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Reachable Set Estimation for Uncertain Linear Systems with Known Inputs

Abstract

This paper studies reachable set estimation for systems with parameter uncertainties and known input. A new method is proposed for estimating real-time reachable sets of systems with parameter uncertainties, known input and non-zero initial condition. In order to reduce the effect of known inputs on the reachable set estimation, we propose a method by separating the uncertain systems into two subsystems: the subsystem with known input and the subsystem with parameter uncertainties. By solving the optimization problem in terms of linear matrix inequalities, real-time reachable sets are obtained. The effectiveness of the proposed method is illustrated by the simulation result of the lateral dynamic system of a vehicle.

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Correspondence to Xin Zhang.

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Recommended by Associate Editor M. Chadli under the direction of Editor Yoshito Ohta. This work was partially supported by the National Natural Science Foundation of China (Grant No. 61773145, 61803127); the Key Laboratory Opening Funds of Harbin Institute of Technology under grant HIT.KLOF.2018.073, and the University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province, China (Grant No. UNPYSCT-2017093).

Zhihao Zhang received his M.Eng. and B.Eng. degrees in electronic engineering from Harbin Institute of Technology, in 2013 and 2016, respectively. He is currently a Ph.D. candidate with the department of control science and engineering, Harbin Institute of Technology. His current research interests include reachable set estimation, fault detection, and observer design.

Xinsheng Wang received her Ph.D. degree from Harbin Institute of Technology in 2002. She is currently an associate professor with Harbin Institute of Technology at Weihai, China. Her current research interests covers robust and nonlinear control, modelling and control of electrical and electronics system.

Wenbo Xie received his B.Eng. and Ph.D. degrees from Harbin Engineering University, in 2008 and 2013, respectively. He is currently an associate professor with Harbin University of Science and Technology, China, and a post-doctoral with Shanghai University, China. He was a post-doctoral with the University of Adelaide, Australia (2015-2016). He was a visiting scholarship in Harbin Institute of Technology, China (2017-2018). His current research interests include nonlinear and fuzzy control systems.

Xin Zhang received his B.S. degree from the Harbin Engineering University in 2009, and his M.S. and Ph.D. degrees from the Harbin Institute of Technology, in 2011 and 2015, respectively. His current research interests include acoustic emission detection in rail, signal processing and pattern recognition.

Yi Shen received his B.S., M.S. and Ph.D. degrees from the Harbin Institute of Technology, in 1985, 1988, and 1995, respectively. He is a professor with the department of control science and engineering, Harbin Institute of Technology. His current research interests include fault diagnosis for control systems, flight vehicle control and ultrasound signal processing.

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Zhang, Z., Wang, X., Xie, W. et al. Reachable Set Estimation for Uncertain Linear Systems with Known Inputs. Int. J. Control Autom. Syst. 18, 2445–2455 (2020). https://doi.org/10.1007/s12555-019-0131-4

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Keywords

  • Linear matrix inequality
  • linear systems
  • parameter uncertainties
  • reachable set estimation
  • system separation