


A. Vicino, CSC director 9.15  12.00
Chaos Control: Theory and Applications
Model Reduction for Systems with LowDimensional
Chaos

NEURAL NETWORKS (i) A Nonlinear Dynamics Perspective of Wolfram's
New Kind of Science
On the Application of Spectral Techniques for
the Analysis of Nonlinear Dynamic Arrays

NEW TRENDS IN STABILITY THEORY FOR COMPLEX SYSTEMS Normal Form, Bifurcation, and Stabilization
of Highly Nonlinear Systems
The InputtoState Stability Approach for Global
Analysis of Nonlinear Systems

CONTROL OF CHAOS AND BIFURCATIONS (ii) Bifurcation Control and Applications
Controller Synthesis for Stabilizing Periodic
Orbits in Chaotic Systems

NEURAL NETWORKS (ii) Programmable Complex Systems, Visual Microprocessors
and Universal Machines on Flows  with Bioinspired Aspects

CHAOS IN COMMUNICATION SYSTEMS Statistical Approach to Chaos: Some Theoretical
Results and Applications
Bifurcation Phenomena in the Behavior of Access
Protocols for Wireless Multimedia Communication Systems
17.30  conclusion of the school 
ABSTRACTS
CONTROL OF CHAOS AND BIFURCATIONS
Chaos Control: Theory and Applications
M. Ogorzalek
This lecture will present basic
techniques available for controlling chaotic dynamical systems. We will
present first special features of chaotic systems which make the approaches
to chaos control different from standard methods available in the control
engineers toolbox. Sensitive dependence on initial conditions, ergodic
properties of trajectories, bifurcation behavior can help in building special
control strategies. Applications in engineering, biology and medicine will
be presented.
Model Reduction for Systems with LowDimensional
Chaos
C. Piccardi
The lecture will discuss a method
for deriving a reduced model of a continuoustime dynamical system with
lowdimensional chaos. The method relies on the identification of peaktopeak
dynamics, i.e. the possibility of approximately (but accurately) predicting
the next peak amplitude of a variable from the knowledge of its two previous
peaks. The reduced model is a simple onedimensional map or, in the most
complex case, a set of onedimensional maps. Its use in control system
design will also be discussed by means of some examples.
Bifurcation Control and Applications
E.H. Abed
The topic of bifurcation control
will be reviewed with a view toward recent results and applications of
current interest. Bifurcation control relates to the design of control
systems that improve the operating characteristics of a nonlinear system
in the vicinity of a bifurcation in its dynamics. Issues such as delay
and stabilization of bifurcating solutions by feedback will be discussed.
System monitoring for the automatic detection of impending bifurcations
will also be considered. Recent developments related to bifurcation control
of nonsmooth systems will be introduced. Applications will be used throughout
the lecture to motivate the theory. This includes control problems for
aircraft, computer networks and heart arrhythmia.
Controller Synthesis for Stabilizing Periodic
Orbits in Chaotic Systems
M. Basso
The lecture deals with the use
of finitedimensional linear timeinvariant controllers for the stabilization
of periodic solutions in sinusoidally forced chaotic systems. Such controllers
can be interpreted as rational approximations of the wellknown Delayed
Feedback Controllers (DFC). By exploiting results concerning absolute stability
of nonlinear systems and robustness of linear systems, it is shown that
controller synthesis techniques based on Linear Matrix Inequalities (LMI)
can be devised. In particular, a synthesis algorithm to maximize the amplitude
of the forcing input ensuring stable periodic solutions is discussed, together
with some application examples.
A Nonlinear Dynamics Perspective of Wolfram's
New Kind of Science
L.O. Chua
This lecture provides a nonlinear
dynamics perspective to Wolfram’s monumental work on “A New Kind of Science”.
By mapping a Boolean local rule, or truth table, onto the point attractors
of a specially tailored nonlinear dynamical system, it is possible to characterize
the complexity of the dynamics of each Boolean local rule. In particular,
Wolfram’s seductive idea of a “threshold of complexity” can
be rigorously defined via a “complexity index”.
On the Application of Spectral Techniques for
the Analysis of Nonlinear Dynamic Arrays
M. Gilli
Regular arrays of nonlinear circuits
present interesting applications in image processing and pattern recognition;
they are also useful for modeling stationary and wave phenomena in many
disciplines, ranging from physics to biology. Such arrays are described
by large systems of locally coupled nonlinear differential equations
and they can exhibit a very complex behaviour. A complete study of their
dynamics would require to classify all the attractors and possibly to estimate
the domains of attraction. This is a formidable task that cannot be faced
