The Experts below are selected from a list of 285 Experts worldwide ranked by ideXlab platform
Panagiotis D. Christofides - One of the best experts on this subject based on the ideXlab platform.
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Nonlinear Feedback Control of Surface Roughness Using a Stochastic PDE: Design and Application to a Sputtering Process
Industrial & Engineering Chemistry Research, 2006Co-Authors: Yiming Lou, Panagiotis D. ChristofidesAbstract:In this work, we develop a method for nonlinear feedback control of the roughness of a one-Dimensional surface whose evolution is described by the stochastic Kuramoto-Sivashinsky equation (KSE), a fourthorder nonlinear stochastic partial differential equation. We initially formulate the stochastic KSE into a System of infinite nonlinear stochastic ordinary differential equations by using Galerkin’s method. A finite-Dimensional approximation of the stochastic KSE is then derived that captures the dominant mode contribution to the surface roughness. A nonlinear feedback controller is then designed based on the finite-Dimensional approximation to control the surface roughness. An analysis of the closed-loop nonlinear infinite-Dimensional System is performed to characterize the closed-loop performance enforced by the nonlinear feedback controller in the closed-loop infinite-Dimensional System. The effectiveness of the proposed nonlinear controller and the advantages of the nonlinear controller over a linear controller resulting from the linearization of the nonlinear controller around the zero solution are demonstrated through numerical simulations. Finally, a successful application of a stochastic KSE-based nonlinear feedback controller to the kinetic Monte Carlo model of a sputtering process is also demonstrated.
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CDC - Nonlinear Feedback Control of Surface Roughness Using a Stochastic PDE
Proceedings of the 45th IEEE Conference on Decision and Control, 2006Co-Authors: Yiming Lou, Panagiotis D. ChristofidesAbstract:In this work, we develop a method for nonlinear feedback control of the roughness of a one-Dimensional surface whose evolution is described by the stochastic Kuramoto-Sivashinsky equation (KSE), a fourth-order nonlinear stochastic partial differential equation. We initially formulate the stochastic KSE into a System of infinite nonlinear stochastic ordinary differential equations by using modal decomposition. A finite-Dimensional approximation of the stochastic KSE is then derived that captures the dominant mode contribution to the surface roughness. A nonlinear feedback controller is then designed based on the finite-Dimensional approximation to control the surface roughness. An analysis of the closed-loop nonlinear infinite-Dimensional System is performed to characterize the closed-loop performance enforced by the nonlinear feedback controller in the closed-loop infinite-Dimensional System. The effectiveness of the proposed nonlinear controller and the advantages of the nonlinear controller over a linear controller resulting from the linearization of the nonlinear controller around the zero solution are demonstrated through numerical simulations.
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CDC - Predictive Control of Infinite Dimensional Systems
Proceedings of the 45th IEEE Conference on Decision and Control, 2006Co-Authors: Stevan Dubljevic, Prashant Mhaskar, Nael H. El-farra, Panagiotis D. ChristofidesAbstract:This paper focuses on predictive control of linear infinite Dimensional Systems with state and control constraints arising in the context of parabolic partial differential equations (PDEs). Initially, a parabolic PDE is presented and formulated as an infinite-Dimensional System in an appropriate Hilbert space. Next, modal decomposition techniques are used to derive a finite-Dimensional System that captures the dominant dynamics of the infinite-Dimensional System, and express the infinite-Dimensional state constraints in terms of the finite-Dimensional System state constraints. A number of model predictive control (MPC) formulations, designed on the basis of different finite-Dimensional approximations, are then presented and compared. The closed-loop stability properties of the infinite-Dimensional System under the low order MPC controller designs are analyzed, and sufficient conditions that guarantee stabilization and state constraint satisfaction for the infinite-Dimensional System under the reduced order MPC formulations are derived. Other formulations are also presented which differ in the way the evolution of the fast eigenmodes is accounted for in the performance objective and state constraints. The impact of these differences on the ability of the predictive controller to enforce closed-loop stability and state constraints satisfaction in the infinite-Dimensional System is analyzed
Andrey A. Amosov - One of the best experts on this subject based on the ideXlab platform.
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Asymptotic approximations for the stationary radiative-conductive heat transfer problem in the two-Dimensional System of plates
Russian Journal of Numerical Analysis and Mathematical Modelling, 2017Co-Authors: Andrey A. AmosovAbstract:AbstractSpecial asymptotic approximations, namely, the first and second homogenized problems are proposed for the boundary value problem describing a stationary radiative-conductive heat transfer in a two-Dimensional System of heat-conducting plates of thickness
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Semidiscrete approximations for the stationary radiative–conductive heat transfer problem in a two-Dimensional System of plates
Russian Journal of Numerical Analysis and Mathematical Modelling, 2016Co-Authors: Andrey A. Amosov, Dmitry A MaslovAbstract:AbstractSpecial semidiscrete approximations, namely, basic, first, and second semidiscrete problems are proposed for a boundary value problem describing a stationary radiative–conductive heat transfer in a two-Dimensional System of heat-conductive plates of width
Yiming Lou - One of the best experts on this subject based on the ideXlab platform.
