Convergence Of Neural Network Research Articles

Global exponential convergence of fuzzy complex-valued neural networks with time-varying delays and impulsive effects

In this paper, the global exponential convergence of T–S fuzzy complex-valued neural networks with time-varying delays and impulsive effects is discussed. By employing Lyapunov functional method and matrix inequality technique, we analyze a type of activation functions with Lipschitz function, and sufficient conditions in terms of complex-valued linear matrix inequality are obtained to ensure the global exponential convergence. Moreover, the framework of the exponential convergence ball in the state space of the considered neural networks and the exponential convergence rate index are also given out. Here, the existence and uniqueness of the equilibrium points need not be considered and the results improve existing results on the Lyapunov exponential stability as special cases. Finally, one numerical example with simulations is given to illustrate the effectiveness of our theoretical results.

Global exponential convergence of fuzzy cellular neural networks with proportional delays and impulsive effects

Global exponential convergence of fuzzy cellular neural networks with proportional delays and impulsive effects

Adaptive near-optimal neuro controller for continuous-time nonaffine nonlinear systems with constrained input

In this paper, an identifier–critic structure is introduced to find an online near-optimal controller for continuous-time nonaffine nonlinear systems having saturated control signal. By employing two Neural Networks (NNs), the solution of Hamilton–Jacobi–Bellman (HJB) equation associated with the cost function is derived without requiring a priori knowledge about system dynamics. Weights of the identifier and critic NNs are tuned online and simultaneously such that unknown terms are approximated accurately and the control signal is kept between the saturation bounds. The convergence of NNs’ weights, identification error, and system states is guaranteed using Lyapunov’s direct method. Finally, simulation results are performed on two nonlinear systems to confirm the effectiveness of the proposed control strategy.

Event-Triggered Optimal Control for Partially Unknown Constrained-Input Systems via Adaptive Dynamic Programming

Event-triggered control has been an effective tool in dealing with problems with finite communication and computation resources. In this paper, we design an event-triggered control for nonlinear constrained-input continuous-time systems based on the optimal policy. Constraints on controls are handled using a bounded function. To learn the optimal solution with partially unknown dynamics, an online adaptive dynamic programming algorithm is proposed. The identifier network, the critic network, and the actor network are employed to approximate the unknown drift dynamics, the optimal value, and the optimal policy, respectively. The identifier is tuned based on online data, which further trains the critic and actor at triggering instants. A concurrent learning technique repeatedly uses past data to train the critic. Stability of the closed-loop system, and convergence of neural networks to the optimal solutions are proved by Lyapunov analysis. In the end, the algorithm is applied to the overhead crane system to observe the performance. The event-triggered optimal controller with constraints stabilizes the system and consumes much less sampling times.

New results on convergence of fuzzy cellular neural networks with multi-proportional delays

In this paper, we propose and study the global exponential convergence of a class of fuzzy cellular neural networks with multi-proportional delays, which has not been studied in the existing literature. Applying the differential inequality technique and Lyapunov functional method, we establish a set of global exponential convergence criteria. The sufficient criteria can be easily tested in practice by simple algebra computations. The obtained results play an important role in designing fuzzy neural networks. Moreover, an illustrative example is given to demonstrate our theoretical results.

Global exponential convergence of neutral-type Hopfield neural networks with multi-proportional delays and leakage delays

This paper is concerned with a class of neutral-type Hopfield neural networks with multi-proportional delays and leakage delays. Using the differential inequality theory, a set of sufficient conditions which guarantee that all solutions of neutral-type Hopfield neural networks with multi-proportional delays and leakage delays converge exponentially to zero vector are derived. Computer simulations are carried out to verify our theoretical findings. The obtained results of this paper are new and complement some previous studies.

The convergence and termination criterion of quantum-inspired evolutionary neural networks

Quantum-inspired evolutionary algorithm (QEA) has proved to be an effective method to design neural networks with few connections and high classification performance. When a quantum-inspired evolutionary neural network (QENN) converges in the training phase, subsequent training is fruitless and time-wasting. Therefore, it is important to control the number of generations of QENN. The analysis on the convergence property of quantum bit evolution can contribute to designing a safe termination criterion that can always be reached. This paper proposes an appropriate termination criterion based on the average convergence rate (ACR). Experiments on classification tasks are conducted to demonstrate the effectiveness of our method. The results show that the termination criterion based on ACR can duly stop the training process of QENN and overcome the limitations of the termination criterion based on the probability of generating the best solution (PBS).

Convergence and Multistability of Nonsymmetric Cellular Neural Networks With Memristors.

