Zeroing neural networks: A survey

The so-called zeroing neural network (ZNN) is an effective recurrent neural network for solving dynamic problems including the dynamic nonlinear equations. There exist numerous unperturbed ZNN models that can converge to the theoretical solution of solvable nonlinear equations in infinity long or finite time. However, when these ZNN models are perturbed by external disturbances, the convergence performance would be dramatically deteriorated. To overcome this issue, this paper for the first time proposes a finite-time convergent ZNN with the noise-rejection capability to endure disturbances and solve dynamic nonlinear equations in finite time. In theory, the finite-time convergence and noise-rejection properties of the finite-time convergent and noise-rejection ZNN (FTNRZNN) are rigorously proved. For potential digital hardware realization, the discrete form of the FTNRZNN model is established based on a recently developed five-step finite difference rule to guarantee a high computational accuracy. The numerical results demonstrate that the discrete-time FTNRZNN can reject constant external noises. When perturbed by dynamic bounded or unbounded linear noises, the discrete-time FTNRZNN achieves the smallest steady-state errors in comparison with those generated by other discrete-time ZNN models that have no or limited ability to handle these noises. Discrete models of the FTNRZNN and the other ZNNs are comparatively applied to redundancy resolution of a robotic arm with superior positioning accuracy of the FTNRZNN verified.

A Finite-Time Convergent and Noise-Rejection Recurrent Neural Network and Its Discretization for Dynamic Nonlinear Equations Solving

The forecast of Singapore condominium prices is important for potential buyers to make informed decisions. This paper applies two algorithms to predict Singapore housing market and to compares the predictive performance of artificial neural network (ANN) model, i.e., the multilayer perceptron, with autoregressive integrated moving average (ARIMA) model. The more superior model is used to predict the future condominium price index (CPI). The lower mean square error (MSE) of the ANN models showed the superiority of ANN over other predictive tools.

Housing price prediction using neural networks

Representations and symbolic computation of generalized inverses over fields

A typical class of recurrent neural networks called zeroing neural network (ZNN) has been considered as a powerful alternative for time-varying problems solving. In this paper, a new ZNN model is proposed and studied to solve the bound-constrained time-varying nonlinear equation (BCTVNE). Specifically, by introducing a time-varying nonnegative vector, the BCTVNE is reformulated as a combined system of nonlinear equations. On the basis of two indefinite error functions and the exponential decay formula, the new ZNN model is thus developed, which can zero in on the combined system. Theoretical analysis and simulation results are provided to verify the effectiveness of the proposed ZNN model. The applicability is further indicated under the simulations on an omnidirectional mobile robot manipulator via the proposed ZNN model.

Zeroing neural network for bound-constrained time-varying nonlinear equation solving and its application to mobile robot manipulators

Zhang dynamics (ZD) and gradient dynamics (GD) are bothpowerful methods. Based on a pendulum system, this paperinvestigates both of the explicit and implicit tracking controlusing the ZD method. For solving the singularity-containingimplicit tracking problems, this paper overcomes the singular-ities by using the ZD method in combination with the GDmethod (i.e., the ZG method). Analyses and simulations ofan explicit tracking example and two implicit tracking exam-ples show the superiority of the ZD and ZG methods. Keywords: Zhang dynamics (ZD); Gradient dynamics (GD); ZG (Zhang-gradient) controller; Pendulum;Explicit and implicit tracking 1. Introduction and pendulum system As two powerful methods, Zhang dynamics (ZD) and gradi-ent dynamics (GD) have recently been studied and compared[1]–[4]. While the GD method is based on a scalar-valuednonnegative energy function and has been designed original-ly for solving constant (or to say, time-invariant) problems, theZD method is based on an indeﬁnite matrix/vector-valued er-ror function (termed Zhang function or Zhangian) and has beenproposed since 2001 for the online solution of various time-varying problems. In addition, the GD method is associatedwith explicit dynamics, while the ZD method is generally de-picted in implicit dynamics [1]–[4]. As shown later in thispaper, by using the ZD method in combination with the GDmethod [i.e., the ZG (Zhang-gradient)method], singularities inthe implicit tracking control problems can be overcome.Tracking control is widely encountered in engineering [5]-[9]. Traditionally and generally speaking, the tracking-controlproblem of a system is to design a controller in terms of theinput u(t)for the system such that the actual outputy(t)tracksthe desired output y

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

A momentous social event prediction attempt is presented in this work. Addition-subtraction frequency (ASF) algorithm with three inputs is investigated and employed to predict a possible date of the event. The important date data which this paper uses are the dates of United States' president death in office (USPDIO) in the past. In order to find a consistent prediction result, three forms of USPDIO dates (i.e., month/day/year form, month/year form, and year form) are chosen as input for numerical experiments. The feasibility of ASF is also verified via previous year confirmation. Finally, May to August in 2027 is presented in the conclusion section as the most possible date of USPDIO occurrence in the future via consistency analysis.

Numerical extrapolation of important date sequence by addition-subtraction frequency (ASF) algorithm

This paper demonstrates the flexibility of Z-type methodology for generating multiple solution-models of time-varying problems. As a case study with examples, we investigate the solution of time-varying generalized inverse (termed Zhang generalized inverse, ZGI). Specifically, to solve for time-varying left generalized inverse (TVLGI or termed Zhang left generalized inverse, ZLGI), five different effective Z-type models are derived by using different Zhang functions (ZFs) as source of derivations and employing the Z-type model design method. In addition, a clear and direct link between model A and the Getz-Marsden (G-M) dynamic system is discovered; and model B with a linear activation function (AF) array has global exponential convergence. Furthermore, two different AFs are adopted for comparisons and verifications.

Different ZFs lead to different nets: Examples of Zhang generalized inverse

Recently, a special class of recurrent neural network (termed Zhang neural network, ZNN) has been generalized for solving systems of time-varying nonlinear equations (STVNE), and a resultant continuous (or say, continuous-time) ZNN model has been proposed and analyzed. To generalize the idea for digital computers and numerical algorithms, this paper discretizes the continuous STVNE-solving ZNN using Euler difference and improves the discrete (or say, discrete time) ZNN models by employing Broyden method. Results of various numerical experiments are presented to verify the effectiveness of the proposed discrete ZNN models, especially the Broyden-method aided ones.

Broyden-Method Aided Discrete ZNN Solving the Systems of Time-Varying Nonlinear Equations

A short-term weather prediction attempt is presented in this paper. Different from the traditional method, a prediction algorithm called addition-subtraction frequency (ASF) algorithm is applied to handling weather prediction. Practically, the snowy weather date data of Guangzhou are chosen as input to ASF algorithm. In order to make the prediction more accurate, three numerical experiments with different forms of input are conducted, and the forms of the input are year form, month/year form, and month/day/year form, respectively. On the basis of consistency analysis, years 2033, 2042 −2044, and 2052 are indicated as the most possible years of snowy winter in Guangzhou within a time span of forty years.

Numerical prediction of short-term snowy weather in Guangzhou via addition-subtraction frequency (ASF) algorithm with unequally half traversal

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