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Finite-dimensional hybrid observer for delayed impulsive model of testosterone regulation
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
2015 (English)In: Mathematical problems in engineering (Print), ISSN 1024-123X, E-ISSN 1563-5147, Vol. 2015, p. 190463:1-12, article id 190463Article in journal (Refereed) Published
Resource type
Text
Place, publisher, year, edition, pages
2015. Vol. 2015, p. 190463:1-12, article id 190463
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:uu:diva-270002DOI: 10.1155/2015/190463ISI: 000365229600001OAI: oai:DiVA.org:uu-270002DiVA, id: diva2:885575
Available from: 2015-12-19 Created: 2015-12-19 Last updated: 2019-04-25Bibliographically approved
In thesis
1. Hybrid observers for systems with intrinsic pulse-modulated feedback
Open this publication in new window or tab >>Hybrid observers for systems with intrinsic pulse-modulated feedback
2017 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

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 (Poincaré) 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.

Place, publisher, year, edition, pages
Uppsala University, 2017
Series
Information technology licentiate theses: Licentiate theses from the Department of Information Technology, ISSN 1404-5117 ; 2017-001
National Category
Control Engineering
Research subject
Electrical Engineering with specialization in Automatic Control
Identifiers
urn:nbn:se:uu:diva-316058 (URN)
Supervisors
Available from: 2017-02-10 Created: 2017-02-23 Last updated: 2017-02-23Bibliographically approved
2. Hybrid observers for systems with intrinsic pulse-modulated feedback
Open this publication in new window or tab >>Hybrid observers for systems with intrinsic pulse-modulated feedback
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Dynamical processes resulting from the interaction of continuous and discrete dynamics are often encountered in living organisms. Time evolutions of such processes constitute continuous variables that are subject to instant changes at discrete points of time. Usually, these discrete events cannot be observed directly and have to be reconstructed from the accessible for measurement continuous variables.

Thus, the problem of hybrid state estimation from measurements of continuous outputs is important to and naturally arises in life sciences but, so far, scarcely covered in the existing literature.

This 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 focus of the work is on a state observation problem for an analytically tractable example of a hybrid oscillator with rich nonlinear dynamics including, e.g., monostable and bistable high-periodic and quasiperiodic solutions as well as deterministic chaos. At the same time, the three-dimensional case of the considered hybrid oscillator constitutes a mathematical model of testosterone regulation in the male validated through system identification on human endocrine data. In a pulsatile endocrine regulation loop, one of the hormones (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 it has to be estimated in some manner from the available data, for instance by applying an observer.

It is desirable for an observer to guarantee asymptotic convergence of the state estimate to that of the observable plant from all feasible initial conditions at a highest possible rate. When the state estimation error is zero, the hybrid observer is in a synchronous mode characterized by the firings of the impulses in the observer feedback and those of the plant occurring simultaneously.

Therefore, the observer design problem can be formulated as synchronization of the plant states with those of the observer. This approach does not formally demand observability of the hybrid plant solution. Further, since the dynamics of the oscillator are highly nonlinear, the state estimation problem is considered with respect to particular solutions of the observed system, whose characteristics are assumed to be known, but not the initial conditions. The observer design problem for the impulsive Goodwin's oscillator consists of the selection of the observer structure and of assigning desired properties to a discrete map that captures the observer state transitions from one impulse firing to another through manipulating the degrees of freedom of the observer. 

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2019. p. 51
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1812
Keywords
hybrid systems, impulsive systems, biomedical systems, Goodwin's oscillator, observers, time-delay
National Category
Control Engineering
Research subject
Electrical Engineering with specialization in Automatic Control
Identifiers
urn:nbn:se:uu:diva-382414 (URN)978-91-513-0665-0 (ISBN)
Public defence
2019-06-14, 2446, ITC, Lägerhyddsvägen 2, Uppsala, 09:15 (English)
Opponent
Supervisors
Available from: 2019-05-27 Created: 2019-04-25 Last updated: 2019-06-18

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Yamalova, DianaMedvedev, Alexander

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