Neural Dynamics for Time-varying Problems


Book Description

This book mainly presents methods based on neural dynamics for the time-varying problems with applications, together with the corresponding theoretical analysis, simulative examples, and physical experiments. Based on these methods, their applications include motion planning of redundant manipulators, filter design, winner-take-all operation, multiple-input multiple-output system configuration, multi-linear tensor equation solving, and manipulability optimization are also presented. In this book, we present the design, proposal, development, analysis, modeling, and simulation of various neural dynamic models, along with their respective applications including motion planning of redundant manipulators, filter design, winner-take-all operation, multiple-input multiple-output system configuration, multi-linear tensor equation solving, and manipulability optimization. Specifically, starting from the top-level considerations of hardware implementation, we integrate computational intelligence methods and control theory to design a series of dynamic and noise-resistant discrete neural dynamic methods. The research work not only owns the theoretical guarantee on its convergence, noise resistance, and accuracy, but demonstrate the effectiveness and robustness in solving various optimization and equation solving problems, particularly in handling time-varying problems and noise perturbations. Moreover, by reducing complexity and avoiding matrix inversion operations, the models’ feasibility and practicality are further enhanced.




Neuronal Dynamics


Book Description

This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.




The Optimal Homotopy Asymptotic Method


Book Description

This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations. The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation.




Zeroing Dynamics, Gradient Dynamics, and Newton Iterations


Book Description

Neural networks and neural dynamics are powerful approaches for the online solution of mathematical problems arising in many areas of science, engineering, and business. Compared with conventional gradient neural networks that only deal with static problems of constant coefficient matrices and vectors, the authors’ new method called zeroing dynamics solves time-varying problems. Zeroing Dynamics, Gradient Dynamics, and Newton Iterations is the first book that shows how to accurately and efficiently solve time-varying problems in real-time or online using continuous- or discrete-time zeroing dynamics. The book brings together research in the developing fields of neural networks, neural dynamics, computer mathematics, numerical algorithms, time-varying computation and optimization, simulation and modeling, analog and digital hardware, and fractals. The authors provide a comprehensive treatment of the theory of both static and dynamic neural networks. Readers will discover how novel theoretical results have been successfully applied to many practical problems. The authors develop, analyze, model, simulate, and compare zeroing dynamics models for the online solution of numerous time-varying problems, such as root finding, nonlinear equation solving, matrix inversion, matrix square root finding, quadratic optimization, and inequality solving.




Zeroing Neural Networks


Book Description

Zeroing Neural Networks Describes the theoretical and practical aspects of finite-time ZNN methods for solving an array of computational problems Zeroing Neural Networks (ZNN) have become essential tools for solving discretized sensor-driven time-varying matrix problems in engineering, control theory, and on-chip applications for robots. Building on the original ZNN model, finite-time zeroing neural networks (FTZNN) enable efficient, accurate, and predictive real-time computations. Setting up discretized FTZNN algorithms for different time-varying matrix problems requires distinct steps. Zeroing Neural Networks provides in-depth information on the finite-time convergence of ZNN models in solving computational problems. Divided into eight parts, this comprehensive resource covers modeling methods, theoretical analysis, computer simulations, nonlinear activation functions, and more. Each part focuses on a specific type of time-varying computational problem, such as the application of FTZNN to the Lyapunov equation, linear matrix equation, and matrix inversion. Throughout the book, tables explain the performance of different models, while numerous illustrative examples clarify the advantages of each FTZNN method. In addition, the book: Describes how to design, analyze, and apply FTZNN models for solving computational problems Presents multiple FTZNN models for solving time-varying computational problems Details the noise-tolerance of FTZNN models to maximize the adaptability of FTZNN models to complex environments Includes an introduction, problem description, design scheme, theoretical analysis, illustrative verification, application, and summary in every chapter Zeroing Neural Networks: Finite-time Convergence Design, Analysis and Applications is an essential resource for scientists, researchers, academic lecturers, and postgraduates in the field, as well as a valuable reference for engineers and other practitioners working in neurocomputing and intelligent control.




Neural Networks for Cooperative Control of Multiple Robot Arms


Book Description

This is the first book to focus on solving cooperative control problems of multiple robot arms using different centralized or distributed neural network models, presenting methods and algorithms together with the corresponding theoretical analysis and simulated examples. It is intended for graduate students and academic and industrial researchers in the field of control, robotics, neural networks, simulation and modelling.




Zhang-Gradient Control


Book Description

This book introduces readers to using the simple but effective Zhang-gradient (ZG) method to solve tracking-control problems concerning various nonlinear systems, while also highlighting the applications of the ZG method to tracking control for practical systems, e.g. an inverted-pendulum-on-a-cart (IPC) system and a two-wheeled mobile robot (showing its potential applications). In addition to detailed theoretical analyses of ZG controllers, the book presents a wealth of computer simulations to demonstrate the feasibility and efficacy of the controllers discussed (as well as the method itself). More importantly, the superiority of ZG controllers in overcoming the division-by-zero (DBZ) problem is also illustrated. Given its scope and format, the book is well suited for undergraduate and graduate students, as well as academic and industrial researchers in the fields of neural dynamics/neural networks, nonlinear control, computer mathematics, time-varying problem solving, modeling and simulation, analog hardware, and robotics.




Neural & Bio-inspired Processing and Robot Control


Book Description

This Research Topic presents bio-inspired and neurological insights for the development of intelligent robotic control algorithms. This aims to bridge the inter-disciplinary gaps between neuroscience and robotics to accelerate the pace of research and development.




Advances in Neural Networks – ISNN 2012


Book Description

The two-volume set LNCS 7367 and 7368 constitutes the refereed proceedings of the 9th International Symposium on Neural Networks, ISNN 2012, held in Shenyang, China, in July 2012. The 147 revised full papers presented were carefully reviewed and selected from numerous submissions. The contributions are structured in topical sections on mathematical modeling; neurodynamics; cognitive neuroscience; learning algorithms; optimization; pattern recognition; vision; image processing; information processing; neurocontrol; and novel applications.