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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
21

STABILITY RESULTS FOR MULTIPLE VOLTERRA INTEGRAL EQUATIONS

DeFranco, Ronald James, 1943- January 1973 (has links)
No description available.
22

Nonlinear controller synthesis for complex chemical and biochemical reaction systems

Leising, Sophie. January 2005 (has links)
Thesis (M.S.) -- Worcester Polytechnic Institute. / Keywords: model predictive control; discrete-time model; continuous-time model; nonlinear systems; Lyapunov design. Includes bibliographical references (p. 99-102).
23

Lyapunov stability analysis of a class of variable speed drives

Lipo, Thomas Anthony, January 1968 (has links)
Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record.
24

Quantifying linear disturbance growth in periodic and aperiodic systems /

Wolfe, Christopher Lee. January 1900 (has links)
Thesis (Ph. D.)--Oregon State University, 2007. / Printout. Includes bibliographical references (leaves 151-157). Also available on the World Wide Web.
25

Controle de sistemas lineares incertos via realimentação derivativa utilizando Funções de Lyapunov dependentes de parâmetros

Silva, Emerson Ravazzi Pires da [UNESP] 23 November 2012 (has links) (PDF)
Made available in DSpace on 2014-06-11T19:30:32Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-11-23Bitstream added on 2014-06-13T19:19:27Z : No. of bitstreams: 1 silva_erp_dr_ilha.pdf: 2155421 bytes, checksum: 4781ef3e29238bac1eacd6e10b9b4b71 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Este trabalho trata do problema de estabilização robusta de sistemas lineares contínuos no tempo sujeitos a incertezas do tipo politópicas no modelo. Todo o trabalho é fundamen- tado em leis de controle por realimentação da derivada do vetor de estado (realimentação derivativa). A motivação em utilizar a realimentação derivativa (u(t) = −Kd x(t)) em ̇ vez da realimentação do vetor de estado convencional é devido à facilidade de imple- mentação em algumas aplicações mecânicas, por exemplo, no controle de vibrações de sistemas mecânicos, nos quais sensores como acelerômetros têm sido utilizados para me- dir a derivada de segunda ordem (aceleração) de uma variável de estado (posição) desses sistemas. A metodologia apresenta condições suficientes na forma de desigualdades ma- triciais lineares (LMIs, acrônimo inglês para Linear Matrix Inequalities) para a síntese de controladores lineares robustos estáticos (Kd ), visando a princípio apenas a estabilização do sistema, na sequência a estabilização com restrição de taxa de decaimento (γ > 0) e por fim projetos que asseguram a D-estabilidade (alocação regional) robusta, restringindo os autovalores a uma determinada região do plano complexo. Os índices de desempenho de taxa de decaimento e D-estabilidade são adicionados no projeto dos controladores visto que, garantir apenas a estabilidade do sistema nem sempre é suficiente para um bom desempenho prático. As formulações LMIs são realizadas através de lemas largamente utilizados (Lema da Projeção Recíproca e Lema de Finsler) em análise de estabilidade e projetos de controladores para os mais diversos problemas. Estes lemas permitem o uso de uma função de Lyapunov dependente de parâmetros (PDLF, acrônimo inglês para Parameter-Dependent Lyapunov Function) para assegurar a estabilidade... / This work deals with the problem of robust stabilization of continuous-time linear sys- tems subjected to polytopic uncertainties in the plant. All our work is based on control techniques using only the state-derivative feedback. The motivation for the use of state- derivative feedback (u(t) = −Kd x(t)) instead of conventional state feedback is due to ease ̇ of implementation in some mechanical applications, for instance, in the vibration control of mechanical systems, in which sensors like accelerometers have been used to measure the second order derivative (acceleration) of one state variable (position) of these systems. The methodology presents sufficient conditions in the form of linear matrix inequalities (LMIs) for the synthesis of static linear robust controllers (Kd ), aiming at first only the system’s stability, followed by the system’s stability with decay rate (γ > 0) and finally designs that ensure the system’s robust D-stability (regional allocation), restricting the eigenvalues at a given region of the complex plane. The performance indexes of decay rate and D-stability are added in the controllers design since ensuring system’s stability only is not always sufficient for a good practical performance. The LMIs formulations are made through widely used lemmas (Reciprocal Projection Lemma and Finsler’s Lemma) in the stability analysis and in the controllers design for many problems. These lemmas allow the use of a parameter-dependent Lyapunov function (PDLF) to ensure the asymptotic stability of the systems in the sense of Lyapunov. Comparing with the existing litera- ture, in which the results consider classical LMIs formulations, based on the existence of a common quadratic Lyapunov function (CQLF) for the solution of the problems, the present work shows to be less conservative in most occasions. In many cases... (Complete abstract click electronic access below)
26

