Education and Qualification for Control and Automation 44.4 New Applications of Systems and Control Theory 771
plete and incomplete markets, consumption–investment
models with or without constraints, portfolio manage-
ment for institutional investors such as pension funds
and banks, and risk assessment and management using
financial derivatives. At the same time, these appli-
cations require and stimulate many new and exciting
theoretical discoveries within the systems and control
field. Take for instance the study of arbitrage theory,
risk assessment, and portfolio management, which have
collectively led to new developments in martingale the-
ory and stochastic control. Moreover, the development
of financial engineering has created a large demand for
graduates at both Master and Ph.D. levels in industry,
resulting in the introduction of the curriculum in many
universities including Kent State University, Princeton
University, Columbia University, and the University of
California at Berkeley.
Another contribution to the control community from
financial engineering and financial mathematics was the
identification and control of stochastic systems with
noise modeledby a fractional Brownian motion[44.11],
a process that can possess a long-range dependence.
Motivated by the need for this type of process in
telecommunications for models of Ethernet and asyn-
chronous transfer mode (AT M) traffic, a new stochastic
calculus for fractional Brownian motion was developed.
This work in financial engineering and financial math-
ematics has since been successfully used in other fields
such as telecommunications and medicine, in particular
epilepsy analysis of brain waves [44.8,9].
44.4.2 Biomedical Models: Epilepsy Model
Epilepsy is a condition where a person has unprovoked
seizures at two or more separate times in her/his life.
A seizure is an abnormal electrical discharge within
the brain resulting in involuntary changes in move-
ment, sensation, perception, behavior, and/or level of
consciousness. It is estimated that 1% of the popula-
tions of industrialized countries have epilepsy whereas
5–10% of the populations of nonindustrialized coun-
tries have epilepsy. One link has been found between
epilepsy and malnutrition [44.26]. In the USA the num-
ber of epilepsy cases is significantly larger than the
number of cases of people who have Parkinson’s dis-
ease, muscular dystrophy, multiple sclerosis, acquired
immunodeficiency syndrome (AIDS)orAlzheimer’s
disease [44.10]. The organizers of the Third Interna-
tional Workshop on Seizure Prediction in Epilepsy held
in Freiburg, Germany stated in the Welcome to the
Workshop that:
The great interest of participants from all over the
world and the highnumber of originalcontributions
presented ... instills confidence in us that seizure
prediction is a promising field for the years to come.
Epilepsy models, with their complexity, can serve
as an example of interdisciplinary and multidisciplinary
research for which systems and control approaches are
showing considerable promise. The methods pioneered
in the financial mathematics and engineering sector de-
scribed above have been successfully used for detection
and prediction of epileptic seizures. There is published
evidencethat the seizure periodsof brain waves of some
patients have long-range dependencies with nonseizure
periods. Based on some initial work, it seems that the
estimates of the Hurst parameter, which is a charac-
terization of the long-range dependence in fractional
Brownian motion, have a noticeable change prior to and
during a seizure. Some of the algorithms [44.8]used
in identifying the Hurst parameter use stochastic calcu-
lus for fractional Brownian motion that was developed
within the financial engineering and financial mathe-
matics sector. A new application for the Hurst param-
eter, real-time event detection, has recently been identi-
fied [44.9]. The high sensitivity to brain state changes,
ability to operate in real time, and small computational
requirements make Hurst parameter estimation well
suited for implementation into miniature implantable
devices for contingent delivery of antiseizure therapies.
This innovative interdisciplinary research has devel-
oped a new technology for future automated therapeutic
intervention devices to lessen, abort or prevent seizures,
opening the possibility of creating a brain pacemaker.
The goal is, by eliminating the unpredictability of
seizures, to minimize or prevent the disability caused
by epilepsy and hardship it imposes on patients and
their families and communities. It brings a hope to
improve productivity and better quality life for those
afflicted with epilepsy and their families as well as
for care-givers and healthcare providers. The creation
of a seizure warning device will minimize risks of in-
jury, the degrading experience associated with having
seizures in public, and the unpredictable disruption of
normal daily-life activities.
Only collaborative work of engineers, computer
scientists, physicists, physicians, biologists, and math-
ematicians can be successful in solving this type of
complex problem. Based partly on the success thus far,
there is a strong desire for a partnership with control
engineers. The University of Kansas (KU) Stochastic
Adaptive Control Group (SACG) has a long history
Part E 44.4