Готові списки джерел за темами / Control of PDEs

Добірка наукової літератури з теми "Control of PDEs"

Автор: Grafiati
Опубліковано: 7 липня 2024
Оновлено: 7 липня 2024

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Статті в журналах з теми "Control of PDEs":

1

Reid, Ian A. "Role of Phosphodiesterase Isoenzymes in the Control of Renin Secretion: Effects of Selective Enzyme Inhibitors." Current Pharmaceutical Design 5, no. 9 (January 1999): 725–35. http://dx.doi.org/10.2174/1381612805666230111201536.

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<p>In most cells, the steady-state level of cAMP ultimately depends on the rate of cAMP synthesis by adenylyl cyclase and the rate of cAMP hydrolysis by cyclic nucleotide phosphodiesterases (PDEs). PDEs exist in multiple forms that have been grouped into seven families based on their substrate specificity, mode of regulation and kinetic properties. Selective inhibitors of many PDE families are now available. Examples are milrinone and trequinsin (PDE3); rolipram and Ro 20-1724 (PDE4); and zaprinast, sildenafil and didyridamole (PDE5). These inhibitors have proven to be valuable tools to investigate the role of PDEs in cell function.</p> <p> Representatives of most PDE families are present in the kidneys, and recent studies in this and other laboratories have provided evidence that some of them participate in the regulation of renin secretion. In particular, administration of selective PDE inhibitors has marked effects on renin secretion. For example, the PDE3 inhibitors milrinone and trequinsin increase resting renin in conscious rabbits and enhance the renin secretory response to beta-adrenergic stimulation. Milrinone also increases renin secretion in human subjects. The PDE4 inhibitors rolipram and Ro 20-1724 both increase renin secretion in rabbits and also enhance the renin response to beta-adrenergic stimulation. Studies in other laboratories have implicated other PDE families in the control of renin secretion. The aim of this review is to present current concepts concerning the PDEs and to discuss their role in the control of renin secretion by the kidneys.</p>
2

Lugnier, Claire. "The Complexity and Multiplicity of the Specific cAMP Phosphodiesterase Family: PDE4, Open New Adapted Therapeutic Approaches." International Journal of Molecular Sciences 23, no. 18 (September 13, 2022): 10616. http://dx.doi.org/10.3390/ijms231810616.

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Cyclic nucleotides (cAMP, cGMP) play a major role in normal and pathologic signaling. Beyond receptors, cyclic nucleotide phosphodiesterases; (PDEs) rapidly convert the cyclic nucleotide in its respective 5′-nucleotide to control intracellular cAMP and/or cGMP levels to maintain a normal physiological state. However, in many pathologies, dysregulations of various PDEs (PDE1-PDE11) contribute mainly to organs and tissue failures related to uncontrolled phosphorylation cascade. Among these, PDE4 represents the greatest family, since it is constituted by 4 genes with multiple variants differently distributed at tissue, cellular and subcellular levels, allowing different fine-tuned regulations. Since the 1980s, pharmaceutical companies have developed PDE4 inhibitors (PDE4-I) to overcome cardiovascular diseases. Since, they have encountered many undesired problems, (emesis), they focused their research on other PDEs. Today, increases in the knowledge of complex PDE4 regulations in various tissues and pathologies, and the evolution in drug design, resulted in a renewal of PDE4-I development. The present review describes the recent PDE4-I development targeting cardiovascular diseases, obesity, diabetes, ulcerative colitis, and Crohn’s disease, malignancies, fatty liver disease, osteoporosis, depression, as well as COVID-19. Today, the direct therapeutic approach of PDE4 is extended by developing allosteric inhibitors and protein/protein interactions allowing to act on the PDE interactome.
3

Cai, Ying-Lan, Mo-Han Zhang, Xu Huang, Jing-Zhi Jiang, Li-Hua Piao, Zheng Jin, and Wen-Xie Xu. "CNP-pGC-cGMP-PDE3-cAMP Signal Pathway Upregulated in Gastric Smooth Muscle of Diabetic Rats." Gastroenterology Research and Practice 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/305258.

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Our previous studies have shown that CNP-NPR-B/pGC-cGMP is upregulated in the diabetic rats. The present study was designed to determine whether the upregulation of CNP-NPR-B/pGC-cGMP signal pathway affects cGMP-PDE3-cAMP signal pathway in diabetic gastric smooth muscle. The gastric smooth muscle motility was observed by using isometric measurement. PDEs expressions in diabetic gastric smooth muscle tissue were observed by using immunohistochemistry, Western blotting, and RT-PCR methods. The results demonstrated that the inhibitory effect of CNP on the spontaneous contraction of gastric antral circular smooth muscle was potentiated in STZ-induced diabetic rat. CNP-induced increase of cGMP and cAMP was much higher in diabetic gastric smooth muscle tissue than in controls. The expression of PDE3 is downregulated while the levels of gene expression of PDE1, PDE2, PDE4, and PDE5 were not altered in the diabetic gastric smooth muscle tissue. The results suggest that the sensitivity of gastric smooth muscle to CNP is potentiated via activation of CNP-pGC-cGMP-PDE3-cAMP signal pathway in STZ-induced diabetic rats, which may be associated with diabetes-induced gastric motility disorder.
4

Krstic, Miroslav, and Andrey Smyshlyaev. "ADAPTIVE CONTROL OF PDES." IFAC Proceedings Volumes 40, no. 13 (2007): 20–31. http://dx.doi.org/10.3182/20070829-3-ru-4911.00004.

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5

Krstic, Miroslav, and Andrey Smyshlyaev. "ADAPTIVE CONTROL OF PDES." IFAC Proceedings Volumes 40, no. 14 (2007): 20–31. http://dx.doi.org/10.3182/20070829-3-ru-4912.00004.

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6

Krstic, Miroslav, and Andrey Smyshlyaev. "Adaptive control of PDEs." Annual Reviews in Control 32, no. 2 (December 2008): 149–60. http://dx.doi.org/10.1016/j.arcontrol.2008.05.001.

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7

Hengge, Regine. "Trigger phosphodiesterases as a novel class of c-di-GMP effector proteins." Philosophical Transactions of the Royal Society B: Biological Sciences 371, no. 1707 (November 5, 2016): 20150498. http://dx.doi.org/10.1098/rstb.2015.0498.

