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Junwei Wang - One of the best experts on this subject based on the ideXlab platform.
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distributed proportional plus second order Spatial Derivative control for distributed parameter systems subject to spatiotemporal uncertainties
Nonlinear Dynamics, 2014Co-Authors: Junwei WangAbstract:In this paper, a robust distributed control design based on proportional plus second-order Spatial Derivative (P-sD $$^2$$ ) is proposed for exponential stabilization and minimization of Spatial variation of a class of distributed parameter systems (DPSs) with spatiotemporal uncertainties, whose model is represented by parabolic partial differential equations with Spatially varying coefficients. Based on the Lyapunov’s direct method, a robust distributed P-sD $$^2$$ controller is developed to not only exponentially stabilize the DPS for all admissible spatiotemporal uncertainties but also minimize the Spatial variation of the process. The outcome of the robust distributed P-sD $$^2$$ control problem is formulated as a Spatial differential bilinear matrix inequality (SDBMI) problem. A local optimization algorithm that the SDBMI is treated as a double Spatial differential linear matrix inequality (SDLMI) is presented to solve this SDBMI problem. Furthermore, the SDLMI optimization problem can be approximately solved via the finite difference method and the existing convex optimization techniques. Finally, the proposed design method is successfully applied to feedback control problem of the FitzHugh–Nagumo equation.
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robust control for a class of nonlinear distributed parameter systems via proportional Spatial Derivative control approach
Abstract and Applied Analysis, 2014Co-Authors: Chengdong Yang, Jianlong Qiu, Junwei WangAbstract:This paper addresses the problem of robust control design via the proportional-Spatial Derivative (P-sD) control approach for a class of nonlinear distributed parameter systems modeled by semilinear parabolic partial differential equations (PDEs). By using the Lyapunov direct method and the technique of integration by parts, a simple linear matrix inequality (LMI) based design method of the robust P-sD controller is developed such that the closed-loop PDE system is exponentially stable with a given decay rate and a prescribed performance of disturbance attenuation. Moreover, a suboptimal controller is proposed to minimize the attenuation level for a given decay rate. The proposed method is successfully employed to address the control problem of the FitzHugh-Nagumo (FHN) equation, and the achieved simulation results show its effectiveness.
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distributed proportional Spatial Derivative control of nonlinear parabolic systems via fuzzy pde modeling approach
Systems Man and Cybernetics, 2012Co-Authors: Junwei WangAbstract:In this paper, a distributed fuzzy control design based on Proportional-Spatial Derivative (P-sD) is proposed for the exponential stabilization of a class of nonlinear Spatially distributed systems described by parabolic partial differential equations (PDEs). Initially, a Takagi-Sugeno (T-S) fuzzy parabolic PDE model is proposed to accurately represent the nonlinear parabolic PDE system. Then, based on the T-S fuzzy PDE model, a novel distributed fuzzy P-sD state feedback controller is developed by combining the PDE theory and the Lyapunov technique, such that the closed-loop PDE system is exponentially stable with a given decay rate. The sufficient condition on the existence of an exponentially stabilizing fuzzy controller is given in terms of a set of Spatial differential linear matrix inequalities (SDLMIs). A recursive algorithm based on the finite-difference approximation and the linear matrix inequality (LMI) techniques is also provided to solve these SDLMIs. Finally, the developed design methodology is successfully applied to the feedback control of the Fitz-Hugh-Nagumo equation.
M Gomes - One of the best experts on this subject based on the ideXlab platform.
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higher Spatial Derivative field theories
Physical Review D, 2012Co-Authors: Pedro R S Gomes, M GomesAbstract:In this work, we employ renormalization group methods to study the general behavior of field theories possessing anisotropic scaling in the spacetime variables. The Lorentz symmetry breaking that accompanies these models are either soft, if no higher Spatial Derivative is present, or it may have a more complex structure if higher Spatial Derivatives are also included. Both situations are discussed in models with only scalar fields and also in models with fermions as a Yukawa-like model.
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fourth order Spatial Derivative gravity
Physical Review D, 2011Co-Authors: F S Bemfica, M GomesAbstract:In this work we study a modified theory of gravity that contains up to fourth order Spatial Derivatives as a model for the Hořava-Lifshitz gravity. The propagator is evaluated and, as a result, it is obtained one extra pole corresponding to a spin two nonrelativistic massless particle, an extra term which jeopardizes renormalizability, besides the unexpected general relativity unmodified propagator. Then, unitarity is proved at the tree-level, where the general relativity pole has shown to have no dynamics, remaining only the two degrees of freedom of the new pole. Next, the nonrelativistic effective potential is determined from a scattering process of two identical massive gravitationally interacting bosons. In this limit, Newton’s potential is obtained, together with a Darwin-like term that comes from the extra non-pole term in the propagator. Regarding renormalizability, this extra term may be harmful, by power counting, but it can be eliminated by adjusting the free parameters of the model. This adjustment is in accord with the detailed balance condition suggested in the literature and shows that the way in which extra Spatial Derivative terms are added is of fundamental importance.
Chengdong Yang - One of the best experts on this subject based on the ideXlab platform.
