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Encouraged by superior convergence performance achieved by a recently-proposed hybrid of recursive neural dynamics for online matrix inversion, we investigate its robustness properties in this paper when there exists large model implementation errors. Theoretical analysis shows that the perturbed dynamic system is still global stable with the tight steady-state bound of solution error estimated. Moreover, this paper analyses global exponential convergence rate and finite convergence time of such a hybrid dynamical model to a relatively loose solution error bound. Computer simulation results substantiate our analysis on the perturbed hybrid neural dynamics for online matrix inversion when having large implementation errors. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, two types of recurrent neural network (RNN) are comparatively developed and exploited for the online solution of the well-known Lyapunov matrix equation with the stationary and nonstationary coefficients. Based on a new design method, the resultant Zhang neural networks (ZNN) are generalized and presented to solve the stationary and nonstationary problems with accuracy and efficiency. For comparison, the conventional gradient-based neural networks (GNN) are also used for the same problems. Computer simulation results show that, when used to solve the whether stationary or nonstationary problems, the convergence performance of ZNN solvers are superior than that of GNN solvers. [Copyright &y& Elsevier]

Abstract: A type of recurrent neural networks called Zhang neural network (ZNN) is presented and investigated to provide an online solution to the time-varying linear matrix equation, by using a novel design method. In contrast to the gradient-based neural network (GNN), the novel design of ZNN is based on a matrix-valued indefinite error function, instead of a scalar-valued norm-based energy function. Therefore, a ZNN model depicted in implicit dynamics can globally and exponentially converge to the time-varying theoretical solution of the given linear matrix equation. Computer simulation results further demonstrate the superior performance of the ZNN model in solving the time-varying linear matrix equation compared with the conventional GNN model. [Copyright &y& Elsevier]

Different from gradient-based neural dynamics, a special kind of recurrent neural dynamics has recently been proposed by Zhang et al. for solving online time-varying problems. Such a recurrent neural dynamics is designed based on an indefinite error-monitoring function instead of a usually norm- or square-based energy function. In addition, Zhang neural dynamics (ZND) are depicted generally in implicit dynamics, whereas gradient-based neural dynamics (GND) are associated with explicit dynamics. In this paper, we generalize the ZND design method to solving online nonlinear time-varying equations in the form of f ( x, t) = 0. For comparative purposes, the GND model is also employed for such time-varying equations' solving. Computer-simulation results via power-sigmoid activation functions substantiate the theoretical analysis and efficacy of the ZND model for solving online nonlinear time-varying equations. [ABSTRACT FROM AUTHOR]

Abstract: Differing from gradient-based neural networks (GNN), a special kind of recurrent neural network has recently been proposed by Zhang et al. for real-time inversion of time-varying matrices. The design of such a recurrent neural network is based on a matrix-valued error function instead of a scalar-valued norm-based energy-function. In addition, it is depicted in an implicit dynamics instead of an explicit dynamics. This paper investigates the simulation and verification of such a Zhang neural network (ZNN). Four important simulation techniques are employed to simulate this system: (1) Kronecker product of matrices is introduced to transform a matrix-differential-equation (MDE) to a vector differential equation (VDE) [i.e., finally, there is a standard ordinary-differential-equation (ODE) formulation]. (2) MATLAB routine “ode45” with a mass-matrix property is introduced to simulate the transformed initial-value implicit ODE system. (3) Matrix derivatives are obtained using the routine “diff” and symbolic math toolbox. (4) Various implementation errors and different types of activation functions are investigated, further demonstrating the advantages of the ZNN model. Three illustrative computer-simulation examples substantiate the theoretical results and efficacy of the ZNN model for online time-varying matrix inversion. [Copyright &y& Elsevier]