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The bacterial second messenger c-di-GMP controls bacterial biofilm formation, motility, cell cycle progression, development and virulence. It is synthesized by diguanylate cyclases (with GGDEF domains), degraded by specific phosphodiesterases (PDEs, with EAL of HD-GYP domains) and sensed by a wide variety of c-di-GMP-binding effectors that control diverse targets. c-di-GMP-binding effectors can be riboswitches as well as proteins with highly diverse structures and functions. The latter include ‘degenerate’ GGDEF/EAL domain proteins that are enzymatically inactive but still able to bind c-di-GMP. Surprisingly, two enzymatically active ‘trigger PDEs’, the Escherichia coli proteins PdeR and PdeL, have recently been added to this list of c-di-GMP-sensing effectors. Mechanistically, trigger PDEs are multifunctional. They directly and specifically interact with a macromolecular target (e.g. with a transcription factor or directly with a promoter region), whose activity they control by their binding and degradation of c-di-GMP—their PDE activity thus represents the c-di-GMP sensor or effector function. In this process, c-di-GMP serves as a regulatory ligand, but in contrast to classical allosteric control, this ligand is also degraded. The resulting kinetics and circuitry of control are ideally suited for trigger PDEs to serve as key components in regulatory switches. This article is part of the themed issue ‘The new bacteriology’.
8

Idres, Sarah, Germain Perrin, Valérie Domergue, Florence Lefebvre, Susana Gomez, Audrey Varin, Rodolphe Fischmeister, Véronique Leblais, and Boris Manoury. "Contribution of BKCa channels to vascular tone regulation by PDE3 and PDE4 is lost in heart failure." Cardiovascular Research 115, no. 1 (June 23, 2018): 130–44. http://dx.doi.org/10.1093/cvr/cvy161.

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Abstract Aims Regulation of vascular tone by 3′,5′-cyclic adenosine monophosphate (cAMP) involves many effectors including the large conductance, Ca2+-activated, K+ (BKCa) channels. In arteries, cAMP is mainly hydrolyzed by type 3 and 4 phosphodiesterases (PDE3, PDE4). Here, we examined the specific contribution of BKCa channels to tone regulation by these PDEs in rat coronary arteries, and how this is altered in heart failure (HF). Methods and results Concomitant application of PDE3 (cilostamide) and PDE4 (Ro-20-1724) inhibitors increased BKCa unitary channel activity in isolated myocytes from rat coronary arteries. Myography was conducted in isolated, U46619-contracted coronary arteries. Cilostamide (Cil) or Ro-20-1724 induced a vasorelaxation that was greatly reduced by iberiotoxin (IBTX), a BKCa channel blocker. Ro-20-1724 and Cil potentiated the relaxation induced by the β-adrenergic agonist isoprenaline (ISO) or the adenylyl cyclase activator L-858051 (L85). IBTX abolished the effect of PDE inhibitors on ISO but did not on L85. In coronary arteries from rats with HF induced by aortic stenosis, contractility and response to acetylcholine were dramatically reduced compared with arteries from sham rats, but relaxation to PDE inhibitors was retained. Interestingly, however, IBTX had no effect on Ro-20-1724- and Cil-induced vasorelaxations in HF. Expression of the BKCa channel α-subunit, of a 98 kDa PDE3A and of a 80 kDa PDE4D were lower in HF compared with sham coronary arteries, while that of a 70 kDa PDE4B was increased. Proximity ligation assays demonstrated that PDE3 and PDE4 were localized in the vicinity of the channel. Conclusion BKCa channels mediate the relaxation of coronary artery induced by PDE3 and PDE4 inhibition. This is achieved by co-localization of both PDEs with BKCa channels, enabling tight control of cAMP available for channel opening. Contribution of the channel is prominent at rest and on β-adrenergic stimulation. This coupling is lost in HF.
9

Vinogradova, Tatiana M., and Edward G. Lakatta. "Dual Activation of Phosphodiesterase 3 and 4 Regulates Basal Cardiac Pacemaker Function and Beyond." International Journal of Molecular Sciences 22, no. 16 (August 5, 2021): 8414. http://dx.doi.org/10.3390/ijms22168414.

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The sinoatrial (SA) node is the physiological pacemaker of the heart, and resting heart rate in humans is a well-known risk factor for cardiovascular disease and mortality. Consequently, the mechanisms of initiating and regulating the normal spontaneous SA node beating rate are of vital importance. Spontaneous firing of the SA node is generated within sinoatrial nodal cells (SANC), which is regulated by the coupled-clock pacemaker system. Normal spontaneous beating of SANC is driven by a high level of cAMP-mediated PKA-dependent protein phosphorylation, which rely on the balance between high basal cAMP production by adenylyl cyclases and high basal cAMP degradation by cyclic nucleotide phosphodiesterases (PDEs). This diverse class of enzymes includes 11 families and PDE3 and PDE4 families dominate in both the SA node and cardiac myocardium, degrading cAMP and, consequently, regulating basal cardiac pacemaker function and excitation-contraction coupling. In this review, we will demonstrate similarities between expression, distribution, and colocalization of various PDE subtypes in SANC and cardiac myocytes of different species, including humans, focusing on PDE3 and PDE4. Here, we will describe specific targets of the coupled-clock pacemaker system modulated by dual PDE3 + PDE4 activation and provide evidence that concurrent activation of PDE3 + PDE4, operating in a synergistic manner, regulates the basal cardiac pacemaker function and provides control over normal spontaneous beating of SANCs through (PDE3 + PDE4)-dependent modulation of local subsarcolemmal Ca2+ releases (LCRs).
10

Murray, Fiona, Hemal H. Patel, Ryan Y. S. Suda, Shen Zhang, Patricia A. Thistlethwaite, Jason X. J. Yuan, and Paul A. Insel. "Expression and activity of cAMP phosphodiesterase isoforms in pulmonary artery smooth muscle cells from patients with pulmonary hypertension: role for PDE1." American Journal of Physiology-Lung Cellular and Molecular Physiology 292, no. 1 (January 2007): L294—L303. http://dx.doi.org/10.1152/ajplung.00190.2006.

