This book acquaints readers with recent developments in dynamical systems theory and its applications, with a strong focus on the control and estimation of nonlinear systems.

Several algorithms are proposed and worked out for a set of model systems, in particular so-called input-affine or bilinear systems, which can serve to approximate a wide class of nonlinear control systems. These can either take the form of state space models or be represented by an input-output equation.

The approach taken here further highlights the role of modern mathematical and conceptual tools, including differential algebraic theory, observer design for nonlinear systems and generalized canonical forms.

Introduces novel approaches to nonlinear control systems Self-contained presentation suitable also for newcomers to the field Contains many worked examples

Autorentext

Rafael Martínez-Guerra obtained the B.Sc. degree in Physics and Mathematics from the National Polytechnic Institute (IPN), Mexico City (Mexico) and the M.Sc. degree in Automatic Control from CINVESTAV-IPN (Center for Research and Advanced Studies of IPN), Mexico City. He also got a M.Sc. degree in Mathematics and Automatic from Ecole des Mines, Paris (France) and earned his Ph.D. Degree from the Universidad Autónoma Metropolitana in 1996. Currently, he is a Researcher at the Automatic Control Department of the CINVESTAV-IPN and a Member of the National System Researchers since 1992 (Level 3, now). He is author and co-author of more than 90 papers in international journals and more than 140 contributions in international conference proceedings. He is co-author of 9 books. His main 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. Juan Pablo Flores-Flores obtained the B.Sc. degree as Aerospace Engineer from the National Polytechnic Institute (IPN) and the M.Sc. degree in Control Theory from the Automatic Control Department of CINVESTAV-IPN (Center for Research and Advanced Studies of IPN). He earned his Ph.D. from the same institution in 2022. He is co-author of the book Encryption and Decryption Algorithms for Plain Text and Images using Fractional Calculus (Springer, 2023) and has published research papers in international journals and conference proceedings. His main research interests are nonlinear systems, differential algebra methods, partial differential equations systems and integer and fractional synchronization of nonlinear systems.

Inhalt

Preface.- Analysis of input-affine nonlinear processes.- Basic Definitions of Differential Algebras.- Algebraic Observability Condition for Nonlinear systems and External behaviour.- Generalized Observability Canonical Forms.- Observer Synthesis.- Tracking and Stabilization Problems.- Parametric and State Estimation.- Observer synthesis for a more general class of Nonlinear Systems.- A Separation Principle for Nonlinear Systems.- Some uncommon observers with interesting applications.- Appendix A Singularity Treatment.- Appendix B Some properties for Nonlinear Systems.