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Journal articles on the topic 'Stabilization of PDEs'

Author: Grafiati

Published: 14 September 2024

Last updated: 31 July 2025

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1

Mokra, Daniela, and Juraj Mokry. "Phosphodiesterase Inhibitors in Acute Lung Injury: What Are the Perspectives?" International Journal of Molecular Sciences 22, no. 4 (2021): 1929. http://dx.doi.org/10.3390/ijms22041929.

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Despite progress in understanding the pathophysiology of acute lung damage, currently approved treatment possibilities are limited to lung-protective ventilation, prone positioning, and supportive interventions. Various pharmacological approaches have also been tested, with neuromuscular blockers and corticosteroids considered as the most promising. However, inhibitors of phosphodiesterases (PDEs) also exert a broad spectrum of favorable effects potentially beneficial in acute lung damage. This article reviews pharmacological action and therapeutical potential of nonselective and selective PDE

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2

Bernard, Pauline, and Miroslav Krstic. "Adaptive output-feedback stabilization of non-local hyperbolic PDEs." Automatica 50, no. 10 (2014): 2692–99. http://dx.doi.org/10.1016/j.automatica.2014.09.001.

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3

Li, Jian, and Yungang Liu. "Adaptive stabilization for ODE systems coupled with parabolic PDES." Journal of Systems Science and Complexity 29, no. 4 (2016): 959–77. http://dx.doi.org/10.1007/s11424-016-5094-4.

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4

Bernard, Pauline, and Miroslav Krstic. "Adaptive Output-Feedback Stabilization of Non-Local Hyperbolic PDEs." IFAC Proceedings Volumes 47, no. 3 (2014): 7755–60. http://dx.doi.org/10.3182/20140824-6-za-1003.00108.

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5

Lhachemi, Hugo, and Christophe Prieur. "Global Output Feedback Stabilization of Semilinear Reaction-Diffusion PDEs." IFAC-PapersOnLine 55, no. 26 (2022): 53–58. http://dx.doi.org/10.1016/j.ifacol.2022.10.376.

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6

Krstic, Miroslav. "Systematization of approaches to adaptive boundary stabilization of PDEs." International Journal of Robust and Nonlinear Control 16, no. 16 (2006): 801–18. http://dx.doi.org/10.1002/rnc.1098.

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7

Yıldız, Hüseyin Alpaslan, and Leyla Gören-Sümer. "Stabilization of a class of underactuated Euler Lagrange system using an approximate model." Transactions of the Institute of Measurement and Control 44, no. 8 (2021): 1569–78. http://dx.doi.org/10.1177/01423312211058556.

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The energy shaping method, Controlled Lagrangian, is a well-known approach to stabilize the underactuated Euler Lagrange (EL) systems. In this approach, to construct a control rule, some nonlinear and nonhomogeneous partial differential equations (PDEs), which are called matching conditions, must be solved. In this paper, a method is proposed to obtain an approximate solution of these matching conditions for a class of underactuated EL systems. To develop this method, the potential energy matching condition is transformed to a set of linear PDEs using an approximation of inertia matrices. Henc

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8

Auriol, Jean, and Florent Di Meglio. "Two-Sided Boundary Stabilization of Heterodirectional Linear Coupled Hyperbolic PDEs." IEEE Transactions on Automatic Control 63, no. 8 (2018): 2421–36. http://dx.doi.org/10.1109/tac.2017.2763320.

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9

Elharfi, Abdelhadi. "Exponential stabilization of a class of 1-D hyperbolic PDEs." Journal of Evolution Equations 16, no. 3 (2016): 665–79. http://dx.doi.org/10.1007/s00028-015-0317-z.

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10

Fornberg, Bengt, and Erik Lehto. "Stabilization of RBF-generated finite difference methods for convective PDEs." Journal of Computational Physics 230, no. 6 (2011): 2270–85. http://dx.doi.org/10.1016/j.jcp.2010.12.014.

