Zhang Y. Zhang Time Discretization (ZTD). Formulas and Applications 2025 torrent

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This book aims to solve the discrete implementation problems of continuous-time neural network models while improving the performance of neural networks by using various Zhang Time Discretization (ZTD) formulas. The authors summarize and present the systematic derivations and complete research of ZTD formulas from special 3S-ZTD formulas to general NS-ZTD formulas. These finally led to their proposed discrete-time Zhang neural network (DTZNN) algorithms, which are more efficient, accurate, and elegant. This book will open the door to scientific and engineering applications of ZTD formulas and neural networks, and will be a major inspiration for studies in neural network modeling, numerical algorithm design, prediction, and robot manipulator control.
In recent decades, with the characteristics of distributed-storage and high-speed parallel processing, superior performance in large-scale online applications, and convenience of hardware implementations, neural networks have widely arisen in scientific computation and optimization, drawing extensive interest and investigation of researchers. Due to the in-depth research in neural networks, the approaches based on recurrent neural networks (RNNs) are now regarded as powerful alternatives, which can online solve various mathematical and engineering problems. Generally, these RNNs can be divided into two classes: the continuous-time RNNs and the discrete-time RNNs.
As a special class of RNNs, originating and extending from the research of Hopfield neural network, zeroing neural network (also termed as Zhang neural network, ZNN) was proposed by Zhang et al. ZNN has been developed and investigated as a systematic and efficient method to solve various time-dependent problems in real time, and it differs from conventional gradient-based RNNs in terms of the problem to be solved, error function, design formula, dynamic equation, and the utilization of derivative information. ZNN can perfectly track the time-dependent solution by fully exploiting the derivative information of time-dependent parameters.
Zeroing neural network (ZNN) is a great alternative to solve time-dependent problems. It is a special class of recurrent neural networks (RNNs), which originates from Hopfield neural network. ZNN is developed to solve time-dependent problems and fully utilizes the information of time derivative and correlation of solutions of adjacent moments. ZNN has been used to solve various problems in science and engineering fields, such as manipulators, control, and time-dependent mathematical operations, ever since its development.
ZNN has the capability of predicting future solutions on the basis of current and past information compared with other methods for time-dependent problems. This characteristic of ZNN satisfies the requirement of strictly real-time computation for time-dependent problems. That is, the solution at this instant should already be obtained when a time instant arrives; thus, practical tasks can be completed in real time. This superior performance of strictly real-time computation originates from an effective discretization of continuous-time ZNN (CTZNN). Therefore, discretization formulas are the key points to the solution of discrete time-dependent problems (also termed as future problems).
Preface
Part I Zhang–Taylor Discretization Formula and Applications
Future Matrix Right Pseudoinversion
Future Equality-Constrained Quadratic Programming
Part II ZTD 6321 Formula and Applications
Future Matrix Inversion with Noises
Future Matrix Pseudoinversion
Part III General Formulas and Applications of ZTD
Future Constrained Nonlinear Optimization with O(g3)
Future Unconstrained Nonlinear Optimization with O(g4)
Future Different-Layer Inequation–Equation System Solving with O(g5)
Future Matrix Square Root Finding with O(g6)