Enhanced discrete-time Zhang neural network for time-variant matrix inversion in the presence of bias noises

A Survey on Biomimetic and Intelligent Algorithms with Applications

The question "How does it work" has motivated many scientists. Through the study of natural phenomena and behaviors, many intelligence algorithms have been proposed to solve various optimization problems. This paper aims to offer an informative guide for researchers who are interested in tackling optimization problems with intelligence algorithms. First, a special neural network was comprehensively discussed, and it was called a zeroing neural network (ZNN). It is especially intended for solving time-varying optimization problems, including origin, basic principles, operation mechanism, model variants, and applications. This paper presents a new classification method based on the performance index of ZNNs. Then, two classic bio-inspired algorithms, a genetic algorithm and a particle swarm algorithm, are outlined as representatives, including their origin, design process, basic principles, and applications. Finally, to emphasize the applicability of intelligence algorithms, three practical domains are introduced, including gene feature extraction, intelligence communication, and the image process.

Two New Discrete-Time Neurodynamic Algorithms Applied to Online Future Matrix Inversion With Nonsingular or Sometimes-Singular Coefficient

In this paper, a high-precision general discretization formula using six time instants is first proposed to approximate the first-order derivative. Then, such a formula is studied to discretize two continuous-time neurodynamic models, both of which are derived by applying the neurodynamic approaches based on neural networks (i.e., zeroing neurodynamics and gradient neurodynamics). Originating from the general six-instant discretization (6ID) formula, a specific 6ID formula is further presented. Subsequently, two new discrete-time neurodynamic algorithms, i.e., 6ID-type discrete-time zeroing neurodynamic (DTZN) algorithm and 6ID-type discrete-time gradient neurodynamic (DTGN) algorithm, are proposed and investigated for online future matrix inversion (OFMI). In addition to analyzing the usual nonsingular situation of the coefficient, this paper investigates the sometimes-singular situation of the coefficient for OFMI. Finally, two illustrative numerical examples, including an application to the inverse-kinematic control of a PUMA560 robot manipulator, are provided to show respective characteristics and advantages of the proposed 6ID-type DTZN and DTGN algorithms for OFMI in different situations, where the coefficient matrix to be inverted is always-nonsingular or sometimes-singular during time evolution.

General Square-Pattern Discretization Formulas via Second-Order Derivative Elimination for Zeroing Neural Network Illustrated by Future Optimization

Previous works provide a few effective discretization formulas for zeroing neural network (ZNN), of which the precision is a square pattern. However, those formulas are separately developed via many relatively blind attempts. In this paper, general square-pattern discretization (SPD) formulas are proposed for ZNN via the idea of the second-order derivative elimination. All existing SPD formulas in previous works are included in the framework of the general SPD formulas. The connections and differences of various general formulas are also discussed. Furthermore, the general SPD formulas are used to solve future optimization under linear equality constraints, and the corresponding general discrete ZNN models are proposed. General discrete ZNN models have at least one parameter to adjust, thereby determining their zero stability. Thus, the parameter domains are obtained by restricting zero stability. Finally, numerous comparative numerical experiments, including the motion control of a PUMA560 robot manipulator, are provided to substantiate theoretical results and their superiority to conventional Euler formula.

A New Varying-Parameter Recurrent Neural-Network for Online Solution of Time-Varying Sylvester Equation

Solving Sylvester equation is a common algebraic problem in mathematics and control theory. Different from the traditional fixed-parameter recurrent neural networks, such as gradient-based recurrent neural networks or Zhang neural networks, a novel varying-parameter recurrent neural network, [called varying-parameter convergent-differential neural network (VP-CDNN)] is proposed in this paper for obtaining the online solution to the time-varying Sylvester equation. With time passing by, this kind of new varying-parameter neural network can achieve super-exponential performance. Computer simulation comparisons between the fixed-parameter neural networks and the proposed VP-CDNN via using different kinds of activation functions demonstrate that the proposed VP-CDNN has better convergence and robustness properties.

Design, Analysis, and Representation of Novel Five-Step DTZD Algorithm for Time-Varying Nonlinear Optimization

Continuous-time and discrete-time forms of Zhang dynamics (ZD) for time-varying nonlinear optimization have been developed recently. In this paper, a novel discrete-time ZD (DTZD) algorithm is proposed and investigated based on the previous research. Specifically, the DTZD algorithm for time-varying nonlinear optimization is developed by adopting a new Taylor-type difference rule. This algorithm is a five-step iteration process, and thus, is referred to as the five-step DTZD algorithm in this paper. Theoretical analysis and results of the proposed five-step DTZD algorithm are presented to highlight its excellent computational performance. The geometric representation of the proposed algorithm for time-varying nonlinear optimization is also provided. Comparative numerical results are illustrated with four examples to substantiate the efficacy and superiority of the proposed five-step DTZD algorithm for time-varying nonlinear optimization compared with the previous DTZD algorithms.