Discrete-Time Neural Observers: Analysis and Applications presents recent advances in the theory of neural state estimation for discrete-time unknown nonlinear systems with multiple inputs and outputs. The book includes rigorous mathematical analyses, based on the Lyapunov approach, that guarantee their properties. In addition, for each chapter, simulation results are included to verify the successful performance of the corresponding proposed schemes. In order to complete the treatment of these schemes, the authors also present simulation and experimental results related to their application in meaningful areas, such as electric three phase induction motors and anaerobic process, which show the applicability of such designs. The proposed schemes can be employed for different applications beyond those presented. The book presents solutions for the state estimation problem of unknown nonlinear systems based on two schemes. For the first one, a full state estimation problem is considered; the second one considers the reduced order case with, and without, the presence of unknown delays. Both schemes are developed in discrete-time using recurrent high order neural networks in order to design the neural observers, and the online training of the respective neural networks is performed by Kalman Filtering. - Presents online learning for Recurrent High Order Neural Networks (RHONN) using the Extended Kalman Filter (EKF) algorithm - Contains full and reduced order neural observers for discrete-time unknown nonlinear systems, with and without delays - Includes rigorous analyses of the proposed schemes, including the nonlinear system, the respective observer, and the Kalman filter learning - Covers real-time implementation and simulation results for all the proposed schemes to meaningful applications

Alma Y. Alanis, was born in Durango, Durango, Mexico, in 1980. She received the B. Sc. degree from Instituto Tecnologico de Durango (ITD), Durango Campus, Durango, Durango, in 2002, the M.Sc. and the Ph.D. degrees in electrical engineering from the Advanced Studies and Research Center of the National Polytechnic Institute (CINVESTAV-IPN), Guadalajara Campus, Mexico, in 2004 and 2007, respectively. Since 2008 she has been with University of Guadalajara, where she is currently a Chair Professor in the Department of Computer Science. She is also member of the Mexican National Research System (SNI-2) and member of the Mexican Academy of Sciences. She has published papers in recognized International Journals and Conferences, besides four International Books. She is a Senior Member of the IEEE and Subject and Associated Editor of the Journal of Franklin Institute (Elsevier) and Intelligent Automation and Soft Computing (Taylor and Francis), moreover she is currently serving on a number of IEEE and IFAC Conference Organizing Committees. In 2013, she receives the grant for women in science by L'Oreal-UNESCOAMC- CONACYT-CONALMEX. In 2015, she receives the Research Award Marcos Moshinsky. Since 2008 she is member for the Accredited Assessors record RCEACONACYT, evaluating a wide range of national research projects, besides she has belonged to important project evaluation committees of national and international research projects. Her research interest centers on neural control, backstepping control, block control, and their applications to electrical machines, power systems and robotics.

Discrete-Time Neural Observers: Analysis and Applications presents recent advances in the theory of neural state estimation for discrete-time unknown nonlinear systems with multiple inputs and outputs. The book includes rigorous mathematical analyses, based on the Lyapunov approach, that guarantee their properties. In addition, for each chapter, simulation results are included to verify the successful performance of the corresponding proposed schemes.

In order to complete the treatment of these schemes, the authors also present simulation and experimental results related to their application in meaningful areas, such as electric three phase induction motors and anaerobic process, which show the applicability of such designs. The proposed schemes can be employed for different applications beyond those presented.

The book presents solutions for the state estimation problem of unknown nonlinear systems based on two schemes. For the first one, a full state estimation problem is considered; the second one considers the reduced order case with, and without, the presence of unknown delays. Both schemes are developed in discrete-time using recurrent high order neural networks in order to design the neural observers, and the online training of the respective neural networks is performed by Kalman Filtering.

• Presents online learning for Recurrent High Order Neural Networks (RHONN) using the Extended Kalman Filter (EKF) algorithm
• Contains full and reduced order neural observers for discrete-time unknown nonlinear systems, with and without delays
• Includes rigorous analyses of the proposed schemes, including the nonlinear system, the respective observer, and the Kalman filter learning
• Covers real-time implementation and simulation results for all the proposed schemes to meaningful applications

1. Introduction 2. Mathematical Preliminaries 3. Full order neural observers 4. Reduced order neural observers 5. Neural observers with unknown time delays 6. Final Remarks