Alberto Isidori - Böcker

The problem of controlling the output of a system so as to achieve asymptotic tracking of prescribed trajectories and/or asymptotic re­ jection of undesired disturbances is a central problem in control the­ ory. A classical setup in which the problem was posed and success­ fully addressed - in the context of linear, time-invariant and finite dimensional systems - is the one in which the exogenous inputs, namely commands and disturbances, may range over the set of all possible trajectories ofa given autonomous linear system, commonly known as the exogeneous system or, more the exosystem. The case when the exogeneous system is a harmonic oscillator is, of course, classical. Even in this special case, the difference between state and error measurement feedback in the problem ofoutput reg­ ulation is profound. To know the initial condition of the exosystem is to know the amplitude and phase of the corresponding sinusoid. On the other hand, to solve the output regulation problem in this case with only error measurement feedback is to track, or attenu­ ate, a sinusoid ofknown frequency but with unknown amplitude and phase. This is in sharp contrast with alternative approaches, such as exact output tracking, where in lieu of the assumption that a signal is within a class of signals generated by an exogenous system, one instead assumes complete knowledge of the past, present and future time history of the trajectory to be tracked.

The world of artificial systems is reaching complexity levels that es­ cape human understanding. Researchers from many different fields are trying to understand and develop theories for complex man-made systems. The book has grown out of activities in the research program Control of Complex Systems (COSY).

Plant control systems are subject to the undesirable influence of exogenous commands and disturbances. To track and reject these the authors have designed a feedback control system based on embedding a model of them within the controller itself - the "internal model".From a review of the principles of internal-model-based feedback control design, this book moves on to expound recent enhancements to such designs and then to their implementation in systems operating under conditions of great uncertainty.The case studies presented involve control systems coping with a high degree of nonlinear behaviour. The key issues addressed in each are the design of an adaptive internal model for the specific tracking task and of stabilizing control capable of steering the tracking error to zero while keeping all internal states bounded for any arbitrarily large but bounded envelope of initial data and uncertain parameters. Nested saturated controls form the basis of novel tools for asymptotic analysis and design.

The purpose of this book is to present a self-contained and coordinated de­ scription of several design methods for nonlinear control systems, with special emphasis on the problem of achieving stability, globally or on arbitrarily large domains, in the presence of model uncertainties.

This book contains the text of the plenary lectures and the mini-courses of the European Control Conference (ECC 95) held in Rome, Italy, September 5-September 8, 1995. In particular, the book includes nine essays in which a selected number of prominent authorities present their views on some of the most recent developments in the theory and practice of control systems design and three self-contained sets of lecture notes. Some of the essays are focused on the topic of robust control. The article by J. Ackermann describes how to robustly control the rotational motions of a vehicle, to the purpose of simplifying the driver's task. The contribution by H. K wakernaak presents a detailed discussion of the requirements that performance and robustness impose on control systems design and of the symmetric roles of sensitivity and complementary sensitivity functions. The article by P. Boulet, B. A. Francis, P. C . Hughes and T. Hong describes an experimental testbed facility, called Daisy, whose dynamics emulate those of a real large flexible space structure and whose purpose is to test advanced identification and control design methods. The article of K. Glover discusses recent advances in uncertain system modeling, analysis and design, with ref­ erence to a flight control case study that has been test flown. The other essays describe advances in fundamental problems of control theory. The article by V. A. Yakubovich is a survey of certain new infinite­ horizon linear-quadratic optimization problems. The contribution by A. S.

The purpose of this book is to present a self-contained description of the fun­ damentals of the theory of nonlinear control systems, with special emphasis on the differential geometric approach.

The problem of controlling the output of a system so as to achieve asymptotic tracking of prescribed trajectories and/or asymptotic re­ jection of undesired disturbances is a central problem in control the­ ory. A classical setup in which the problem was posed and success­ fully addressed - in the context of linear, time-invariant and finite dimensional systems - is the one in which the exogenous inputs, namely commands and disturbances, may range over the set of all possible trajectories ofa given autonomous linear system, commonly known as the exogeneous system or, more the exosystem. The case when the exogeneous system is a harmonic oscillator is, of course, classical. Even in this special case, the difference between state and error measurement feedback in the problem ofoutput reg­ ulation is profound. To know the initial condition of the exosystem is to know the amplitude and phase of the corresponding sinusoid. On the other hand, to solve the output regulation problem in this case with only error measurement feedback is to track, or attenu­ ate, a sinusoid ofknown frequency but with unknown amplitude and phase. This is in sharp contrast with alternative approaches, such as exact output tracking, where in lieu of the assumption that a signal is within a class of signals generated by an exogenous system, one instead assumes complete knowledge of the past, present and future time history of the trajectory to be tracked.

This book incorporates recent advances in the design of feedback laws to the purpose of globally stabilizing nonlinear systems via state or output feedback. It is a continuation of the first volume by Alberto Isidori on Nonlinear Control Systems. Specifically this second volume will cover: *Stability analysis of interconnected nonlinear systems. The notion of Input-to-State stability and its role in analysing stability of cascade-connected or feedback-connected systems. The notion of dissipativity and its consequences (passivity and "gain"). *Robust stabilization in the case of parametric uncertainties. The case of state feedback: global or semi-global stabilization. The case of output feedback: semi-global stabilization. *Robust stabilization in the case of unstructured perturbations. Feedback design via the small-gain approach. Robust semi-global stabilization via output feedback. *Methods for asymptotic tracking, disturbance rejection and model following. Global and semi-global analysis. *Normal forms for multi-input multi-output nonlinear systems form a global point of view. Their role in feedback design.