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Pulmonary hypertension (PHT) is associated with increased vascular resistance due to sustained contraction and enhanced proliferation of pulmonary arterial smooth muscle cells (PASMC); the abnormal tone and remodeling in the pulmonary vasculature may relate, at least in part, to decreased cyclic nucleotide levels. Cyclic nucleotide phosphodiesterases (PDEs), of which 11 families have been identified, catalyze the hydrolysis of cAMP and cGMP. We tested the hypothesis that PASMC isolated from patients with PHT, either idiopathic pulmonary arterial hypertension (IPAH) or secondary pulmonary hypertension (SPH), have increased expression and activity of PDE isoforms that reduce the responsiveness of agents that raise cellular cAMP. Real-time PCR and immunoblotting demonstrated that the expression of PDE1A, PDE1C, PDE3B, and PDE5A was enhanced in PASMC from both IPAH and SPH patients compared with control PASMC. Consistent with this enhanced expression of PDEs, agonist-stimulated cAMP levels were significantly reduced in IPAH and SPH PASMC unless a PDE inhibitor was present. The use of specific PDE inhibitors revealed that an increase in PDE1 and PDE3 activity largely accounted for reduced agonist-induced cAMP levels and increased proliferation in IPAH and SPH PASMC. Treatment with PDE1C-targeted small interference RNA enhanced cAMP accumulation and inhibited cellular proliferation to a greater extent in PHT PASMC than controls. The results imply that an increase in PDE isoforms, in particular PDE1C, contributes to decreased cAMP and increased proliferation of PASMC in patients with PHT. PDE1 isoforms may provide novel targets for the treatment of both primary and secondary forms of the disease.
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Статті в журналах Дисертації Книги

Дисертації з теми "Control of PDEs":

1

BACCOLI, ANTONELLO. "Boundary control and observation of coupled parabolic PDEs." Doctoral thesis, Università degli Studi di Cagliari, 2016. http://hdl.handle.net/11584/266880.

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Reaction-diffusion equations are parabolic Partial Differential Equations (PDEs) which often occur in practice, e.g., to model the concentration of one or more substances, distributed in space, under the in uence of different phenomena such as local chemical reactions, in which the substances are transformed into each other, and diffusion, which causes the substances to spread out over a surface in space. Certainly, reaction-diffusion PDEs are not confined to chemical applications but they also describe dynamical processes of non-chemical nature, with examples being found in thermodynamics, biology, geology, physics, ecology, etc. Problems such as parabolic Partial Differential Equations (PDEs) and many others require the user to have a considerable background in PDEs and functional analysis before one can study the control design methods for these systems, particularly boundary control design. Control and observation of coupled parabolic PDEs comes in roughly two settingsdepending on where the actuators and sensors are located \in domain" control, where the actuation penetrates inside the domain of the PDE system or is evenly distributed everywhere in the domain and \boundary" control, where the actuation and sensing are applied only through the boundary conditions. Boundary control is generally considered to be physically more realistic because actuation and sensing are nonintrusive but is also generally considered to be the harder problem, because the \input operator" and the "output operator" are unbounded operators. The method that this thesis develops for control of PDEs is the so-called backstepping control method. Backstepping is a particular approach to stabilization of dynamic systems and is particularly successful in the area of nonlinear control. The backstepping method achieves Lyapunov stabilization, which is often achieved by collectively shifting all the eigenvalues in a favorable direction in the complex plane, rather than by assigning individual eigenvalues. As the reader will soon learn, this task can be achieved in a rather elegant way, where the control gains are easy to compute symbolically, numerically, and in some cases even explicitly. In addition to presenting the methods for boundary control design, we present the dual methods for observer design using boundary sensing. Virtually every one of our control designs for full state stabilization has an observer counterpart. The observer gains are easy to compute symbolically or even explicitly in some cases. They are designed in such a way that the observer error system is exponentially stabilized. As in the case of finite-dimensional observer-based control, a separation principle holds in the sense that a closed-loop system remains stable after a full state stabilizing feedback is replaced by a feedback that employs the observer state instead of the plant state.
2

Hein, Sabine. "MPC/LQG-Based Optimal Control of Nonlinear Parabolic PDEs." Doctoral thesis, Universitätsbibliothek Chemnitz, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-201000134.

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The topic of this thesis is the theoretical and numerical research of optimal control problems for uncertain nonlinear systems, described by semilinear parabolic differential equations with additive noise, where the state is not completely available. Based on a paper by Kazufumi Ito and Karl Kunisch, which was published in 2006 with the title "Receding Horizon Control with Incomplete Observations", we analyze a Model Predictive Control (MPC) approach where the resulting linear problems on small intervals are solved with a Linear Quadratic Gaussian (LQG) design. Further we define a performance index for the MPC/LQG approach, find estimates for it and present bounds for the solutions of the underlying Riccati equations. Another large part of the thesis is devoted to extensive numerical studies for an 1+1- and 3+1-dimensional problem to show the robustness of the MPC/LQG strategy. The last part is a generalization of the MPC/LQG approach to infinite-dimensional problems.
3

Torres, Ixbalank. "Simulation and control of denitrification biofilters described by PDEs." Toulouse 3, 2010. http://thesesups.ups-tlse.fr/1204/.

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Cette thèse concerne la simulation et la commande d'un biofiltre de dénitrification. Selon que l'on considère ou que l'on néglige la diffusion, des modèles d'EDP paraboliques ou hyperboliques sont considérés. En plus des classiques méthodes des lignes, des approches spécifiques au type d'EDP sont évaluées pour simuler le système. La méthode des caractéristiques s'applique aux systèmes d'EDP hyperboliques. L'analyse modale utilisée pour les systèmes d'EDP paraboliques permet de manipuler un système d'ordre réduit. L'objectif de commande est alors de réduire la concentration en azote en sortie du réacteur sous une certaine limite, en dépit des perturbations externes et des incertitudes du modèle. Deux stratégies de commande sont considérées. Une approche "early lumping" permet la synthèse d'une loi de commande linéaire H2 de type retour de sortie avec observateur. Une approche "late lumping" associe une loi de commande linéarisante à un observateur à paramètres distribués
This thesis addresses the simulation and control of a denitrification biofilter. Parabolic and hyperbolic PDE models may be considered, which depends on the fact of considering or neglecting the diffusion phenomenon. In plus of the classical methods of lines, approaches specific to the type of PDE system are evaluated to simulate the biofilter. The method of characteristics applies to hyperbolic PDE systems. The modal analysis used on the parabolic PDE system allows manipulating a reduced order model. The control objective is then the reduction of the nitrogen concentration at the output of the reactor below some pre-specified upper limit, in spite of the external disturbances and uncertainties of the model. Two control strategies are considered. An early lumping approach is used to synthesize an observer-based H2 output feedback linear controller. A late lumping approach associates a linearizing control to a distributed parameter observer
4

Liu, Bainan. "Boundary Observer-based 0utput Feedback Control of Coupled Parabolic PDEs." Thesis, Bourges, INSA Centre Val de Loire, 2018. http://www.theses.fr/2018ISAB0011.

