Bøger i Systems & Control: Foundations & Applications serien

This contributed volume aims to build the foundation of a framework for computationally aware algorithmic design for cyber-physical systems (CPSs), focusing on approaches that take computation into account at the design stage to address their impact on performance and safety. It demonstrates how novel techniques may emerge from the combination of formal methods, model predictive control, distributed optimization, data-driven methods, reconfigurable/adaptive methods, and information-theoretic techniques.Chapters are written by both researchers and practitioners and cover such topics as analysis and design of uncertain CPSs, cooperative and non-cooperative paradigms for handling complexity in large scale CPSs,task-relevant environment abstractions for autonomous systems based on information theory,information flow in event-based stabilization of CPSs,set-valued model predictive control, andautomated synthesis of certifiable controllers for CPSs.State-of-the-art applications and case studies are provided throughout with a special focus on intelligent transportation systems and autonomous vehicles.Graduate students and researchers with an interest in CPS verification and control will find this volume to be a valuable resource in their work. It will also appeal to researchers from disciplines other than control, such as computer science, operations research, applied mathematics, and robotics.

Unifying two decades of research, this book is the first to establish a comprehensive foundation for a systematic analysis and design of linear systems with general state and input constraints. For such systems, which can be used as models for most nonlinear systems, the issues of stability, controller design, additonal constraints, and satisfactory performance are addressed.The book is an excellent reference for practicing engineers, graduate students, and researchers in control systems theory and design. It may also serve as an advanced graduate text for a course or a seminar in nonlinear control systems theory and design in applied mathematics or engineering departments. Minimal prerequisites include a first graduate course in state-space methods as well as a first course in control systems design.

The book deals with several closely related topics concerning approxima- tions and perturbations of random processes and their applications to some important and fascinating classes of problems in the analysis and design of stochastic control systems and nonlinear filters. The basic mathematical methods which are used and developed are those of the theory of weak con- vergence. The techniques are quite powerful for getting weak convergence or functional limit theorems for broad classes of problems and many of the techniques are new. The original need for some of the techniques which are developed here arose in connection with our study of the particular applica- tions in this book, and related problems of approximation in control theory, but it will be clear that they have numerous applications elsewhere in weak convergence and process approximation theory. The book is a continuation of the author's long term interest in problems of the approximation of stochastic processes and its applications to problems arising in control and communication theory and related areas. In fact, the techniques used here can be fruitfully applied to many other areas. The basic random processes of interest can be described by solutions to either (multiple time scale) Ito differential equations driven by wide band or state dependent wide band noise or which are singularly perturbed. They might be controlled or not, and their state values might be fully observable or not (e. g. , as in the nonlinear filtering problem).

This book is about the theory of system representations. The systems that are considered are linear, time-invariant, deterministic and finite- dimensional. The observation that some representations are more suitable for handling a particular problem than others motivates the study of rep- resentations. In modeling a system, a representation often arises naturally from certain laws that underlie the system. In its most general form the representation then consists of dynamical equations for the system compo- nents and of constraint equations reflecting the connection between these components. Depending on the particular problem that is to be inves- tigated, it will sometimes be useful to rewrite the equations, that is, to transform the representation. For this reason it is of special importance to derive transformations that enable one to switch from one representation to another. A new approach of the past decade has been the so-called "e;behavioral ap- proach"e; introduced by Willems. One of the main features of the behavioral approach is that it is well suited for modeling the interconnection of sys- tems. It is for this reason that the behavioral approach is a natural choice in the context of modeling. In this book we adopt the behavioral approach: we define a system as a "e;behavior"e; , that is, a set of trajectories whose math- ematical representation by means of differential or difference equations is nonunique. An aspect of this approach that is important in the context of representation theory is the fact that a natural type of equivalence arises.

