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Hybrid state observer for time-delay systems under intrinsic impulsive feedback
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för systemteknik. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Reglerteknik.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för systemteknik. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Reglerteknik.
2014 (engelsk)Inngår i: Proc. 21st International Symposium on Mathematical Theory of Networks and Systems, The Netherlands: University of Groningen , 2014, s. 977-984Konferansepaper, Publicerat paper (Fagfellevurdert)
sted, utgiver, år, opplag, sider
The Netherlands: University of Groningen , 2014. s. 977-984
HSV kategori
Identifikatorer
URN: urn:nbn:se:uu:diva-315989ISBN: 978-90-367-6321-9 (tryckt)OAI: oai:DiVA.org:uu-315989DiVA, id: diva2:1076691
Konferanse
MTNS 2014, July 7–11, Groningen, The Netherlands
Tilgjengelig fra: 2014-07-11 Laget: 2017-02-23 Sist oppdatert: 2019-04-25bibliografisk kontrollert
Inngår i avhandling
1. Hybrid observers for systems with intrinsic pulse-modulated feedback
Åpne denne publikasjonen i ny fane eller vindu >>Hybrid observers for systems with intrinsic pulse-modulated feedback
2017 (engelsk)Licentiatavhandling, med artikler (Annet vitenskapelig)
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.

sted, utgiver, år, opplag, sider
Uppsala University, 2017
Serie
IT licentiate theses / Uppsala University, Department of Information Technology, ISSN 1404-5117 ; 2017-001
HSV kategori
Forskningsprogram
Elektroteknik med inriktning mot reglerteknik
Identifikatorer
urn:nbn:se:uu:diva-316058 (URN)
Veileder
Tilgjengelig fra: 2017-02-10 Laget: 2017-02-23 Sist oppdatert: 2017-02-23bibliografisk kontrollert
2. Hybrid observers for systems with intrinsic pulse-modulated feedback
Åpne denne publikasjonen i ny fane eller vindu >>Hybrid observers for systems with intrinsic pulse-modulated feedback
2019 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
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. 

sted, utgiver, år, opplag, sider
Uppsala: Acta Universitatis Upsaliensis, 2019. s. 51
Serie
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1812
Emneord
hybrid systems, impulsive systems, biomedical systems, Goodwin's oscillator, observers, time-delay
HSV kategori
Forskningsprogram
Elektroteknik med inriktning mot reglerteknik
Identifikatorer
urn:nbn:se:uu:diva-382414 (URN)978-91-513-0665-0 (ISBN)
Disputas
2019-06-14, 2446, ITC, Lägerhyddsvägen 2, Uppsala, 09:15 (engelsk)
Opponent
Veileder
Tilgjengelig fra: 2019-05-27 Laget: 2019-04-25 Sist oppdatert: 2019-06-18

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