Controle de sistemas lineares incertos via realimentação derivativa utilizando Funções de Lyapunov dependentes de parâmetros /

Silva, Emerson Ravazzi Pires da. January 2012 (has links)
Orientador: Edvaldo Assunção / Banca: Marcelo Carvalho Minhoto Teixeira / Banca: Rodrigo Cardim / Banca: Roberto Kawakami Harrop Galvão / Banca: Flávio Andrade Faria / Resumo: Este trabalho trata do problema de estabilização robusta de sistemas lineares contínuos no tempo sujeitos a incertezas do tipo politópicas no modelo. Todo o trabalho é fundamen- tado em leis de controle por realimentação da derivada do vetor de estado (realimentação derivativa). A motivação em utilizar a realimentação derivativa (u(t) = −Kd x(t)) em ̇ vez da realimentação do vetor de estado convencional é devido à facilidade de imple- mentação em algumas aplicações mecânicas, por exemplo, no controle de vibrações de sistemas mecânicos, nos quais sensores como acelerômetros têm sido utilizados para me- dir a derivada de segunda ordem (aceleração) de uma variável de estado (posição) desses sistemas. A metodologia apresenta condições suficientes na forma de desigualdades ma- triciais lineares (LMIs, acrônimo inglês para Linear Matrix Inequalities) para a síntese de controladores lineares robustos estáticos (Kd ), visando a princípio apenas a estabilização do sistema, na sequência a estabilização com restrição de taxa de decaimento (γ > 0) e por fim projetos que asseguram a D-estabilidade (alocação regional) robusta, restringindo os autovalores a uma determinada região do plano complexo. Os índices de desempenho de taxa de decaimento e D-estabilidade são adicionados no projeto dos controladores visto que, garantir apenas a estabilidade do sistema nem sempre é suficiente para um bom desempenho prático. As formulações LMIs são realizadas através de lemas largamente utilizados (Lema da Projeção Recíproca e Lema de Finsler) em análise de estabilidade e projetos de controladores para os mais diversos problemas. Estes lemas permitem o uso de uma função de Lyapunov dependente de parâmetros (PDLF, acrônimo inglês para Parameter-Dependent Lyapunov Function) para assegurar a estabilidade... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This work deals with the problem of robust stabilization of continuous-time linear sys- tems subjected to polytopic uncertainties in the plant. All our work is based on control techniques using only the state-derivative feedback. The motivation for the use of state- derivative feedback (u(t) = −Kd x(t)) instead of conventional state feedback is due to ease ̇ of implementation in some mechanical applications, for instance, in the vibration control of mechanical systems, in which sensors like accelerometers have been used to measure the second order derivative (acceleration) of one state variable (position) of these systems. The methodology presents sufficient conditions in the form of linear matrix inequalities (LMIs) for the synthesis of static linear robust controllers (Kd ), aiming at first only the system's stability, followed by the system's stability with decay rate (γ > 0) and finally designs that ensure the system's robust D-stability (regional allocation), restricting the eigenvalues at a given region of the complex plane. The performance indexes of decay rate and D-stability are added in the controllers design since ensuring system's stability only is not always sufficient for a good practical performance. The LMIs formulations are made through widely used lemmas (Reciprocal Projection Lemma and Finsler's Lemma) in the stability analysis and in the controllers design for many problems. These lemmas allow the use of a parameter-dependent Lyapunov function (PDLF) to ensure the asymptotic stability of the systems in the sense of Lyapunov. Comparing with the existing litera- ture, in which the results consider classical LMIs formulations, based on the existence of a common quadratic Lyapunov function (CQLF) for the solution of the problems, the present work shows to be less conservative in most occasions. In many cases... (Complete abstract click electronic access below) / Doutor
27