Infinite dimensional systems can be used to describe many phenomena in the real world. As is well known, heat conduction, properties of elastic- plastic material, fluid dynamics, diffusion-reaction processes, etc., all lie within this area. The object that we are studying (temperature, displace- ment, concentration, velocity, etc.) is usually referred to as the state. We are interested in the case where the state satisfies proper differential equa- tions that are derived from certain physical laws, such as Newton's law, Fourier's law etc. The space in which the state exists is called the state space, and the equation that the state satisfies is called the state equation. By an infinite dimensional system we mean one whose corresponding state space is infinite dimensional. In particular, we are interested in the case where the state equation is one of the following types: partial differential equation, functional differential equation, integro-differential equation, or abstract evolution equation. The case in which the state equation is being a stochastic differential equation is also an infinite dimensional problem, but we will not discuss such a case in this book.

The engineering objective of high performance control using the tools of optimal control theory, robust control theory, and adaptive control theory is more achiev- able now than ever before, and the need has never been greater. Of course, when we use the term high peiformance control we are thinking of achieving this in the real world with all its complexity, uncertainty and variability. Since we do not expect to always achieve our desires, a more complete title for this book could be "e;Towards High Performance Control"e;. To illustrate our task, consider as an example a disk drive tracking system for a portable computer. The better the controller performance in the presence of eccen- tricity uncertainties and external disturbances, such as vibrations when operated in a moving vehicle, the more tracks can be used on the disk and the more memory it has. Many systems today are control system limited and the quest is for high performance in the real world.

The analysis, processing, evolution, optimization and/or regulation, and control of shapes and images appear naturally in engineering (shape optimization, image processing, visual control), numerical analysis (interval analysis), physics (front propagation), biological morphogenesis, population dynamics (migrations), and dynamic economic theory.   These problems are currently studied with tools forged out of differential geometry and functional analysis, thus requiring shapes and images to be smooth.  However, shapes and images are basically sets, most often not smooth.  J.-P. Aubin thus constructs another vision, where shapes and images are just any compact set.  Hence their evolution -- which requires a kind of differential calculus -- must be studied in the metric space of compact subsets.  Despite the loss of linearity, one can transfer most of the basic results of differential calculus and differential equations in vector spaces to mutational calculus and mutational equations in any mutational space, including naturally the space of nonempty compact subsets.   "e;Mutational and Morphological Analysis"e; offers a structure that embraces and integrates the various approaches, including shape optimization and mathematical morphology.   Scientists and graduate students will find here other powerful mathematical tools for studying problems dealing with shapes and images arising in so many fields.

Loosely speaking, adaptive systems are designed to deal with, to adapt to, chang- ing environmental conditions whilst maintaining performance objectives. Over the years, the theory of adaptive systems evolved from relatively simple and intuitive concepts to a complex multifaceted theory dealing with stochastic, nonlinear and infinite dimensional systems. This book provides a first introduction to the theory of adaptive systems. The book grew out of a graduate course that the authors taught several times in Australia, Belgium, and The Netherlands for students with an engineering and/or mathemat- ics background. When we taught the course for the first time, we felt that there was a need for a textbook that would introduce the reader to the main aspects of adaptation with emphasis on clarity of presentation and precision rather than on comprehensiveness. The present book tries to serve this need. We expect that the reader will have taken a basic course in linear algebra and mul- tivariable calculus. Apart from the basic concepts borrowed from these areas of mathematics, the book is intended to be self contained.

This monograph introduces breakthrough control algorithms for partial differential equation models with moving boundaries, the study of which is known as the Stefan problem.

The common experience in solving control problems shows that optimal control as a function of time proves to be piecewise analytic, having a finite number of jumps (called switches) on any finite-time interval.

Self-Oscillations in Dynamic Systems

The second edition of this monograph describes the set-theoretic approach for the control and analysis of dynamic systems, both from a theoretical and practical standpoint.

The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme.

The beginning of the 21st century can be characterized as the" time-delay boom" leading to numerous important results. This book is based on the course "Introduction to time-delay systems" for graduate students in Engineering and Applied Mathematics that the author taught in Tel Aviv University in 2011-2012 and 2012-2013 academic years.

Attractive Ellipsoids in Robust Control

Stability of Dynamical Systems