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robust exponential synchronization for a class of master slave distributed parameter systems with Spatially variable coefficients and nonlinear perturbation
Mathematical Problems in Engineering, 2015Co-Authors: Chengdong Yang, Kejia Yi, Xiangyong Chen, Ancai Zhang, Xiao Chen, Liuqing YangAbstract:This paper addresses the exponential synchronization problem of a class of master-slave distributed parameter systems (DPSs) with Spatially variable coefficients and spatiotemporally variable nonlinear perturbation, modeled by a couple of semilinear parabolic partial differential equations (PDEs). With a locally Lipschitz constraint, the perturbation is a continuous function of time, space, and system state. Firstly, a sufficient condition for the robust exponential synchronization of the unforced semilinear master-slave PDE systems is investigated for all admissible nonlinear perturbations. Secondly, a robust distributed proportional-Spatial Derivative (P-sD) state feedback controller is desired such that the closed-loop master-slave PDE systems achieve exponential synchronization. Using Lyapunov’s direct method and the technique of integration by parts, the main results of this paper are presented in terms of Spatial differential linear matrix inequalities (SDLMIs). Finally, two numerical examples are provided to show the effectiveness of the proposed methods applied to the robust exponential synchronization problem of master-slave PDE systems with nonlinear perturbation.
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distributed proportional Spatial Derivative control design for 3 dimensional parabolic pde systems
International Conference on Information Science and Technology, 2015Co-Authors: Chengdong Yang, Xiangyong Chen, Ancai Zhang, Xiao Chen, Jianlong Qiu, Liuqing YangAbstract:This paper addresses the problem of distributed proportional-Spatial Derivative (P-sD) control design for a class of linear distributed parameter systems (DPSs) modeled by 3-dimensional parabolic partial differential equations (PDEs). Based on the Lyapunov direct method and the technique of integration by parts, the P-sD control design is developed in terms of standard linear matrix inequality (LMI) such that the closed-loop 3-dimensional PDE system is exponentially stable. Finally, numerical simulation result illustrates its effectiveness.
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exponential synchronization for a class of complex spatio temporal networks with space varying coefficients
Neurocomputing, 2015Co-Authors: Chengdong Yang, Haibo HeAbstract:Abstract This paper addresses the problem of exponential synchronization for a class of complex spatio-temporal networks with space-varying coefficients, where the dynamics of nodes are described by coupled partial differential equations (PDEs). The goal of this research is to design distributed proportional-Spatial Derivative (P-sD) state feedback controllers to ensure exponential synchronization of the complex spatio-temporal network. Using Lyapunov׳s direct method, the problem of exponential synchronization of the complex spatio-temporal network is formulated as the feasibility problem of Spatial differential linear matrix inequality (SDLMI) in space. The feasible solutions to this SDLMI in space can be approximately derived via the standard finite difference method and the linear matrix inequality (LMI) optimization technique. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed design method.
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robust control for a class of nonlinear distributed parameter systems via proportional Spatial Derivative control approach
Abstract and Applied Analysis, 2014Co-Authors: Chengdong Yang, Jianlong Qiu, Junwei WangAbstract:This paper addresses the problem of robust control design via the proportional-Spatial Derivative (P-sD) control approach for a class of nonlinear distributed parameter systems modeled by semilinear parabolic partial differential equations (PDEs). By using the Lyapunov direct method and the technique of integration by parts, a simple linear matrix inequality (LMI) based design method of the robust P-sD controller is developed such that the closed-loop PDE system is exponentially stable with a given decay rate and a prescribed performance of disturbance attenuation. Moreover, a suboptimal controller is proposed to minimize the attenuation level for a given decay rate. The proposed method is successfully employed to address the control problem of the FitzHugh-Nagumo (FHN) equation, and the achieved simulation results show its effectiveness.
Mehdi Dehghan - One of the best experts on this subject based on the ideXlab platform.
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simulation of activator inhibitor dynamics based on cross diffusion brusselator reaction diffusion system via a differential quadrature radial point interpolation method dq rpim technique
European Physical Journal Plus, 2021Co-Authors: Mostafa Abbaszadeh, Mobina Golmohammadi, Mehdi DehghanAbstract:The current paper proposes an efficient numerical procedure for solving the two-dimensional Brusselator reaction–diffusion system. First, the time Derivative is discretized by a semi-implicit finite difference scheme such that the nonlinear terms are approximated by using one term of the Taylor expansion. It is shown if the nonlinear terms satisfy the Lipshitz condition, then the proposed difference scheme is stable. In the next, the Spatial Derivative is discretized by the differential quadrature technique based upon the shape functions of radial point interpolation method. We study some practical problems to show the efficiency and acceptable results of the developed technique.
