Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild conditions on the system nonlinearities, setting it apart from other techniques such as those – well-known – based on differential geometry. The authors cover many aspects of nonlinear systems including stability theory, control design and extensions to distributed parameter systems. Many of the classical and modern control design methods which can be applied to linear, time-varying systems can be extended to nonlinear systems by this technique. The implementation of the control is therefore simple and can be done with well-established classical methods. Many aspects of nonlinear systems, such as spectral theory which is important for the generalisation of frequency domain methods, can be approached by this method.

The aim of this book is to propose a new approach to analysis and control of linear time-varying systems. These systems are defined in an intrinsic way, i.e., not by a particular representation (e.g., a transfer matrix or a state-space form) but as they are actually. The system equations, derived, e.g., from the laws of physics, are gathered to form an intrinsic mathematical object, namely a finitely presented module over a ring of operators. This is strongly connected with the engineering point of view, according to which a system is not a specific set of equations but an object of the material world which can be described by equivalent sets of equations. This viewpoint makes it possible to formulate and solve efficiently several key problems of the theory of control in the case of linear time-varying systems. The solutions are based on algebraic analysis. This book, written for engineers, is also useful for mathematicians since it shows how algebraic analysis can be applied to solve engineering problems. Henri Bourlès is a Professor and holds the industrial automation chair at the Conservatoire national des arts et métiers in France. He has been teaching automation for over 20 years in engineering and graduate schools. Bogdan Marinescu is currently research engineer at the French Transmission System Operator (RTE) and Associate Professor at SATIE-Ecole Normale Supérieure de Cachan.

The underlying theory on which much modern robust and nonlinear control is based can be difficult to grasp. This volume is a collection of lecture notes presented by experts in advanced control engineering. The book is designed to provide a better grounding in the theory underlying several important areas of control. It is hoped the book will help the reader to apply otherwise abstruse ideas of nonlinear control in a variety of real systems.

This research monograph summarizes solutions to reconfigurable fault-tolerant control problems for nonlinear dynamical systems that are based on the fault-hiding principle. It emphasizes but is not limited to complete actuator and sensor failures. In the first part, the monograph starts with a broad introduction of the control reconfiguration problems and objectives as well as summaries and explanations of solutions for linear dynamical systems. The solution is always a reconfiguration block, which consists of linear virtual actuators in the case of actuator faults and linear virtual sensors in the case of sensor faults. The main advantage of the fault-hiding concept is the reusability of the nominal controller, which remains in the loop as an active system while the virtual actuator and sensor adapt the control input and the measured output to the fault scenario. The second and third parts extend virtual actuators and virtual sensors towards the classes of Hammerstein-Wiener systems and piecewise affine systems. The main analyses concern stability recovery, setpoint tracking recovery, and performance recovery as reconfiguration objectives. The fourth part concludes the monograph with descriptions of practical implementations and case studies. The book is primarily intended for active researchers and practicing engineers in the field of fault-tolerant control. Due to many running examples it is also suitable for interested graduate students.

The theory of linear functional observers, which is the subject of this book, is increasingly becoming a popular researched topic because of the many advantages it presents in state observation and control system design. This book presents recent information on the current state of the art research in this field. This book will serve as a useful reference to researchers in this area of research to understand the fundamental concepts relevant to the theory of functional observers and to gather most recent advancements in the field. This book is useful to academics and postgraduate students researching into the theory of linear functional observers. This book can also be useful for specialized final year undergraduate courses in control systems engineering and applied mathematics with a research focus.

This monograph covers some selected problems of positive fractional 1D and 2D linear systems. It is an extended and modified English version of its preceding Polish edition published by Technical University of Bialystok in 2009. This book is based on the lectures delivered by the author to the Ph.D. students of the Faculty of Electrical Engineering of Bialystok University of Technology and of Warsaw University of Technology and on invited lectures in several foreign universities in the last three years.

Robot Motion Control 2011 presents very recent results in robot motion and control. Forty short papers have been chosen from those presented at the sixth International Workshop on Robot Motion and Control held in Poland in June 2011. The authors of these papers have been carefully selected and represent leading institutions in this field. The following recent developments are discussed: Design of trajectory planning schemes for holonomic and nonholonomic systems with optimization of energy, torque limitations and other factors. New control algorithms for industrial robots, nonholonomic systems and legged robots. Different applications of robotic systems in industry and everyday life, like medicine, education, entertainment and others. Multiagent systems consisting of mobile and flying robots with their applications The book is suitable for graduate students of automation and robotics, informatics and management, mechatronics, electronics and production engineering systems as well as scientists and researchers working in these fields.

This book comprises a selection of the presentations made at the “Workshop on Dynamics and Control of Micro and Nanoscale Systems” held at IBM Research – Zurich, Switzerland, on the 10th and 11th of December 2009. The aim of the workshop was to bring together some of the leading researchers in the field of dynamics and control of micro- and nanoscale systems. It proved an excellent forum for discussing new ideas and approaches.

For nonlinear dynamical systems, which represent the majority of real devices, any study of stability requires the investigation of the domain of attraction of an equilibrium point, i.e. the set of initial conditions from which the trajectory of the system converges to equilibrium. Unfortunately, both estimating and attempting to control the domain of attraction are very difficult problems, because of the complex relationship of this set with the model of the system. Domain of Attraction addresses the estimation and control of the domain of attraction of equilibrium points via SOS programming, i.e. optimization techniques based on the sum of squares of polynomials (SOS) that have been recently developed and that amount to solving convex problems with linear matrix inequality constraints. A unified framework for addressing these issues is presented for in various cases depending on the nature of the nonlinear systems considered, including the cases of polynomial, non-polynomial, certain and uncertain systems. The methods proposed are illustrated various example systems such as electric circuits, mechanical devices, and nuclear plants. Domain of Attraction also deals with related problems that can be considered within the proposed framework, such as characterizing the equilibrium points and bounding the trajectories of nonlinear systems, and offers a concise and simple description of the main features of SOS programming, which can be used for general purpose in research and teaching.

The book presents the newest results of the major world research groups working in the area of Variable Structure Systems and Sliding Mode Control (VSS/SMC). The research activity of these groups is coordinated by the IEEE Technical Committee on Variable Structure Systems (VSS) and Sliding Modes (SM). The presented results include the reports of the research groups collaborating in a framework of the Unión European Union – México project of Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICyT) 93302 titled "Automatization and Monitoring of Energy Production Processes via Sliding Mode Control". The book starts with the overview of the sliding mode control concepts and algorithms that were developed and discussed in the last two decades The research papers are combined in three sections: Part I: VSS and SM Algorithms and their Analysis Part II: SMC Design Part III: Applications of VSS and SMC The book will be of interests of engineers, researchers and graduate students working in the area of the control systems design. Novel mathematical theories and engineering concepts of control systems are rigorously discussed and supported by numerous applications to practical tasks.