Stability and Control of Dynamical Systems with Applications - Derong Liu and Panos J. Antsaklis (New York, NY: Birkhauser-Boston, 2003). Reviewed by: Huaguang Zhang, School of Information Science and Engineering, Northeastern University, Shenyang, Liaoning 110004, People’s Republic of China
This book is an extensive compilation of papers
presented at the workshop held at the University
of Notre Dame on 5 April 2003. It presents recent important research results on stability
and control of dynamical systems by 41 researchers.
The book is organized into three major parts incorporating 21 chapters.
The first part of the book contains
seven chapters on stability
analysis of dynamical systems. Chapter
1 expands wave digital concepts
and relativity theory through some
modifications to Newton’s laws. Chapter
2 studies the notion of time and
establishes a consistent Lyapunov
methodology for nonlinear systems.
Moreover, the extended concept of
the vector Lyapunov function is introduced.
Chapter 3 develops a mathematical
model for a multibody
attitude system that exposes the
dynamic coupling between the rotational
degrees of freedom of the base
body and the deformation or shape
degrees of freedom of the elastic subsystems. Furthermore, results that
guarantee asymptotic stability of this
multibody attitude system are
obtained. Chapter 4 discusses robust
control of uncertain hybrid systems
affected by both parameter variations
and exterior disturbances, and it provides
a method for checking attainability.
Chapter 5 overviews stability
properties of swarms, and it analyzes
swarm cohesion under very noisy
measurements using Lyapunov stability
theory. Chapter 6 presents a necessary
and sufficient asymptotic
stability condition for discrete-time,
time-varying, uncertain delay systems,
and it applies the result to control problems of a communication
network. Chapter 7 investigates stability
and L2 gain properties for
switched symmetric systems. The key
idea is to establish a common Lyapunov
function for all of the subsystems
in the switched systems.
Comprising six chapters, the second
part of the book is concerned
with neural networks and signal processing.
Chapter 8 investigates the
approximation capabilities of Gaussian
radial basis functions and the
concept of locally compact metric
spaces. Chapter 9 provides a generalized
state-space formulation and
learning algorithms for blind source
recovery based on the theory of multivariable
optimization. Chapter 10
discusses the theme of approximate
dynamic programming. Furthermore,
it presents a method of direct neural-dynamic
programming and its application
to helicopter command
tracking. Chapter 11 studies online
approximator-based aircraft state
estimation. Chapter12 proposes and
analyzes a novel dynamic multiobjective
evolutionary algorithm.
Chapter 13 introduces set membership
adaptive filtering and its novel
feature of data-dependent selective
update of parameter estimates.
The final part of the book covers
power systems and control systems
(Chapters 14–21). Chapter 14 is concerned
with trajectory sensitivity
theory and its practical application
to power systems. Chapter 15 investigates
the design of a corrective
control strategy after substantial disturbances
in large-scale electric
power systems. An analytical
approach in which the system is separated
into smaller islands at a slightly
reduced capacity is developed.
Chapter 16 expands control methods
for maintaining the stability of the
electric power generation transmission
distribution grid. This chapter
also presents a roadmap for the
development of new controls for
power system stability.
Chapter 17 introduces data fusion modeling for groundwater system
identification based on Kalman filtering
methods and a Markov random
field representation for spatial variations.
Chapter 18 provides an introduction
to the nominal design problem
along with results for feedback synthesis
in an algebraic framework. Chapter
19 introduces the adaptive dynamic
programming algorithm and gives a
detailed proof. Chapter 20 analyzes the
reliability of supervisory control and
data acquisition systems used in offshore
oil and gas platforms. Chapter
21 develops call admission control
algorithms, based on signal-to-interference
ratio, for power-controlled CDMA
cellular networks. In particular, call
admission control algorithms are
developed based on the necessary and
sufficient conditions under which the
power control algorithm will have a
feasible solution.
One welcome feature of the book
is that each chapter includes an
abstract, a detailed introduction,
and a concise conclusion, thereby
significantly assisting the readers’
comprehension. Each chapter is a
helpful guide for anyone engaged in
the analysis and control of dynamical
systems, offering ample opportunity
for further exploration of the
approaches covered. Rigid mathematical
descriptions and logical
derivations are another feature. The
main ideas presented are original,
and the results stated are advanced
and appropriate. The reviewer
believes that the book is an excellent
reference source for
researchers and practitioners in the
areas of dynamical systems
research and applications. The book
is well written and well organized,
and it is clear that the authors have
made important research contributions
in this field.