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DelayDependent Robust Stability Analysis and Stabilization for Uncertain Systems with TimeVarying DelayChen, JunShen 04 September 2010 (has links)
This thesis concerns delaydependent robust stability analysis and stabilization for timedelay system with uncertainties. By choosing new LyapunovKrasovskii functional and using methods which can reduce conservativeness of stability condition in the literature, new delaydependent sufficient stability conditions are obtained in terms of linear matrix inequality. It is shown that the new stability conditions can provide less conservative results than some existing ones. Furthermore, the new stability conditions are also used to design the state feedback controllers. Finally, numerical examples are given to show the derived results and compared with results in the literature.

2 
Analysis and synthesis of distributed control systems under communication constraintsChen, Yuanye 21 December 2017 (has links)
With the help of rapidly advancing communication technology, control systems
are increasingly integrated via communication networks. Networked control systems
(NCSs) bring significant advantages such as flexible and scalable structures, easy
implementation and maintenance, and efficient resources distribution and allocation.
NCSs empowers to finish some complicated tasks using some relatively simple systems
in a collaborated manner. However, there are also some challenges and constraints
subject to the imperfection of communication channels. In this thesis, the stabilization
problems and the performance limitation problems of control systems subject to
networkedinduced constraints are studied.
Overall, the thesis mainly includes two parts: 1) Consensus and consensusability
of multiagent systems (MASs); 2) Delay margins of NCSs. Chapter 2 and Chapter 3
deal with the consensus problems of MASs, which aim to properly design the control
protocols to ensure the state convergence of all the agents. Chapter 4 and Chapter 5
focus on the consensusability analysis, exploring how the dynamics of the agents and
the networked induced constraints impact the overall systems for achieving consensus.
Chapter 6 pays attention to the delay margins of discretetime linear timeinvariant
(LTI) systems, studying how the dynamics of the plants limit the time delays that
can be tolerated by LTI controllers.
In Chapter 2, the leaderfollowing consensus problem of MASs with general linear
dynamics and arbitrary switching topologies is considered. The MAS with arbitrary
switching topologies is formulated as a switched system. Then the leaderfollowing
consensus problem is transformed to the stability problem of the corresponding
switched system. A necessary and sufficient consensus condition is derived.
The condition is also extended to MASs with timevarying delays.
In Chapter 3, the consensus problem of MASs with general linear dynamics is
studied. Motivated by the multipleinput multipleoutput (MIMO) communication
technique, a general framework is considered in which different state variables are
exchanged in different independent communication topologies. This novel framework
could improve the control system design flexibility and potentially improve the system
performance. Fully distributed consensus protocols are proposed and analyzed for
the settings of fixed and switching multiple topologies. The protocols can be applied
using only local information. And the control gains can be designed depending on
the dynamics of the individual agent. By transforming the overall MASs into cascade
systems, necessary and sufficient conditions are provided to guarantee the consensus
under fixed and switching statevariablesdependent topologies, respectively.
Chapter 4 investigates the consensusability problem for MASs with timevarying
delays. The bounded delays can be arbitrarily fast timevarying. The communication
topology is assumed to be undirected and fixed. Considering general linear dynamics
under average state protocols, the consensus problem is then transformed into a
robust control problem. Sufficient frequency domain criteria are established in terms
of smallgain theorem by analyzing the delay dependent gains for both continuoustime
and discretetime systems. The controller synthesis problems can be solved by
applying the frequency domain design methods.
The consensusablity problem of general linear MASs considering directed topologies
are explored from a frequency domain perspective in Chapter 5. By investigating
the properties of Laplacian spectra, a consensus criterion is established based on the
stability of several complex weighted closedloop systems. Furthermore, for singleinput
MASs, frequency domain consensusability criteria are proposed on the basis of
the stability margins, which depend on the H∞ norm of the complementary sensitivity
function determined by the agents’ unstable poles. The corresponding design
procedure is also developed.
Chapter 6 studies the delay margin problem of discretetime LTI systems. For
general LTI plants with multiple unstable poles and nonminimum phase zeros, we
employ analytic function interpolation and rational approximation techniques to derive
bounds on delay margins. Readily computable and explicit lower bounds are
found by computing the real eigenvalues of a constant matrix, and LTI controllers can
be synthesized based on the H∞ control theory to achieve the bounds. The results
can be also consistently extended to the case of systems with timevarying delays.
For firstorder unstable plants, we also obtain bounds achievable by proportionalintergral
derivative (PID) controllers, which are of interest to PID control design and
implementation. It is worth noting that unlike its continuoustime counterpart, the
discretetime delay margin problem being considered herein constitutes a simultaneous
stabilization problem, which is known to be rather difficult. While previous work
on the discretetime delay margin led to negative results, the bounds developed in
this chapter provide instead a guaranteed range of delays within which the delayed
plants can be robustly stabilized, and in turn solve the special class of simultaneous
stabilization problems in question.
Finally, in Chapter 7, the thesis is summarized and some future research topics
are also presented. / Graduate