neither through computer simulation, nor through classical timedomain
techniques, that are suitable for loworder dynamical systems. The lecture
will briefly summarize the properties of stable arrays, i.e dynamical systems,
where each trajectory (with the exception of a set of measure zero) converges
towards an equilibrium point. Then it will focus on the application of
spectral techniques to nonlinear arrays that exhibits either a periodic
or a nonperiodic behavior. It will be shown that: a) the whole set of
periodic attractors can be characterized through a suitable extension of
the describing function technique; b) the main properties and characteristics
of such attractors can be determined through a harmonic balance (HB) based
method; c) the limit cycle bifurcation processes, leading to a complex
behavior, can be studied through a suitable combination of HB based and
timedomain techniques.
Programmable Complex Systems, Visual Microprocessors
and Universal Machines on Flows  with Bioinspired Aspects
T. Roska
Following the formal computing
machine models on integers (Turing Machine and VonNeumann computers) and
on reals (BlumSchubSmale), recently, a new computing paradigm on flows
(Roska and Chua) has been introduced. The basic idea of the latter, the
CNN Universal Machine, will be introduced first with key notions and practical
aspects. The possibility to algorithmically program and implement complex
systems will be explored. Next, the various physical implementations will
be reviewed, including visual microprocessors, and the computational and
computer complexity issues will be described. Application case studies
will follow for superhighspeed sensorycomputing tasks (Xkframe per sec).
Finally, the biological relevance will be highlighted culminating in a
programmable mammalian retinal model implemented on a single chip.
NEW TRENDS IN STABILITY THEORY FOR COMPLEX SYSTEMS
Normal Form, Bifurcation, and Stabilization
of Highly Nonlinear Systems
W. Kang
The first part of the talk is
an introduction to the normal forms and invariants of nonlinear control
systems. In the second part, bifurcations of control systems are defined.
Classification of the bifurcations for systems with uncontrollable modes
is derived using normal forms. Furthermore, feedbacks for the qualitative
control of classical bifurcations will be introduced. The third part of
the talk is on the feedback stabilization of nonlinear systems with a positive
uncontrollable mode. Its feedback design takes the advantage of the bifurcation
on controllability. In the last part, the speaker will announce some open
problems and talk about possible directions for future research.
The InputtoState Stability Approach for Global
Analysis of Nonlinear Systems
D. Angeli
The notion of Input to State
Stability allows in a unified framework to deal with a variety of systems
theoretic properties. The focus of this talk are techniques which are in
our opinion most relevant in order to analyze complex behaviours: incremental
ISS and almost global ISS.
CHAOS IN COMMUNICATION SYSTEMS
Statistical Approach to Chaos: Some Theoretical
Results and Applications
G. Setti (joint research with R. Rovatti and G.
Mazzini)
Recent developments have highlighted
that a statistical approach may greatly benefit the study of discretetime
chaotic systems (maps). The key idea is to consider a set of trajectories
of nonvanishing measure of a chaotic map, whose study allows to track
the mechanism causing the complex behavior and to characterize it quantitatively
despite the wellknown critical dependence on initial condition. A set
of tools will be introduced which permits to assess the statistical features
of the quantized process generated by a chaotic map in terms of the exact
computation of highorder moments. Such a welldeveloped theoretical framework
will be then applied to three hot information engineering topics, namely
DSCDMA communication system performance optimization, electromagnetic
interference reduction and artificial multimedia traffic generation.
Bifurcation Phenomena in the Behavior of Access
Protocols for Wireless Multimedia Communication Systems
G. Giambene
The steady increase of mobile
traffic requires new solutions to coordinate the transmissions of wireless
terminals. The first part of this talk will survey Medium Access Control
(MAC) protocols, focusing on the techniques used in thirdgeneration (3G)
mobile communication systems and in Low Earth Orbit Systems. The second
part of this talk will focus on MAC protocols based on uncoordinated access
attempts from mobile terminals. A novel protocol will be proposed that
adopts suitable control parameters to regulate the transmission of terminals
belonging to different traffic classes. Such scheme will be modeled through
nonlinear equations by means of the Equilibrium Point Analysis (EPA) that
will permit to highlight a bifurcation behavior.
(May 30, 2003)