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Cette thèse vise à concevoir un contrôleur basé observateur au bord pour une classede systèmes modélisés par des équations aux dérivées partielles (EDP) paraboliquescouplées en utilisant la méthode dite backstepping. Grosso modo, la méthode dubackstepping pour les EDP consiste principalement à les transformer sous certainesformes faciles à analyser et à stabiliser à l’aide de contrôleurs ou d’observateurs. Cesformes seront appelées les systèmes cibles. Tout d’abord, ce travail considère un cassimple d’équations couplées avec des paramètres de diffusion constants. Pour ce cas,on met en évidence des conditions de stabilité moins contraignantes que les conditionsproposées dans la littérature sur ce sujet. De plus, pour le même cas, on conçoitune commande par retour d’état basé observateur. Ensuite, on donne une simulationsur un exemple pour prouver la consistance de la méthode proposée. Ce travail traiteégalement d’une classe de systèmes modélisés par équations de réaction-advectiondiffusionavec le même paramètre de diffusion constant en proposant des conditionsparticulières sur les systèmes cibles. Dans un second temps, on traite le cas des équationscouplées réaction-diffusion avec différentes diffusions. Cependant, comme lestermes de diffusions sont différents, il est plus difficile de calculer le noyau de la transformationbackstepping. Pour surmonter cette difficulté, on fait une hypothèse sur lenoyau qui définit la transformation backstepping. De plus, on conçoit également uncontrôleur basé observateur avec les mêmes conditions de stabilité proposées pour lesdeux premières situations. Ensuite, on utilise le principe de séparation pour concevoirun contrôleur basé observateur. Enfin, on utilise un modèle simplifié de réacteurtubulaire pour mettre en évidence la cohérence de la méthode proposée. Dans unetroisième partie, cette thèse étend ces résultats à une classe de systèmes modéliséspar des équations couplées de réaction-advection-diffusion à coefficients dépendantde la variable d’espace, ce qui rend la détermination du noyau de la transformationbackstepping plus difficile. Pour ce faire, on transforme les équations aux dérivéespartielles paraboliques qui définissent le noyau de la transformation en un ensembled’équations hyperboliques. Par conséquent, on peut prouver que le problème est bienposé en fixant des conditions aux limites appropriées pour la fonction noyau. De plus,on fournit également les conditions de stabilité pour les systèmes cibles. La performancede l’observateur proposé est illustrée sur un modèle numérique. Puis, on étendle contrôleur basé observateur aux systèmes EDP d’ordre fractionnaire. Enfin, desconclusions sont présentées avec quelques perspectives
This thesis aims to design a boundary observer-based output feedback controllerfor a class of systems modelled by linear coupled parabolic PDEs by using the backsteppingmethod.Roughly speaking, the backstepping method for PDEs mainly consists oftransforming some kinds of PDEs into some particular PDEs, that are easy to analyzeand stabilize by using controllers or observers. This kind of particular PDEs will becalled target systems. Firstly, it considers an easy case of coupled reaction-diffusionequations with the same constant diffusion parameter. For this case, it proposes amore relaxed stability condition for the target system of the backstepping transformation.Moreover, for the same case, it designs a backstepping boundary observer-basedoutput feedback controller. Then, it takes an example to verify the proposed method.It also deals with a class of systems modelled by reaction-advection-diffusion equationswith the same constant diffusion parameter, which are realized by proposingparticular conditions on the target systems. Secondly, it deals with a kind of systemsmodelled by coupled reaction-diffusion equations with different diffusions. In a similarway, it designs a boundary observer for this kind of systems. However, due to thefact that the constant diffusions are not the same, it is more difficult to solve the kernelfunctions of the backstepping transformation than the same diffusion case. Forthis, an assumption on the kernel functions is made to enable us to solve the problem.Moreover, it also designs a backstepping boundary controller based on the proposedstability conditions. Those stability conditions are more relaxed than the conditionswe can find in the literatures on this topic. Then, based on the Separation Principle,it designs an observer-based output feedback controller. It takes a simplified modelof Chemical Tubular Reactor to highlight the proposed method. Thirdly, this thesisdesigns a boundary observer as a more general extension by studying a class of systemsmodelled by coupled reaction-advection-diffusion equations with spatially-varyingcoefficients, which is more challenged to solve kernel functions of the backsteppingtransformation. To achieve this, it transforms the parabolic kernel equations into a setof hyperbolic equations. Then, it proves the well-posedness by setting suitable boundaryconditions for the kernel functions. Moreover, it also provides the stability conditionsfor the target systems. The performance of the proposed observer is illustrated bytaking a numerical model. Fourthly, it extends the above backstepping observer-basedoutput feedback controller to fractional-order PDE systems. Finally, conclusions areoutlined with some perspectives
5

Cirant, Marco A. "Nonlinear PDEs in ergodic control, Mean Field Games and prescribed curvature problems." Doctoral thesis, Università degli studi di Padova, 2014. http://hdl.handle.net/11577/3423511.