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Nouvelles stratégies de contrôle avancé pour les procédés sidérurgiques / New Advanced Control Strategy for Steel Making ProcessAsghar, Mohamad Taki 03 May 2018 (has links)
L'industrie sidérurgique rencontre depuis des années un développement important. Les caractéristiques des produits destinés aux différents secteurs industriels deviennent de plus en plus exigeantes. Actuellement des régulateurs avancés de type PID sont utilisés avec une structure multiboucles locales. Afin de traiter les cahiers des charges de plus en plus contraints, il devient intéressant de revoir cette stratégie de contrôle. Ce sujet de thèse CIFRE entre ArcelorMittal et le CRAN a pour objectif de proposer de nouvelles stratégies de contrôle avancé pour le laminage à froid des bandes d'acier de type tôle fine, notamment des stratégies centralisées de contrôle remplaçant des boucles de régulation locales et indépendantes, afin d'élargir le champ des matériaux traitables, d'augmenter et d'optimiser la productivité et les capabilités du procédé ainsi que de minimiser les coûts de production. Dans une première partie, une étude bibliographique sera effectuée afin de mieux cerner les différents modèles métallurgiques et dynamiques du système à piloter. Dans une seconde partie, le cahier des charges sera traduit en termes d'un problème d'optimisation dont la solution est un contrôleur de type retour d'état. Enfin dans une troisième et dernière partie, une synthèse de retour de sortie dynamique sera proposée pour résoudre le problème des mesures manquantes / The steel industry has been developing for years. The characteristics of the products intended for the various industrial sectors are becoming more and more demanded. Currently advanced PID controllers are used with a local multiloop structure. In order to deal with the increasingly constrained specifications, it is interesting to review this control strategy. This CIFRE PhD thesis between ArcelorMittal and CRAN aims to propose new advanced control strategies for the cold rolling of thin sheet steel strips, including centralized control strategies replacing local and independent control loops, to broaden the scope of treatable materials, increase and optimize process productivity and capabilities, and minimize production costs. In a first part, a bibliographic study will be carried out in order to better define the various metallurgical and dynamic models of the system to be controlled. In a second part, the specifications will be translated in terms of an optimization problem whose solution is the state feedback controller. Finally, in a third and final part, a dynamic output feedback synthesis will be proposed to solve the problem of missing measurements

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Quasilinear Control of Systems with TimeDelays and Nonlinear Actuators and SensorsHuang, WeiPing 01 January 2018 (has links)
This thesis investigates Quasilinear Control (QLC) of timedelay systems with nonlinear actuators and sensors and analyzes the accuracy of stochastic linearization for these systems. QLC leverages the method of stochastic linearization to replace each nonlinearity with an equivalent gain, which is obtained by solving a transcendental equation. The idea of QLC is to stochastically linearize the system in order to analyze and design controllers using classical linear control theory. In this thesis, the existence of the equivalent gain for a closedloop timedelay system is discussed. To compute the equivalent gain, two methods are explored. The first method uses an explicit but complex algorithm based on delay Lyapunov equation to study the timedelay, while the second method uses Pade approximant. It is shown that, under a suitable criterion, Pade approximant can be effectively applied for QLC of timedelay systems. Furthermore, the method of SaturatedRoot Locus (SRL) is extended to nonlinear timedelay systems. It turns out that, in a timedelay system, SRL always terminates prematurely as opposed to a delayfree system, which may or may not terminate prematurely. Statistical experiments are performed to investigate the accuracy of stochastic linearization compared to a system without timedelay. The impact of increasing the timedelay in the approach of stochastic linearization is also investigated. Results show that stochastic linearization effectively linearizes a nonlinear timedelay system, even though delays generally degrade accuracy. Overall, the accuracy remains relatively high over the selected parameters. Finally, this approach is applied to pitch control in a wind turbine system as a practical example of a nonlinear timedelay system, and its performance is analyzed to demonstrate the efficacy of the approach.

