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
1. THE SOURCE
This book is an extensive compilation of papers
presented at the workshop held at the University
of Notre Dame on 5 April 2003. The workshop honored Anthony N. Michel, who has made
distinguished contributions in several areas of systems theory and control theory, on the occasion
of his retirement, and was also a forum to
explore topics and applications related to the
stability and control of dynamical systems. The book presents recent research results on stability
and control of dynamic systems by 41 of Michel’s
colleagues, friends, and former PhD students.
2. THE CONTENT
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. The second part of the
book, comprising six chapters, is concerned with neural networks and signal processing. The final part of the book consists of eight chapters which
cover power systems and control systems.
Part I of the book consists of Chapters 1–7.
Chapter 1 (by A. Fettweis) starts with introducing
the nonlinear passive Kirchhoff circuits, the wave-digital
method, nonlinear relativistic mass and
direct derivation of the alternative results. This
chapter expands the wave-digital concepts and
relativity theory through some modifications to
Newton’s Law. An unnecessary additional earlier
requirement that had led to an unavoidable factor of 1/2 in the expression for the equivalence between
mass and energy is abandoned. The chapter
clarifies some of the issues involved, by accurate
and unequivocal measurements, to obtain results
with the closest connection to reality.
Chapter 2 (by L. T. Gruyitch) studies the notion
of time and defines the complete transfer function
matrix for continuous-time MIMO time-invariant
linear systems. This matrix is crucial for zero-pole
cancelation, system minimal realization, stability
analysis, and stabilizing, tracking and/or optimal
control synthesis. A new Lyapunov methodology
for nonlinear systems, called consistent Lyapunov
methodology, enables us to establish the necessary
and sufficient conditions for (1) asymptotic stability
of x=0, (2) a set to be the exact domain of
asymptotic stability and (3) a direct construction
of a Lyapunov function for a given nonlinear
dynamical system. Moreover, the extended concepts
of vector Lyapunov function are introduced.
Chapter 3 (by J. Shen, A. K. Sanyal and N. H.
Mc-Clamroch) develops a mathematical model
for multibody attitude systems that expose the
dynamic coupling between the rotational degree
of freedom of the base body and the deformation
or shape degree of freedom of the elastic
subsystems. Furthermore, a number of results
that guarantee asymptotic stability for this multibody
attitude system are obtained. Finally, two
examples including a system with elastic rotational
degree of freedom and a system with elastic
transnational degree of freedom are introduced.
Chapter 4 (by H. Lin and P. J. Antsaklis)
concentrates on robust regulation of uncertain
hybrid systems that affected by both parameter
variations and exterior disturbances. In particular,
a robust one-step predecessor operator for the
uncertain linear hybrid systems serves as the basic
tool for analysis. This chapter provides a method
for checking the safety, reachability and attainability.
Further, the authors apply the results to
networked control systems (NCS) and formulate
the ultimate boundedness control problem for the
NCS with uncertain delay, package-dropout and
quantization effects as a regulation problem for an
uncertain hybrid system.
Chapter 5 (by K. M. Passino) gives stability
properties of swarms, and analyses swarms’
cohesion under very noisy measurements using
Lyapunov stability theory. The author gives a
simple example of how to consider the effect of
sensor noise and noise in sensing the gradient of a ‘resource profile’.
Chapter 6 (by M. L. Sichitiu and P. H. Bauer)
presents a necessary and suffcient asymptotic
stability condition for discrete time-varying uncertain
delay systems, where the uncertainty set is finite and additional constraints on the time
variance of the system exist, and applies the result
to communication network control problems.
Chapter 7 (by G. Zhai) investigates the stability
and the L2 gain properties for switched symmetric
systems, and shows two results. The first
result is that when all the subsystems are stable,
the switched system is exponentially stable under
arbitrary switching. Another one is that when all
the subsystems have L2 gains less than a positive
scalar g, the switched system has L2 gains less
than the same g under arbitrary switching. The
key idea is to establish a common Lyapunov
function for all the subsystems in the switched
systems.
Chapters 8–13 constitutes Part II of the book.
Chapter 8 (by I. W. Sandberg) researches the
approximation capabilities of Gaussian radial
basis functions and the concept of locally compact
metric spaces. It is shown that the members of
some interesting families of shift-varying input–output maps can be uniformly approximated in
certain special way. The proposed results have
theoretical guidance to many aspects of system
identification and adaptive systems.
Chapter 9 (by K. Waheed and F. M. Salem) provides a generalized state-space blind source recovery framework based on the theory of multivariable optimization and the Kullback–Lieblar divergence as the performance functional. The multivariable optimization technique is used to derive update laws for nonlinear time-varying dynamical systems. Moreover, the various possible state-space demixing network structures are exploited to develop learning rules. In particular, linear state-space algorithms are presented for the minimum phase and non-minimum phase mixing environment models.
Chapter 10 (by L. Yang, R. Enns, Y. T.Wang and J. Si) discusses the theme of approximate dynamic programming (ADP). It presents direct neural dynamic programming (NDP) and applies it to a challenging continuous state control problem of helicopter command tracking. It is noted that direct NDP mechanism for helicopter control is probably the first time that an ADP type of algorithm has been applied to a complex real-life continuous state problem.
In Chapter 11 (by J. Farrell, M, Sharma and M.
Polycarpo), algorithms for estimating the aircraft
state vector and for approximating the nonlinear
forces and moments acting on the aircraft are
proposed. First, the authors give aircraft dynamics
and model structure, and then discuss
the unknown forces and moments and their
representation as ‘non-dimensional coeffcient’
functions over an operating envelope denoted by delta. Finally, a Lyapunov-like function is used to
prove the convergence of the estimator state
and to discuss suffcient conditions for the
convergence of the approximated force and
moment functions.
