The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Reinaldo M. Palhares - One of the best experts on this subject based on the ideXlab platform.
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avoiding Matrix Inversion in takagi sugeno based advanced controllers and observers
IEEE Transactions on Fuzzy Systems, 2018Co-Authors: Thomas Laurain, Jimmy Lauber, Reinaldo M. PalharesAbstract:Many of the recent advances on control and estimation of systems described by Takagi–Sugeno (TS) fuzzy models are based on Matrix Inversion, which could be a trouble in the case of real-time implementation. This paper is devoted to the development of alternative solutions to this Matrix Inversion problem in the discrete-time case. Two different methods are proposed: The first one relies on replacing the Matrix Inversion by multiple sums and the second methodology is based on an estimation of the Matrix Inversion by an observer structure. For the first methodology, a new class of controllers and observers are introduced which are called, respectively, the counterpart of an advanced TS-based (CATS) controller and the replica of an advanced TS-based (RATS) observer. Instead of relaxations for the linear Matrix inequalities conditions, an original use of the membership functions is presented. In the second methodology, it is proposed the estimation-based control law for approximating TS-based (ECLATS) controller that uses a fuzzy state observer. The Lyapunov theory is used to ensure stability conditions for either the closed-loop system as well as the estimation error. Numerical examples and comparisons highlight the efficiency of the procedures that can be used to replace any inverted Matrix in any advanced fuzzy controller or observer. Finally, advantages and drawbacks of the proposed method are discussed.
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Avoiding Matrix Inversion in Takagi–Sugeno-Based Advanced Controllers and Observers
IEEE Transactions on Fuzzy Systems, 2018Co-Authors: Thomas Laurain, Jimmy Lauber, Reinaldo M. PalharesAbstract:Many of the recent advances on control and estimation of systems described by Takagi–Sugeno (TS) fuzzy models are based on Matrix Inversion, which could be a trouble in the case of real-time implementation. This paper is devoted to the development of alternative solutions to this Matrix Inversion problem in the discrete-time case. Two different methods are proposed: The first one relies on replacing the Matrix Inversion by multiple sums and the second methodology is based on an estimation of the Matrix Inversion by an observer structure. For the first methodology, a new class of controllers and observers are introduced which are called, respectively, the counterpart of an advanced TS-based (CATS) controller and the replica of an advanced TS-based (RATS) observer. Instead of relaxations for the linear Matrix inequalities conditions, an original use of the membership functions is presented. In the second methodology, it is proposed the estimation-based control law for approximating TS-based (ECLATS) controller that uses a fuzzy state observer. The Lyapunov theory is used to ensure stability conditions for either the closed-loop system as well as the estimation error. Numerical examples and comparisons highlight the efficiency of the procedures that can be used to replace any inverted Matrix in any advanced fuzzy controller or observer. Finally, advantages and drawbacks of the proposed method are discussed.
Yunong Zhang - One of the best experts on this subject based on the ideXlab platform.
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ICNC - Three nonlinearly-activated discrete-Time ZNN models for time-varying Matrix Inversion
2012 8th International Conference on Natural Computation, 2012Co-Authors: Yunong Zhang, Dongsheng Guo, Long Jin, Lin XiaoAbstract:Since March 2001, a special class of recurrent neural network termed Zhang neural network (ZNN) has been proposed by Zhang et al for time-varying Matrix Inversion. For the purpose of possible hardware implementation, the resultant ZNN model is discretized by employing Euler forward-difference rule. In this paper, three discrete-time ZNN models using nonlinear activation functions (e.g., power-sigmoid activation functions) are presented and investigated for time-varying Matrix Inversion. In addition, a criterion is proposed to measure the rapidity and accuracy of the presented discrete-time ZNN models for time-varying Matrix Inversion. Numerical results further demonstrate the efficacy of the presented discrete-time ZNN models for time-varying Matrix Inversion.
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performance analysis of gradient neural network exploited for online time varying Matrix Inversion
IEEE Transactions on Automatic Control, 2009Co-Authors: Yunong Zhang, Ke Chen, Hongzhou TanAbstract:This technical note presents theoretical analysis and simulation results on the performance of a classic gradient neural network (GNN), which was designed originally for constant Matrix Inversion but is now exploited for time-varying Matrix Inversion. Compared to the constant Matrix-Inversion case, the gradient neural network inverting a time-varying Matrix could only approximately approach its time-varying theoretical inverse, instead of converging exactly. In other words, the steady-state error between the GNN solution and the theoretical/exact inverse does not vanish to zero. In this technical note, the upper bound of such an error is estimated firstly. The global exponential convergence rate is then analyzed for such a Hopfield-type neural network when approaching the bound error. Computer-simulation results finally substantiate the performance analysis of this gradient neural network exploited to invert online time-varying matrices.