Qualitative and quantitative properties of solutions of ordinary differential equations

Ogundare, Babatunde Sunday January 2009 (has links)
This thesis is concerned with the qualitative and quantitative properties of solutions of certain classes of ordinary di erential equations (ODEs); in particular linear boundary value problems of second order ODE's and non-linear ODEs of order at most four. The Lyapunov's second method of special functions called Lyapunov functions are employed extensively in this thesis. We construct suitable complete Lyapunov functions to discuss the qualitative properties of solutions to certain classes of non-linear ordinary di erential equations considered. Though there is no unique way of constructing Lyapunov functions, We adopt Cartwright's method to construct complete Lyapunov functions that are required in this thesis. Su cient conditions were established to discuss the qualitative properties such as boundedness, convergence, periodicity and stability of the classes of equations of our focus. Another aspect of this thesis is on the quantitative properties of solutions. New scheme based on interpolation and collocation is derived for solving initial value problem of ODEs. This scheme is derived from the general method of deriving the spline functions. Also by exploiting the Trigonometric identity property of the Chebyshev polynomials, We develop a new scheme for approximating the solutions of two-point boundary value problems. These schemes are user-friendly, easy to develop algorithm (computer program) and execute. They compare favorably with known standard methods used in solving the classes of problems they were derived for
28

