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This book is about algebraic and differential methods, as well as
fractional calculus, applied to diagnose and reject faults in
nonlinear systems, which are of integer or fractional order. This
represents an extension of a very important and widely studied
problem in control theory, namely fault diagnosis and rejection
(using differential algebraic approaches), to systems presenting
fractional dynamics, i.e. systems whose dynamics are represented by
derivatives and integrals of non-integer order. The authors offer a
thorough overview devoted to fault diagnosis and fault-tolerant
control applied to fractional-order and integer-order dynamical
systems, and they introduce new methodologies for control and
observation described by fractional and integer models, together
with successful simulations and real-time applications. The basic
concepts and tools of mathematics required to understand the
methodologies proposed are all clearly introduced and explained.
Consequently, the book is useful as supplementary reading in
courses of applied mathematics and nonlinear control theory. This
book is meant for engineers, mathematicians, physicists and, in
general, to researchers and postgraduate students in diverse areas
who have a minimum knowledge of calculus. It also contains advanced
topics for researchers and professionals interested in the area of
states and faults estimation.
This book is about algebraic and differential methods, as well as
fractional calculus, applied to diagnose and reject faults in
nonlinear systems, which are of integer or fractional order. This
represents an extension of a very important and widely studied
problem in control theory, namely fault diagnosis and rejection
(using differential algebraic approaches), to systems presenting
fractional dynamics, i.e. systems whose dynamics are represented by
derivatives and integrals of non-integer order. The authors offer a
thorough overview devoted to fault diagnosis and fault-tolerant
control applied to fractional-order and integer-order dynamical
systems, and they introduce new methodologies for control and
observation described by fractional and integer models, together
with successful simulations and real-time applications. The basic
concepts and tools of mathematics required to understand the
methodologies proposed are all clearly introduced and explained.
Consequently, the book is useful as supplementary reading in
courses of applied mathematics and nonlinear control theory. This
book is meant for engineers, mathematicians, physicists and, in
general, to researchers and postgraduate students in diverse areas
who have a minimum knowledge of calculus. It also contains advanced
topics for researchers and professionals interested in the area of
states and faults estimation.
After a short introduction to the fundamentals, this book provides
a detailed account of major advances in applying fractional
calculus to dynamical systems. Fractional order dynamical systems
currently continue to gain further importance in many areas of
science and engineering. As with many other approaches to
mathematical modeling, the first issue to be addressed is the need
to couple a definition of the fractional differentiation or
integration operator with the types of dynamical systems that are
analyzed. As such, for the fundamentals the focus is on basic
aspects of fractional calculus, in particular stability analysis,
which is required to tackle synchronization in coupled fractional
order systems, to understand the essence of estimators for related
integer order systems, and to keep track of the interplay between
synchronization and parameter observation. This serves as the
common basis for the more advanced topics and applications
presented in the subsequent chapters, which include an introduction
to the 'Immersion and Invariance' (I&I) methodology, the
masterslave synchronization scheme for partially known nonlinear
fractional order systems, Fractional Algebraic Observability (FAO)
and Fractional Generalized quasi-Synchronization (FGqS) to name but
a few. This book is intended not only for applied mathematicians
and theoretical physicists, but also for anyone in applied science
dealing with complex nonlinear systems.
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.
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.
The high reliability required in industrial processes has created
the necessity of detecting abnormal conditions, called faults,
while processes are operating. The term fault generically refers to
any type of process degradation, or degradation in equipment
performance because of changes in the process's physical
characteristics, process inputs or environmental conditions. This
book is about the fundamentals of fault detection and diagnosis in
a variety of nonlinear systems which are represented by ordinary
differential equations. The fault detection problem is approached
from a differential algebraic viewpoint, using residual generators
based upon high-gain nonlinear auxiliary systems ('observers'). A
prominent role is played by the type of mathematical tools that
will be used, requiring knowledge of differential algebra and
differential equations. Specific theorems tailored to the needs of
the problem-solving procedures are developed and proved.
Applications to real-world problems, both with constant and
time-varying faults, are made throughout the book and include
electromechanical positioning systems, the Continuous Stirred Tank
Reactor (CSTR), bioreactor models and belt drive systems, to name
but a few.
This book provides a general overview of several concepts of
synchronization and brings together related approaches to secure
communication in chaotic systems. This is achieved using a
combination of analytic, algebraic, geometrical and asymptotical
methods to tackle the dynamical feedback stabilization problem. In
particular, differential-geometric and algebraic differential
concepts reveal important structural properties of chaotic systems
and serve as guide for the construction of design procedures for a
wide variety of chaotic systems. The basic differential algebraic
and geometric concepts are presented in the first few chapters in a
novel way as design tools, together with selected experimental
studies demonstrating their importance. The subsequent chapters
treat recent applications. Written for graduate students in applied
physical sciences, systems engineers, and applied mathematicians
interested in synchronization of chaotic systems and in secure
communications, this self-contained text requires only basic
knowledge of integer ordinary and fractional ordinary differential
equations. Design applications are illustrated with the help of
several physical models of practical interest.