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This thesis is concerned with nonlinear elliptic PDEs and system of PDEs arising in various problems of stochastic control, differential games, specifically Mean Field Games, and differential geometry. It is divided in three parts. The first part is focused on stochastic ergodic control problems where both the state and the control space is R^d. The interest is in giving conditions on the fixed drift, the cost function and the Lagrangian function that are sufficient for synthesizing an optimal control of feedback type. In order to obtain such conditions, an approach that combines the Lyapunov method and the approximation of the problem on bounded sets with reflection of the diffusions at the boundary is proposed. A general framework is developed first, and then particular cases are considered, which show how Lyapunov functions can be constructed from the solutions of the approximating problems. The second part is devoted to the study of Mean Field Games, a recent theory which aims at modeling and analyzing complex decision processes involving a very large number of indistinguishable rational agents. The attention is given to existence results for the multi- population MFG system of PDEs with homogeneous Neumann boundary conditions, that are obtained combining elliptic a-priori estimates and fixed point arguments. A model of segregation between human populations, inspired by ideas of T. Schelling is then proposed. The model, that fits into the theoretical framework developed in the thesis, is analyzed from the qualitative point of view using numerical finite-difference techniques. The phenomenon of segregation between the population densities arises in the numerical experiments on the particular mean field game model, assuming mild ethnocentric attitude of people as in the original model of Schelling. In the last part of the thesis some results on existence and uniqueness of solutions for the prescribed k-th principal curvature equation are presented. The Dirichlet problem for such a family of degenerate elliptic fully nonlinear partial differential equations is solved using the theory of Viscosity solutions, by implementing a version of the Perron method which involves semiconvex subsolutions; the restriction to this class of functions is sufficient for proving a Lipschitz estimate on the elliptic operator with respect to the gradient entry which is also required for obtaining the comparison principle. Existence and uniqueness are stated under general assumptions, and examples of data which satisfy the general hypotheses are provided.
Questa tesi ha come oggetto di studio EDP ellittiche nonlineari e sistemi di EDP che si presentano in problemi di controllo stocastico, giochi differenziali, in particolare Mean Field Games e geometria differenziale. I risultati contenuti si possono suddividere in tre parti. Nella prima parte si pone l'attenzione su problemi di controllo ergodico stocastico dove lo spazio degli stati e dei controlli coincide con l'intero Rd. L'interesse è posto sul formulare condizioni sul drift, il funzionale di costo e la Lagrangiana sufficienti a sintetizzare un controllo ottimo di tipo feedback. Al fine di ottenere tali condizioni, viene proposto un approccio che combina il metodo delle funzioni di Lyapunov e l'approssimazione del problema su domini limitati con riflessione delle traiettorie al bordo. Le tecniche vengono formulate in termini generali e successivamente sono presi in considerazione esempi specifici, che mostrano come opportune funzioni di Lyapunov possono essere costruite a partire dalle soluzioni dei problemi approssimanti. La seconda parte è incentrata sullo studio di Mean Fielda Games, una recente teoria che mira a elaborare modelli per analizzare processi di decisione in cui è coinvolto un grande numero di agenti indistinguibili. Sono ottenuti nella tesi alcuni risultati di esistenza di soluzioni per sistemi MFG a più popolazioni con condizioni al bordo omogenee di tipo Neumann, attraverso stime a-priori ellittiche e argomenti di punto fisso. Viene in seguito proposto un modello di segregazione tra popolazioni umane che prende ispirazione da alcune idee di T. Schelling. Tale modello si inserisce nel contesto teorico sviluppato nella tesi, e viene analizzato dal punto di vista qualitativo tramite tecniche numeriche alle differenze finite. Il fenomeno di segregazione tra popolazioni si riscontra negli esperimenti numerici svolti sul particolare modello mean field, assumendo l'ipotesi di moderata mentalità etnocentrica delle persone, similmente all’originale modello di Schelling. L'ultima parte della tesi riguarda alcuni risultati di esistenza e unicità di soluzioni per l’equazione di k-esima curvatura principale prescritta. Il problema di Dirichlet per tale famiglia di equazioni ellittiche degeneri nonlineari è risolto implementando la teoria delle soluzioni di Viscosità, applicando in particolare una versione del metodo di Perron basata su soluzioni semiconvesse; la restrizione a tale classe di funzioni risulta sufficiente per dimostrare una stima di tipo Lipschitz sull'operatore ellittico, essenziale per ottenere un principio di confronto. Esistenza e unicità di soluzioni sono formulate in termini generali; vengono forniti infine esempi in cui condizioni particolari sui dati soddisfano tali ipotesi.
6

Götschel, Sebastian [Verfasser]. "Adaptive Lossy Trajectory Compression for Optimal Control of Parabolic PDEs / Sebastian Götschel." Berlin : Freie Universität Berlin, 2015. http://d-nb.info/1066645221/34.

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7

Tan, Xiaolu. "Stochastic control methods for optimal transportation and probabilistic numerical schemes for PDEs." Palaiseau, Ecole polytechnique, 2011. https://theses.hal.science/docs/00/66/10/86/PDF/These_TanXiaolu.pdf.

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Cette thèse porte sur les méthodes numériques pour les équations aux dérivées partielles (EDP) non-linéaires dégénérées, ainsi que pour des problèmes de contrôle d'EDP non-linéaires résultants d'un nouveau problème de transport optimal. Toutes ces questions sont motivées par des applications en mathématiques financières. La thèse est divisée en quatre parties. Dans une première partie, nous nous intéressons à la condition nécessaire et suffisante de la monotonie du thêta-schéma de différences finies pour l'équation de diffusion en dimension un. Nous donnons la formule explicite dans le cas de l'équation de la chaleur, qui est plus faible que la condition classique de Courant-Friedrichs-Lewy (CFL). Dans une seconde partie, nous considérons une EDP parabolique non-linéaire dégénérée et proposons un schéma de type ''splitting'' pour la résoudre. Ce schéma réunit un schéma probabiliste et un schéma semi-lagrangien. Au final, il peut être considéré comme un schéma Monte-Carlo. Nous donnons un résultat de convergence et également un taux de convergence du schéma. Dans une troisième partie, nous étudions un problème de transport optimal, où la masse est transportée par un processus d'état type ''drift-diffusion'' controllé. Le coût associé est dépendant des trajectoires de processus d'état, de son drift et de son coefficient de diffusion. Le problème de transport consiste à minimiser le coût parmi toutes les dynamiques vérifiant les contraintes initiales et terminales sur les distributions marginales. Nous prouvons une formule de dualité pour ce problème de transport, étendant ainsi la dualité de Kantorovich à notre contexte. La formulation duale maximise une fonction valeur sur l'espace des fonctions continues bornées, et la fonction valeur correspondante à chaque fonction continue bornée est la solution d'un problème de contrôle stochastique optimal. Dans le cas markovien, nous prouvons un principe de programmation dynamique pour ces problèmes de contrôle optimal, proposons un algorithme de gradient projeté pour la résolution numérique du problème dual, et en démontrons la convergence. Enfin dans une quatrième partie, nous continuons à développer l'approche duale pour le problème de transport optimal avec une application à la recherche de bornes de prix sans arbitrage des options sur variance étant donnés les prix des options européennes. Après une première approximation analytique, nous proposons un algorithme de gradient projeté pour approcher la borne et la stratégie statique correspondante en options vanilles
This thesis deals with the numerical methods for a fully nonlinear degenerate parabolic partial differential equations (PDEs), and for a controlled nonlinear PDEs problem which results from a mass transportation problem. The manuscript is divided into four parts. In a first part of the thesis, we are interested in the necessary and sufficient condition of the monotonicity of finite difference thêta-scheme for a one-dimensional diffusion equations. An explicit formula is given in case of the heat equation, which is weaker than the classical Courant-Friedrichs-Lewy (CFL) condition. In a second part, we consider a fully nonlinear degenerate parabolic PDE and propose a splitting scheme for its numerical resolution. The splitting scheme combines a probabilistic scheme and the semi-Lagrangian scheme, and in total, it can be viewed as a Monte-Carlo scheme for PDEs. We provide a convergence result as well as a rate of convergence. In the third part of the thesis, we study an optimal mass transportation problem. The mass is transported by the controlled drift-diffusion dynamics, and the associated cost depends on the trajectories, the drift as well as the diffusion coefficient of the dynamics. We prove a strong duality result for the transportation problem, thus extending the Kantorovich duality to our context. The dual formulation maximizes a value function on the space of all bounded continuous functions, and every value function corresponding to a bounded continuous function is the solution to a stochastic control problem. In the Markovian cases, we prove the dynamic programming principle of the optimal control problems, and we propose a gradient-projection algorithm for the numerical resolution of the dual problem, and provide a convergence result. Finally, in a fourth part, we continue to develop the dual approach of mass transportation problem with its applications in the computation of the model-independent no-arbitrage price bound of the variance option in a vanilla-liquid market. After a first analytic approximation, we propose a gradient-projection algorithm to approximate the bound as well as the corresponding static strategy in vanilla options
8