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a multigrid compact finite difference method for solving the one dimensional nonlinear sine gordon equation
Mathematical Methods in The Applied Sciences, 2015Co-Authors: Hamid Moghaderi, Mehdi DehghanAbstract:The aim of this paper is to propose a multigrid method to obtain the numerical solution of the one-dimensional nonlinear sine-Gordon equation. The finite difference equations at all interior grid points form a large sparse linear system, which needs to be solved efficiently. The solution cost of this sparse linear system usually dominates the total cost of solving the discretized partial differential equation. The proposed method is based on applying a compact finite difference scheme of fourth-order for discretizing the Spatial Derivative and the standard second-order central finite difference method for the time Derivative. The proposed method uses the Richardson extrapolation method in time variable. The obtained system has been solved by V-cycle multigrid (VMG) method, where the VMG method is used for solving the large sparse linear systems. The numerical examples show the efficiency of this algorithm for solving the one-dimensional sine-Gordon equation. Copyright © 2014 John Wiley & Sons, Ltd.
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high order solution of one dimensional sine gordon equation using compact finite difference and dirkn methods
Mathematical and Computer Modelling, 2010Co-Authors: Akbar Mohebbi, Mehdi DehghanAbstract:In this work we propose a high-order and accurate method for solving the one-dimensional nonlinear sine-Gordon equation. The proposed method is based on applying a compact finite difference scheme and the diagonally implicit Runge-Kutta-Nystrom (DIRKN) method for Spatial and temporal components, respectively. We apply a compact finite difference approximation of fourth order for discretizing the Spatial Derivative and a fourth-order A-stable DIRKN method for the time integration of the resulting nonlinear second-order system of ordinary differential equations. The proposed method has fourth-order accuracy in both space and time variables and is unconditionally stable. The results of numerical experiments show that the combination of a compact finite difference approximation of fourth order and a fourth-order A-stable DIRKN method gives an efficient algorithm for solving the one-dimensional sine-Gordon equation.
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fourth order compact solution of the nonlinear klein gordon equation
Numerical Algorithms, 2009Co-Authors: Mehdi Dehghan, Akbar Mohebbi, Zohreh AsgariAbstract:In this work we propose a fourth-order compact method for solving the one-dimensional nonlinear Klein-Gordon equation. We apply a compact finite difference approximation of fourth-order for discretizing Spatial Derivative and a fourth-order A-stable diagonally-implicit Runge-Kutta-Nystrom (DIRKN) method for the time integration of the resulting nonlinear second-order system of ordinary differential equations. The proposed method has fourth order accuracy in both space and time variables and is unconditionally stable. Numerical results obtained from solving several problems possessing periodic, kinks, single and double-soliton waves show that the combination of a compact finite difference approximation of fourth order and a fourth-order A-stable DIRKN method gives an efficient algorithm for solving these problems.
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high order compact solution of the one space dimensional linear hyperbolic equation
Numerical Methods for Partial Differential Equations, 2008Co-Authors: Akbar Mohebbi, Mehdi DehghanAbstract:In this article, we introduce a high-order accurate method for solving one-space dimensional linear hyperbolic equation. We apply a compact finite difference approximation of fourth order for discretizing Spatial Derivative of linear hyperbolic equation and collocation method for the time component. The main property of this method additional to its high-order accuracy due to the fourth order discretization of Spatial Derivative, is its unconditionally stability. In this technique the solution is approximated by a polynomial at each grid point that its coefficients are determined by solving a linear system of equations. Numerical results show that the compact finite difference approximation of fourth order and collocation method produce a very efficient method for solving the one-space-dimensional linear hyperbolic equation. We compare the numerical results of this paper with numerical results of (Mohanty, Appl Math Lett 17 (2004), 101–105).© 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008
Maohua Ran - One of the best experts on this subject based on the ideXlab platform.
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an effective algorithm for delay fractional convection diffusion wave equation based on reversible exponential recovery method
IEEE Access, 2019Co-Authors: Qifeng Zhang, Wahidullah Niazi, Maohua RanAbstract:In this paper, we investigate a linearized finite difference scheme for the variable coefficient semi-linear fractional convection-diffusion wave equation with delay. Based on reversible recovery technique, the original problems are transformed into an equivalent variable coefficient semi-linear fractional delay reaction-diffusion equation. Then, the temporal Caputo Derivative is discreted by using $L_{1}$ approximation and the second-order Spatial Derivative is approximated by the centered finite difference scheme. The numerical solution can be obtained by an inverse exponential recovery method. By introducing a new weighted norm and applying discrete Gronwall inequality, the solvability, unconditionally stability, and convergence in the sense of $L_{2}$ - and $L_{\infty }$ - norms are proved rigorously. Finally, we present a numerical example to verify the effectiveness of our algorithm.
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analysis of the compact difference scheme for the semilinear fractional partial differential equation with time delay
Applicable Analysis, 2017Co-Authors: Qifeng Zhang, Maohua RanAbstract:In the paper, a linearized compact finite difference scheme is presented for the semilinear fractional delay convection-reaction–diffusion equation. Firstly, the equation is transformed into an equivalent semilinear fractional delay reaction–diffusion equation by using a special transformation. Then, the temporal Caputo Derivative is discreted by using approximation and the second-order Spatial Derivative is approximated by the compact finite difference scheme. The solvability, unconditional stability, and convergence in the sense of - and - norms are proved rigorously. Finally, numerical examples are carried out extensively to support our theoretical analysis.