5 
Approximation and applications of distributed delayLu, Hao 01 October 2013 (has links) (PDF)
A distributed delay is a linear inputoutput operators and appears in many control problems. We investigate distributed delay and its applications. After introducing the definition and the main properties of the distributed delay, the numerical implementation problem of distributed delays is analyzed and a general method for its approximation is given. Then three applications are focused on where distributed delay appears. The first application is the stable inversion and model matching. A new class of stable inversion and model matching problem for finite dimensional linear timeinvariant systems is defined. The stable inversion (resp. model matching) is an approximation of the inverse of a given model (resp. model matching), where exact inversion (resp. exact matching) is reached after a time $t=h$, which is a parameter of our procedure. The second application is concerned with stabilization and finite spectrum assignment for a class of infinite dimensional systems. The last application concerns observer synthesis for estimation or output control. For linear finite dimensional systems. A closedloop memoryless observer by input injection is introduced. Asymptotic convergence as well as finite time convergence of the estimation are analyzed by output injection and input information via distributed delay. At last, we introduce a new class for approximation of distributed parameter systems. We work on the graph topology, and show that under some weak assumptions, such an approximation can be realized using distributed delay.

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Symmetric bifurcation analysis of synchronous states of timedelay oscillators networks. / Análise de bifurcações simétricas de estados síncronos em redes de osciladores com atraso de tempo.Ferruzzo Correa, Diego Paolo 30 May 2014 (has links)
In recent years, there has been increasing interest in studying timedelayed coupled networks of oscillators since these occur in many real life applications. In many cases symmetry, patterns can emerge in these networks; as a consequence, a part of the system might repeat itself, and properties of this symmetric subsystem represent the whole dynamics. In this thesis, an analysis of a second order Nnode timedelay fully connected network is made. This study is carried out using symmetry groups. The existence of multiple eigenvalues forced by symmetry is shown, as well as the possibility of uncoupling the linearization at equilibria, into irreducible representations due to the symmetry. The existence of steadystate and Hopf bifurcations in each irreducible representation is also proved. Three different models are used to analyze the network dynamics, namely, the fullphase, the phase, and the phasedifference model. A finite set of frequencies ω is also determined, which might correspond to Hopf bifurcations in each case for critical values of the delay. Although we restrict our attention to second order nodes, the results could be extended to higher order networks provided the timedelay in the connections between nodes remains equal. / Nos últimos anos, tem havido um crescente interesse em estudar redes de osciladores acopladas com retardo de tempo uma vez que estes ocorrem em muitas aplicações da vida real. Em muitos casos, simetria e padrões podem surgir nessas redes; em consequência, uma parte do sistema pode repetirse, e as propriedades deste subsistema simétrico representam a dinâmica da rede toda. Nesta tese é feita uma análise de uma rede de N nós de segunda ordem totalmente conectada com atraso de tempo. Este estudo é realizado utilizando grupos de simetria. É mostrada a existência de múltiplos valores próprios forçados por simetria, bem como a possibilidade de desacoplamento da linearização no equilíbrio, em representações irredutíveis. É também provada a existência de bifurcações de estado estacionário e Hopf em cada representação irredutível. São usados três modelos diferentes para analisar a dinâmica da rede: o modelo de fase completa, o modelo de fase, e o modelo de diferença de fase. É também determinado um conjunto finito de frequências ω, que pode corresponder a bifurcações de Hopf em cada caso, para valores críticos do atraso. Apesar de restringir a nossa atenção para nós de segunda ordem, os resultados podem ser estendido para redes de ordem superior, desde que o tempo de atraso nas conexões entre nós permanece igual.

