Noise-Resistant Discrete-Time Neural Dynamics for Computing Time-Dependent Lyapunov Equation

Xiang, Qiuhong; Li, Weibing; Liao, Bolin; Huang, Zhiguan

doi:10.1109/access.2018.2863736

Cited by 19 publications

(7 citation statements)

References 34 publications

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“…This Paper Time-Dependent Lyapunov Complex-Valued Double Integral Strong Strong [30] time-dependent Lyapunov real-valued single integral weak weak [32] time-dependent Lyapunov real-valued single integral weak weak [36] time-dependent Lyapunov real-valued single integral weak weak [31] time-dependent Lyapunov real-valued absence weak weak [22] time-dependent Lyapunov real-valued absence none none [28] time-dependent Sylvester complex-valued absence none none [25] time-dependent Sylvester real-valued absence none none…”

Section: Quadratic Noise Rejectionmentioning

confidence: 99%

“…Although one can preprocess these noises, such as employing a prefilter, this will undoubtedly reduce the efficiency of the real-time solution. Therefore, some ZNN models with noise tolerance were further studied and widely used in the solution of TDLE [29][30][31][32][33][34][35][36]. Jin et al studied a classical integral-enhanced ZNN (IEZNN) model in [29].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Quadratic Noise Rejectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2022

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“…where (t) ∈ C n×m denotes the unpredictable noise. (t) is represented in matrix-form, the noises fall into three categories: the constant noise, the linear noise, the random noise [29].…”

Section: Design Of Naznn Modelmentioning

confidence: 99%

“…In some cases, they cause failure in online computing process. In view of this, Xiang et al [29] first proposed a noise-resistant neural dynamics for computing time-dependent lyapunov equation in real-domain. However, few literatures investigate complex-valued time-dependent matrix pseudoinverse with different noise.…”

Section: Introductionmentioning

confidence: 99%

A Noise-Acceptable ZNN for Computing Complex-Valued Time-Dependent Matrix Pseudoinverse

2019

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The issue of complex-valued time-dependent pseudoinverse often exists in science and engineering fields. In the existing studies, many models were presented for solving complex-valued timedependent pseudoinverse in the noiseless environments. However, the appearance of noise is unavoidable in practice. In this paper, a novel noise-acceptable zeroing neural network (NAZNN) model is first proposed for computing complex-valued time-dependent matrix pseudoinverse with different noise situations. For comparison, the traditional zeroing neural network and the gradient neural network are adopted to complete the same task. Theoretical analyses prove that the proposed NAZNN model obtains the global exponential convergence performance. Moreover, the proposed NAZNN is also proven to obtain strong resistance to various sorts of noise. Finally, the results of numerical experiments further substantiate the theoretical analysis and indicate the effectiveness and superiority of the proposed NAZNN model for computing complex-valued time-dependent matrix pseudoinverse in various kinds of noise. INDEX TERMS Zeroing neural network, time-dependent, complex-valued, noise-acceptable, matrix pseudoinverse.

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“…Up to now, a large number of approaches and techniques for the synchronization of chaotic systems have been creatively proposed and effectively employed, such as the sliding-mode-control approach [2], the neurodynamic approach [24]- [29], the active-control approach [14], [30], and the adaptive-backstepping control approach [31]. For instances, Ahmad et al [14] studied and investigated a new global chaotic synchronization problem for identical chaotic systems as well as nonidentical chaotic systems by novelly utilizing a linear-active control (LAC) approach.…”

Section: Introductionmentioning

confidence: 99%

A Novel Disturbance Rejection Zeroing Neurodynamic Approach for Robust Synchronization of Chaotic Systems

Chen¹,

Li²,

Wu³

2019

IEEE Access

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Robust synchronization of chaotic systems becomes a hot topic in scientific and engineering fields because of the ubiquitous existence of time-variant external disturbances in complex application scenarios. In contrast with existing studies that the resultant synchronization error has a supremum or even diverges under the influence of time-variant external disturbances, this paper proposes a disturbance rejection zeroing neurodynamic (DRZN) approach and its related controller for the robust synchronization of chaotic systems against time-variant external disturbances. The controller designed by the proposed DRZN approach distinctively features the rejection of external disturbances with the generated synchronization error being convergence toward zero. Theoretical analyses guarantee that the DRZN approach and its related controller inherently possess robustness. Moreover, numerical studies including three examples substantiate the effectiveness of the proposed DRZN approach and its related controller for the synchronization of chaotic systems against the time-variant external disturbances. Comparisons with existing approaches, e.g., the conventional zeroing neurodynamic (CZN) approach and the linear-active control (LAC) approach, show the superiority of the proposed DRZN approach. Extensive tests further verify that the proposed DRZN approach possesses the outstanding anti-disturbance performance, and thus is suitable for the practical applications with time-variant external disturbances.INDEX TERMS Zeroing neurodynamic approach, robustness, zeroing neural networks, chaotic systems, external disturbances.

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Noise-Resistant Discrete-Time Neural Dynamics for Computing Time-Dependent Lyapunov Equation

Cited by 19 publications

References 34 publications

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

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

A Noise-Acceptable ZNN for Computing Complex-Valued Time-Dependent Matrix Pseudoinverse

A Novel Disturbance Rejection Zeroing Neurodynamic Approach for Robust Synchronization of Chaotic Systems

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