Αριθμητική κατασκευή συναρτήσεων Lyapunov

Αλωνιάτη, Μαρία 14 October 2013 (has links)
Σε αυτή την εργασία παρουσιάζουμε μεθόδους για την κατασκευή συναρτήσεων Lyapunov για δυναμικά συστήματα αλλά και για τον καθορισμό του ελκτικού συνόλου ενός σημείου ισορροπίας. Η μελέτη των διαφορικών εξισώσεων έχει ως κίνητρο τις πολλαπλές εφαρμογές τους στη Φυσική, τη Χημεία, τα Οικονομικά, τη Βιολογία, κ.λ.π.. Εστιάζουμε στις αυτόνομες διαφορικές εξισώσεις της μορφής οι οποίες ορίζουν ένα δυναμικό σύστημα. Οι πιο απλές λύσεις μίας τέτοιας εξίσωσης καλούνται σημεία ισορροπίας. Πολύ σημαντικός είναι επίσης και ο καθορισμός του ελκτικού συνόλου. Ο καθορισμός του ελκτικού συνόλου επιτυγχάνεται μέσω υποεπίπεδων συνόλων μίας συνάρτησης Lyapunov, δηλαδή μίας συνάρτησης με αρνητική παράγωγο κατά μήκος των τροχιών στη περιοχή ισορροπίας. Σε αυτή την εργασία παρουσιάζουμε μεθόδους κατασκευής συναρτήσεων Lyapunov για ένα σημείο ισορροπίας. Υπάρχει πλούσια βιβλιογραφία πάνω στις συναρτήσεις Lyapunov. Το 1893, ο Lyapunov εισήγαγε την άμεση ή δεύτερη μέθοδό του, όπου κατάφερε να εξασφαλίσει αποτελέσματα για την ευστάθεια ενός σημείου ισορροπίας χωρίς να γνωρίζει τη λύση της διαφορικής εξίσωσης, αλλά χρησιμοποιώντας μόνο την ίδια τη διαφορική εξίσωση. Από τότε έχει δοθεί πλήθος αντίστροφων θεωρημάτων, που εξασφαλίζουν την ύπαρξη μίας συνάρτησης Lyapunov, από διάφορους συγγραφείς. Το πρώτο κύριο θεώρημα για ασυμπτωτική ευστάθεια δόθηκε από τον Massera το 1949 και από τότε έχει βελτιωθεί από πολλούς συγγραφείς προς διάφορες κατευθύνσεις. Ωστόσο, κανένα από τα θεωρήματα ύπαρξης δεν παρέχει μία μέθοδο σαφούς κατασκευής μίας συνάρτησης Lyapunov. Για γραμμικά συστήματα μπορεί κάποιος να κατασκευάσει μία τετραγωνικής μορφής συνάρτηση Lyapunov της μορφής με ένα συμμετρικό, θετικά ορισμένο πίνακα , όπου συμβολίζει το σημείο ισορροπίας. Ο Hahn περιγράφει πως μπορεί κάποιος, ξεκινώντας από ένα μη-γραμμικό σύστημα, να χρησιμοποιήσει την τετραγωνικής μορφής συνάρτηση Lyapunov του γραμμικοποιημένου συστήματος σα μία συνάρτηση Lyapunov για το μη-γραμμικό σύστημα. Πολλές προσεγγίσεις θεωρούν ειδικές συναρτήσεις Lyapunov, όπως τετραγωνικής μορφής, πολυωνυμικές, κατά τμήματα γραμμικές, ή κατά τμήματα τετραγωνικής μορφής. Οι μέθοδοι όμως αυτές μπορούν να χρησιμοποιηθούν μόνο σε συγκεκριμμένες διαφορικές εξισώσεις. Σε αυτή την εργασία θα ασχοληθούμε με δύο μεθόδους κατασκευής συναρτήσεων Lyapunov. Για τη πρώτη μέθοδο κατασκευής συναρτήσεων Lyapunov για ένα σημείο ισορροπίας, ξεκινούμε με ένα θεώρημα που εξασφαλίζει την ύπαρξη μίας συνάρτησης Lyapunov η οποία ικανοποιεί την ισότητα , όπου είναι μία γνωστή σταθερά. Βασικός στόχος της μεθόδου είναι να προσεγγίσει τη λύση αυτής της μερικής διαφορικής εξίσωσης με τη χρήση συναρτήσεων ακτινωτής βάσης. Τότε και η προσέγγιση είναι μία συνάρτηση Lyapunov και έτσι, μπορούμε να τη χρησιμοποιήσουμε για να καθορίσουμε το ελκτικό σύνολο. Επειδή η συνάρτηση δεν ορίζεται στο , μελετούμε και μία δεύτερη κλάση συναρτήσεων Lyapunov , οι οποίες ορίζονται και είναι ομαλές στο . Αυτές ικανοποιούν την ισότητα , όπου είναι μία δοθείσα συνάρτηση με συγεκριμμένες ιδιότητες, μία εκ των οποίων είναι ότι . Για την προσέγγιση χρησιμοποιούμε συναρτήσεις ακτινωτής βάσης. Στη δεύτερη μέθοδο κατασκευάζουμε μια κατά τμήματα γραμμική συνάρτηση Lyapunov για το αρχικό μη-γραμμικό σύστημα χρησιμοποιώντας γραμμικό προγραμματισμό. / In this diploma work we present methods for the construction of Lyapunov functions for dynamical systems but also we determine the basin of attraction of an equilibrium. The study of differential equations is motivated from numerous applications in physics, chemistry, economics, biology, etc. We focus on autonomous differential equations x’ = f(x), x ∈ Rn which define a dynamical system. The simplest solutions x(t) of such an equation are equilibria, i.e. solutions x(t) = x0 which remain constant. An important and non-trivial task is thedetermination of their basin of attraction. The determination of the basin of attraction is achieved through sublevel sets of a Lyapunov function, i.e. a function with negative orbital derivative. The orbital derivative V ‘(x) of a function V (x) is the derivative along solutions of the differential equation. In this book we present a method to construct Lyapunov functions for an equilibrium. There is a rich literature on the functions of Lyapunov. In 1893, Lyapunov introduced the direct method, where he managed to secure results for the stability of an equilibrium point without knowing the solution of the differential equation, but using only the same differential equation. Since then many inverse theorems have been given that ensure the existence of a function Lyapunov, by various authors. The first main theorem on asymptotic stability given by Massera in 1949 and since then has been improved by many authors in different directions. However, none of the theorem of existence does not provide a clear method of manufacturing a Lyapunov function. For linear systems, one can construct a quadratic form of a Lyapunov function with a symmetric positive definite table. The Hahn describes how people, starting from a non-linear system, use the like it were a Lyapunov function for the nonlinear system. Many approaches consider special functions Lyapunov, such as quadratic form, polynomial. These methods can be used only in specific differential equations. In this book we present a method to construct Lyapunov functions for an equilibrium. We start from a theorem which ensures the existence of a Lyapunov function T which satisfies the equation T’(x) = −c, where -c > 0 is a given constant. This equation is a linear first-order partial differential equation. The main goal of this method is to approximate the solution T of this partial differential equation using radial basis functions. Then the approximation itself is a Lyapunov function, and thus can be used to determine the basin of attraction. Since the function T is not defined at x0, we also study a second class of Lyapunov functions V which are defined and smooth at x0. They satisfy the equation V ‘(x) = −p(x), where p(x) is a given function with certain properties, in particular p(x0) = 0. For the approximation we use radial basis functions, a powerful meshless approximation method. In the second method we construct a linear Lyapunov function for the original non-linear system using linear programming.
29

