The Experts below are selected from a list of 7572 Experts worldwide ranked by ideXlab platform
Xiaodong Liu - One of the best experts on this subject based on the ideXlab platform.
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local analysis of continuous time takagi sugeno fuzzy system with disturbances bounded by magnitude or energy a Lagrange Multiplier Method
Information Sciences, 2013Co-Authors: Likui Wang, Xiaodong LiuAbstract:Abstract This paper is concerned with the problem of computing the bounds of disturbances for continuous-time Takagi–Sugeno fuzzy model. Two kinds of disturbances are investigated by applying the non-parallel distributed compensation (non-PDC) law, non-quadratic Lyapunov function and Lagrange Multiplier Method. One is bounded by magnitude, the other is bounded by energy. If the exogenous disturbances are bounded by magnitude, the maximal value of the magnitude under which the closed-loop system can be controlled is obtained by solving an optimization problem. On the other hand, if the disturbances are bounded by energy, except for the maximal bound, some conditions are derived to get two local regions (a smaller and a bigger) such that all the trajectories starting from the smaller region will remain in the bigger one which is required to be contained in a specific compact set (where the original system can be represented as T–S model exactly). In the end, the effectiveness of the proposed results is demonstrated by two examples.
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Local analysis of continuous-time Takagi–Sugeno fuzzy system with disturbances bounded by magnitude or energy: A Lagrange Multiplier Method
Information Sciences, 2013Co-Authors: Likui Wang, Xiaodong LiuAbstract:Abstract This paper is concerned with the problem of computing the bounds of disturbances for continuous-time Takagi–Sugeno fuzzy model. Two kinds of disturbances are investigated by applying the non-parallel distributed compensation (non-PDC) law, non-quadratic Lyapunov function and Lagrange Multiplier Method. One is bounded by magnitude, the other is bounded by energy. If the exogenous disturbances are bounded by magnitude, the maximal value of the magnitude under which the closed-loop system can be controlled is obtained by solving an optimization problem. On the other hand, if the disturbances are bounded by energy, except for the maximal bound, some conditions are derived to get two local regions (a smaller and a bigger) such that all the trajectories starting from the smaller region will remain in the bigger one which is required to be contained in a specific compact set (where the original system can be represented as T–S model exactly). In the end, the effectiveness of the proposed results is demonstrated by two examples.
Likui Wang - One of the best experts on this subject based on the ideXlab platform.
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local analysis of continuous time takagi sugeno fuzzy system with disturbances bounded by magnitude or energy a Lagrange Multiplier Method
Information Sciences, 2013Co-Authors: Likui Wang, Xiaodong LiuAbstract:Abstract This paper is concerned with the problem of computing the bounds of disturbances for continuous-time Takagi–Sugeno fuzzy model. Two kinds of disturbances are investigated by applying the non-parallel distributed compensation (non-PDC) law, non-quadratic Lyapunov function and Lagrange Multiplier Method. One is bounded by magnitude, the other is bounded by energy. If the exogenous disturbances are bounded by magnitude, the maximal value of the magnitude under which the closed-loop system can be controlled is obtained by solving an optimization problem. On the other hand, if the disturbances are bounded by energy, except for the maximal bound, some conditions are derived to get two local regions (a smaller and a bigger) such that all the trajectories starting from the smaller region will remain in the bigger one which is required to be contained in a specific compact set (where the original system can be represented as T–S model exactly). In the end, the effectiveness of the proposed results is demonstrated by two examples.
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Local analysis of continuous-time Takagi–Sugeno fuzzy system with disturbances bounded by magnitude or energy: A Lagrange Multiplier Method
Information Sciences, 2013Co-Authors: Likui Wang, Xiaodong LiuAbstract:Abstract This paper is concerned with the problem of computing the bounds of disturbances for continuous-time Takagi–Sugeno fuzzy model. Two kinds of disturbances are investigated by applying the non-parallel distributed compensation (non-PDC) law, non-quadratic Lyapunov function and Lagrange Multiplier Method. One is bounded by magnitude, the other is bounded by energy. If the exogenous disturbances are bounded by magnitude, the maximal value of the magnitude under which the closed-loop system can be controlled is obtained by solving an optimization problem. On the other hand, if the disturbances are bounded by energy, except for the maximal bound, some conditions are derived to get two local regions (a smaller and a bigger) such that all the trajectories starting from the smaller region will remain in the bigger one which is required to be contained in a specific compact set (where the original system can be represented as T–S model exactly). In the end, the effectiveness of the proposed results is demonstrated by two examples.
Ajit Patel - One of the best experts on this subject based on the ideXlab platform.