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from zhang neural network to newton iteration for Matrix Inversion
IEEE Transactions on Circuits and Systems, 2009Co-Authors: Yunong Zhang, Binghuang CaiAbstract:Different from gradient-based neural networks, a special kind of recurrent neural network (RNN) has recently been proposed by Zhang for online Matrix Inversion. Such an RNN is designed based on a Matrix-valued error function instead of a scalar-valued error function. In addition, it was depicted in an implicit dynamics instead of an explicit dynamics. In this paper, we develop and investigate a discrete-time model of Zhang neural network (termed as such and abbreviated as ZNN for presentation convenience), which is depicted by a system of difference equations. Comparing with Newton iteration for Matrix Inversion, we find that the discrete-time ZNN model incorporates Newton iteration as its special case. Noticing this relation, we perform numerical comparisons on different situations of using ZNN and Newton iteration for Matrix Inversion. Different kinds of activation functions and different step-size values are examined for superior convergence and better stability of ZNN. Numerical examples demonstrate the efficacy of both ZNN and Newton iteration for online Matrix Inversion.
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The link between newton iteration for Matrix Inversion and Zhang neural network (ZNN)
2008 IEEE International Conference on Industrial Technology, 2008Co-Authors: Yunong ZhangAbstract:Different from gradient-based neural networks, a special kind of recurrent neural network has recently been proposed by Zhang et al for online Matrix Inversion. Such a neural network is designed based on a Matrix-valued error function instead of a scalar-valued norm-based error function. In this paper, we develop and investigate a discrete-time model of Zhang neural network (termed as such and abbreviated to ZNN for presentation convenience), which is depicted by a system of difference equations. Compared with Newton iteration for Matrix Inversion, we find that the discrete-time ZNN model incorporates Newton iteration as one of its special cases. Noticing this relation, we perform numerical comparisons on different situations of using Zhang neural network and Newton iteration for the Matrix Inversion. Different kinds of activation functions and different step-size values are examined as well for the superior convergence and better stability of ZNN model. Numerical examples demonstrate the effectiveness of both ZNN model and Newton iteration for constant Matrix Inversion.
Thomas Laurain - One of the best experts on this subject based on the ideXlab platform.
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avoiding Matrix Inversion in takagi sugeno based advanced controllers and observers
IEEE Transactions on Fuzzy Systems, 2018Co-Authors: Thomas Laurain, Jimmy Lauber, Reinaldo M. PalharesAbstract:Many of the recent advances on control and estimation of systems described by Takagi–Sugeno (TS) fuzzy models are based on Matrix Inversion, which could be a trouble in the case of real-time implementation. This paper is devoted to the development of alternative solutions to this Matrix Inversion problem in the discrete-time case. Two different methods are proposed: The first one relies on replacing the Matrix Inversion by multiple sums and the second methodology is based on an estimation of the Matrix Inversion by an observer structure. For the first methodology, a new class of controllers and observers are introduced which are called, respectively, the counterpart of an advanced TS-based (CATS) controller and the replica of an advanced TS-based (RATS) observer. Instead of relaxations for the linear Matrix inequalities conditions, an original use of the membership functions is presented. In the second methodology, it is proposed the estimation-based control law for approximating TS-based (ECLATS) controller that uses a fuzzy state observer. The Lyapunov theory is used to ensure stability conditions for either the closed-loop system as well as the estimation error. Numerical examples and comparisons highlight the efficiency of the procedures that can be used to replace any inverted Matrix in any advanced fuzzy controller or observer. Finally, advantages and drawbacks of the proposed method are discussed.
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Avoiding Matrix Inversion in Takagi–Sugeno-Based Advanced Controllers and Observers
IEEE Transactions on Fuzzy Systems, 2018Co-Authors: Thomas Laurain, Jimmy Lauber, Reinaldo M. PalharesAbstract:Many of the recent advances on control and estimation of systems described by Takagi–Sugeno (TS) fuzzy models are based on Matrix Inversion, which could be a trouble in the case of real-time implementation. This paper is devoted to the development of alternative solutions to this Matrix Inversion problem in the discrete-time case. Two different methods are proposed: The first one relies on replacing the Matrix Inversion by multiple sums and the second methodology is based on an estimation of the Matrix Inversion by an observer structure. For the first methodology, a new class of controllers and observers are introduced which are called, respectively, the counterpart of an advanced TS-based (CATS) controller and the replica of an advanced TS-based (RATS) observer. Instead of relaxations for the linear Matrix inequalities conditions, an original use of the membership functions is presented. In the second methodology, it is proposed the estimation-based control law for approximating TS-based (ECLATS) controller that uses a fuzzy state observer. The Lyapunov theory is used to ensure stability conditions for either the closed-loop system as well as the estimation error. Numerical examples and comparisons highlight the efficiency of the procedures that can be used to replace any inverted Matrix in any advanced fuzzy controller or observer. Finally, advantages and drawbacks of the proposed method are discussed.
