Licentiate thesis 2017-001

Hybrid Observers for Systems with Intrinsic Pulse-Modulated Feedback

Diana Yamalova

3 March 2017


This licentiate thesis deals with a special class of hybrid systems, where the continuous linear part is controlled by an intrinsic impulsive feedback that contributes discrete dynamics. The impacting pulsatile feedback signal is not available for measurement and, therefore, has to be reconstructed. To estimate all the elements of the hybrid state vector, an observation problem is considered.

The motivation for the research performed in this thesis comes from mathematical modelling of pulsatile endocrine regulation, where one of the hormones (a releasing hormone) is secreted in pulses from neurons in the hypothalamus of the brain. Thus a direct measurement of the concentration of this hormone in the human is not possible for ethical reasons and has to be estimated.

Several hybrid observer structures are proposed and evaluated. The observer design is reduced to a problem of synchronizing the impulsive sequence produced by the observer with that of the plant. It utilizes a local approach of assigning, through the output error feedback in both the discrete and continuous parts of the plant model, a guaranteed convergence rate to the local dynamics of a synchronous mode. Performance of the proposed observer schemes is analyzed by means of pointwise discrete (Poincare) maps.

The first two papers of the thesis address the effects of observer design degrees of freedom on the convergence of the hybrid state estimation error. A generalization of the proposed observation scheme to hybrid impulsive systems with a time delay in continuous part of the plant is investigated in Paper III and Paper IV.

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