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A priori error analysis of the stabilized Lagrange Multiplier Method for elliptic problems with natural norms
Journal of Applied Mathematics and Computing, 2018Co-Authors: Sanjib Kumar Acharya, Ajit PatelAbstract:In this article the error analysis in the paper, stabilized Lagrange Multiplier Method for elliptic and parabolic interface problems are extended to the case of natural norm which is independent of mesh size for the case of elliptic interface problems. A stabilized Lagrange Multiplier Method for second order elliptic interface problems is presented in the framework of mortar Method. The requirement of Ladyzhenskaya–Babuska–Brezzi condition for mortar Method is alleviated by introducing penalty terms in the formulation. Optimal convergence results are established. Numerical experiments are conducted in support of the theoretical derivations.
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Convergence results with natural norms: Stabilized Lagrange Multiplier Method for elliptic interface problems
arXiv: Numerical Analysis, 2017Co-Authors: Sanjib Kumar Acharya, Ajit PatelAbstract:A stabilized Lagrange Multiplier Method for second order elliptic interface problems is presented in the framework of mortar Method. The requirement of LBB (Ladyzhenskaya-Babu\v{s}ka-Brezzi) condition for mortar Method is alleviated by introducing penalty terms in the formulation. Optimal convergence results are established in natural norm which is independent of mesh. Numerical experiments are conducted in support of the theoretical derivations.
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Stabilized Lagrange Multiplier Method for elliptic and parabolic interface problems
Applied Numerical Mathematics, 2017Co-Authors: Ajit Patel, Sanjib Kumar Acharya, Amiya K. PaniAbstract:Abstract In this paper, we discuss a new stabilized Lagrange Multiplier Method for finite element solution of multi-domain elliptic and parabolic initial-boundary value problems with non-matching grid across the subdomain interfaces. The proposed Method is consistent with the original problem and its stability is established without using the inf-sup (well known as LBB) condition. In the first part of this article, optimal error estimates are derived for second order elliptic interface problems. Then, the analysis is extended to parabolic initial and boundary value problems with interface and optimal error estimates are established for both semi-discrete and completely discrete schemes. The results of numerical experiments support the theoretical results obtained in this article.
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Lagrange Multiplier Method with penalty for elliptic and parabolic interface problems
Journal of Applied Mathematics and Computing, 2010Co-Authors: Ajit PatelAbstract:The basic requirement for the stability of the mortar element Method is to construct finite element spaces which satisfy certain criteria known as inf-sup (well known as LBB, i.e., Ladyzhenskaya-Babuska-Brezzi) condition. Many natural and convenient choices of finite element spaces are ruled out as these spaces may not satisfy the inf-sup condition. In order to alleviate this problem Lagrange Multiplier Method with penalty is used in this paper. The existence and uniqueness results of the discrete problem are discussed without using the discrete LBB condition. We have also analyzed the Lagrange Multiplier Method with penalty for parabolic initial-boundary value problems using semidiscrete and fully discrete schemes. We have derived sub-optimal order of estimates for both semidiscrete and fully discrete schemes. The results of numerical experiments support the theoretical results obtained in this article.
Jun Wang - One of the best experts on this subject based on the ideXlab platform.
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Decoupling Capacitor Placement Optimization With Lagrange Multiplier Method
2020 IEEE International Symposium on Electromagnetic Compatibility & Signal Power Integrity (EMCSI), 2020Co-Authors: Jun Wang, Jun FanAbstract:This paper proposes a decoupling capacitor placement optimization Method based on the cavity model and Lagrange Multiplier. The variable conditions associating with coordinates (x,y) of input impedance expression based on the cavity model are combined with the Lagrange Multiplier Method. The decoupling capacitor optimum placement within a defined area of the board can be found through the proposed analytical Method. The example of finding an optimum location of the decoupling capacitor within a defined area of the power delivery network is exposed, the results are compared to the brute-force Method to prove the effectiveness of the proposed Method.
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double noise dual problem approach to the augmented Lagrange Multiplier Method for robust principal component analysis
Soft Computing, 2017Co-Authors: Dansong Cheng, Jianzhe Yang, Jun WangAbstract:Robust principal component analysis (RPCA) is one of the most useful tools to recover a low-rank data component from the superposition of a sparse component. The augmented Lagrange Multiplier (ALM) Method enjoys the highest accuracy among all the approaches to the RPCA. However, it still suffers from two problems, namely, a brutal force initialization phase resulting in low convergence speed and ignorance of other types of noise resulting in low accuracy. To this end, this paper proposes a double-noise, dual-problem approach to the augmented Lagrange Multiplier Method, referred to as DNDP-ALM, for robust principal component analysis. Firstly, the original ALM Method considers sparse noise only, ignoring Gaussian noise, which generally exists in real-world data. In our proposed DNDP-ALM, the data consist of low-rank component, sparse component and Gaussian noise component, with RPCA problem converted to convex optimization. Secondly, the original ALM uses a rough initialization of Multipliers, leading to more work of iterative calculation and lower calculation accuracy. In our proposed DNDP-ALM, the initialization is carried out by solving a dual problem to obtain the optimal Multiplier. The experimental results show that the proposed approach super-performs in solving robust principal component analysis problems in terms of speed and accuracy, compared to the state-of-the-art techniques.
