Robust repetitive control of semi-Markovian jump systems

ABSTRACT

This paper considers the periodic reference tracking problem for continuous-time semi-Markovian jump systems. An observer-based robust $H_{\mathrm{\infty }}$ modified repetitive controller with logarithmically quantised output measurements is proposed. By using a lifting technique, the semi-Markovian jump system and the modified repetitive controller structure are transformed into a stochastic two-dimensional (2D) model to differentiate the control and learning actions involved in the repetitive controller structure. For the transformed 2D model, first, sufficient conditions are derived for the closed-loop control system to be mean square asymptotically stable by utilising tools from stochastic systems theory and multiple Lyapunov functional technique. Subsequently, a robust modified repetitive controller is synthesised to ensure a prescribed $H_{\mathrm{\infty }}$ attenuation performance in the presence of a bounded exogenous disturbance input. A numerical example on a switched boost converter circuit is considered and simulation results are provided to evaluate the proposed control strategy.

Keywords:

• Robust $H_{\mathrm{\infty }}$ repetitive control
• periodic reference tracking
• semi-Markovian jump systems
• observer
• output quantisation

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Prabhakar R. Pagilla http://orcid.org/0000-0001-8553-4658

Additional information

Notes on contributors

Guoqi Ma

Guoqi Ma is currently pursuing the Ph.D. degree in mechanical engineering in J. Mike Walker ’66 Department of Mechanical Engineering, Texas A&M University, College Station, TX, USA. His current research interests include hybrid dynamical systems, autonomous vehicles, and event-triggered control.

Xinghua Liu

Xinghua Liu received the B.Sc. degree from Jilin University, Changchun, China, in 2009; and the Ph.D. degree in Automation from the University of Science and Technology of China, Hefei, in 2014. From 2014 to 2015, he was invited as a visiting fellow at RMIT University in Melbourne, Australia. From 2015 to 2018, he was a Research Fellow at the School of Electrical and Electronic Engineering in Nanyang Technological University, Singapore. Dr Liu has joined Xi’an University of Technology as a professor since September 2018. His research interest includes state estimation and control, intelligent systems, autonomous vehicles, cyber-physical systems, robotic systems, etc.

Prabhakar R. Pagilla

Prabhakar R. Pagilla received the B.Eng. degree in mechanical engineering from Osmania University, Hyderabad, India, in 1990, and the M.S. and Ph.D. degrees in mechanical engineering from the University of California at Berkeley, Berkeley, CA, USA, in 1994 and 1996, respectively. He is currently the James J. Cain ’51 Professor II and Associate Department Head in J. Mike Walker ’66 Department of Mechanical Engineering, Texas A&M University, College Station, TX, USA. He is currently interested in the broad area of modeling and control of dynamics systems with applications in roll-to-roll manufacturing, large-scale systems, robotics, and mechatronics. He was a recipient of the National Science Foundation CAREER Award in 2000. He was an Associate Editor of the ASME Journal of Dynamic Systems, Measurement and Control and a Technical Editor of the IEEE/ASME Transactions on Mechatronics. He is a fellow of the American Society of Mechanical Engineers.