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11

Lhachemi, Hugo, and Robert Shorten. "Boundary output feedback stabilization of state delayed reaction–diffusion PDEs." Automatica 156 (October 2023): 111188. http://dx.doi.org/10.1016/j.automatica.2023.111188.

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12

Bertoluzza, Silvia, Erik Burman, and Cuiyu He. "WAN Discretization of PDEs: Best Approximation, Stabilization, and Essential Boundary Conditions." SIAM Journal on Scientific Computing 46, no. 6 (2024): C688—C715. https://doi.org/10.1137/23m1588196.

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13

Auriol, Jean, and Florent Di Meglio. "Robust output feedback stabilization for two heterodirectional linear coupled hyperbolic PDEs." Automatica 115 (May 2020): 108896. http://dx.doi.org/10.1016/j.automatica.2020.108896.

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14

Phan, Tuấn Đình, and Ha Ngoc Hoang. "NONLINEAR CONTROL OF TEMPERATURE PROFILE OF UNSTABLE HEAT CONDUCTION SYSTEMS: A PORT HAMILTONIAN APPROACH." Journal of Computer Science and Cybernetics 32, no. 1 (2016): 61–74. http://dx.doi.org/10.15625/1813-9663/32/1/6401.

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This paper focuses on boundary control of distributed parameter systems (also called infinite dimensional systems). More precisely, a passivity based approach for the stabilization of temperature profile inside a well-insulated bar with heat conduction in a one-dimensional described by parabolic partial differential equations (PDEs) is developed. This approach is motivated by an appropriate model reduction schema using the finite difference approximation method. On this basis, it allows to discretize and then, write the original parabolic PDEs into a Port Hamiltonian (PH) representation. From

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15

Cristofaro, A., and F. Ferrante. "Boundary stabilization of systems of high order PDEs arising from flexible robotics." IFAC-PapersOnLine 53, no. 2 (2020): 7807–12. http://dx.doi.org/10.1016/j.ifacol.2020.12.1876.

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16

Wang, Jun-Min, Han-Wen Zhang, and Xiu-Fang Yu. "Input-to-state stabilization of coupled parabolic PDEs subject to external disturbances." IMA Journal of Mathematical Control and Information 39, no. 1 (2021): 185–218. http://dx.doi.org/10.1093/imamci/dnab040.

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Abstract In this paper, we are concerned with the input-to-state stabilization of coupled parabolic partial differential equations, which is suffering the disturbances in all channels. By using the sliding mode control integrated with the backstepping approach, we design two boundary feedback controllers to reject the matched boundary disturbances, stabilize the whole coupled system in the absence of unmatched disturbances and achieve the input-to-state stability property of the closed-loop system with respect to the unmatched disturbances. We show the existence of the generalized solutions of

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17

Zhang, Jin, Wen Kang, Emilia Fridman, and Alexandre Seuret. "Delayed stabilization of parabolic PDEs via augmented Lyapunov functionals and Legendre polynomials." Systems & Control Letters 156 (October 2021): 105003. http://dx.doi.org/10.1016/j.sysconle.2021.105003.

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18

Chen, Juan, Aleksei Tepljakov, Eduard Petlenkov, YangQuan Chen, and Bo Zhuang. "Stabilization and Stability Robustness of Coupled Non-Constant Parameter Time Fractional PDEs." IEEE Access 7 (2019): 163969–80. http://dx.doi.org/10.1109/access.2019.2951058.

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19

Kang, Wen, Emilia Fridman, and Chuan-Xin Liu. "Stabilization by switching of parabolic PDEs with spatially scheduled actuators and sensors." Automatica 147 (January 2023): 110668. http://dx.doi.org/10.1016/j.automatica.2022.110668.

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20

Lhachemi, Hugo, and Christophe Prieur. "Output feedback stabilization of reaction–diffusion PDEs with a non-collocated boundary condition." Systems & Control Letters 164 (June 2022): 105238. http://dx.doi.org/10.1016/j.sysconle.2022.105238.

