior member of IEEE.

Kai-Yuan Cai

Kai-Yuan Cai is a Cheung Kong Scholar (Chair Professor), jointly appointed by the Ministry of Education of China and the Li Ka Shing Foundation of Hong Kong in 1999. He has been a full Professor at Beihang University (Beijing University of Aeronautics and Astronautics) since 1995. He was born in April 1965 and entered Beihang University as an undergraduate student in 1980. He received his BS degree in 1984, MS degree in 1987 and PhD degree in 1991, all from Beihang University. He was a research fellow at City University, London, and a visiting scholar at Purdue University (USA). He was also a Visiting Professorial Fellow with the University of Wollongong, Australia. Dr Cai has published many research papers in international journals and is the author of three books: Software Defect and Operational Profile Modeling (Kluwer, Boston, 1998); Introduction to Fuzzy Reliability (Kluwer, Boston, 1996); Elements of Software Reliability Engineering (Tshinghua University Press, Beijing, 1995, in Chinese). He serves on the editorial board of the international journal Fuzzy Sets and Systems. He also served as guest editor for Fuzzy Sets and Systems (1996), the International Journal of Software Engineering and Knowledge Engineering (2006), the Journal of Systems and Software (2006) and IEEE Transactions on Reliability (2011). His main research interests include software reliability and testing, reliable flight control and software cybernetics.