New Noise-Tolerant ZNN Models With Predefined-Time Convergence for Time-Variant Sylvester Equation Solving

Sylvester equation is often applied to various fields, such as mathematics and control systems due to its importance. Zeroing neural network (ZNN), as a systematic design method for time-variant problems, has been proved to be effective on solving Sylvester equation in the ideal conditions. In this paper, in order to realize the predefined-time convergence of the ZNN model and modify its robustness, two new noise-tolerant ZNNs (NNTZNNs) are established by devising two novelly constructed nonlinear activation functions (AFs) to find the accurate solution of the time-variant Sylvester equation in the presence of various noises. Unlike the original ZNN models activated by known AFs, the proposed two NNTZNN models are activated by two novel AFs, therefore, possessing the excellent predefined-time convergence and strong robustness even in the presence of various noises. Besides, the detailed theoretical analyses of the predefined-time convergence and robustness ability for the NNTZNN models are given by considering different kinds of noises. Simulation comparative results further verify the excellent performance of the proposed NNTZNN models, when applied to online solution of the time-variant Sylvester equation

A Novel Disturbance Rejection Zeroing Neurodynamic Approach for Robust Synchronization of Chaotic Systems

Robust synchronization of chaotic systems becomes a hot topic in scientific and engineering fields because of the ubiquitous existence of time-variant external disturbances in complex application scenarios. In contrast with existing studies that the resultant synchronization error has a supremum or even diverges under the influence of time-variant external disturbances, this paper proposes a disturbance rejection zeroing neurodynamic (DRZN) approach and its related controller for the robust synchronization of chaotic systems against time-variant external disturbances. The controller designed by the proposed DRZN approach distinctively features the rejection of external disturbances with the generated synchronization error being convergence toward zero. Theoretical analyses guarantee that the DRZN approach and its related controller inherently possess robustness. Moreover, numerical studies including three examples substantiate the effectiveness of the proposed DRZN approach and its related controller for the synchronization of chaotic systems against the time-variant external disturbances. Comparisons with existing approaches, e.g., the conventional zeroing neurodynamic (CZN) approach and the linear-active control (LAC) approach, show the superiority of the proposed DRZN approach. Extensive tests further verify that the proposed DRZN approach possesses the outstanding anti-disturbance performance, and thus is suitable for the practical applications with time-variant external disturbances

Simultaneous identification, tracking control and disturbance rejection of uncertain nonlinear dynamics systems: A unified neural approach

Previous works of traditional zeroing neural networks (or termed Zhang neural networks, ZNN) show great success for solving specific time-variant problems of known systems in an ideal environment. However, it is still a challenging issue for the ZNN to effectively solve time-variant problems for uncertain systems without the prior knowledge. Simultaneously, the involvement of external disturbances in the neural network model makes it even hard for time-variant problem solving due to the intensively computational burden and low accuracy. In this paper, a unified neural approach of simultaneous identification, tracking control and disturbance rejection in the framework of the ZNN is proposed to address the time-variant tracking control of uncertain nonlinear dynamics systems (UNDS). The neural network model derived by the proposed approach captures hidden relations between inputs and outputs of the UNDS. The proposed model shows outstanding tracking performance even under the influences of uncertainties and disturbances. Then, the continuous-time model is discretized via Euler forward formula (EFF). The corresponding discrete algorithm and block diagram are also presented for the convenience of implementation. Theoretical analyses on the convergence property and discretization accuracy are presented to verify the performance of the neural network model. Finally, numerical studies, robot applications, performance comparisons and tests demonstrate the effectiveness and advantages of the proposed neural network model for the time-variant tracking control of UNDS

A Noise-Tolerant Zeroing Neural Network for Time-Dependent Complex Matrix Inversion Under Various Kinds of Noises

Complex-valued time-dependent matrix inversion (TDMI) is extensively exploited in practical industrial and engineering fields. Many current neural models are presented to find the inverse of a matrix in an ideal noise-free environment. However, the outer interferences are normally believed to be ubiquitous and avoidable in practice. If these neural models are applied to complex-valued TDMI in a noise environment, they need to take a lot of precious time to deal with outer noise disturbances in advance. Thus, a noise-suppression model is urgent to be proposed to address this problem. In this article, a complex-valued noise-tolerant zeroing neural network (CVNTZNN) on the basis of an integral-type design formula is established and investigated for finding complex-valued TDMI under a wide variety of noises. Furthermore, both convergence and robustness of the CVNTZNN model are carefully analyzed and rigorously proved. For comparison and verification purposes, the existing zeroing neural network (ZNN) and gradient neural network (GNN) have been presented to address the same problem under the same conditions. Numerical simulation consequences demonstrate the effectiveness and excellence of the proposed CVNTZNN model for complex-valued TDMI under various kinds of noises, by comparing the existing ZNN and GNN models

Design and analysis of three nonlinearly activated ZNN models for solving time-varying linear matrix inequalities in finite time

To obtain the superiority property of solving time-varying linear matrix inequalities (LMIs), three novel finite-time convergence zeroing neural network (FTCZNN) models are designed and analyzed in this paper. First, to make the Matlab toolbox calculation processing more conveniently, the matrix vectorization technique is used to transform matrix-valued FTCZNN models into vector-valued FTCZNN models. Then, considering the importance of nonlinear activation functions on the conventional zeroing neural network (ZNN), the sign-bi-power activation function (AF), the improved sign-bi-power AF and the tunable sign-bi-power AF are explored to establish the FTCZNN models. Theoretical analysis shows that the FTCZNN models not only can accelerate the convergence speed, but also can achieve finite-time convergence. Computer numerical results ulteriorly confirm the effectiveness and advantages of the FTCZNN models for finding the solution set of time-varying LMIs