Recent work has considered a class of cellular neural networks (CNNs) where each cell contains an ideal capacitor and an ideal flux-controlled memristor. One main feature is that during the analog computation the memristor is assumed to be a dynamic element, hence each cell is second-order with state variables given by the capacitor voltage and the memristor flux. Such CNNs, named dynamic memristor (DM)-CNNs, were proved to be convergent when a symmetry condition for the cell interconnections is satisfied. The goal of this paper is to investigate convergence and multistability of DM-CNNs in the general case of nonsymmetric interconnections. The main result is that convergence holds when there are (possibly) nonsymmetric, non-negative interconnections between cells and an irreducibility assumption is satisfied. This result appears to be similar to the classic convergence result for standard (S)-CNNs with positive cell-linking templates. Yet, due to the presence of DMs, a DM-CNN displays some basically different and peculiar dynamical properties with respect to S-CNNs. One key difference is that the DM-CNN processing is based on the time evolution of memristor fluxes instead of capacitor voltages as it happens for S-CNNs. Moreover, when a steady state is reached, all voltages and currents, and hence power consumption of a DM-CNN vanish. This notwithstanding the memristors are able to store in a nonvolatile way the result of the processing. Voltages, currents and power instead do not vanish when an S-CNN reaches a steady state.

A Spintronic Memristor-Based Neural Network With Radial Basis Function for Robotic Manipulator Control Implementation

A radial basis function (RBF) neural network control algorithm can effectively improve the robotic manipulators’ performance against a large amount of uncertainty. The adaptive law can be derived by using the Lyapunov method so that the stability of robotic manipulator control system and the weight self-adaptive convergence of RBF neural networks will be guaranteed. Meanwhile, system fluctuations and even overshot phenomenon under every start-up process, which are caused by the system’s convergence from the given nonoptimal initial weight value to the optimal weight value, can be avoided by using memristors to remember the optimal weight after the system’s first operation. According to the above analysis, this correspondence paper designs a kind of RBF neural network control algorithm based on spintronic memristors, and then analyzes its theoretical derivation process and core design idea. Finally, the system simulation model, which uses a two-link robotic manipulator as control object, is built to prove the algorithm’s validity and feasibility. Simulation results show that the proposed algorithm can satisfy the effect of presupposition.

Global exponential convergence of non-autonomous cellular neural networks with multi-proportional delays

The paper is concerned with the exponential convergence for a class of non-autonomous cellular neural networks with multi-proportional delays. By employing the differential inequality techniques, we establish a novel result to ensure that all solutions of the addressed system converge exponentially to zero vector. Our results complement with some recent ones. Moreover, an illustrative example and its numerical simulation are given to demonstrate the effectiveness of the obtained results.

Accelerating convergence of backpropagation for multilayer perceptron neural networks: a case study on character bit-mapped pixel image to ASCII conversion

In this paper, we introduced a modified version of backpropagation algorithm which is able to converge faster than the traditional backpropagation for multilayer perceptron neural networks. We also proposed a dynamic technique for specifying the number of hidden layers and number of neuron in each hidden layer along with an initialization technique to set start values of the synaptic weights. A novel two activation functions have been proposed, which are proved experimentally that they accelerate convergence of neural networks while maintaining the accuracy of the trained network. Experimental results showed that the average number of epochs required to reach approximation using exponential hyperbolic tangent is less than the half of average number using traditional sigmoid function. Finally, a case study is performed on converting alphanumeric character bit-mapped pixel image to its ASCII equivalent code.

A non-penalty recurrent neural network for solving a class of constrained optimization problems

In this paper, we explain a methodology to analyze convergence of some differential inclusion-based neural networks for solving nonsmooth optimization problems. For a general differential inclusion, we show that if its right hand-side set valued map satisfies some conditions, then solution trajectory of the differential inclusion converges to optimal solution set of its corresponding in optimization problem. Based on the obtained methodology, we introduce a new recurrent neural network for solving nonsmooth optimization problems. Objective function does not need to be convex on Rn nor does the new neural network model require any penalty parameter. We compare our new method with some penalty-based and non-penalty based models. Moreover for differentiable cases, we implement circuit diagram of the new neural network.

Deriving a New Divergence Measure from Extended Cross-Entropy Error Function

Relative entropy is a divergence measure between two probability density functions of a random variable. Assuming that the random variable has only two alphabets, the relative entropy becomes a cross-entropy error function that can accelerate training convergence of multi-layer perceptron neural networks. Also, the n-th order extension of cross-entropy (nCE) error function exhibits an improved performance in viewpoints of learning convergence and generalization capability. In this paper, we derive a new divergence measure between two probability density functions from the nCE error function. And the new divergence measure is compared with the relative entropy through the use of three-dimensional plots.

Convergence and attractivity of memristor-based cellular neural networks with time delays

This paper presents theoretical results on the convergence and attractivity of memristor-based cellular neural networks (MCNNs) with time delays. Based on a realistic memristor model, an MCNN is modeled using a differential inclusion. The essential boundedness of its global solutions is proven. The state of MCNNs is further proven to be convergent to a critical-point set located in saturated region of the activation function, when the initial state locates in a saturated region. It is shown that the state convergence time period is finite and can be quantitatively estimated using given parameters. Furthermore, the positive invariance and attractivity of state in non-saturated regions are also proven. The simulation results of several numerical examples are provided to substantiate the results.

Assessment of Transmission Line Icing State Based on Multi-Sensor Information Fusion

Due to considerations limited for the current monitoring techniques and computational models and other reasons,the accuracy rate of line icing condition assessment is not high. Transmission line icing are affected by many factors, having greater relevance with micro-meteorological parameters. To improve the assessment accuracy of transmission line icing condition,multi-sensor information fusion method are put forward for a comprehensive assessment to Line icing state, based on online monitoring system,considering the equivalent ice thickness of monitoring system, micro-meteorological parameters and duration of ice cover.BP neural network convergence line icing membership value, the output state is cing probability. Then ,the probability of the state of uncertainty output line integrated assessmen through Fuzzy Reasoning

Assessment of Transmission Line Condition Based on Neural Networks and Fuzzy Logic Decision

Accurate assessment of the operational status of transmission line,and the line status timely warning, can protect the stable operation of the transmission line. Not high accuracy assessment for the current state of the transmission line,assessment model of transmission line state based on neural networks and fuzzy logic decisions are put forward,built on online monitoring system, Considering the conductor temperature, angle, tension and other parameters.Using BP neural network convergence line fault membership values, and the output state is line fault probability. Then ,the uncertainty of the state probability output line integrated assessmen through Fuzzy Reasoning.

Correction to “Convergence and Rate Analysis of Neural Networks for Sparse Approximation” [Sep 12 1377-1389

Correction to “Convergence and Rate Analysis of Neural Networks for Sparse Approximation” [Sep 12 1377-1389

Tool life prediction based on particle swarm optimization–back-propagation neural network

As one of the most important factors affecting shop floor management, tool life is determined by the tool flank wear or break, which is related to the tool parameters, cutting conditions and workpiece parameters. It is found that the relationship between these factors and the tool life is too nonlinear to be analytically formulated. For this reason, back-propagation neural network model is used to predict the tool life for its strong ability of nonlinear fitness. To avoid the local optimum, slow convergence and low generalization capability of the back-propagation neural network, a tool life prediction model, which is based on improved particle swarm optimization–back-propagation neural networks, is proposed in this article. The particle swarm optimization is applied to optimize the weights and thresholds of the back-propagation algorithm for improving the ability of global search and generality. Existing sample data of tools are used to train the proposed model for predicting the life of the tools that are similar to the sample data in tool style. The face milling tools and workpiece of 45 steel are selected for experiment. Theoretical analysis and comparative experiments with back-propagation neural network indicate that the life predicted by the particle swarm optimization–back-propagation model is much better than that of the back-propagation model. It proves that particle swarm optimization–back-propagation model has better convergence, stronger robustness and higher generality. This model also provides a theoretical basis for the economization of tool demand analysis and production planning.

An Improved Modeling of Nonlinear Circuits based on Elman Neural Network

In this paper, an improved modeling based on Elman neural network was proposed to analyze the nonlinear features of nonlinear circuits with the memory effect. The input vector of the hidden layer in neural network is normalized to enhance the neural network convergence precision. A group of Chebyshev orthogonal basis functions was employed to activate hidden layer neurons. Computer simulation results of the nonlinear power amplifier (PA) have shown that the proposed behavioral modeling not only accurately describes the nonlinear distortions of PAs, but also well depicts memory effect of PAs. And, the proposed approach could be also applied to analyze linear circuits and RF power amplifiers.

Exponential convergence of Cohen-Grossberg neural networks with continuously distributed leakage delays

This paper is concerned with the global exponential convergence of Cohen-Grossberg neural networks with continuously distributed leakage delays. By using the Lyapunov functional method and differential inequality techniques, we propose a new approach to establishing some sufficient conditions ensuring that all solutions of the networks converge exponentially to the zero point. Our results complement some recent ones.MSC: 34C25, 34K13, 34K25.