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Hybrid observers for systems with intrinsic pulse-modulated 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.
2019 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
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. 

Ort, förlag, år, upplaga, sidor
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
Nyckelord [en]
hybrid systems, impulsive systems, biomedical systems, Goodwin's oscillator, observers, time-delay
Nationell ämneskategori
Reglerteknik
Forskningsämne
Elektroteknik med inriktning mot reglerteknik
Identifikatorer
URN: urn:nbn:se:uu:diva-382414ISBN: 978-91-513-0665-0 (tryckt)OAI: oai:DiVA.org:uu-382414DiVA, id: diva2:1306831
Disputation
2019-06-14, 2446, ITC, Lägerhyddsvägen 2, Uppsala, 09:15 (Engelska)
Opponent
Handledare
Tillgänglig från: 2019-05-27 Skapad: 2019-04-25 Senast uppdaterad: 2019-06-18
Delarbeten
1. Bifurcation analysis for non-local design of a hybrid observer for the impulsive Goodwin's oscillator
Öppna denna publikation i ny flik eller fönster >>Bifurcation analysis for non-local design of a hybrid observer for the impulsive Goodwin's oscillator
2019 (Engelska)Ingår i: Artikel i tidskrift (Övrigt vetenskapligt) Submitted
Nationell ämneskategori
Reglerteknik
Identifikatorer
urn:nbn:se:uu:diva-382411 (URN)
Tillgänglig från: 2019-04-25 Skapad: 2019-04-25 Senast uppdaterad: 2019-05-07Bibliografiskt granskad
2. Hybrid observer with finite-memory output error correction for linear systems under intrinsic impulsive feedback
Öppna denna publikation i ny flik eller fönster >>Hybrid observer with finite-memory output error correction for linear systems under intrinsic impulsive feedback
2019 (Engelska)Ingår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836Artikel i tidskrift (Övrigt vetenskapligt) Submitted
Nationell ämneskategori
Reglerteknik
Identifikatorer
urn:nbn:se:uu:diva-382412 (URN)
Tillgänglig från: 2019-04-25 Skapad: 2019-04-25 Senast uppdaterad: 2019-05-07Bibliografiskt granskad
3. Robustification of the synchronous mode in a hybrid observer for a continuous system under an intrinsic pulse-modulated feedback
Öppna denna publikation i ny flik eller fönster >>Robustification of the synchronous mode in a hybrid observer for a continuous system under an intrinsic pulse-modulated feedback
2018 (Engelska)Ingår i: Proc. 16th European Control Conference, IEEE, 2018, s. 107-112Konferensbidrag, Publicerat paper (Refereegranskat)
Ort, förlag, år, upplaga, sidor
IEEE, 2018
Nationell ämneskategori
Reglerteknik
Identifikatorer
urn:nbn:se:uu:diva-354827 (URN)10.23919/ECC.2018.8550264 (DOI)000467725300018 ()978-3-9524-2698-2 (ISBN)
Konferens
ECC 2018, June 12–15, Limassol, Cyprus
Tillgänglig från: 2018-11-29 Skapad: 2018-06-22 Senast uppdaterad: 2019-06-19Bibliografiskt granskad
4. Hybrid observers for an impulsive Goodwin’s oscillator subject to continuous exogenous signals
Öppna denna publikation i ny flik eller fönster >>Hybrid observers for an impulsive Goodwin’s oscillator subject to continuous exogenous signals
2017 (Engelska)Ingår i: 2017 IEEE 56Th Annual Conference on Decision and Control (Cdc), Piscataway, NJ: IEEE, 2017, s. 2396-2401Konferensbidrag, Publicerat paper (Refereegranskat)
Abstract [en]

This paper deals with the state estimation problemin an impulsive model of Goodwin’s oscillator forced by acontinuous exogenous signal. The continuous linear part of themodel is controlled by an intrinsic impulsive feedback thatcontributes discrete dynamics to the closed-loop system. Theimpacting pulsatile feedback signal is not available for mea-surement and, therefore, has to be reconstructed. To estimateall the elements of the hybrid state vector, an observationproblem is considered. Two hybrid observer structures areproposed and evaluated: one based on reconstructing both thestates of the Goodwin’s oscillator and those of the exogenoussystem and another assuming that the exogenous signal, or afunction of it, is known. The observer design is reduced to aproblem of synchronizing the impulsive sequence produced bythe observer with that of the plant. It utilizes a local approach ofassigning a guaranteed convergence rate to the local dynamicsof a synchronous mode through output error feedback. Thedynamics of the proposed observer schemes are analyzed bymeans of pointwise discrete (Poincar ́e) maps and illustrated bynumerical simulation for a case of bistability in the oscillator.