A fully connected deep learning approach to upper limb gesture recognition in a secure FES rehabilitation environment

Stroke is one of the leading causes of death and disability in the world. The rehabilitation of Patients' limb functions has great medical value, for example, the therapy of functional electrical stimulation (FES) systems, but suffers from effective rehabilitation evaluation. In this paper, six gestures of upper limb rehabilitation were monitored and collected using microelectromechanical systems sensors, where data stability was guaranteed using data preprocessing methods, that is, deweighting, interpolation, and feature extraction. A fully connected neural network has been proposed investigating the effects of different hidden layers, and determining its activation functions and optimizers. Experiments have depicted that a three‐hidden‐layer model with a softmax function and an adaptive gradient descent optimizer can reach an average gesture recognition rate of 97.19%. A stop mechanism has been used via recognition of dangerous gesture to ensure the safety of the system, and the lightweight cryptography has been used via hash to ensure the security of the system. Comparison to the classification models, for example, k‐nearest neighbor, logistic regression, and other random gradient descent algorithms, was conducted to verify the outperformance in recognition of upper limb gesture data. This study also provides an approach to creating health profiles based on large‐scale rehabilitation data and therefore consequent diagnosis of the effects of FES rehabilitation

Path Planning and Energy Efficiency of Heterogeneous Mobile Robots Using Cuckoo–Beetle Swarm Search Algorithms with Applications in UGV Obstacle Avoidance

In this paper, a new meta-heuristic path planning algorithm, the cuckoo–beetle swarm search (CBSS) algorithm, is introduced to solve the path planning problems of heterogeneous mobile robots. Traditional meta-heuristic algorithms, e.g., genetic algorithms (GA), particle swarm search (PSO), beetle swarm optimization (BSO), and cuckoo search (CS), have problems such as the tenancy to become trapped in local minima because of premature convergence and a weakness in global search capability in path planning. Note that the CBSS algorithm imitates the biological habits of cuckoo and beetle herds and thus has good robustness and global optimization ability. In addition, computer simulations verify the accuracy, search speed, energy efficiency and stability of the CBSS algorithm. The results of the real-world experiment prove that the proposed CBSS algorithm is much better than its counterparts. Finally, the CBSS algorithm is applied to 2D path planning and 3D path planning in heterogeneous mobile robots. In contrast to its counterparts, the CBSS algorithm is guaranteed to find the shortest global optimal path in different sizes and types of maps

Wind Power Forecasting Based on Echo State Networks and Long Short-Term Memory

Wind power generation has presented an important development around the world. However, its integration into electrical systems presents numerous challenges due to the variable nature of the wind. Therefore, to maintain an economical and reliable electricity supply, it is necessary to accurately predict wind generation. The Wind Power Prediction Tool (WPPT) has been proposed to solve this task using the power curve associated with a wind farm. Recurrent Neural Networks (RNNs) model complex non-linear relationships without requiring explicit mathematical expressions that relate the variables involved. In particular, two types of RNN, Long Short-Term Memory (LSTM) and Echo State Network (ESN), have shown good results in time series forecasting. In this work, we present an LSTM+ESN architecture that combines the characteristics of both networks. An architecture similar to an ESN is proposed, but using LSTM blocks as units in the hidden layer. The training process of this network has two key stages: (i) the hidden layer is trained with a descending gradient method online using one epoch; (ii) the output layer is adjusted with a regularized regression. In particular, the case is proposed where Step (i) is used as a target for the input signal, in order to extract characteristics automatically as the autoencoder approach; and in the second stage (ii), a quantile regression is used in order to obtain a robust estimate of the expected target. The experimental results show that LSTM+ESN using the autoencoder and quantile regression outperforms the WPPT model in all global metrics used

Learning as a Nonlinear Line of Attraction for Pattern Association, Classification and Recognition

Development of a mathematical model for learning a nonlinear line of attraction is presented in this dissertation, in contrast to the conventional recurrent neural network model in which the memory is stored in an attractive fixed point at discrete location in state space. A nonlinear line of attraction is the encapsulation of attractive fixed points scattered in state space as an attractive nonlinear line, describing patterns with similar characteristics as a family of patterns. It is usually of prime imperative to guarantee the convergence of the dynamics of the recurrent network for associative learning and recall. We propose to alter this picture. That is, if the brain remembers by converging to the state representing familiar patterns, it should also diverge from such states when presented by an unknown encoded representation of a visual image. The conception of the dynamics of the nonlinear line attractor network to operate between stable and unstable states is the second contribution in this dissertation research. These criteria can be used to circumvent the plasticity-stability dilemma by using the unstable state as an indicator to create a new line for an unfamiliar pattern. This novel learning strategy utilizes stability (convergence) and instability (divergence) criteria of the designed dynamics to induce self-organizing behavior. The self-organizing behavior of the nonlinear line attractor model can manifest complex dynamics in an unsupervised manner. The third contribution of this dissertation is the introduction of the concept of manifold of color perception. The fourth contribution of this dissertation is the development of a nonlinear dimensionality reduction technique by embedding a set of related observations into a low-dimensional space utilizing the result attained by the learned memory matrices of the nonlinear line attractor network. Development of a system for affective states computation is also presented in this dissertation. This system is capable of extracting the user\u27s mental state in real time using a low cost computer. It is successfully interfaced with an advanced learning environment for human-computer interaction