uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Hybrid observers for systems with intrinsic pulse-modulated feedback
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.
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 [en]
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: urn:nbn:se:uu:diva-382414ISBN: 978-91-513-0665-0 (print)OAI: oai:DiVA.org:uu-382414DiVA, id: diva2:1306831
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
List of papers
1. Bifurcation analysis for non-local design of a hybrid observer for the impulsive Goodwin's oscillator
Open this publication in new window or tab >>Bifurcation analysis for non-local design of a hybrid observer for the impulsive Goodwin's oscillator
2019 (English)In: Article in journal (Other academic) Submitted
National Category
Control Engineering
Identifiers
urn:nbn:se:uu:diva-382411 (URN)
Available from: 2019-04-25 Created: 2019-04-25 Last updated: 2019-05-07Bibliographically approved
2. Hybrid observer with finite-memory output error correction for linear systems under intrinsic impulsive feedback
Open this publication in new window or tab >>Hybrid observer with finite-memory output error correction for linear systems under intrinsic impulsive feedback
2019 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836Article in journal (Other academic) Submitted
National Category
Control Engineering
Identifiers
urn:nbn:se:uu:diva-382412 (URN)
Available from: 2019-04-25 Created: 2019-04-25 Last updated: 2019-05-07Bibliographically approved
3. Robustification of the synchronous mode in a hybrid observer for a continuous system under an intrinsic pulse-modulated feedback
Open this publication in new window or tab >>Robustification of the synchronous mode in a hybrid observer for a continuous system under an intrinsic pulse-modulated feedback
2018 (English)In: Proc. 16th European Control Conference, IEEE, 2018, p. 107-112Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
IEEE, 2018
National Category
Control Engineering
Identifiers
urn:nbn:se:uu:diva-354827 (URN)10.23919/ECC.2018.8550264 (DOI)000467725300018 ()978-3-9524-2698-2 (ISBN)
Conference
ECC 2018, June 12–15, Limassol, Cyprus
Available from: 2018-11-29 Created: 2018-06-22 Last updated: 2019-06-19Bibliographically approved
4. Hybrid observers for an impulsive Goodwin’s oscillator subject to continuous exogenous signals
Open this publication in new window or tab >>Hybrid observers for an impulsive Goodwin’s oscillator subject to continuous exogenous signals
2017 (English)In: 2017 IEEE 56Th Annual Conference on Decision and Control (Cdc), Piscataway, NJ: IEEE, 2017, p. 2396-2401Conference paper, Published paper (Refereed)
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.

Place, publisher, year, edition, pages
Piscataway, NJ: IEEE, 2017
Series
Proceedings / IEEE Conference on Decision and Control, ISSN 0743-1546
National Category
Control Engineering
Identifiers
urn:nbn:se:uu:diva-342163 (URN)10.1109/CDC.2017.8264000 (DOI)000424696902052 ()978-1-5090-2873-3 (ISBN)
Conference
CDC 2017, IEEE 56:th Annual Conference on Decision and Control, December 12–15,2017, Melbourne, Australia
Funder
Swedish Research Council, 2015-05256
Available from: 2018-01-23 Created: 2018-02-19 Last updated: 2019-04-25Bibliographically approved
5. Attractivity of the synchronous mode in hybrid observers for the impulsive Goodwin's oscillator subject to harmonic exogenous excitation
Open this publication in new window or tab >>Attractivity of the synchronous mode in hybrid observers for the impulsive Goodwin's oscillator subject to harmonic exogenous excitation
2019 (English)In: Proc. American Control Conference: ACC 2019, American Automatic Control Council , 2019, p. 2334-2339Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
American Automatic Control Council, 2019
National Category
Control Engineering
Identifiers
urn:nbn:se:uu:diva-382413 (URN)978-1-5386-7926-5 (ISBN)
Conference
ACC 2019, July 10–12, Philadelphia, PA
Available from: 2019-08-29 Created: 2019-04-25 Last updated: 2019-09-30Bibliographically approved
6. Finite-dimensional hybrid observer for delayed impulsive model of testosterone regulation
Open this publication in new window or tab >>Finite-dimensional hybrid observer for delayed impulsive model of testosterone regulation
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
National Category
Control Engineering
Identifiers
urn:nbn:se:uu:diva-270002 (URN)10.1155/2015/190463 (DOI)000365229600001 ()
Available from: 2015-12-19 Created: 2015-12-19 Last updated: 2019-04-25Bibliographically approved
7. Hybrid state observer for time-delay systems under intrinsic impulsive feedback
Open this publication in new window or tab >>Hybrid state observer for time-delay systems under intrinsic impulsive feedback
2014 (English)In: Proc. 21st International Symposium on Mathematical Theory of Networks and Systems, The Netherlands: University of Groningen , 2014, p. 977-984Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
The Netherlands: University of Groningen, 2014
National Category
Control Engineering
Identifiers
urn:nbn:se:uu:diva-315989 (URN)978-90-367-6321-9 (ISBN)
Conference
MTNS 2014, July 7–11, Groningen, The Netherlands
Available from: 2014-07-11 Created: 2017-02-23 Last updated: 2019-04-25Bibliographically approved

Open Access in DiVA

fulltext(894 kB)84 downloads
File information
File name FULLTEXT01.pdfFile size 894 kBChecksum SHA-512
b463f074004668d41c359cfb2b0b6b90d20b1c29529d93d43ac9ce90810990c83998c5a30e4a5f6dd78f4d18595baeeb41ccc8ccda30a4fef7efad317261c18b
Type fulltextMimetype application/pdf
Buy this publication >>

Authority records BETA

Yamalova, Diana

Search in DiVA

By author/editor
Yamalova, Diana
By organisation
Division of Systems and ControlAutomatic control
Control Engineering

Search outside of DiVA

GoogleGoogle Scholar
Total: 84 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 385 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf