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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]

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]