An Arctan-Type Varying-Parameter ZNN for Solving Time-Varying Complex Sylvester Equations in Finite Time

Xiao, Lin; Tao, Juan; Li, Weibing

doi:10.1109/tii.2021.3111816

Cited by 26 publications

(8 citation statements)

References 22 publications

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“…Besides activation functions, varying parameters are also utilised to improve the convergence rate. Xiao et al designed an Arctan-Type varying-parameter ZNN model, where the parameter includes the exponential of time and the power of time [28]. In addition, Gerontitis et al proposed a novel ZNN model exploiting a time-varying parameter to accelerate the convergence rate.…”

Section: Introductionmentioning

confidence: 99%

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An activated variable parameter gradient‐based neural network for time‐variant constrained quadratic programming and its applications

Wang

Hao

et al. 2023

CAAI Trans on Intel Tech

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This study proposes a novel gradient‐based neural network model with an activated variable parameter, named as the activated variable parameter gradient‐based neural network (AVPGNN) model, to solve time‐varying constrained quadratic programming (TVCQP) problems. Compared with the existing models, the AVPGNN model has the following advantages: (1) avoids the matrix inverse, which can significantly reduce the computing complexity; (2) introduces the time‐derivative of the time‐varying parameters in the TVCQP problem by adding an activated variable parameter, enabling the AVPGNN model to achieve a predictive calculation that achieves zero residual error in theory; (3) adopts the activation function to accelerate the convergence rate. To solve the TVCQP problem with the AVPGNN model, the TVCQP problem is transformed into a non‐linear equation with a non‐linear compensation problem function based on the Karush Kuhn Tucker conditions. Then, a variable parameter with an activation function is employed to design the AVPGNN model. The accuracy and convergence rate of the AVPGNN model are rigorously analysed in theory. Furthermore, numerical experiments are also executed to demonstrate the effectiveness and superiority of the proposed model. Moreover, to explore the feasibility of the AVPGNN model, applications to the motion planning of a robotic manipulator and the portfolio selection of marketed securities are illustrated.

show abstract

Section: Introductionmentioning

confidence: 99%

“…Xiao et al. designed an Arctan‐Type varying‐parameter ZNN model, where the parameter includes the exponential of time and the power of time [28]. In addition, Gerontitis et al.…”

Section: Introductionmentioning

confidence: 99%

An activated variable parameter gradient‐based neural network for time‐variant constrained quadratic programming and its applications

Wang

Hao

et al. 2023

CAAI Trans on Intel Tech

View full text Add to dashboard Cite

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“…At present, RNNs were universally applied in practical engineering and application problems [9][10][11][12][13][14][15][16][17][18][19][20][21]. Additionally, RNNs have the characteristics of parallel distributed processing; hence, they have been extensively employed for solving the time-dependent Lyapunov equation (TDLE) [22][23][24][25][26]. In [22], Zhang et al compared two types of RNN (i.e., gradient neural network, GNN and zeroing neural network, ZNN) for solving TDLE, and they concluded that ZNN has a better solving performance than GNN.…”

Section: Introductionmentioning

confidence: 99%

“…Ding et al presented an improved complex ZNN model for computing complex timedependent Sylvester equations (CTDSE) [28]. In [26], Xiao et al presented an arctan-type VP-ZNN model for solving time-dependent Sylvester equations (TDSE), which can realize convergence in finite time and adjust the design parameters of its final convergence to a constant.…”

Section: Introductionmentioning

confidence: 99%

Complex Noise-Resistant Zeroing Neural Network for Computing Complex Time-Dependent Lyapunov Equation

et al. 2022

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Complex time-dependent Lyapunov equation (CTDLE), as an important means of stability analysis of control systems, has been extensively employed in mathematics and engineering application fields. Recursive neural networks (RNNs) have been reported as an effective method for solving CTDLE. In the previous work, zeroing neural networks (ZNNs) have been established to find the accurate solution of time-dependent Lyapunov equation (TDLE) in the noise-free conditions. However, noises are inevitable in the actual implementation process. In order to suppress the interference of various noises in practical applications, in this paper, a complex noise-resistant ZNN (CNRZNN) model is proposed and employed for the CTDLE solution. Additionally, the convergence and robustness of the CNRZNN model are analyzed and proved theoretically. For verification and comparison, three experiments and the existing noise-tolerant ZNN (NTZNN) model are introduced to investigate the effectiveness, convergence and robustness of the CNRZNN model. Compared with the NTZNN model, the CNRZNN model has more generality and stronger robustness. Specifically, the NTZNN model is a special form of the CNRZNN model, and the residual error of CNRZNN can converge rapidly and stably to order 10−5 when solving CTDLE under complex linear noises, which is much lower than order 10−1 of the NTZNN model. Analogously, under complex quadratic noises, the residual error of the CNRZNN model can converge to 2∥A∥F/ζ3 quickly and stably, while the residual error of the NTZNN model is divergent.

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“…In addition to the characteristic of parallel processing, RNN models can be implemented expediently by circuit components in the wake of the rapid development of field-programmable gate array and integrated circuit technology [13][14][15]. As the result of these two outstanding features, a growing number of RNN models that aim at solving the Sylvester equation and related problems (e.g., matrix pseudoinverse) have been successively put forward and discussed in recent years [16][17][18][19][20][21][22][23][24][25]. ZNN (zeroing neural network) and GNN (gradient neural network) are two popular RNN categories that are extensively investigated in the literature.…”

Section: Introductionmentioning

confidence: 99%

Fixed-Time Convergent Gradient Neural Network for Solving Online Sylvester Equation

Tan

2022

Mathematics

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This paper aims at finding a fixed-time solution to the Sylvester equation by using a gradient neural network (GNN). To reach this goal, a modified sign-bi-power (msbp) function is presented and applied on a linear GNN as an activation function. Accordingly, a fixed-time convergent GNN (FTC-GNN) model is developed for solving the Sylvester equation. The upper bound of the convergence time of such an FTC-GNN model can be predetermined if parameters are given regardless of the initial conditions. This point is corroborated by a detailed theoretical analysis. In addition, the convergence time is also estimated utilizing the Lyapunov stability theory. Two examples are then simulated to demonstrate the validation of the theoretical analysis, as well as the superior convergence performance of the presented FTC-GNN model as compared to the existing GNN models.

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An Arctan-Type Varying-Parameter ZNN for Solving Time-Varying Complex Sylvester Equations in Finite Time

Cited by 26 publications

References 22 publications

An activated variable parameter gradient‐based neural network for time‐variant constrained quadratic programming and its applications

An activated variable parameter gradient‐based neural network for time‐variant constrained quadratic programming and its applications

Complex Noise-Resistant Zeroing Neural Network for Computing Complex Time-Dependent Lyapunov Equation

Fixed-Time Convergent Gradient Neural Network for Solving Online Sylvester Equation

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