Xia, Xiaonyu. "Singular BSDEs and PDEs Arising in Optimal Liquidation Problems." Doctoral thesis, Humboldt-Universität zu Berlin, 2020. http://dx.doi.org/10.18452/21040.

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Diese Dissertation analysiert BSDEs und PDEs mit singulären Endbedingungen, welche in Problemen der optimalen Portfolioliquidierung auftreten. In den vergangenen Jahren haben Portfolioliquidierungsprobleme in der Literatur zur Finanzmathematik große Aufmerksamkeit erhalten. Ihre wichtigste Eigenschaft ist die singuläre Endbedingung der durch die Liquidierungsbedingung induzierten Wertfunktion, welche eine singuläre Endbedingung der zugehörigen BSDE oder PDE impliziert. Diese Arbeit besteht aus drei Kapiteln. Das erste Kapitel analysiert ein Portfolioliquidierungsproblem für mehrere Wertpapiere mit sofortigem und anhaltendem Preiseinfluss und stochastischer Resilienz. Wir zeigen, dass die Wertfunktion durch eine mehrdimensionale BSRDE mit singulärer Endbedingung beschrieben werden kann. Wir weisen die Existenz einer Lösung dieser BSRDE nach und zeigen, dass diese durch eine Folge von Lösungen von BSRDEs mit endlicher und wachsender Endbedingung approximiert werden kann. Eine neue a priori-Abschätzung für die approximierenden BSRDEs wird für den Nachweis hergeleitet. Das zweite Kapitel betrachtet ein Portfolioliquidierungsproblem mit unbeschränkten Kostenkoeffizienten. Wir weisen die Existenz einer eindeutigen nichtnegativen Viskositätslösung der HJB-Gleichung nach. Das Existenzresultat basiert auf einem neuartigen Vergleichsprinzip für semi-stetige Viskositätssub-/-superlösungen für singuläre PDEs. Stetigkeit der Viskositätslösung ist hinreichend für das Verifikationsargument. Im dritten Kapitel untersuchen wir ein optimales Liquidierungsproblem unter Mehrdeutigkeit der Parameter des Preiseinflusses. In diesem Fall kann die Wertfunktion durch die Lösung einer semilinearen PDE mit superlinearem Gradienten beschrieben werden. Zuerst zeigen wir die Existenz einer Viskositätslösung indem wir unser Vergleichsprinzip für singuläre PDEs erweitern. Sodann weisen wir die Regularität mit einer asymptotischen Entwicklung der Lösung am Endzeitpunkt nach.
This dissertation analyzes BSDEs and PDEs with singular terminal condition arising in models of optimal portfolio liquidation. Portfolio liquidation problems have received considerable attention in the financial mathematics literature in recent years. Their main characteristic is the singular terminal condition of the value function induced by the liquidation constraint, which translates into a singular terminal state constraint on the associated BSDE or PDE. The dissertation consists of three chapters. The first chapter analyzes a multi-asset portfolio liquidation problem with instantaneous and persistent price impact and stochastic resilience. We show that the value function can be described by a multi-dimensional BSRDE with a singular terminal condition. We prove the existence of a solution to this BSRDE and show that it can be approximated by a sequence of the solutions to BSRDEs with finite increasing terminal condition. A novel a priori estimate for the approximating BSRDEs is established for the verification argument. The second chapter considers a portfolio liquidation problem with unbounded cost coefficients. We establish the existence of a unique nonnegative continuous viscosity solution to the HJB equation. The existence result is based on a novel comparison principle for semi-continuous viscosity sub-/supersolutions for singular PDEs. Continuity of the viscosity solution is enough to carry out the verification argument. The third chapter studies an optimal liquidation problem under ambiguity with respect to price impact parameters. In this case the value function can be characterized by the solution to a semilinear PDE with superlinear gradient. We first prove the existence of a solution in the viscosity sense by extending our comparison principle for singular PDEs. Higher regularity is then established using an asymptotic expansion of the solution at the terminal time.
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Trenz, Stefan [Verfasser]. "POD-Based A-posteriori Error Estimation for Control Problems Governed by Nonlinear PDEs / Stefan Trenz." Konstanz : Bibliothek der Universität Konstanz, 2017. http://d-nb.info/1142113868/34.

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10

Branco, Meireles Joao. "Singular Perturbations and Ergodic Problems for degenerate parabolic Bellman PDEs in R^m with Unbounded Data." Doctoral thesis, Università degli studi di Padova, 2015. http://hdl.handle.net/11577/3424194.