Huachun Tan - One of the best experts on this subject based on the ideXlab platform.
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Mixture Augmented Lagrange Multiplier Method for Tensor Recovery and Its Applications
Discrete Dynamics in Nature and Society, 2014Co-Authors: Huachun Tan, Bin Cheng, Jianshuai Feng, Li Liu, Wuhong WangAbstract:The problem of data recovery inmultiway arrays (i.e., tensors) arises in many fields such as computer vision, image processing, and traffic data analysis. In this paper, we propose a scalable and fast algorithm for recovering a low-n-rank tensor with an unknown fraction of its entries being arbitrarily corrupted. In the new algorithm, the tensor recovery problem is formulated as a mixture convex multilinear Robust Principal Component Analysis (RPCA) optimization problem by minimizing a sum of the nuclear norm and the l(1)-norm. The problem is well structured in both the objective function and constraints. We apply augmented Lagrange Multiplier Method which can make use of the good structure for efficiently solving this problem. In the experiments, the algorithm is compared with the state-of-art algorithm both on synthetic data and real data including traffic data, image data, and video data.
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Low-n-rank tensor recovery based on multi-linear augmented Lagrange Multiplier Method
Neurocomputing, 2013Co-Authors: Huachun Tan, Bin Cheng, Jianshuai Feng, Guangdong Feng, Wuhong Wang, Yujin ZhangAbstract:The problem of recovering data in multi-way arrays (i.e., tensors) arises in many fields such as image processing and computer vision, etc. In this paper, we present a novel Method based on multi-linear n-rank and @?"0 norm optimization for recovering a low-n-rank tensor with an unknown fraction of its elements being arbitrarily corrupted. In the new Method, the n-rank and @?"0 norm of the each mode of the given tensor are combined by weighted parameters as the objective function. In order to avoid relaxing the observed tensor into penalty terms, which may cause less accuracy problem, the minimization problem along each mode is accomplished by applying the augmented Lagrange Multiplier Method. In experiments, we test the influence of parameters on the results of the proposed Method, and then compare with one state-of-the-art Method on both simulated data and real data. Numerical results show that the Method can reliably solve a wide range of problems at a speed at least several times faster than the state-of-the-art Method while the results of the Method are comparable to the previous Method in terms of accuracy.
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tensor recovery via multi linear augmented Lagrange Multiplier Method
International Conference on Image and Graphics, 2011Co-Authors: Huachun Tan, Bin Cheng, Jianshuai Feng, Guangdong Feng, Yujin ZhangAbstract:The problem of recovering data in multi-way arrays (i.e., tensors) arises in many fields such as image processing and computer vision, etc. In this paper, we present a novel Method based on multi-linear n-rank and l_0 norm optimization for recovering a low-n-rank tensor with an unknown fraction of its elements being arbitrarily corrupted. In the new Method, the n-rank and l_0 norm of the each mode of the given tensor are combined by weighted parameters as the objective function. In order to avoid relaxing the observed tensor into penalty terms, which may cause less accuracy problem, the minimization problem along each mode is accomplished by applying the augmented Lagrange Multiplier Method. The proposed approach is evaluated both on simulated data and real world data. Experimental results show that our proposed Method tends to deliver higher-quality solutions with faster convergence rate compared with previous Methods.
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ICIG - Tensor Recovery via Multi-linear Augmented Lagrange Multiplier Method
2011 Sixth International Conference on Image and Graphics, 2011Co-Authors: Huachun Tan, Bin Cheng, Jianshuai Feng, Guangdong Feng, Yujin ZhangAbstract:The problem of recovering data in multi-way arrays (i.e., tensors) arises in many fields such as image processing and computer vision, etc. In this paper, we present a novel Method based on multi-linear n-rank and l_0 norm optimization for recovering a low-n-rank tensor with an unknown fraction of its elements being arbitrarily corrupted. In the new Method, the n-rank and l_0 norm of the each mode of the given tensor are combined by weighted parameters as the objective function. In order to avoid relaxing the observed tensor into penalty terms, which may cause less accuracy problem, the minimization problem along each mode is accomplished by applying the augmented Lagrange Multiplier Method. The proposed approach is evaluated both on simulated data and real world data. Experimental results show that our proposed Method tends to deliver higher-quality solutions with faster convergence rate compared with previous Methods.
