Saturation-Allowed Neural Dynamics Applied to Perturbed Time-Dependent System of Linear Equations and Robots

Jin, Long; Liufu, Ying; Lu, Huosheng; Zhang, Zhijun

doi:10.1109/tie.2020.3029478

Cited by 50 publications

(10 citation statements)

References 30 publications

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“…In general, for the solution of nonlinear equations, since there is no exact solution formula, the commonly used RNN model [27][28][29] is to iterate the error function, thus approximating…”

Section: Continuous-time Prnn Modelmentioning

confidence: 99%

“…Proof The traditional Lyapunov method [29] is applied to demonstrate the global convergence of PRNN model (5). First, a Lyapunov function candidate is defined as follows:…”

Section: Global Convergence Of Prnn Model With Noise Freementioning

confidence: 99%

“…Recently, recurrent neural network (RNN) has attracted considerable attention as candidates for novel computational systems, which can be used for solving time-varying nonlinear equations [26]. Besides, RNN is often designed as an ordinary differential equation for zeroing finding in the field of industrial system tracking control [27][28][29][30]. However, in actual industrial control, the convergence rate of the controller for errors is often limited by the influence of hardware devices, which causes the convergence performance of the traditional RNN with convex constraints to be seriously affected as the error decays.…”

Section: Introductionmentioning

confidence: 99%

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Lower limb movement intention recognition for rehabilitation robot aided with projected recurrent neural network

Liu

Peng

Shang

2021

Complex Intell. Syst.

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For the lower limb rehabilitation robot, how to better realize intention recognition is the key issue in the practical application. Recognition of the patient’s movement intention is a challenging research work, which needs to be studied from the shallow to the deep. Specifically, it is necessary to ensure that the movement intention of the normal person can be accurately recognized, and then improve the model to realize the recognition of the movement intention of the patients. Therefore, before studying the patient’s movement intention, it is essential to consider the normal person first, which is also for safety considerations. In recent years, a new Hill-based muscle model has been demonstrated to be capable of directly estimating the joint angle intention in an open-loop form. On this basis, by introducing a recurrent neural network (RNN), the whole prediction process can achieve more accuracy in a closed-loop form. However, for the traditional RNN algorithms, the activation function must be convex, which brings some limitations to the solution of practical problems. Especially, when the convergence speed of the traditional RNN model is limited in the practical applications, as the error continues to decrease, the convergence performance of the traditional RNN model will be greatly affected. To this end, a projected recurrent neural network (PRNN) model is proposed, which relaxes the condition of the convex function and can be used in the saturation constraint case. In addition, the corresponding theoretical proof is given, and the PRNN method with saturation constraint has been successfully applied in the experiment of intention recognition of lower limb movement compared with the traditional RNN model.

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Section: Continuous-time Prnn Modelmentioning

confidence: 99%

“…Proof The traditional Lyapunov method [29] is applied to demonstrate the global convergence of PRNN model (5). First, a Lyapunov function candidate is defined as follows:…”

Section: Global Convergence Of Prnn Model With Noise Freementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Lower limb movement intention recognition for rehabilitation robot aided with projected recurrent neural network

Liu

Peng

Shang

2021

Complex Intell. Syst.

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show abstract

“…ZNN models are proposed to overcome the disadvantages of previous static numerical algorithms and neural networks, which can real-time solve dynamic problems in a predictable manner aided by developing the time derivative information [11][12][13]. Noise perturbation serves as an essential surrogate to evaluate the robustness of the dynamic solution model before being deployed [14][15][16]. However, it has been reported that the original ZNNs are shown easily interfered with by perturbed measurement noises crafted during model implementation, thereby severely limiting the applications in complicated environments [17,18].…”

Section: Introductionmentioning

confidence: 99%

Robust neural dynamics with adaptive coefficient applied to solve the dynamic matrix square root

Jiang

Xiao

et al. 2022

Complex Intell. Syst.

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Zeroing neural networks (ZNN) have shown their state-of-the-art performance on dynamic problems. However, ZNNs are vulnerable to perturbations, which causes reliability concerns in these models owing to the potentially severe consequences. Although it has been reported that some models possess enhanced robustness but cost worse convergence speed. In order to address these problems, a robust neural dynamic with an adaptive coefficient (RNDAC) model is proposed, aided by the novel adaptive activation function and robust evolution formula to boost convergence speed and preserve robustness accuracy. In order to validate and analyze the performance of the RNDAC model, it is applied to solve the dynamic matrix square root (DMSR) problem. Related experiment results show that the RNDAC model reliably solves the DMSR question perturbed by various noises. Using the RNDAC model, we are able to reduce the residual error from 10$$^1$$ 1 to 10$$^{-4}$$ - 4 with noise perturbed and reached a satisfying and competitive convergence speed, which converges within 3 s.

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“…In order to eliminate the influence of measurement noise on the solution of zeroingtype models and improve the robustness of the system, Jin et al present the modified zeroing neural network (MZNN) model in [27], which introduces the integral information into the solution evolution formula for the first time. However, the parameters of the MZNN model still require tedious manual adjustments, which leads to a lot of additional computational resources and redundant adjustment processes [28]. The rest of this paper is arranged as the following five sections.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Zeroing-Type Neural Dynamics for Solving Quadratic Minimization and Applied to Target Tracking

Jiang¹,

Jin²,

Xiao³

2021

Preprint

Self Cite

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The time-dependent quadratic minimization (TDQM) problem appears in many applications and research projects. It has been reported that the zeroing neural network (ZNN) models can effectively solve the TDQM problem. However, the convergent and robust performance of the existing ZNN models are restricted for lack of a joint-action mechanism of adaptive coefficient and integration enhanced term. Consequently, the residual-based adaption coefficient zeroing neural network (RACZNN) model with integration term is proposed in this paper for solving the TDQM problem. The adaptive coefficient is proposed to improve the performance of convergence and the integration term is embedded to ensure the RACZNN model can maintain reliable robustness while perturbed by variant measurement noises. Compared with the state-of-the-art models, the proposed RACZNN model owns faster convergence and more reliable robustness. Then, theorems are provided to prove the convergence of the RACZNN model. Finally, corresponding quantitative numerical experiments are designed and performed in this paper to verify the performance of the proposed RACZNN model.

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Saturation-Allowed Neural Dynamics Applied to Perturbed Time-Dependent System of Linear Equations and Robots

Cited by 50 publications

References 30 publications

Lower limb movement intention recognition for rehabilitation robot aided with projected recurrent neural network

Lower limb movement intention recognition for rehabilitation robot aided with projected recurrent neural network

Robust neural dynamics with adaptive coefficient applied to solve the dynamic matrix square root

Adaptive Zeroing-Type Neural Dynamics for Solving Quadratic Minimization and Applied to Target Tracking

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