Ort, förlag, år, upplaga, sidor
Piscataway, NJ: IEEE, 2017
Serie
Proceedings / IEEE Conference on Decision and Control, ISSN 0743-1546
Nationell ämneskategori
Reglerteknik
Identifikatorer
urn:nbn:se:uu:diva-342163 (URN)10.1109/CDC.2017.8264000 (DOI)000424696902052 ()978-1-5090-2873-3 (ISBN)
Konferens
CDC 2017, IEEE 56:th Annual Conference on Decision and Control, December 12–15,2017, Melbourne, Australia
Forskningsfinansiär
Vetenskapsrådet, 2015-05256
Tillgänglig från: 2018-01-23 Skapad: 2018-02-19 Senast uppdaterad: 2019-04-25Bibliografiskt granskad
5. Attractivity of the synchronous mode in hybrid observers for the impulsive Goodwin's oscillator subject to harmonic exogenous excitation
Öppna denna publikation i ny flik eller fönster >>Attractivity of the synchronous mode in hybrid observers for the impulsive Goodwin's oscillator subject to harmonic exogenous excitation
2019 (Engelska)Ingår i: Proc. American Control Conference: ACC 2019, American Automatic Control Council , 2019, s. 2334-2339Konferensbidrag, Publicerat paper (Refereegranskat)
Ort, förlag, år, upplaga, sidor
American Automatic Control Council, 2019
Nationell ämneskategori
Reglerteknik
Identifikatorer
urn:nbn:se:uu:diva-382413 (URN)978-1-5386-7926-5 (ISBN)
Konferens
ACC 2019, July 10–12, Philadelphia, PA
Tillgänglig från: 2019-08-29 Skapad: 2019-04-25 Senast uppdaterad: 2019-09-30Bibliografiskt granskad
6. Finite-dimensional hybrid observer for delayed impulsive model of testosterone regulation
Öppna denna publikation i ny flik eller fönster >>Finite-dimensional hybrid observer for delayed impulsive model of testosterone regulation
2015 (Engelska)Ingår i: Mathematical problems in engineering (Print), ISSN 1024-123X, E-ISSN 1563-5147, Vol. 2015, s. 190463:1-12, artikel-id 190463Artikel i tidskrift (Refereegranskat) Published
Nationell ämneskategori
Reglerteknik
Identifikatorer
urn:nbn:se:uu:diva-270002 (URN)10.1155/2015/190463 (DOI)000365229600001 ()
Tillgänglig från: 2015-12-19 Skapad: 2015-12-19 Senast uppdaterad: 2019-04-25Bibliografiskt granskad
7. Hybrid state observer for time-delay systems under intrinsic impulsive feedback
Öppna denna publikation i ny flik eller fönster >>Hybrid state observer for time-delay systems under intrinsic impulsive feedback
2014 (Engelska)Ingår i: Proc. 21st International Symposium on Mathematical Theory of Networks and Systems, The Netherlands: University of Groningen , 2014, s. 977-984Konferensbidrag, Publicerat paper (Refereegranskat)
Ort, förlag, år, upplaga, sidor
The Netherlands: University of Groningen, 2014
Nationell ämneskategori
Reglerteknik
Identifikatorer
urn:nbn:se:uu:diva-315989 (URN)978-90-367-6321-9 (ISBN)
Konferens
MTNS 2014, July 7–11, Groningen, The Netherlands
Tillgänglig från: 2014-07-11 Skapad: 2017-02-23 Senast uppdaterad: 2019-04-25Bibliografiskt granskad

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