@article{ab0aadfeda0f4568b09a295fbb3be666,
title = "Sliding mode control to stabilization of cascaded heat PDE-ODE systems subject to boundary control matched disturbance",
abstract = "In this paper, we are concerned with the boundary feedback stabilization of a cascade of heat PDE-ODE system with Dirichlet/Neumann interconnection and with the external disturbance flowing the control end. In order to deal with the disturbance, the sliding model control (SMC) is integrated with the backstepping approach, where the disturbance is supposed to be bounded only. The existence and uniqueness of the solution for the closed-loop system are proved, and the monotonicity of the {"}reaching condition{"} is presented without differentiation of the sliding mode function, for which it may not always exist for the weak solution of the closed-loop system. Finally the numerical simulations validate the effectiveness of this method for the system with periodic and normal random disturbances respectively.",
keywords = "Backstepping, Boundary control, Cascade systems, Disturbance rejection, Sliding mode control",
author = "Wang, {Jun Min} and Liu, {Jun Jun} and Beibei Ren and Jinhao Chen",
note = "Funding Information: Jun-Min Wang received his B.S. degree in Mathematics from Shanxi University in 1995, and M.S. degree in Applied Mathematics from Bering Institute of Technology in 1998, respectively, and Ph.D. degree in Applied Mathematics from the University of Hong Kong in 2004. From 1998 to 2000, he worked as a teaching assistant at the Beijing Institute of Technology. He was a postdoctoral fellow at the University of the Witwatersrand, South Africa from 2004 to 2006. From 2006 to 2009 he was an associate professor at the Beijing Institute of Technology. Since 2009, he has been with Beijing Institute of Technology as a full professor in Applied Mathematics. His research interests focus on the control theory of distributed parameter systems. Dr. Wang is the recipient for New Century Excellent Talents Program from Ministry of Higher Education of China (2007). Funding Information: This work was supported by the National Natural Science Foundation of China (No. 61273130 ). The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Miroslav Krstic under the direction of Editor Xiaobo Tan. Publisher Copyright: {\textcopyright} 2014 Elsevier. Ltd All rights reserved.",
year = "2015",
month = feb,
day = "1",
doi = "10.1016/j.automatica.2014.10.117",
language = "English",
volume = "52",
pages = "23--34",
journal = "Automatica",
issn = "0005-1098",
}