Due to the time delay and some unavoidable noise factors, obtaining a real-time solution of dynamic time-varying linear matrix equation (LME) problems is of great importance in the scientific and engineering fields. In this paper, based on the philosophy of zeroing neural networks (ZNN), we propose an integration-enhanced combined accelerating zeroing neural network (IEAZNN) model to solve LME problem accurately and efficiently. Different from most of the existing ZNNs research, there are two error functions combined in the IEAZNN model, among which the gradient of the energy function is the first design for the purpose of decreasing the norm-based error to zero and the second one is adding an integral term to resist additive noise. On the strength of novel combination in two error functions, the IEAZNN model is capable of converging in finite time and resisting noise at the same time. Moreover, theoretical proof and numerical verification results show that the IEAZNN model can achieve high accuracy and fast convergence speed in solving time-varying LME problems compared with the conventional ZNN (CZNN) and integration-enhanced ZNN (IEZNN) models, even in various kinds of noise environments. [ABSTRACT FROM AUTHOR]

The time-variant Sylvester equation (TVSE) plays a highly crucial role in many areas of scientific research and engineering applications. Recently, zeroing neural network (ZNN) has been prevailed as an effective solution for time-variant problem. However, the majority of the existing ZNN solution schemes for TVSE are either only considered in noiseless environments or are unable to converge in a finite amount of time, and while there is a pressing need for effective and noise-resisting ZNNs to fulfill real-time applications' requirements in the actual world. For this reason, inspired by the advantages offered by super-twisting algorithm (STA), being a well-accepted second order sliding mode method, this paper introduces STA into ZNN and establishes a novel STZNN model for TVSE solving. Actually, the intrinsic properties of STA, such as finite-time convergence and anti-noise robustness, are perfectly in line with what an efficient and noise-resisting ZNN model desired to be. Hence, the STZNN model can realize a much quick convergence time and a much great resistance against noise. Moreover, rigorous theoretical analyses on the case of zero noise, constant noise and dynamic bounded noise are conducted, and the illustrative verification not only verifies the STZNN's convergence property, validates its superior ability in convergence time and noise resisting compared to the gradient-based neural network (GNN), the conventional ZNN (CZNN) model and the integration-enhanced ZNN (IEZNN) model, but also shows the STZNN model's capability in addressing moving localization problems based on angle of arrival (AoA) and time difference of arrival (TDOA). [ABSTRACT FROM AUTHOR]

Breast cancer has become one of the leading causes of death in female population due to its high morbidity and mortality. However, the treatment options for benign or malignant tumors are different, which makes the diagnosis of breast cancer important. In this paper, the subset method is proposed to improve the single-output Chebyshev-polynomial neural network (SOCPNN), and the modified SOCPNN has a 100.00% testing accuracy in pattern classification on the Wisconsin breast cancer dataset. Specifically, the subset method generates the optimal number of cross-validation folds and constructs the initial structure of the modified SOCPNN automatically and rapidly, with a group of basis functions based on Chebyshev-polynomials exploited to activate the neural network. In addition, the weights of the hidden-layer neurons are directly determined by the weights-direct-determination (WDD) method. Besides, the optimal structure of the neural network is determined by a growing method. Moreover, to improve the generalization performance, the multi-fold cross-validation algorithm is exploited in the modified SOCPNN. Finally, comparative experiments on the Wisconsin breast cancer dataset are conducted and the results show that the modified SOCPNN has higher accuracy in classification of breast cancer on this dataset compared to the traditional machine learning algorithms. [ABSTRACT FROM AUTHOR]

This paper presents a distributed scheme for the control of multiple redundant manipulators to simultaneously achieve four objectives, i.e., the task to reach global cooperation, joint-physical limits compliance, limited communications among manipulators and optimality in terms of a specified performance index. In addition, corresponding theoretical analyses are provided, which guarantee that, with the communication network being connected, all manipulators can jointly obtain the same desired motion information. Then, the proposed scheme is converted into a quadratic program (QP) formed formulation and solved by a dynamic neural network with rigorously provable convergence. Furthermore, simulations and comparisons are provided to illustrate the effectiveness of the proposed distributed scheme as well as the presented dynamic neural network. [ABSTRACT FROM AUTHOR]