The authors present a completely new and highly application-oriented field of nonlinear analysis. The work covers the theory of non-smooth input-output systems and presents various methods to non-standard applications in mathematics and physics. A particular focus lies on hysteresis and relay phenomena, electric circuits with diode nonlinearities, and biological systems with constraints.
Many of the non-smooth, non-linear phenomena covered in this well-balanced book are of vital importance in almost any field of engineering. Contributors from all over the world ensure that no one area’s slant on the subjects predominates.
Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics reports some of the latest research on modeling, identification and adaptive control for systems with nonsmooth dynamics (e.g., backlash, dead zone, friction, saturation, etc). The authors present recent research results for the modelling and control designs of uncertain systems with nonsmooth dynamics, such as friction, dead-zone, saturation and hysteresis, etc., with particular applications in servo systems. The book is organized into 19 chapters, distributed in five parts concerning the four types of nonsmooth characteristics, namely friction, dead-zone, saturation and hysteresis, respectively. Practical experiments are also included to validate and exemplify the proposed approaches. This valuable resource can help both researchers and practitioners to learn and understand nonlinear adaptive control designs. Academics, engineers and graduate students in the fields of electrical engineering, control systems, mechanical engineering, applied mathematics and computer science can benefit from the book. It can be also used as a reference book on adaptive control for servo systems for students with some background in control engineering. - Explains the latest research outputs on modeling, identification and adaptive control for systems with nonsmooth dynamics - Provides practical application and experimental results for robotic systems, and servo motors
The book combines vehicle systems dynamics with the latest theoretical developments in dynamics of non-smooth systems and numerical analysis of differential-algebraic dynamical systems with discontinuities. These two fields are fundamental for the modelling and analysis of vehicle dynamical sytems. The results are also applicable to other non-smooth dynamical systems.
Thank you for opening the second edition of this monograph, which is devoted to the study of a class of nonsmooth dynamical systems of the general form: ::i; = g(x,u) (0. 1) f(x, t) 2: 0 where x E JRn is the system's state vector, u E JRm is the vector of inputs, and the function f (-, . ) represents a unilateral constraint that is imposed on the state. More precisely, we shall restrict ourselves to a subclass of such systems, namely mechanical systems subject to unilateral constraints on the position, whose dynamical equations may be in a first instance written as: ii= g(q,q,u) (0. 2) f(q, t) 2: 0 where q E JRn is the vector of generalized coordinates of the system and u is an in put (or controller) that generally involves a state feedback loop, i. e. u= u(q, q, t, z), with z= Z(z, q, q, t) when the controller is a dynamic state feedback. Mechanical systems composed of rigid bodies interacting fall into this subclass. A general prop erty of systems as in (0. 1) and (0. 2) is that their solutions are nonsmooth (with respect to time): Nonsmoothness arises primarily from the occurence of impacts (or collisions, or percussions) in the dynamical behaviour, when the trajectories attain the surface f(x, t) = O. They are necessary to keep the trajectories within the subspace = {x : f(x, t) 2: O} of the system's state space.
Nonsmooth Lyapunov Analysis in Finite and Infinite Dimensions provides helpful tools for the treatment of a broad class of dynamical systems that are governed, not only by ordinary differential equations but also by partial and functional differential equations. Existing Lyapunov constructions are extended to discontinuous systems—those with variable structure and impact—by the involvement of nonsmooth Lyapunov functions. The general theoretical presentation is illustrated by control-related applications; the nonsmooth Lyapunov construction is particularly applied to the tuning of sliding-mode controllers in the presence of mismatched disturbances and to orbital stabilization of the bipedal gate. The nonsmooth construction is readily extendible to the control and identification of distributed-parameter and time-delay systems. The first part of the book outlines the relevant fundamentals of benchmark models and mathematical basics. The second concentrates on the construction of nonsmooth Lyapunov functions. Part III covers design and applications material. This book will benefit the academic research and graduate student interested in the mathematics of Lyapunov equations and variable-structure control, stability analysis and robust feedback design for discontinuous systems. It will also serve the practitioner working with applications of such systems. The reader should have some knowledge of dynamical systems theory, but no background in discontinuous systems is required—they are thoroughly introduced in both finite- and infinite-dimensional settings.
System Modeling and Optimization is an indispensable reference for anyone interested in the recent advances in these two disciplines. The book collects, for the first time, selected articles from the 21st and most recent IFIP TC 7 conference in Sophia Antipolis, France. Applied mathematicians and computer scientists can attest to the ever-growing influence of these two subjects. The practical applications of system modeling and optimization can be seen in a number of fields: environmental science, transport and telecommunications, image analysis, free boundary problems, bioscience, and non-cylindrical evolution control, to name just a few. New developments in each of these fields have contributed to a more complex understanding of both system modeling and optimization. Editors John Cagnol and Jean-Paul Zolésio, chairs of the conference, have assembled System Modeling and Optimization to present the most up-to-date developments to professionals and academics alike.
This edited book contains selected papers presented at the Louisiana Conference on Mathematical Control Theory (MCT'03), which brought together over 35 prominent world experts in mathematical control theory and its applications. The book forms a well-integrated exploration of those areas of mathematical control theory in which nonsmooth analysis is having a major impact. These include necessary and sufficient conditions in optimal control, Lyapunov characterizations of stability, input-to-state stability, the construction of feedback mechanisms, viscosity solutions of Hamilton-Jacobi equations, invariance, approximation theory, impulsive systems, computational issues for nonlinear systems, and other topics of interest to mathematicians and control engineers. The book has a strong interdisciplinary component and was designed to facilitate the interaction between leading mathematical experts in nonsmooth analysis and engineers who are increasingly using nonsmooth analytic tools.
This book presents the synthesis and analysis of fuzzy controllers and its application to a class of mechanical systems. It mainly focuses on the use of type-2 fuzzy controllers to account for disturbances known as hard or nonsmooth nonlinearities. The book, which summarizes the authors’ research on type-2 fuzzy logic and control of mechanical systems, presents models, simulation and experiments towards the control of servomotors with dead-zone and Coulomb friction, and the control of both wheeled mobile robots and a biped robot. Closed-loop systems are analyzed in the framework of smooth and nonsmooth Lyapunov functions.