John Mccanny - One of the best experts on this subject based on the ideXlab platform.
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QR Decomposition-Based Matrix Inversion for High Performance Embedded MIMO Receivers
IEEE Transactions on Signal Processing, 2011Co-Authors: Lei Ma, K. Dickson, John Mcallister, John MccannyAbstract:Real-time Matrix Inversion is a key enabling technology in multiple-input multiple-output (MIMO) communications systems, such as 802.11n. To date, however, no Matrix Inversion implementation has been devised which supports real-time operation for these standards. In this paper, we overcome this barrier by presenting a novel Matrix Inversion algorithm which is ideally suited to high performance floating-point implementation. We show how the resulting architecture offers fundamentally higher performance than currently published Matrix Inversion approaches and we use it to create the first reported architecture capable of supporting real-time 802.11n operation. Specifically, we present a Matrix Inversion approach based on modified squared Givens rotations (MSGR). This is a new QR decomposition algorithm which overcomes critical limitations in other QR algorithms that prohibits their application to MIMO systems. In addition, we present a novel modification that further reduces the complexity of MSGR by almost 20%. This enables real-time implementation with negligible reduction in the accuracy of the Inversion operation, or the BER of a MIMO receiver based on this.
Jimmy Lauber - One of the best experts on this subject based on the ideXlab platform.
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avoiding Matrix Inversion in takagi sugeno based advanced controllers and observers
IEEE Transactions on Fuzzy Systems, 2018Co-Authors: Thomas Laurain, Jimmy Lauber, Reinaldo M. PalharesAbstract:Many of the recent advances on control and estimation of systems described by Takagi–Sugeno (TS) fuzzy models are based on Matrix Inversion, which could be a trouble in the case of real-time implementation. This paper is devoted to the development of alternative solutions to this Matrix Inversion problem in the discrete-time case. Two different methods are proposed: The first one relies on replacing the Matrix Inversion by multiple sums and the second methodology is based on an estimation of the Matrix Inversion by an observer structure. For the first methodology, a new class of controllers and observers are introduced which are called, respectively, the counterpart of an advanced TS-based (CATS) controller and the replica of an advanced TS-based (RATS) observer. Instead of relaxations for the linear Matrix inequalities conditions, an original use of the membership functions is presented. In the second methodology, it is proposed the estimation-based control law for approximating TS-based (ECLATS) controller that uses a fuzzy state observer. The Lyapunov theory is used to ensure stability conditions for either the closed-loop system as well as the estimation error. Numerical examples and comparisons highlight the efficiency of the procedures that can be used to replace any inverted Matrix in any advanced fuzzy controller or observer. Finally, advantages and drawbacks of the proposed method are discussed.
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Avoiding Matrix Inversion in Takagi–Sugeno-Based Advanced Controllers and Observers
IEEE Transactions on Fuzzy Systems, 2018Co-Authors: Thomas Laurain, Jimmy Lauber, Reinaldo M. PalharesAbstract:Many of the recent advances on control and estimation of systems described by Takagi–Sugeno (TS) fuzzy models are based on Matrix Inversion, which could be a trouble in the case of real-time implementation. This paper is devoted to the development of alternative solutions to this Matrix Inversion problem in the discrete-time case. Two different methods are proposed: The first one relies on replacing the Matrix Inversion by multiple sums and the second methodology is based on an estimation of the Matrix Inversion by an observer structure. For the first methodology, a new class of controllers and observers are introduced which are called, respectively, the counterpart of an advanced TS-based (CATS) controller and the replica of an advanced TS-based (RATS) observer. Instead of relaxations for the linear Matrix inequalities conditions, an original use of the membership functions is presented. In the second methodology, it is proposed the estimation-based control law for approximating TS-based (ECLATS) controller that uses a fuzzy state observer. The Lyapunov theory is used to ensure stability conditions for either the closed-loop system as well as the estimation error. Numerical examples and comparisons highlight the efficiency of the procedures that can be used to replace any inverted Matrix in any advanced fuzzy controller or observer. Finally, advantages and drawbacks of the proposed method are discussed.
