Road Map for Sliding Mode Control Design

Vadim Utkin graduated from Moscow Power Institute (Dipl. Eng.) and received PhD and Doctor of Science degrees from the Institute of Control Sciences (Moscow, Russia). He worked at the Institute of Control Sciences from 1960 to 1994, and in 1973 was appointed as Head of the Discontinuous Control Systems Laboratory. Currently he is a professor at Ohio State University. Professor Utkin is one of the originators of the concepts of variable structure systems and sliding mode control. His application interests are control of power converters and electric drives, robotics, and automotive control. He is the author or co-author of five books and 350 papers.Alexander Poznyak graduated from Moscow Physical Technical Institute (MPhTI) in 1970. He earned PhD and Doctor of Science degrees from the Institute of Control Sciences of the Russian Academy of Sciences in 1978 and 1989, respectively. From 1973 to 1993 he served first as a researcher and then as leading researcher at this institute, before accepting a post as full professor (3-F) at the Center for Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV-IPN) in Mexico, where for 8 years he was head of the Automatic Control Department. He has been the supervisor for 43 PhD theses. He has published more than 240 papers in different international journals and 14 books. His areas of interest are robust nonlinear deterministic and stochastic control, identification theory, Markov processes, and game theory with economics applications. Yury Orlov is a Professor in the Electronics and Telecommunication Department, Scientific Research and Advanced Studies Center of Ensenada, Mexico. His research interests lie in the analysis and synthesis of discontinuous as well as time delay and distributed parameter systems. He has authored or co-authored about 250 journal and conference papers in the above areas as well as five monographs. He is an Associate Editor of IEEE Transactions on Control Systems Technology, of the International Journal of Robust and Nonlinear Control, and of the IMA Journal of Mathematical Control and Information. Andrey Polyakov received his PhD in Systems Analysis and Control from Voronezh State University in 2005. Until 2010 he was an Associate Professor with this university. In 2007–8, Dr. Polyakov worked at CINVESTAV-PIN in Mexico. From 2010 to 2013 he was a lead researcher of the Institute of Control Sciences of the Russian Academy of Sciences, and he then joined INRIA, Lille, France. His main research interests include robust and nonlinear control. He has authored or co-authored more than 150 papers.

“This book surveys the basic ideas of sliding mode control (SMC) theory. The main design principles are discussed and investigated, and their application to a wide range of problems is analyzed. The authors explicitly recognize that the scientific arsenal accumulated in the theory of SMC during more than 50 years offers such a wide range of both problem statements and solution methods that any attempt to prepare a state-of-the-art survey paper would hardly be successful.” (Maria Letizia Corradini, Mathematical Reviews, June, 2022)

• 1 Introduction.- 2 Mathematical Methods.- 3 Design Principles.- 4. Lyapunov stability tools for sliding modes.- 5 SM observers.- 6 Chattering Problem.- 7 High Order Sliding Mode Control.- 8 Discrete-Time Systems.- 9 Adaptive SMC.- 10 SMC in Infinite-dimensional Systems.- 11 Open Problems in SMC.- 12 Conclusions.