This book is about algebraic and differential methods, as well as fractional calculus, applied to diagnose and reject faults in nonlinear systems, which are of integer or fractional order. This represents an extension of a very important and widely studied problem in control theory, namely fault diagnosis and rejection (using differential algebraic approaches), to systems presenting fractional dynamics, i.e. systems whose dynamics are represented by derivatives and integrals of non-integer order.

The authors offer a thorough overview devoted to fault diagnosis and fault-tolerant control applied to fractional-order and integer-order dynamical systems, and they introduce new methodologies for control and observation described by fractional and integer models, together with successful simulations and real-time applications. The basic concepts and tools of mathematics required to understand the methodologies proposed are all clearly introduced and explained. Consequently, thebook is useful as supplementary reading in courses of applied mathematics and nonlinear control theory.

This book is meant for engineers, mathematicians, physicists and, in general, to researchers and postgraduate students in diverse areas who have a minimum knowledge of calculus. It also contains advanced topics for researchers and professionals interested in the area of states and faults estimation.

Autorentext

Rafael Martínez-Guerra earned his Ph.D. degree from Metropolitan Autonomous University (UAM) in 1996. Currently, he is a researcher at the Automatic Control Department of the Center for Research and Advanced Studies (CINVESTAV IPN) and member of the National System of Researchers (SNI) since 1992. He is author and co-author of more than 80 papers in international journals and more than 130 contributions in international conference and proceedings. He is co-author of 7 books. His research interests are in the areas of nonlinear systems, differential geometric and differential algebraic methods, fractional nonlinear observers, fractional fault detection and diagnosis, secure communications, fractional synchronization and chaos. Fidel Meléndez-Vázquez obtained the M.Eng. degree at the National Polytechnic Institute (IPN) and the Ph.D. degree in Science at the Center for Research and Advanced Studies (CINVESTAV IPN), in Mexico City, where his research focused on fault diagnosis and rejection in integer and fractional-order systems. Currently, he is a Postdoctoral Assistant Researcher at the Universidad Iberoamericana in Mexico City, where he works on the theory and applications of fractional calculus. He has recently obtained the Appointment as Candidate in the National System of Researchers (SNI), awarded by the National Council of Science and Technology (CONACYT) from Mexico.

Iván Trejo-Zúñiga is Fulltime Professor in mechatronics at the Technological University of San Juan del Rio, Querétaro, Mexico. He obtained his Ph.D. in Automatic Control from the Center for Research and Advanced Studies (CINVESTAV IPN). He is a member of the National System of Researchers (SNI) and conducts research on topics such as fault diagnosis, fault-tolerant control for integer and fractional-order systems, robust control, fractional differentiators and observers for dynamical systems.

Inhalt

Overview.- Fundamentals of differential algebra.- Fault diagnosis by means of invariant observer.- Multi-fault tolerant control in integer-order systems.- Fundamentals of fractional calculus and fractional dynamical systems.- Observer-based fault diagnosis for fractional order nonlinear systems.- Multi-fault-tolerant control in fractional-order systems.- Fractional-order controller based on a robust Pi observer for uncertain fractional-order systems.- Appendix.