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On Observer-Based Control of Nonlinear Systems

Robertsson, Anders LU (1999) In PhD Theses TFRT-1056.
Abstract
Filtering and reconstruction of signals play a fundamental role in modern signal processing, telecommunications, and control theory and are used in numerous applications.



The feedback principle is an important concept in control theory. Many different control strategies are based on the assumption that all internal states of the control object are available for feedback. In most cases, however, only a few of the states or some functions of the states can be measured. This circumstance raises the need for techniques, which makes it possible not only to estimate states, but also to derive control laws that guarantee stability when using the estimated states instead of the true ones. For linear systems, the separation... (More)
Filtering and reconstruction of signals play a fundamental role in modern signal processing, telecommunications, and control theory and are used in numerous applications.



The feedback principle is an important concept in control theory. Many different control strategies are based on the assumption that all internal states of the control object are available for feedback. In most cases, however, only a few of the states or some functions of the states can be measured. This circumstance raises the need for techniques, which makes it possible not only to estimate states, but also to derive control laws that guarantee stability when using the estimated states instead of the true ones. For linear systems, the separation principle assures stability for the use of converging state estimates in a stabilizing state feedback control law. In general, however, the combination of separately designed state observers and state feedback controllers does not preserve performance, robustness, or even stability of each of the separate designs. In this thesis, the problems of observer design and observer-based control for nonlinear systems are addressed. The deterministic continuous-time systems have been in focus.



Stability analysis related to the Positive Real Lemma with relevance for output feedback control is presented. Separation results for a class of nonholonomic nonlinear systems, where the combination of independently designed observers and state-feedback controllers assures stability in the output tracking problem are shown. In addition, a generalization to the observer-backstepping method where the controller is designed with respect to estimated states, taking into account the effects of the estimation errors, is presented. Velocity observers with application to ship dynamics and mechanical manipulators are also presented. (Less)
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author
opponent
  • Siciliano, Bruno, Dipartimento di Informatica e Sistemistica, Universit√† degli Studi di Napoli Federico II, Italy
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Observers, Output feedback, Separation principle, The Positive Real lemma, Kalman filter, Backstepping, Robotics, Automation, Chained form systems, reglerteknik, robotteknik, Automatiska system, control engineering, Lyapunov stability, Nonlinear systems, State estimation
in
PhD Theses
volume
TFRT-1056
pages
229 pages
publisher
Department of Automatic Control, Lund Institute of Technology (LTH)
defense location
Room M:B, Mechanical Engineering Building, Lund Institute of Technology
defense date
1999-12-16 10:15
ISSN
0280-5316
language
English
LU publication?
yes
id
035aa649-c353-4177-b6bc-cbfc320f5ffa (old id 40156)
date added to LUP
2007-08-01 10:53:05
date last changed
2016-09-19 08:44:57
@phdthesis{035aa649-c353-4177-b6bc-cbfc320f5ffa,
  abstract     = {Filtering and reconstruction of signals play a fundamental role in modern signal processing, telecommunications, and control theory and are used in numerous applications.<br/><br>
<br/><br>
The feedback principle is an important concept in control theory. Many different control strategies are based on the assumption that all internal states of the control object are available for feedback. In most cases, however, only a few of the states or some functions of the states can be measured. This circumstance raises the need for techniques, which makes it possible not only to estimate states, but also to derive control laws that guarantee stability when using the estimated states instead of the true ones. For linear systems, the separation principle assures stability for the use of converging state estimates in a stabilizing state feedback control law. In general, however, the combination of separately designed state observers and state feedback controllers does not preserve performance, robustness, or even stability of each of the separate designs. In this thesis, the problems of observer design and observer-based control for nonlinear systems are addressed. The deterministic continuous-time systems have been in focus.<br/><br>
<br/><br>
Stability analysis related to the Positive Real Lemma with relevance for output feedback control is presented. Separation results for a class of nonholonomic nonlinear systems, where the combination of independently designed observers and state-feedback controllers assures stability in the output tracking problem are shown. In addition, a generalization to the observer-backstepping method where the controller is designed with respect to estimated states, taking into account the effects of the estimation errors, is presented. Velocity observers with application to ship dynamics and mechanical manipulators are also presented.},
  author       = {Robertsson, Anders},
  issn         = {0280-5316},
  keyword      = {Observers,Output feedback,Separation principle,The Positive Real lemma,Kalman filter,Backstepping,Robotics,Automation,Chained form systems,reglerteknik,robotteknik,Automatiska system,control engineering,Lyapunov stability,Nonlinear systems,State estimation},
  language     = {eng},
  pages        = {229},
  publisher    = {Department of Automatic Control, Lund Institute of Technology (LTH)},
  school       = {Lund University},
  series       = {PhD Theses},
  title        = {On Observer-Based Control of Nonlinear Systems},
  volume       = {TFRT-1056},
  year         = {1999},
}