The high reliability required in industrial processes has created
the necessity of detecting abnormal conditions, called faults,
while processes are operating. The term fault generically refers to
any type of process degradation, or degradation in equipment
performance because of changes in the process's physical
characteristics, process inputs or environmental conditions. This
book is about the fundamentals of fault detection and diagnosis in
a variety of nonlinear systems which are represented by ordinary
differential equations. The fault detection problem is approached
from a differential algebraic viewpoint, using residual generators
based upon high-gain nonlinear auxiliary systems ('observers'). A
prominent role is played by the type of mathematical tools that
will be used, requiring knowledge of differential algebra and
differential equations. Specific theorems tailored to the needs of
the problem-solving procedures are developed and proved.
Applications to real-world problems, both with constant and
time-varying faults, are made throughout the book and include
electromechanical positioning systems, the Continuous Stirred Tank
Reactor (CSTR), bioreactor models and belt drive systems, to name
but a few.
This book addresses the problem of multi-agent systems, considering
that it can be interpreted as a generalized multi-synchronization
problem. From manufacturing tasks, through encryption and
communication algorithms, to high-precision experiments, the
simultaneous cooperation between multiple systems or agents is
essential to successfully carrying out different modern activities,
both in academy and industry. For example, the coordination of
multiple assembler robots in manufacturing lines. These agents need
to synchronize. The first two chapters of the book describe the
synchronization of dynamical systems, paying special attention to
the synchronization of non-identical systems. Following, the third
chapter presents an interesting application of the synchronization
phenomenon for state estimation. Subsequently, the authors fully
address the multi-agent problem interpreted as
multi-synchronization. The final chapters introduce the reader to a
more complex problem, the synchronization of systems governed by
partial differential equations, both of integer and fractional
order. The book aimed at graduates, postgraduate students and
researchers closely related to the area of automatic control.
Previous knowledge of linear algebra, classical and fractional
calculus is requested, as well as some fundamental notions of graph
theory.
This book is a short primer in engineering mathematics with a view
on applications in nonlinear control theory. In particular, it
introduces some elementary concepts of commutative algebra and
algebraic geometry which offer a set of tools quite different from
the traditional approaches to the subject matter. This text begins
with the study of elementary set and map theory. Chapters 2 and 3
on group theory and rings, respectively, are included because of
their important relation to linear algebra, the group of invertible
linear maps (or matrices) and the ring of linear maps of a vector
space. Homomorphisms and Ideals are dealt with as well at this
stage. Chapter 4 is devoted to the theory of matrices and systems
of linear equations. Chapter 5 gives some information on
permutations, determinants and the inverse of a matrix. Chapter 6
tackles vector spaces over a field, Chapter 7 treats linear maps
resp. linear transformations, and in addition the application in
linear control theory of some abstract theorems such as the concept
of a kernel, the image and dimension of vector spaces are
illustrated. Chapter 8 considers the diagonalization of a matrix
and their canonical forms. Chapter 9 provides a brief introduction
to elementary methods for solving differential equations and,
finally, in Chapter 10, nonlinear control theory is introduced from
the point of view of differential algebra.
After a short introduction to the fundamentals, this book provides
a detailed account of major advances in applying fractional
calculus to dynamical systems. Fractional order dynamical systems
currently continue to gain further importance in many areas of
science and engineering. As with many other approaches to
mathematical modeling, the first issue to be addressed is the need
to couple a definition of the fractional differentiation or
integration operator with the types of dynamical systems that are
analyzed. As such, for the fundamentals the focus is on basic
aspects of fractional calculus, in particular stability analysis,
which is required to tackle synchronization in coupled fractional
order systems, to understand the essence of estimators for related
integer order systems, and to keep track of the interplay between
synchronization and parameter observation. This serves as the
common basis for the more advanced topics and applications
presented in the subsequent chapters, which include an introduction
to the 'Immersion and Invariance' (I&I) methodology, the
masterslave synchronization scheme for partially known nonlinear
fractional order systems, Fractional Algebraic Observability (FAO)
and Fractional Generalized quasi-Synchronization (FGqS) to name but
a few. This book is intended not only for applied mathematicians
and theoretical physicists, but also for anyone in applied science
dealing with complex nonlinear systems.
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