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21

Vazquez, Rafael, and Miroslav Krstic. "Explicit integral operator feedback for local stabilization of nonlinear thermal convection loop PDEs." Systems & Control Letters 55, no. 8 (2006): 624–32. http://dx.doi.org/10.1016/j.sysconle.2005.09.019.

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22

Xu, Zaihua, and Yungang Liu. "Adaptive boundary stabilization for first-order hyperbolic PDEs with unknown spatially varying parameter." International Journal of Robust and Nonlinear Control 26, no. 3 (2015): 613–28. http://dx.doi.org/10.1002/rnc.3331.

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23

Zhang, Jing, and Jie Qi. "Robust stabilization of 2 × 2 first-order hyperbolic PDEs with uncertain input delay." Automatica 157 (November 2023): 111235. http://dx.doi.org/10.1016/j.automatica.2023.111235.

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24

Kitsos, Constantinos, Rami Katz, and Emilia Fridman. "Internal stabilization of three interconnected semilinear reaction-diffusion PDEs with one actuated state." IFAC-PapersOnLine 56, no. 2 (2023): 8934–39. http://dx.doi.org/10.1016/j.ifacol.2023.10.101.

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25

Yu, Xin, Chao Xu, Huacheng Jiang, Arthi Ganesan, and Guojie Zheng. "Backstepping Synthesis for Feedback Control of First-Order Hyperbolic PDEs with Spatial-Temporal Actuation." Abstract and Applied Analysis 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/643640.

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This paper deals with the stabilization problem of first-order hyperbolic partial differential equations (PDEs) with spatial-temporal actuation over the full physical domains. We assume that the interior actuator can be decomposed into a product of spatial and temporal components, where the spatial component satisfies a specific ordinary differential equation (ODE). A Volterra integral transformation is used to convert the original system into a simple target system using the backstepping-like procedure. Unlike the classical backstepping techniques for boundary control problems of PDEs, the in

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26

Kang, Wen, Shan Li, and Da-Wei Ding. "Input-to-State Stabilization of Uncertain Parabolic PDEs Using an Observer-Based Fuzzy Control." IEEE Access 7 (2019): 3581–91. http://dx.doi.org/10.1109/access.2018.2889650.

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27

Lehrenfeld, Christoph, and Maxim Olshanskii. "An Eulerian finite element method for PDEs in time-dependent domains." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 2 (2019): 585–614. http://dx.doi.org/10.1051/m2an/2018068.

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The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in a triangulated computational domain and can overlap the time-independent background mesh in an arbitrary way. The numerical method is based on finite difference discretizations of time derivatives and a standard geometrically unfitted finite element method with an additional stabilization term in the spatial domain. The performance and analysis of the method

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28

Chehab, Jean-Paul. "Damping, stabilization, and numerical filtering for the modeling and the simulation of time dependent PDEs." Discrete & Continuous Dynamical Systems - S 14, no. 8 (2021): 2693. http://dx.doi.org/10.3934/dcdss.2021002.

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29

Anfinsen, Henrik, and Ole Morten Aamo. "Adaptive Output Feedback Stabilization of $n + m$ Coupled Linear Hyperbolic PDEs with Uncertain Boundary Conditions." SIAM Journal on Control and Optimization 55, no. 6 (2017): 3928–46. http://dx.doi.org/10.1137/16m1099662.

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30

Auriol, Jean, and Florent Di Meglio. "Corrigendum to “Robust output feedback stabilization for two heterodirectional linear coupled hyperbolic PDEs” [Automatica 115]." Automatica 119 (September 2020): 109107. http://dx.doi.org/10.1016/j.automatica.2020.109107.

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31

Su, Lingling, Stephen Chen, Jun-Min Wang, and Miroslav Krstic. "Stabilization of a 2 × 2 system of hyperbolic PDEs with recirculation in the unactuated channel." Automatica 120 (October 2020): 109147. http://dx.doi.org/10.1016/j.automatica.2020.109147.

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32

Srivastava, Neeraj. "Optimization of Convergence of Mixed Finite Element Approximations Analysis." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 9, no. 2 (2018): 692–702. http://dx.doi.org/10.17762/turcomat.v9i2.13871.

