Information Technology Reference
In-Depth Information
circadian cells using differential flatness theory and the Derivative-free nonlinear
Kalman Filter.
With the application of differential geometric methods and differential flatness
theory it was shown that the nonlinear model of the coupled circadian cells can be
written in the linear canonical form. It was also shown that by applying differential
geometric methods and by computing Lie derivatives exact linearization of the
model of the coupled circadian cells can be succeeded. Moreover, it was proven
that the model of the coupled circadian cells is a differentially flat one and by
defining appropriate flat outputs it can be transformed to the MIMO (multi-input
multi-output) linear canonical form. For the linearized representation of the coupled
neuron's model the design of a feedback control is possible and synchronization
between the two neurons can be attained.
Next, the problem of synchronization of the coupled circadian cells under
external perturbations and parametric uncertainties was examined. As explained,
synchronization of coupled circadian oscillators becomes more difficult when there
is uncertainty about the parameters of the dynamical model of the circadian cells
and when the parameters of the dynamical models of these cells are uneven. To
obtain simultaneous state and disturbances estimation, a disturbance observer based
on the Derivative-free nonlinear Kalman Filter has been used. The Derivative-
free nonlinear Kalman Filter consists of the standard Kalman Filter recursion
on the linearized equivalent model of the coupled cells and on computation of
state and disturbance estimates using the diffeomorphism (relations about state
variables transformation) provided by differential flatness theory. After estimating
the disturbance terms in the model of the coupled circadian cells their compensation
has become possible.
The performance of the synchronizing control loop has been tested through
simulation experiments. It was shown that the proposed method assures that
the circadian cells will remain synchronized, despite parametric variations and
uncertainties in the associated dynamical model and despite the existence of external
perturbations. Robust synchronizing control of biological oscillators is a developing
research field while the application of elaborated control and estimation methods in
biological models is anticipated to give nontrivial results for further advancements
in the fields of biophysics and biomedical engineering.
