Yonghua Yin

Taylor-type 1-step-ahead numerical differentiation rule for first-order derivative approximation and ZNN discretization

In order to achieve higher computational precision in approximating the first-order derivative and discretize more effectively the continuous-time Zhang neural network (ZNN), a Taylor-type numerical differentiation rule is proposed and investigated in this paper. This rule not only greatly remedies some intrinsic weaknesses of the backward and central numerical differentiation rules, but also overcomes the limitation of the Lagrange-type numerical differentiation rules in ZNN discretization. In addition, a formula is proposed to obtain the optimal step-length of the Taylor-type numerical differentiation rule. Moreover, based on the proposed numerical differentiation rule, the stability, convergence and residual error of the Taylor-type discrete-time ZNN (DTZNN) are analyzed. Numerical experimental results further substantiate the efficacy and advantages of the proposed Taylor-type numerical differentiation rule for first-order derivative approximation and ZNN discretization. A formula is proposed to approximate the first-order derivative.An optimal step length rule for the proposed formula is investigated.A Taylor-type ZNN model is derived for time-varying matrix inversion.

Singularity-conquering ZG controllers of z2g1 type for tracking control of the IPC system

With wider investigations and applications of autonomous robotics and intelligent vehicles, the inverted pendulum on a cart (IPC) system has become more attractive for numerous researchers due to its concise and representative structure. In this article, the tracking-control problem of the IPC system is considered and investigated. Based on Zhang dynamics (ZD) and gradient dynamics (GD), a novel kind of ZG controllers are developed and investigated for achieving the tracking-control purpose, which contains controllers of z2g0 and z2g1 types according to the number of times of using the ZD and GD methods. Besides, theoretical analyses are presented to guarantee the global and exponential convergence performance of both z2g0 and z2g1 controllers. Computer simulations are further performed to substantiate the feasibility and effectiveness of ZG controllers. More importantly, comparative simulation results demonstrate that controllers of z2g1 type can conquer the singularity problem (i.e. the division-by-zero problem).

Cross-validation based weights and structure determination of Chebyshev-polynomial neural networks for pattern classification

Abstract This paper first proposes a new type of single-output Chebyshev-polynomial feed-forward neural network (SOCPNN) for pattern classification. A new type of multi-output Chebyshev-polynomial feed-forward neural network (MOCPNN) is then proposed based on such an SOCPNN. Compared with multi-layer perceptron, the proposed SOCPNN and MOCPNN have lower computational complexity and superior performance, substantiated by both theoretical analyses and numerical verifications. In addition, two weight-and-structure-determination (WASD) algorithms, one for the SOCPNN and another for the MOCPNN, are proposed for pattern classification. These WASD algorithms can determine the weights and structures of the proposed neural networks efficiently and automatically. Comparative experimental results based on different real-world classification datasets with and without added noise prove that the proposed SOCPNN and MOCPNN have high accuracy, and that the MOCPNN has strong robustness in pattern classification when equipped with WASD algorithms.

Zhang Dynamics and Gradient Dynamics with Tracking-Control Application

Via solving time-varying linear equations, this paper shows the Zhang dynamics (ZD) method. Besides, the gradient dynamics (GD) method, which was originally designed for constant problems solving, is generalized for time-varying linear equations solving. Then, the ZD and GD methods are exploited together to solve the tracking-control problem of a nonlinear system as a new application. Simulation results on the nonlinear system further demonstrate the feasibility of the ZD and GD methods for tracking control of nonlinear systems.

ZG Control for Ship Course Tracking with Singularity Considered and Solved

Zhang dynamics (ZD) and gradient dynamics (GD) are both effective methods for online problems solving. By combining ZD and GD methods, an innovative ZG (Zhang-gradient) control method is thus proposed and investigated in this paper, which is applied to ship course tracking for the first time. Firstly, for a constant parameter setting, we design a ZD-based controller to solve the tracking-control problem of a ship course system with no singularity appearing. Then, for a time-varying parameter setting, the ZG method is applied generally to solve the singularity-containing tracking-control problem of such a system. Simulation results further demonstrate and verify the feasibility and superiority of the unified ZG method in fulfilling the tracking-control task while conquering the singularity problem for the ship course system.

ZG controllers for output tracking of nonlinear mass-spring-damper mechanical system with division-by-zero problem solved

Recently, two classes of dynamical methods, i.e., Zhang dynamics (ZD) and gradient dynamics (GD), have been widely investigated individually and comparatively for online time-varying problems solving. In this paper, by combining ZD and GD, an innovative method called Zhang-gradient (ZG) method is proposed for tracking control of a nonlinear mass-spring-damper (MSD) mechanical system. Simulation results substantiate the feasibility and effectiveness of the combined ZG method for handling both the explicit and implicit tracking-control problems. Especially, the z1g1 controller based on the ZG method for the implicit tracking control is also capable of conquering the division-by-zero problem.

ZD and ZG controllers for explicit and implicit tracking of pendulum with singularity finally conquered

Zhang dynamics (ZD) and gradient dynamics (GD) are both powerful methods. Based on a pendulum system, this paper investigates both of the explicit and implicit tracking control using the ZD method. For solving the singularity-containing implicit tracking problems, this paper overcomes the singularities by using the ZD method in combination with the GD method (i.e., the ZG method). Analyses and simulations of an explicit tracking example and two implicit tracking examples show the superiority of the ZD and ZG methods.

Zhang-Gradient controllers of z0g0, z1g0 and z1g1 types for output tracking of time-varying linear systems with control-singularity conquered finally

Recently, Zhang dynamics (ZD) and gradient dynamics (GD) have been used frequently to solve various kinds of online problems. In this paper, the output tracking of time-varying linear (TVL) systems is considered. Then, for such a problem, three different types of tracking controllers (i.e., Z0G0, Z1G0 and Z1G1 controllers) are designed by exploiting the ZD and GD methods. Simulation results on different TVL systems show that such three types of controllers can be feasible and effective for the output-tracking problem solving. Especially, the Z1G1 controller is capable of conquering the control-singularity of systems.

Pruning-included weights and structure determination of 2-input neuronet using Chebyshev polynomials of Class 1

A new type of feed-forward 2-input neuronet using Chebyshev polynomials of Class 1 (2INCP1) is constructed and investigated in this paper. In addition, with the weights-direct-determination method exploited to obtain the optimal weights from hidden layer to output layer directly (i.e., just in one step), a new structure-automatic-determination method called weights-and-structure-determination (WASD) algorithm is proposed to determine the optimal number of hidden-layer neurons of the 2INCP1. Such a WASD algorithm includes a procedure of pruning the proposed neuronet (after the net grows up). Numerical results further substantiate the efficacy of the 2INCP1 equipped with the so-called WASD algorithm.

Weights and structure determination of multiple-input feed-forward neural network activated by Chebyshev polynomials of Class 2 via cross-validation

Differing from conventional improvements on backpropagation (BP) neural network, a novel neural network is proposed and investigated in this paper to overcome the BP neural-network weaknesses, which is called the multiple-input feed-forward neural network activated by Chebyshev polynomials of Class 2 (MINN-CP2). In addition, to obtain the optimal number of hidden-layer neurons and the optimal linking weights of the MINN-CP2, the paper develops an algorithm of weights and structure determination (WASD) via cross-validation. Numerical studies show the effectiveness and superior abilities (in terms of approximation and generalization) of the MINN-CP2 equipped with the algorithm of WASD via cross-validation. Moreover, an application to gray image denoising demonstrates the effective implementation and application prospect of the proposed MINN-CP2 equipped with the algorithm of WASD via cross-validation.