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The numerical approximation of partial differential equations (PDEs) plays a vital role in many scientific and engineering applications. Mixed finite element methods have emerged as powerful techniques for solving a wide range of PDEs due to their ability to handle problems with mixed variables, such as fluid flow and elasticity. However, ensuring the convergence of mixed finite element approximations remains a challenging task. It presents a comprehensive analysis of the optimization strategies employed to enhance the convergence of mixed finite element approximations. We investigate the key

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33

Dong, Zhaonan, and Alexandre Ern. "Hybrid high-order method for singularly perturbed fourth-order problems on curved domains." ESAIM: Mathematical Modelling and Numerical Analysis 55, no. 6 (2021): 3091–114. http://dx.doi.org/10.1051/m2an/2021081.

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We propose a novel hybrid high-order method (HHO) to approximate singularly perturbed fourth-order PDEs on domains with a possibly curved boundary. The two key ideas in devising the method are the use of a Nitsche-type boundary penalty technique to weakly enforce the boundary conditions and a scaling of the weighting parameter in the stabilization operator that compares the singular perturbation parameter to the square of the local mesh size. With these ideas in hand, we derive stability and optimal error estimates over the whole range of values for the singular perturbation parameter, includi

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34

Farahani, Hamed Shirinabadi, Heidar Ali Talebi, and Mohammad Baghermenhaj. "An adaptive control scheme for hyperbolic partial differential equation system (drilling system) with unknown coefficient." Archives of Control Sciences 27, no. 1 (2017): 63–76. http://dx.doi.org/10.1515/acsc-2017-0004.

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Abstract The adaptive boundary stabilization is investigated for a class of systems described by second-order hyperbolic PDEs with unknown coefficient. The proposed control scheme only utilizes measurement on top boundary and assume anti-damping dynamics on the opposite boundary which is the main feature of our work. To cope with the lack of full state measurements, we introduce Riemann variables which allow us reformulate the second-order in time hyperbolic PDE as a system with linear input-delay dynamics. Then, the infinite-dimensional time-delay tools are employed to design the controller.

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35

Bekiaris-Liberis, Nikolaos. "Hybrid boundary stabilization of linear first-order hyperbolic PDEs despite almost quantized measurements and control input." Systems & Control Letters 146 (December 2020): 104809. http://dx.doi.org/10.1016/j.sysconle.2020.104809.

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36

Karafyllis, Iasson, and Miroslav Krstic. "Small-Gain-Based Boundary Feedback Design for Global Exponential Stabilization of One-Dimensional Semilinear Parabolic PDEs." SIAM Journal on Control and Optimization 57, no. 3 (2019): 2016–36. http://dx.doi.org/10.1137/18m1213129.

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37

Di Meglio, Florent, Rafael Vazquez, and Miroslav Krstic. "Stabilization of a System of $n+1$ Coupled First-Order Hyperbolic Linear PDEs With a Single Boundary Input." IEEE Transactions on Automatic Control 58, no. 12 (2013): 3097–111. http://dx.doi.org/10.1109/tac.2013.2274723.

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38

DIAGNE, Mamadou, Peipei SHANG, and Zhiqiang WANG. "Feedback Stabilization of a Food Extrusion Process Described by 1D PDEs Defined on Coupled Time-Varying Spatial Domains." IFAC-PapersOnLine 48, no. 12 (2015): 51–56. http://dx.doi.org/10.1016/j.ifacol.2015.09.352.

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39

Arfaoui, H. "Robust Robin Boundary Controls for the Finite-Time Stabilization of Caputo Fractional Nonlinear Systems of PDEs with Time-Delay." Lobachevskii Journal of Mathematics 46, no. 2 (2025): 578–93. https://doi.org/10.1134/s1995080224607689.

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40

He, Cang, Fang Zhang, and Jinhui Jiang. "Adaptive Boundary Control of Flexible Manipulators with Parameter Uncertainty Based on RBF Neural Network." Shock and Vibration 2020 (November 16, 2020): 1–13. http://dx.doi.org/10.1155/2020/8261423.

