Academic literature on the topic 'Control of PDEs'
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Journal articles on the topic "Control of PDEs":
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Dissertations / Theses on the topic "Control of PDEs":
BACCOLI, ANTONELLO. "Boundary control and observation of coupled parabolic PDEs." Doctoral thesis, Università degli Studi di Cagliari, 2016. http://hdl.handle.net/11584/266880.
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.
Torres, Ixbalank. "Simulation and control of denitrification biofilters described by PDEs." Toulouse 3, 2010. http://thesesups.ups-tlse.fr/1204/.
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
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.
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
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
Books on the topic "Control of PDEs":
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.
Meurer, Thomas. Control of Higher–Dimensional PDEs. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-30015-8.
Smyshlyaev, Andrey. Adaptive control of parabolic PDEs. Princeton: Princeton University Press, 2010.
Smyshlyaev, Andrey. Adaptive control of parabolic PDEs. Princeton: Princeton University Press, 2010.
Smyshlyaev, Andrey. Adaptive control of parabolic PDEs. Princeton: Princeton University Press, 2010.
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.
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.
Lasiecka, I. Mathematical control theory of coupled PDEs. Philadelphia: Society for Industrial and Applied Mathematics, 2002.
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.
Meurer, Thomas. Control of Higher–Dimensional PDEs: Flatness and Backstepping Designs. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013.
Book chapters on the topic "Control of PDEs":
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Conference papers on the topic "Control of PDEs":
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Reports on the topic "Control of PDEs":
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.
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.