Concentration phenomena for singularly perturbed problems on two dimensional domains. / CUHK electronic theses & dissertations collection

January 2007 (has links)
Firstly, we establish the existence of a solution u epsilon concentrating along a curve Gammaepsilon near the non-degenerate Gamma, exponentially small in epsilon at any positive distance from the curve, provided epsilon is small and away from certain critical numbers. The concentrating curve Gammaepsilon will collapse to Gamma as epsilon → 0. / In this thesis, we consider the following problem 32Du-u+up= 0 and u>0 in W , 6u6n= 0 on 6W, where O is a bounded domain in R2 with smooth boundary, epsilon is a small positive parameter, nu denotes the outward normal of O and p > 1. Let Gamma be a straight line intersecting orthogonally with ∂O at exactly two points. We use the infinite dimensional Lyapunov-Schmidt reduction method, introduced by M. del Pino, M. Kowalczyk and J. Wei in [14], to deal with the non-invertibility caused by the critical eigenvalues of the linearized operator in the perturbed problems and then construct interior concentration layers near Gamma, which interact with the boundary. Moreover, the method of successive improvements of the approximation helps us decompose the interaction between the boundary and the interior layers. / Secondly, for any given integer N with N ≥ 2 and for small epsilon away from certain critical numbers, we construct another solution uepsilon exhibiting N concentration layers at mutual distances O(epsilon∣ ln epsilon∣), whose concentration set will approach the non-degenerate and non-minimal Gamma as epsilon → 0, provided that the exponent p ≥ 2. Asymptotic location of these layers is governed by a Toda type system. / Yang, Jun. / "July 2007." / Adviser: Juncheng Wei. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0357. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 129-136). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.
30

Nonlinear adaptive control of highly maneuverable high performance aircraft

Cho, Sul 14 October 1993 (has links)
This thesis presents an effective control design methodology using a one-step-ahead prediction adaptive control law and an adaptive control law based on a Lyapunov function. These control law were applied to a highly maneuverable high performance aircraft, in particular, a modified F/A-18. An adaptive controller is developed to maneuver an aircraft at a high angle of attack even if the aircraft is required to fly over a highly nonlinear flight regime. The adaptive controller presented in this thesis is based on linear, bilinear, and nonlinear prediction models with input constraints. It is shown that the linear, bilinear, and nonlinear adaptive controllers can be constructed to minimize the given cost function or Lyapunov function with respect to the control input at each step. The control is calculated such that the system follows the reference trajectory, and such that control signal remains within its constraints. From several simulation results, the nonlinear controller is controller is better than the linear controller. A nonlinear adaptive control law based on a Lyapunov function is designed such that control inputs are smoother than for the one-step-ahead prediction adaptive controller. / Graduation date: 1994

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