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In this paper, nonlinear dynamical equations of the flexible manipulator with a lumped payload at the free end are derived from Hamilton's principle. The obtained model consists of both distributed parameters and lumped parameters, namely, partial differential equations (PDEs) governing the flexible motion of links and boundary conditions in the form of ordinary differential equations (ODEs). Considering the great nonlinear approximation ability of the radial basis function (RBF) neural network, we propose a combined control algorithm that includes two parts: one is a boundary controller to tr

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41

Lhachemi, Hugo, Christophe Prieur, and Robert Shorten. "Robustness of constant-delay predictor feedback for in-domain stabilization of reaction–diffusion PDEs with time- and spatially-varying input delays." Automatica 123 (January 2021): 109347. http://dx.doi.org/10.1016/j.automatica.2020.109347.

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42

Guerrero-Sánchez, María-Eusebia, Omar Hernández-González, Rogelio Lozano, Carlos-D. García-Beltrán, Guillermo Valencia-Palomo, and Francisco-R. López-Estrada. "Energy-Based Control and LMI-Based Control for a Quadrotor Transporting a Payload." Mathematics 7, no. 11 (2019): 1090. http://dx.doi.org/10.3390/math7111090.

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This paper presents the control of a quadrotor with a cable-suspended payload. The proposed control structure is a hierarchical scheme consisting of an energy-based control (EBC) to stabilize the vehicle translational dynamics and to attenuate the payload oscillation, together with a nonlinear state feedback controller based on an linear matrix inequality (LMI) to control the quadrotor rotational dynamics. The payload swing control is based on an energy approach and the passivity properties of the system’s translational dynamics. The main advantage of the proposed EBC strategy is that it does

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43

Mavi, Anele, and Tiri Chinyoka. "Finite Volume Computational Analysis of the Heat Transfer Characteristic in a Double-Cylinder Counter-Flow Heat Exchanger with Viscoelastic Fluids." Defect and Diffusion Forum 424 (May 8, 2023): 19–43. http://dx.doi.org/10.4028/p-j482zy.

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This work presents a computational analysis of the heat-exchange characteristics in a double-cylinder (also known as a double-pipe) geometrical arrangement. The heat-exchange is from a hotter viscoelastic fluid flowing in the core (inner) cylinder to a cooler Newtonian fluid flowing in the shell (outer) annulus. For optimal heat-exchange characteristics, the core and shell fluid flow in opposite directions, the so-called counter-flow arrangement.The mathematical modelling of the given problem reduces to a system of nonlinear coupled Partial Differential Equations (PDEs). Specifically, the rheo

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44

Kumari, Neeraj, Maya Ferrell, Carolina G. Garcia, and Cullen M. Taniguchi. "Abstract 1107: Exploring the hypoxia pathway for gastrointestinal radioprotection in human minigut model." Cancer Research 83, no. 7_Supplement (2023): 1107. http://dx.doi.org/10.1158/1538-7445.am2023-1107.

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Abstract Introduction: When pancreatic cancer cannot be removed by surgery, radiation can be used to approximate a resection. Unfortunately, conventional radiation therapy cannot achieve ablative doses in the pancreas due to potential radiotoxicity to the nearby intestinal tissues. Thus, treatment-related gastrointestinal (GI) toxicity may be the most significant barrier to improving treatment responses for unresectable pancreatic cancer. There are no medications that can selectively protect the intestine from radiation damage, but we previously demonstrated that the genetic or pharmacologic i

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45

Dubljevic, Stevan. "Model predictive control of diffusion-reaction processes." Chemical Industry and Chemical Engineering Quarterly 11, no. 1 (2005): 10–18. http://dx.doi.org/10.2298/ciceq0501010d.