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Nonlinear Feedback Control of Surface Roughness Using a Stochastic PDE: Design and Application to a Sputtering Process
Industrial & Engineering Chemistry Research, 2006Co-Authors: Yiming Lou, Panagiotis D. ChristofidesAbstract:In this work, we develop a method for nonlinear feedback control of the roughness of a one-Dimensional surface whose evolution is described by the stochastic Kuramoto-Sivashinsky equation (KSE), a fourthorder nonlinear stochastic partial differential equation. We initially formulate the stochastic KSE into a System of infinite nonlinear stochastic ordinary differential equations by using Galerkin’s method. A finite-Dimensional approximation of the stochastic KSE is then derived that captures the dominant mode contribution to the surface roughness. A nonlinear feedback controller is then designed based on the finite-Dimensional approximation to control the surface roughness. An analysis of the closed-loop nonlinear infinite-Dimensional System is performed to characterize the closed-loop performance enforced by the nonlinear feedback controller in the closed-loop infinite-Dimensional System. The effectiveness of the proposed nonlinear controller and the advantages of the nonlinear controller over a linear controller resulting from the linearization of the nonlinear controller around the zero solution are demonstrated through numerical simulations. Finally, a successful application of a stochastic KSE-based nonlinear feedback controller to the kinetic Monte Carlo model of a sputtering process is also demonstrated.
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CDC - Nonlinear Feedback Control of Surface Roughness Using a Stochastic PDE
Proceedings of the 45th IEEE Conference on Decision and Control, 2006Co-Authors: Yiming Lou, Panagiotis D. ChristofidesAbstract:In this work, we develop a method for nonlinear feedback control of the roughness of a one-Dimensional surface whose evolution is described by the stochastic Kuramoto-Sivashinsky equation (KSE), a fourth-order nonlinear stochastic partial differential equation. We initially formulate the stochastic KSE into a System of infinite nonlinear stochastic ordinary differential equations by using modal decomposition. A finite-Dimensional approximation of the stochastic KSE is then derived that captures the dominant mode contribution to the surface roughness. A nonlinear feedback controller is then designed based on the finite-Dimensional approximation to control the surface roughness. An analysis of the closed-loop nonlinear infinite-Dimensional System is performed to characterize the closed-loop performance enforced by the nonlinear feedback controller in the closed-loop infinite-Dimensional System. The effectiveness of the proposed nonlinear controller and the advantages of the nonlinear controller over a linear controller resulting from the linearization of the nonlinear controller around the zero solution are demonstrated through numerical simulations.
Hugo Lhachemi - One of the best experts on this subject based on the ideXlab platform.
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PI Regulation of a Reaction-Diffusion Equation with Delayed Boundary Control
IEEE Transactions on Automatic Control, 2021Co-Authors: Hugo Lhachemi, Christophe Prieur, Emmanuel TrélatAbstract:The general context of this work is the feedback control of an infinite-Dimensional System so that the closed-loop System satisfies a fading-memory property and achieves the setpoint tracking of a given reference signal. More specifically , this paper is concerned with the Proportional Integral (PI) regulation control of the left Neumann trace of a one-Dimensional reaction-diffusion equation with a delayed right Dirichlet boundary control. In this setting, the studied reaction-diffusion equation might be either open-loop stable or unstable. The proposed control strategy goes as follows. First, a finite-Dimensional truncated model that captures the unstable dynamics of the original infinite-Dimensional System is obtained via spectral decomposition. The truncated model is then augmented by an integral component on the tracking error of the left Neumann trace. After resorting to the Artstein transformation to handle the control input delay, the PI controller is designed by pole shifting. Stability of the resulting closed-loop infinite-Dimensional System, consisting of the original reaction-diffusion equation with the PI controller, is then established thanks to an adequate Lyapunov function. In the case of a time-varying reference input and a time-varying distributed disturbance, our stability result takes the form of an exponential Input-to-State Stability (ISS) estimate with fading memory. Finally, another exponential ISS estimate with fading memory is established for the tracking performance of the reference signal by the System output. In particular, these results assess the setpoint regulation of the left Neumann trace in the presence of distributed perturbations that converge to a steady-state value and with a time-derivative that converges to zero. Numerical simulations are carried out to illustrate the efficiency of our control strategy.
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Neumann trace tracking of a constant reference input for 1-D boundary controlled heat-like equations with delay
2020Co-Authors: Hugo Lhachemi, Christophe Prieur, Emmanuel TrélatAbstract:This paper discusses the Proportional Integral (PI) regulation control of the left Neumann trace of a one-Dimensional reaction-diffusion equation with a delayed right Dirichlet boundary control. Specifically, a PI controller is designed based on a finite-Dimensional truncated model that captures the unstable dynamics of the original infinite-Dimensional System. In this setting, the control input delay is handled by resorting to the Artstein transformation. The stability of the resulting infinite-Dimensional System, as well as the tracking of a constant reference signal in the presence of a constant distributed perturbation, is assessed based on the introduction of an adequate Lyapunov function. The theoretical results are illustrated with numerical simulations.
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Boundary feedback stabilization of a reaction–diffusion equation with Robin boundary conditions and state-delay
Automatica, 2020Co-Authors: Hugo Lhachemi, Robert ShortenAbstract:This paper discusses the boundary feedback stabilization of a reaction–diffusion equation with Robin boundary conditions and in the presence of a time-varying state-delay. The proposed control design strategy is based on a finite-Dimensional truncated model obtained via a spectral decomposition. By an adequate selection of the number of modes of the original infinite-Dimensional System, we show that the design performed on the finite-Dimensional truncated model achieves the exponential stabilization of the original infinite-Dimensional System. In the presence of distributed disturbances, we show that the closed-loop System is exponentially input-to-state stable with fading memory.
Yaqin Wang - One of the best experts on this subject based on the ideXlab platform.
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Adaptive control for synchronization of a four-Dimensional chaotic System via a single variable
Nonlinear Dynamics, 2010Co-Authors: Xingyuan Wang, Yaqin WangAbstract:This paper studies the control for synchronization of a four-Dimensional System via a single variable, and a linear feedback controller and an adaptive controller are proposed. Based on the Lyapunov stability theory, the correctness of the proposed methods is strictly demonstrated. The numerical simulations further show their effectiveness.