Real-time reachable set estimation for linear time-delay systems based on zonotopes

ABSTRACT

This paper considers reachable set estimation for discrete-time linear time-delay systems. With the assumption that the unknown initial condition and disturbances are bounded by zonotopes, three zonotope-based methods are proposed to estimate the real-time reachable sets. We find that the couplings in the time-delay systems lead to conservative estimation results and propose a reachable set estimation method based on state augmentation. The augmentation-based method can reduce the conservatisms caused by the time-delay and achieve more accurate reachable set estimation. Simulation results demonstrate the performances of the proposed methods.

KEYWORDS:

• Reachable set estimation
• time-delay
• zonotope

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Additional information

Notes on contributors

Tuochen Li

Tuochen Li received his B.Sc. degree from Jilin University, Changchun, China, in 1988, his M.S. degree from Nankai University, Tianjin, China, in 1995, and his Ph.D. degree from Harbin Engineering University, Harbin, China, in 2006. He is currently a Professor at the School of Economics and Management, Harbin Engineering University, China. His research interests include applied economics and engineering management. 

Cunxi Zheng

Cunxi Zheng received her B.Sc. degree from Northeast Agricultural University, Harbin, China, in 2012 and her M.S. degree from Harbin Engineering University, Harbin, China, in 2015. She is currently a Ph.D. student at the School of Economics and Management, Harbin Engineering University, China. Her research interests include reachable set estimation and its application to economics.  

Zhiguang Feng

Zhiguang Feng received the B.S. degree in automation from Qufu Normal University in 2006, the M.S. degree in control Science and Engineering from Harbin Institute of Technology in 2009, and the Ph.D. degree in the Department of Mechanical Engineering, The University of Hong Kong, China in 2013. He is currently a full Professor at the College of Intelligent Systems Science and Engineering, Harbin Engineering University. His research interests include singular systems, time-delay systems, robust control, dissipative control, and reachable set estimation. 

Thach N. Dinh

Thach Ngoc Dinh obtained his M.S. degree in Electrical Engineering from INSA de Lyon, France in 2011 and his Ph.D. degree from Université Paris-Saclay, France in 2014. He is currently a tenured Associate Professor at Conservatoire National des Arts et Métiers, France. His research interests include robust control, observer and fault detection. He is a member of the IFAC Technical Committee “Linear Control Systems”. 

Tarek Raïssi

Tarek Raïssi received the Ph.D. degree from the University of Paris XII in 2004 and the Accreditation to Supervise/Conduct Research (HDR) from the University of Bordeaux in 2012. From 2005 to 2011 he was an Associate Professor at the University of Bordeaux. Currently, he is a Full Professor at the Conservatoire National des Arts et Métiers, Paris, France. He is a member of the IFAC Technical Committee “Modelling, Identification and Signal Processing” and a Senior member of IEEE. His research interests include fault detection and isolation, nonlinear systems estimation and robust control.