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Parabolic partial differential equations naturally arise as an adequate representation of a large class of spatially distributed systems, such as diffusion-reaction processes, where the interplay between diffusive and reaction forces introduces complexity in the characterization of the system, for the purpose of process parameter identification and subsequent control. In this work we introduce a model predictive control (MPC) framework for the control of input and state constrained parabolic partial differential equation (PDEs) systems. Model predictive control (MPC) is one of the most popular

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46

Priyanka, R., and S. Ramadevi. "A Hyperbolic PDE-ODE System with Delay-Robust Stabilization." International Journal of Trend in Scientific Research and Development Volume-2, Issue-5 (2018): 1988–90. http://dx.doi.org/10.31142/ijtsrd17157.

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47

Chen, Jiyun, Brahmam Pujala, Ashu Gupta, et al. "A novel orally bioavailable small molecular ENPP1 inhibitor (OC-1) for cancer immunotherapy." Journal of Clinical Oncology 41, no. 16_suppl (2023): e15136-e15136. http://dx.doi.org/10.1200/jco.2023.41.16_suppl.e15136.

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e15136 Background: Ectonucleotide pyrophosphatase/phosphodiesterase I (ENPP1) is a type II transmembrane glycoprotein with nucleotide pyrophosphatase and phosphodiesterase enzymatic activities. Inhibiting ENPP1 activity has emerged as an attractive approach in cancer immunotherapy, based on two distinct mechanisms. One mechanism is the stabilization of cyclic GMP–AMP (2’3’-cGAMP), which binds to stimulator of IFN genes (STING) and functions as an endogenous second messenger to activate the innate immune system; the other is the lowering of adenosine concentrations in the tumor microenvironment

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48

Crescioli, Clara, and Maria Paola Paronetto. "The Emerging Role of Phosphodiesterase 5 Inhibition in Neurological Disorders: The State of the Art." Cells 13, no. 20 (2024): 1720. http://dx.doi.org/10.3390/cells13201720.

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Growing evidence suggests that neuroinflammation is not just a consequence of neurodegeneration in pathologies such as Alzheimer’s disease, Parkinson’s disease, Huntington’s disease or Amyotrophic lateral sclerosis, but it is rather a determinant factor, which plays a pivotal role in the onset and progression of these disorders. Neuroinflammation can affect cells and processes in the central nervous system (CNS) as well as immune cells, and might precede protein aggregation, which is a hallmark of the neurodegenerative process. Standard treatment methods are far from being able to counteract i

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49

Cedervall, Peder, Ann Aulabaugh, Kieran F. Geoghegan, Thomas J. McLellan, and Jayvardhan Pandit. "Engineered stabilization and structural analysis of the autoinhibited conformation of PDE4." Proceedings of the National Academy of Sciences 112, no. 12 (2015): E1414—E1422. http://dx.doi.org/10.1073/pnas.1419906112.

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Phosphodiesterase 4 (PDE4) is an essential contributor to intracellular signaling and an important drug target. The four members of this enzyme family (PDE4A to -D) are functional dimers in which each subunit contains two upstream conserved regions (UCR), UCR1 and -2, which precede the C-terminal catalytic domain. Alternative promoters, transcriptional start sites, and mRNA splicing lead to the existence of over 25 variants of PDE4, broadly classified as long, short, and supershort forms. We report the X-ray crystal structure of long form PDE4B containing UCR1, UCR2, and the catalytic domain,

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50

Temmesfeld-Wollbrück, Bettina, Bernhard Brell, Corinna zu Dohna, et al. "Adrenomedullin reduces intestinal epithelial permeability in vivo and in vitro." American Journal of Physiology-Gastrointestinal and Liver Physiology 297, no. 1 (2009): G43—G51. http://dx.doi.org/10.1152/ajpgi.90532.2008.

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Leakage of the gut mucosal barrier in the critically ill patient may allow translocation of bacteria and their virulence factors, thereby perpetuating sepsis and inflammation. Present evidence suggests that adrenomedullin (AM) improves endothelial barrier function and stabilizes circulatory function in systemic inflammation. We tested the hypothesis that exogenously applied AM stabilizes gut epithelial barrier function. Infusion of Staphylococcus aureus α-toxin induced septic shock in rats. AM infusion in a therapeutic setting reduced translocation of labeled dextran from the gut into the syst

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