Chapter 12 (by G. G. Yen) presents some
results about dynamic multiobjective evolutionary
algorithm (DMOEA). In the proposed DMOEA,
a cell-based rank and density estimation strategy,
a population growing strategy, a population
declining strategy, and an objective space compression
strategy are designed. In order to validate
the proposed DMOEA, its performance is compared
to five other advanced MOEAs. Moreover,
DMOEA with different parameter settings is
exploited by the chosen test function to show its
robustness in converging to an optimal population
size independent of the initial population.
Chapter 13 (by Y. F. Huang) is focused on set-membership adaptive filtering (SMAF). One unique feature of the proposed SMAF is data-dependent selective update of parameter estimates, and thus the SMAF could offer performance comparable to what can be achieved with conventional algorithms such as RLS and LMS.
The final part of the book contains Chapters
14–21. Chapter 14 (by M. A. Pai and T. B.
Nguyen) is concerned with trajectory sensitivity
theory and practical application to power systems.
It also discusses the technique to compute critical
values of any parameter that induces stability in
the system using trajectory sensitivity.
Chapter 15 (by V. Vittal) investigates the design
of a corrective control strategy after large
disturbances in large electric power systems. An
analytical approach by which the system is
separated into smaller islands at a slightly reduced
capacity is developed. The basis for forming the
islands is to minimize the generation-load imbalance
in each island, thereby facilitating the
restoration process. Then, a carefully designed
load-shedding scheme based on the rate of
frequency decline is explored.
Chapter 16 (by A. Bose) expands control
methods of maintaining the stability of the electric
power generation-transmission-distribution grid.
It presents a roadmap for the development of new
controls for power system stability.
Chapter 17 (by D. W. Porter) introduces data
fusion modelling (DFM) for groundwater systems
identification. It is shown that DFM is a spatial
and temporal state estimation and system identification methodology that uses three sources of
information: measured data, physical laws and
statistical models for uncertainty in spatial heterogeneities
and for temporal variation in driving
terms. DFM provides predictive modeling to
help close the management control loop.
Kalman-filtering methods are generalized using
information filtering methods coupled with a
Markov random field representation for spatial
variations.
Chapter 18 (by M. K. Sain and B. F. Wyman)
provides a tutorial study of the nominal design
problem (NDP) and results for feedback synthesis
in an algebraic framework. The NDP can be
understood as an abstract kernel problem on localized modules and the design freedom
amounts to the choice of a single morphism in
this chapter. It is important that model matching
does not determine the design morphism associated
with total synthesis problem.
Chapter 19 (by J. J. Murray, C. J. Cox and R. E. Saeks) proposes the adaptive dynamic programming
algorithm, and gives detailed four step
proof of the adaptive dynamic programming
theorem.
Chapter 20 (by K. T. Erickson, E. K. Stanek, E.
Cetinkaya, S. Dunn-Norman and A. Miller)
analyses the reliability of the supervisory control
and data acquisition (SCADA) system used in
offshore oil and gas platforms. A fault tree is
constructed to show the effect of contributing
events on system-level reliability. Probability
methods provide a unifying method to assess
physical faults, contributing effect, human actions
and other events having a high degree of
uncertainty. Results of the reliability study
indicate that communication system failures are
the predominant failure modes in the SCADA
systems.
Chapter 21 (by D. Liu, Y. Zhang and S. Hu)
develops call admission control algorithms for
signal-to-interference ratio-based power-controlled
CDMA cellular networks based on calculated
power control set-points for all users in the
network. The proposed call admission control
algorithms are derived from the viewpoint of
controlling the SIR levels for all users at a base
station. In particular, it gives several admission
control algorithms when necessary and suffcient
conditions under which the power control algorithm
will have a feasible solution.
3. COMMENTS
One feature of the book is that each chapter gives
a detailed introduction and a concise conclusion
so that readers could easily penetrate the proposed
methods. Moreover, an abstract at the
beginning of each chapter helps the readers
capture the topic of each chapter. Every chapter
is a helpful guide for anyone engaged in research
for analysis and applications of dynamical systems,
providing the readers with all necessaryreferences to relevant bibliography, thus offering
ample opportunity for further exploration on the
algorithms covered in the book.
The book reads very well. The mathematical
descriptions are quite rigorous, derivations are
logical, the main ideas presented are original and
results stated in the book are accurate and
appropriate. The book emphasizes theoretical
analyses and derivations, but no lack of rich
examples. The many examples bridge the gap
between control system theory and practical
applications by approaches and issues proposed
in this book, such as swarm dynamics, blind
source recovery, direct NDP-based tracking control
and so on.
Last, but not least, this book provides breadth
to the methods/techniques used, depth to literature
review, and reviews on the current status and
future developments of several research and
application areas.
This book is a valuable resource for researchers
and practitioners interested in expanding their
knowledge of dynamical systems research and
applications. The book is different from textbooks
of a graduate course. It is light on link of the
whole book and heavy on consistency and depth of each chapter, which discusses currently very
active research topics. It provides an excellent
extension to a graduate course in dynamical
systems. In any case, the book could be a valuable
addition to a well-stocked academic or corporate
library, particularly for universities or organizations
that interested in the subject.
4. SUMMARY
In summary, this is a very well-written book, and
it is clear that the authors have made important
research contributions in the area of researches
and applications of dynamical systems and presented
a very special tribute to Anthony N.
Michel who has made significant contributions
to the systems and control community.