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Approximation and applications of distributed delay / Approximation et applications de retard distributéLu, Hao 01 October 2013 (has links)
Dans ce manuscrit, nous étudions le retard distribué et ses applications. Nous présentons la définition du retard distribué et l'étude de ses propriétés. Nous expliquons aussi le problème de la mise en œuvre du retard distribué et donnons une méthode générale pour son approximation. Ensuite nous présentons trois applications à l'aide de retard distribué, qui sont différentes avec les applications apparaissent dans la littérature. Le premier est l'inversion stable et le modèle appariement. Nous introduisons une nouvelle classe d'inversion stable et modèle d'appariement pour les systèmes linéaires de dimension finie invariables dans le temps. L'inversion stable (resp. modèle d'appariement) est une sorte d'inversion (resp. modèle d'appariement) de rapprochement. En fait, nous obtenons l'inversion exacte (resp. exacte modèle d'appariement) après un temps t = h, où le temps t = h peut être choisi arbitrairement. La deuxième application est le contrôle de la stabilité et du pôle placement finie pour une classe de système de dimension infinie. La dernière application du retard distribué est la synthèse de l'observateur pour l'estimation ou la commande de sortie. Nous craignons seulement avec les systèmes linéaires de dimension finie. Nous introduisons une boucle fermée observateurs sans mémoire par injection d'entrée. Convergence asymptotique ainsi que la convergence en temps fini de l'estimation sont analysés par injection de sortie et des informations d'entrée via retard distribué. Enfin, nous introduisons une nouvelle classe de l’approximation des systèmes à paramètres distribués. Nous travaillons sur la topologie du graphe, et montrons que sous certaines hypothèses faibles, une telle approximation peut être réalisé en utilisant retard distribué. / A distributed delay is a linear inputoutput operators and appears in many control problems. We investigate distributed delay and its applications. After introducing the definition and the main properties of the distributed delay, the numerical implementation problem of distributed delays is analyzed and a general method for its approximation is given. Then three applications are focused on where distributed delay appears. The first application is the stable inversion and model matching. A new class of stable inversion and model matching problem for finite dimensional linear timeinvariant systems is defined. The stable inversion (resp. model matching) is an approximation of the inverse of a given model (resp. model matching), where exact inversion (resp. exact matching) is reached after a time $t=h$, which is a parameter of our procedure. The second application is concerned with stabilization and finite spectrum assignment for a class of infinite dimensional systems. The last application concerns observer synthesis for estimation or output control. For linear finite dimensional systems. A closedloop memoryless observer by input injection is introduced. Asymptotic convergence as well as finite time convergence of the estimation are analyzed by output injection and input information via distributed delay. At last, we introduce a new class for approximation of distributed parameter systems. We work on the graph topology, and show that under some weak assumptions, such an approximation can be realized using distributed delay.

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Symmetric bifurcation analysis of synchronous states of timedelay oscillators networks. / Análise de bifurcações simétricas de estados síncronos em redes de osciladores com atraso de tempo.Diego Paolo Ferruzzo Correa 30 May 2014 (has links)
In recent years, there has been increasing interest in studying timedelayed coupled networks of oscillators since these occur in many real life applications. In many cases symmetry, patterns can emerge in these networks; as a consequence, a part of the system might repeat itself, and properties of this symmetric subsystem represent the whole dynamics. In this thesis, an analysis of a second order Nnode timedelay fully connected network is made. This study is carried out using symmetry groups. The existence of multiple eigenvalues forced by symmetry is shown, as well as the possibility of uncoupling the linearization at equilibria, into irreducible representations due to the symmetry. The existence of steadystate and Hopf bifurcations in each irreducible representation is also proved. Three different models are used to analyze the network dynamics, namely, the fullphase, the phase, and the phasedifference model. A finite set of frequencies ω is also determined, which might correspond to Hopf bifurcations in each case for critical values of the delay. Although we restrict our attention to second order nodes, the results could be extended to higher order networks provided the timedelay in the connections between nodes remains equal. / Nos últimos anos, tem havido um crescente interesse em estudar redes de osciladores acopladas com retardo de tempo uma vez que estes ocorrem em muitas aplicações da vida real. Em muitos casos, simetria e padrões podem surgir nessas redes; em consequência, uma parte do sistema pode repetirse, e as propriedades deste subsistema simétrico representam a dinâmica da rede toda. Nesta tese é feita uma análise de uma rede de N nós de segunda ordem totalmente conectada com atraso de tempo. Este estudo é realizado utilizando grupos de simetria. É mostrada a existência de múltiplos valores próprios forçados por simetria, bem como a possibilidade de desacoplamento da linearização no equilíbrio, em representações irredutíveis. É também provada a existência de bifurcações de estado estacionário e Hopf em cada representação irredutível. São usados três modelos diferentes para analisar a dinâmica da rede: o modelo de fase completa, o modelo de fase, e o modelo de diferença de fase. É também determinado um conjunto finito de frequências ω, que pode corresponder a bifurcações de Hopf em cada caso, para valores críticos do atraso. Apesar de restringir a nossa atenção para nós de segunda ordem, os resultados podem ser estendido para redes de ordem superior, desde que o tempo de atraso nas conexões entre nós permanece igual.

