Circadian rhythms exist in almost all of living species, and they occupy an important role in daily biological activities of these species. This thesis deals with reduction of measurements in circadian models, and recovery of circadian phases. Two mathematical models of circadian rhythms are considered, with a 3rd order model for Neurospora, and a 7th order model for Mammals. The reduction of measurements of circadian models is shown by the proposals of observer designs to the two mathematical models of circadian rhythms. Both mathematical models contain strong nonlinearities, which make the observer design challenging. Two observer designs, reduced-order and one-sided Lipschitz, are applied to the circadian models to tackle the nonlinearities. Reduced-order observer design is based on a state transformation to make certain nonlinearities have no impact on the observer errors, and the design of one-sided Lipschitz observer is based on systems with one-sided Lipschitz nonlinearities. Both observer designs are based on the existing methods in literature. The existing method of reduced-order observer has been applied to a class of multi-output nonlinear systems. A new reduced-order observer design which extends the existing one in literature is presented in this thesis. In this new reduced-order observer method, the observer error dynamics can be designed by choosing the observer gain, unlike the existing one, of which the observer error dynamics depend on the invariant zeros under certain input-output map. The recovery of circadian phases is carried out to provide a solution to phase shifts occurred in circadian disorders. The restoration of circadian phases is performed by the synchronizations of trajectories of a controlled model with trajectories of a reference model. The reference model and the controlled model have phase differences, and both these models are based on a given 3rd order model of Neurospora circadian rhythms. The phase differences are reflected by different initial conditions, and by parameter uncertainty. The synchronizations of the two models are performed by using back-stepping method for the case of different initial conditions, and by using adaptive back-stepping method for the remaining case. Several simulation studies of the proposed observer designs and the proposed schemes of synchronizations are carried out with the results shown in this thesis.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:551351 |
| Date | January 2011 |
| Creators | Ton That, Long |
| Contributors | Ding, Zhengtao |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/nonlinear-control-studies-for-circadian-models-in-system-biology(f616f360-99e4-4314-ba51-be7a49e9ff0e).html |
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