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In this thesis we treat the first singular perturbation problem of a stochastic model with unbounded and controlled fast variables with success. Our methods are based on the theory of viscosity solutions, homogenisation of fully nonlinear PDEs and a careful analysis of the associated ergodic stochastic control problem in the whole space R^m. The text is divided in two parts. In the first chapter, we investigate the existence and uniqueness as well as a suitable stability of the solution to the associated ergodic problem that are crucial to characterize the effective Hamiltonian of the limit (effective) Cauchy problem in Chapter II of this thesis. The main achievement obtained in this part is a purely analytical proof for the uniqueness of solution to such ergodic problem. Since the state space of the problem is not compact, in general there are infinitely many solutions to the ergodic problem. However, if one restrict the class of solutions to the set of bounded-below functions, then it is known that uniqueness holds up to an additive constant. The existing proof relies on some probabilistic techniques employing the invariant probability measure for the associated stochastic process. Here we give a new proof, purely analytic, based on the strong maximum principle. We believe that our results can be interesting and useful for researchers in the PDE community. In the second chapter, we introduce our singular perturbation model of a stochastic control problem and we prove our main result: the convergence of the value function $V^\epsilon$ associated to the problem to the solution of the limiting equation. More precisely, we prove that the functions \underline{V} (t,x):=\liminf_{(\epsilon,t',x') \to (0,t,x)} \inf_{y \in \mathbb{R}^m} V^\epsilon (t',x',y) and \bar{V} (t,x) :=(\sup_{R} \bar{V}_R)^* (t,x) \text{ (upper semi-continuous envelope of $\sup_{R} \bar{V}_R$ )} where $\bar{V}_{R} (t,x):=\limsup_{(\epsilon, t',x') \to (0,t,x)} \sup_{y \in B_R (0)} V^\epsilon (t',x',y)$, are, respectively, a super and a subsolution of the effective Cauchy problem. As a corollary of this result, $V^\epsilon$ converges to the unique solution $V$ of the effective equation provided the equation admits the comparison principle for discontinuous viscosity solutions. The justification of this convergence is not trivial at all. It especially involves some regularity issues and a careful treatment of viscosity techniques and stochastic analysis. This result has never been obtained before.
In questa tesi viene trattato con successo il primo problema di perturbazione singolare di un modello stocastico con variabili veloci controllate e non limitate. I metodi si basano sulla teoria delle soluzioni di viscosità, omogeinizzazione dei PDE completamente non lineari, e su un'attenta analisi del problema stocastico ergodico associato, valido nell'intero spazio R^m. Il testo è diviso in due parti. Nel primo capitolo, saranno studiate l'esistenza, l'unicità e alcune proprietà di stabilità della soluzione del problema ergodico, riferito sopra, che sono essenziali per caratterizzare il Hamiltoniano effettivo che appare in un Problema di Cauchy "limite", che sarà descritto nel capitolo II di questa tesi. Il principale contributo, presentato in questa parte, è una prova puramente analitica dell'unicità della soluzione di questo problema ergodico. Siccome lo stato dello spazio del problema non è compatto, in generale ci sono un numero infinito di soluzioni a questo problema. Tuttavia, se uno limitasse la classe di soluzioni all'insieme di funzioni limitate inferiormente, allora è noto che l'unicità sarà mantenuta a meno di una costante. La prova esistente si basa su alcune tecniche probabilistiche che impiegano la misura di probabilità invariante per l'associato processo stocastico. Qua verrà data una nuova prova, puramente analitica, basata sul principio del massimo. Si ritiene che il risultato potrà essere interessante ed utile per i ricercatori che lavorano all'interno della comunità di ricerca delle Equazioni Differenziali alle derivate Parziali (PDE). Nel secondo capitolo, sarà introdotto un modello di perturbazione singolare di un problema di controllo stocastico, e provato il risultato principale: la convergenza della funzione valore $V^\epsilon$, associata al nostro problema, per soluzione dell'equazione limite. Più precisamente, sarà provato che le funzioni: \underline{V} (t,x):=\liminf_{(\epsilon,t',x') \to (0,t,x)} \inf_{y \in \mathbb{R}^m} V^\epsilon (t',x',y) e \bar{V} (t,x) :=(\sup_{R} \bar{V}_R)^* (t,x) \text{ (upper semi-continuous envelope of $\sup_{R} \bar{V}_R$ )} dove $\bar{V}_{R} (t,x):=\limsup_{(\epsilon, t',x') \to (0,t,x)} \sup_{y \in B_R (0)} V^\epsilon (t',x',y)$, sono, rispettivamente, una super soluzione e una sottosoluzione del problema effettivo di Cauchy. Come corollario di questo risultato, $V^\epsilon$ converge all'unica soluzione V della equazione effettiva se l'equazione limite permette il principio di comparazione per le soluzioni di viscosità discontinue. La motivazione di questa convergenza non è ovvia del tutto. Coinvolge specialmente alcuni problemi di regolarità e un trattamento attento delle tecniche di viscosità e di analisi stocastica. Questo risultato è nuovo e non è mai stato ottenuto, prima d'ora, nella letteratura Matematica.
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Книги з теми "Control of PDEs":

1

Anfinsen, Henrik, and Ole Morten Aamo. Adaptive Control of Hyperbolic PDEs. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-05879-1.

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2

Meurer, Thomas. Control of Higher–Dimensional PDEs. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-30015-8.

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3

Smyshlyaev, Andrey. Adaptive control of parabolic PDEs. Princeton: Princeton University Press, 2010.

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4

Smyshlyaev, Andrey. Adaptive control of parabolic PDEs. Princeton: Princeton University Press, 2010.

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5

Smyshlyaev, Andrey. Adaptive control of parabolic PDEs. Princeton: Princeton University Press, 2010.

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6

Guo, Bao-Zhu, and Jun-Min Wang. Control of Wave and Beam PDEs. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-12481-6.

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7

Martínez-Frutos, Jesús, and Francisco Periago Esparza. Optimal Control of PDEs under Uncertainty. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-98210-6.

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8

Lasiecka, I. Mathematical control theory of coupled PDEs. Philadelphia: Society for Industrial and Applied Mathematics, 2002.

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9

Doubova, Anna, Manuel González-Burgos, Francisco Guillén-González, and Mercedes Marín Beltrán, eds. Recent Advances in PDEs: Analysis, Numerics and Control. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97613-6.

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10

Meurer, Thomas. Control of Higher–Dimensional PDEs: Flatness and Backstepping Designs. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013.