The world of artificial systems is reaching hitherto undreamed-of levels of complexity. Surface traffic, electricity distribution, mobile communications, etc., demonstrate that problems are arising that are beyond classical scientific or engineering knowledge. In order that our ability to control such systems should not be hindered by lack of comprehension, there is an on-going effort to understand them.This book is an example of the types of approach that European researchers are using to tackle problems derived from systems' complexity. It has grown out of activities in the Control of Complex Systems (COSY) research program the goals of which are to promote multi-disciplinary activity leading to a deeper understanding and further development of control technologies for complex systems and if possible, to develop the theory underlying such systems. The material in this book represents a selection of the results of the COSY program and is organised as a collection of essays of varying nature: surveys of essential areas, discussion of specific problems, case studies, and benchmark problems.Topics covered include:Modelling complex physical systems;Passivity-based control of non-linear systems;Aspects of fault identification and fault tolerance;Control design;Learning control;Satellite attitude control.Complex systems appear in many different fields and for this reason this book should be of interest to scientists, researchers and industrial engineers with a broad spectrum of experience.

Control of nonlinear systems, one of the most active research areas in control theory, has always been a domain of natural convergence of research interests in applied mathematics and control engineering. The theory has developed from the early phase of its history, when the basic tool was essentially only the Lyapunov second method, to the present day, where the mathematics ranges from differential geometry, calculus of variations, ordinary and partial differential equations, functional analysis, abstract algebra and stochastic processes, while the applications to advanced engineering design span a wide variety of topics, which include nonlinear controllability and observability, optimal control, state estimation, stability and stabilization, feedback equivalence, motion planning, noninteracting control, disturbance attenuation, asymptotic tracking. The reader will find in the book methods and results which cover a wide variety of problems: starting from pure mathematics (like recent fundamental results on (non)analycity of small balls and the distance function), through its applications to all just mentioned topics of nonlinear control, up to industrial applications of nonlinear control algorithms.

Control of nonlinear systems, one of the most active research areas in control theory, has always been a domain of natural convergence of research interests in applied mathematics and control engineering. The theory has developed from the early phase of its history, when the basic tool was essentially only the Lyapunov second method, to the present day, where the mathematics ranges from differential geometry, calculus of variations, ordinary and partial differential equations, functional analysis, abstract algebra and stochastic processes, while the applications to advanced engineering design span a wide variety of topics, which include nonlinear controllability and observability, optimal control, state estimation, stability and stabilization, feedback equivalence, motion planning, noninteracting control, disturbance attenuation, asymptotic tracking. The reader will find in the book methods and results which cover a wide variety of problems: starting from pure mathematics (like recent fundamental results on (non)analycity of small balls and the distance function), through its applications to all just mentioned topics of nonlinear control, up to industrial applications of nonlinear control algorithms.

A typical plant control system will be subject to the undesirable influence of exogenous commands and disturbances. In order to track and reject these Professor Isidori and his co-authors have designed a feedback control system based on embedding a model of these disturbances within the controller itself - the so-called "internal model". Beginning with a review of the fundamental principles of internal-model-based feedback control design, Robust Autonomous Guidance moves on to expound recent enhancements to such designs and then to their implementation in systems operating under conditions of great uncertainty. The three case studies presented: attitude control of a low-Earth-orbit satellite and the landing of fixed- and rotary-winged aircraft on a ship involve control systems coping with a high degree of nonlinear behaviour. The key issues addressed in each case study are the design of an adaptive internal model for the specific tracking task and of stabilizing control capable of steering the tracking error to zero while keeping all internal states bounded for any arbitrarily large but bounded envelope of initial data and uncertain parameters.Nested saturated controls form the basis of novel tools for asymptotic analysis and design. Robust Autonomous Guidance will be of great interest to academic and industrial researchers working with nonlinear control systems and to engineers involved in the design of aerospatial guidance systems. It will also be a useful reference for graduate students working with non-linear systems.

This book focuses on methods that relate, in one form or another, to the “small-gain theorem”. It is aimed at readers who are interested in learning methods for the design of feedback laws for linear and nonlinear multivariable systems in the presence of model uncertainties. With worked examples throughout, it includes both introductory material and   more advanced topics.Divided into two parts, the first covers relevant aspects of linear-systems theory, the second, nonlinear theory. In order to deepen readers’ understanding, simpler single-input–single-output systems generally precede treatment of more complex multi-input–multi-output (MIMO) systems and linear systems precede nonlinear systems. This approach is used throughout, including in the final chapters, which explain the latest advanced ideas governing the stabilization, regulation, and tracking of nonlinear MIMO systems. Two major design problems are considered, both in the presence of model uncertainties: asymptotic stabilization with a “guaranteed region of attraction” of a given equilibrium point and asymptotic rejection of the effect of exogenous (disturbance) inputs on selected regulated outputs.Much of the introductory instructional material in this book has been developed for teaching students, while the final coverage of nonlinear MIMO systems offers readers a first coordinated treatment of completely novel results. The worked examples presented provide the instructor with ready-to-use material to help students to understand the mathematical theory.Readers should be familiar with the fundamentals of linear-systems and control theory. This book is a valuable resource for students following postgraduate programs in systems and control, as well as engineers working on the control of robotic, mechatronic and power systems.

In order to deepen readers’ understanding, simpler single-input–single-output systems generally precede treatment of more complex multi-input–multi-output (MIMO) systems and linear systems precede nonlinear systems.

This text focuses on the design and analysis of nonlinear control systems. It considers recent research results and techniques and gives examples from mechanical, electrical and aerospace engineering. The book employs a rigorous mathematical formulation of control problems and respective methods of solution. The book's two appendices outline the most important concepts of differential geometry.