MODEL-INDEPENDENT CONTROL OF DYNAMICAL SYSTEMS IN PHYSIOLOGY
DAVID J. CHRISTINI
Boston University, College of Engineering, 1997
Advisor: James
J. Collins, Ph.D.
Professor of Biomedical Engineering
Abstract:
Quantitative, analytical system models are often unavailable for
physiological systems. Thus, traditional model-based control
techniques are usually not applicable to the control of physiological
dynamics. Recently, however, model-independent control techniques have
been developed for nonlinear dynamical systems. These techniques do
not require explicit knowledge of the underlying system equations and
are thus inherently well-suited for the control of dynamical
physiological systems. To date, a detailed analysis of the feasibility
of applying these model-independent techniques to physiological
systems has not been reported. This project investigated this
feasibility by developing, implementing, and testing model-independent
control techniques for dynamical physiological systems. First, we
investigated the control of low-dimensional physiological systems
which have no accessible system parameter. We developed a control
technique for such systems, and successfully controlled chaotic and
nonchaotic neuronal models. Second, we developed a control technique
for high-dimensional chaotic systems and used it in an experimental
setting to control a driven double pendulum - a chaotic system with
dynamical characteristics similar to those of high-dimensional
physiological systems. Third, we developed a technique to stabilize
unstable low-period rhythms which underlie stable high-period
oscillations in nonchaotic systems. We demonstrated the physiological
utility of this technique by suppressing a period-2 rhythm in a
cardiac model. We then showed that this technique is applicable to
real-world physiological systems by using it to suppress a period-2
rhythm in an in vitro rabbit heart experiment. Fourth, we
developed a real-time and adaptive model-independent technique for
low-dimensional dynamical systems. We demonstrated the versatility of
this technique by using it to control the Henon map (in its chaotic
and nonchaotic regimes), a cardiac model (in its nonchaotic regime),
and a continuous-time chemical reaction model (in its chaotic and
nonchaotic regimes). Importantly, the real-time and adaptive nature of
this control technique makes it more appropriate for real-world
systems than existing model-independent control techniques. The
computational and experimental results of this project clearly
demonstrate that model-independent control techniques are applicable
to physiological systems. These results may have important clinical
implications given that many pathological conditions are characterized
by chaotic or nonchaotic dynamics.