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Essays on Agricultural and Financial Markets in PakistanChaudhry, Muhammad Imran January 2016 (has links)
No description available.

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Contribution à la commande robuste des systèmes à échantillonnage variable ou contrôlé / Contribution to the control of systems with timevarying and statedependent samplingFiter, Christophe 25 September 2012 (has links)
Cette thèse est dédiée à l'analyse de stabilité des systèmes à pas d'échantillonnage variable et à la commande dynamique de l'échantillonnage. L'objectif est de concevoir des lois d'échantillonnage permettant de réduire la fréquence d'actualisation de la commande par retour d'état, tout en garantissant la stabilité du système.Tout d'abord, un aperçu des récents défis et axes de recherche sur les systèmes échantillonnés est présenté. Ensuite, une nouvelle approche de contrôle dynamique de l'échantillonnage, "échantillonnage dépendant de l'état", est proposée. Elle permet de concevoir horsligne un échantillonnage maximal dépendant de l'état défini sur des régions coniques de l'espace d'état, grâce à des LMIs.Plusieurs types de systèmes sont étudiés. Tout d'abord, le cas de système LTI idéal est considéré. La fonction d'échantillonnage est construite au moyen de polytopes convexes et de conditions de stabilité exponentielle de type LyapunovRazumikhin. Ensuite, la robustesse visàvis des perturbations est incluse. Plusieurs applications sont proposées: analyse de stabilité robuste visàvis des variations du pas d'échantillonnage, contrôles eventtriggered et selftriggered, et échantillonnage dépendant de l'état. Enfin, le cas de système LTI perturbé à retard est traité. La construction de la fonction d'échantillonnage est basée sur des conditions de stabilité L2 et sur un nouveau type de fonctionnelles de LyapunovKrasovskii avec des matrices dépendant de l'état. Pour finir, le problème de stabilisation est traité, avec un nouveau contrôleur dont les gains commutent en fonction de l'état du système. Un codesign contrôleur/fonction d'échantillonnage est alors proposé / This PhD thesis is dedicated to the stability analysis of sampleddata systems with timevarying sampling, and to the dynamic control of the sampling instants. The main objective is to design sampling laws that allow for reducing the sampling frequency of statefeedback control for linear systems while ensuring the system's stability.First, an overview of the recent problems, challenges, and research directions regarding sampleddata systems is presented. Then, a novel dynamic sampling control approach, "statedependent sampling", is proposed. It allows for designing offline a maximal statedependent sampling map over conic regions of the state space, thanks to LMIs.Various classes of systems are considered throughout the thesis. First, we consider the case of ideal LTI systems, and propose a sampling map design based on the use of polytopic embeddings and LyapunovRazumikhin exponential stability conditions. Then, the robustness with respect to exogenous perturbations is included. Different applications are proposed: robust stability analysis with respect to timevarying sampling, as well as eventtriggered, selftriggered, and statedependent sampling control schemes. Finally, a sampling map design is proposed in the case of perturbed LTI systems with delay in the feedback control loop. It is based on L2stability conditions and a novel type of LyapunovKrasovskii functionals with statedependent matrices. Here, the stabilization issue is considered, and a new controller with gains that switch according to the system's state is presented. A codesign controller gains/sampling map is then proposed

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