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Частини книг з теми "Control of PDEs":

1

Vazquez, Rafael, and Miroslav Krstic. "Backstepping for PDEs." In Encyclopedia of Systems and Control, 1–4. London: Springer London, 2019. http://dx.doi.org/10.1007/978-1-4471-5102-9_100023-1.

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Vazquez, Rafael, and Miroslav Krstic. "Backstepping for PDEs." In Encyclopedia of Systems and Control, 129–32. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-44184-5_100023.

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3

Anfinsen, Henrik, and Ole Morten Aamo. "Adaptive Control of PDEs." In Encyclopedia of Systems and Control, 1–7. London: Springer London, 2020. http://dx.doi.org/10.1007/978-1-4471-5102-9_100022-1.

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4

Anfinsen, Henrik, and Ole Morten Aamo. "Adaptive Control of PDEs." In Encyclopedia of Systems and Control, 11–17. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-44184-5_100022.

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Meurer, Thomas. "Motion Planning for PDEs." In Encyclopedia of Systems and Control, 786–93. London: Springer London, 2015. http://dx.doi.org/10.1007/978-1-4471-5058-9_14.

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6

Meurer, Thomas. "Motion Planning for PDEs." In Encyclopedia of Systems and Control, 1–10. London: Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-5102-9_14-1.

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7

Meurer, Thomas. "Motion Planning for PDEs." In Encyclopedia of Systems and Control, 1–9. London: Springer London, 2019. http://dx.doi.org/10.1007/978-1-4471-5102-9_14-2.

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8

Meurer, Thomas. "Motion Planning for PDEs." In Encyclopedia of Systems and Control, 1338–46. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-44184-5_14.

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9

Christofides, Panagiotis D., Antonios Amaou, Yiming Lou, and Amit Varsheny. "Feedback Control Using Stochastic PDEs." In Control and Optimization of Multiscale Process Systems, 1–52. Boston: Birkhäuser Boston, 2008. http://dx.doi.org/10.1007/978-0-8176-4793-3_5.

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10

Beauchard, Karine, and Pierre Rouchon. "Bilinear Control of Schrödinger PDEs." In Encyclopedia of Systems and Control, 77–82. London: Springer London, 2015. http://dx.doi.org/10.1007/978-1-4471-5058-9_12.

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Тези доповідей конференцій з теми "Control of PDEs":

1

Carnevale, Daniele, and Alessandro Astolfi. "Integrator forwarding without PDEs." In 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC). IEEE, 2009. http://dx.doi.org/10.1109/cdc.2009.5400617.

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2

Dubljevic, S., and P. D. Christofides. "Boundary predictive control of parabolic PDEs." In 2006 American Control Conference. IEEE, 2006. http://dx.doi.org/10.1109/acc.2006.1655329.

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3

Siranosian, Antranik A., Miroslav Krstic, Andrey Smyshlyaev, and Matt Bement. "Gain Scheduling-Inspired Control for Nonlinear Partial Differential Equations." In ASME 2009 Dynamic Systems and Control Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/dscc2009-2532.

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We present a control design method for nonlinear partial differential equations (PDEs) based on a combination of gain scheduling and backstepping theory for linear PDEs. A benchmark first-order hyperbolic system with a destabilizing in-domain nonlinearity is considered first. For this system a nonlinear feedback law based on gain scheduling is derived explicitly, and a statement of stability is presented for the closed-loop system. Control designs are then presented for a string and shear beam PDE, both with Kelvin-Voigt damping and potentially destabilizing free-end nonlinearities. String and beam simulation results illustrate the merits of the gain scheduling approach over the linearization-based design.
4

Dubljevic, S., and P. D. Christofides. "Predictive output feedback control of parabolic PDEs." In 2006 American Control Conference. IEEE, 2006. http://dx.doi.org/10.1109/acc.2006.1656373.

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5

Vatankhah, Ramin, Mohammad Abediny, Hoda Sadeghian, and Aria Alasty. "Backstepping Boundary Control for Unstable Second-Order Hyperbolic PDEs and Trajectory Tracking." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87038.

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In this paper, a problem of boundary feedback stabilization of second order hyperbolic partial differential equations (PDEs) is considered. These equations serve as a model for physical phenomena such as oscillatory systems like strings and beams. The controllers are designed using a backstepping method, which has been recently developed for parabolic PDEs. With the integral transformation and boundary feedback the unstable PDE is converted into a system which is stable in sense of Lyapunov. Then taylorian expansion is used to achieve the goal of trajectory tracking. It means design a boundary controller such that output of the system follows an arbitrary map. The designs are illustrated with simulations.
6

Sonawane, Ramdas B., Anil Kumar, and S. B. Nimse. "Numerical optimal control for bilinear hyperbolic PDEs." In 2013 Nirma University International Conference on Engineering (NUiCONE). IEEE, 2013. http://dx.doi.org/10.1109/nuicone.2013.6780203.

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7

Hasan, Agus. "Backstepping boundary control for semilinear parabolic PDEs." In 2015 54th IEEE Conference on Decision and Control (CDC). IEEE, 2015. http://dx.doi.org/10.1109/cdc.2015.7402594.

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8

Krstic, Miroslav. "Dead-time compensation for wave/string PDEs." In 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC). IEEE, 2009. http://dx.doi.org/10.1109/cdc.2009.5400099.

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9

Acosta, J. A., and A. Astolfi. "On the PDEs arising in IDA-PBC." In 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC 2009). IEEE, 2009. http://dx.doi.org/10.1109/cdc.2009.5400580.

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10

Ahmadi, Mohamadreza, Giorgio Valmorbida, and Antonis Papachristodoulou. "Barrier functionals for output functional estimation of PDEs." In 2015 American Control Conference (ACC). IEEE, 2015. http://dx.doi.org/10.1109/acc.2015.7171125.

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Звіти організацій з теми "Control of PDEs":

1

Burns, John A., Eugene M. Cliff, and Lizette Zietsman. Computational Methods for Identification, Optimization and Control of PDE Systems. Fort Belvoir, VA: Defense Technical Information Center, April 2010. http://dx.doi.org/10.21236/ada523367.

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2

Tannenbaum, Allen R. Geometric PDE's and Invariants for Problems in Visual Control Tracking and Optimization. Fort Belvoir, VA: Defense Technical Information Center, January 2005. http://dx.doi.org/10.21236/ada428955.

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