Fuzzy sliding-mode control with rule adaptation for nonlinear systems

Abstract: A fuzzy sliding-mode control with rule adaptation design approach with decoupling method is proposed. It provides a simple way to achieve asymptotic stability by a decoupling method for a class of uncertain nonlinear systems. The adaptive fuzzy sliding-mode control system is composed of a fuzzy controller and a compensation controller. The fuzzy controller is the main rule regulation controller, which is used to approximate an ideal computational controller. The compensation controller is designed to compensate for the difference between the ideal computational controller and the adaptive fuzzy controller. Fuzzy regulation is used as an approximator to identify the uncertainty. The simulation results for two cart–pole systems and a ball–beam system are presented to demonstrate the effectiveness and robustness of the method. In addition, the experimental results for a tunnelling robot manipulator are given to demonstrate the effectiveness of the system.     

A simulation study of artificial neural networks for nonlinear time-series forecasting

This study presents an experimental evaluation of neural networks for nonlinear time-series forecasting. The effects of three main factors — input nodes, hidden nodes and sample size, are examined through a simulated computer experiment. Results show that neural networks are valuable tools for modeling and forecasting nonlinear time series while traditional linear methods are not as competent for this task. The number of input nodes is much more important than the number of hidden nodes in neural network model building for forecasting. Moreover, large sample is helpful to ease the overfitting problem.Scope and purposeInterest in using artificial neural networks for forecasting has led to a tremendous surge in research activities in the past decade. Yet, mixed results are often reported in the literature and the effect of key modeling factors on performance has not been thoroughly examined. The lack of systematic approaches to neural network model building is probably the primary cause of inconsistencies in reported findings. In this paper, we present a systematic investigation of the application of neural networks for nonlinear time-series analysis and forecasting. The purpose is to have a detailed examination of the effects of certain important neural network modeling factors on nonlinear time-series modeling and forecasting.     

Hopfield network with constraint parameter adaptation foroverlapped shape recognition

We propose an energy formulation for homomorphic graph matching by the Hopfield network and a Lyapunov indirect method-based learning approach to adaptively learn the constraint parameter in the energy function. The adaptation scheme eliminates the need to specify the constraint parameter empirically and generates valid and better quality mappings than the analog Hopfield network with a fixed constraint parameter. The proposed Hopfield network with constraint parameter adaptation is applied to match silhouette images of keys and results are presented.     

Identification of time-series signals using a dynamic neural network with GA-based training

We propose a dynamic neural network (DNN) that realizes a dynamic property and has a network structure with the properties of inertia, viscosity, and stiffness without time-delayed input elements, and a training algorithm based on a genetic algorithm (GA). In a previous study, we proposed a modified training algorithm for the DNN based on the error back-propagation method. However, in the previous method it was necessary to determine the values of the DNN property parameters by trial and error. In the newly proposed DNN, the GA is designed to train not only the connecting weights but also the property parameters of the DNN. Simulation results show that the DNN trained by the GA obtains good performance for time-series patterns generated from an unknown system, and provides a higher performance than the conventional neural network. This work was presented in part at the 10th International Symposium on Artificial Life and Robotics, 0ita, Japan, February 4–6, 2005     

A local linear radial basis function neural network for financial time-series forecasting

In this paper a Local Linear Radial Basis Function Neural Network (LLRBFN) is presented. The difference between the proposed neural network and the conventional Radial Basis Function Neural Network (RBFN) is connection weights between the hidden layer and the output layer which are replaced by a local linear model in the LLRBFN. A modified Particle Swarm Optimization (PSO) with hunter particles is introduced for training the LLRBFN. The proposed methods have been applied for prediction of financial time-series and the result shows the feasibility and effectiveness.     

Fuzzy neural network with fuzzy signals and weights

We discuss the direct fuzzification of a standard layered, feedforward, neural network where the signals and weights are fuzzy sets. A fuzzified delta rule is presented for learning. Three applications are given including fuzzy expert systems, fuzzy hierarchical analysis, and fuzzy systems modeling. © 1993 John Wiley & Sons, Inc.     

A general regression neural network

A memory-based network that provides estimates of continuous variables and converges to the underlying (linear or nonlinear) regression surface is described. The general regression neural network (GRNN) is a one-pass learning algorithm with a highly parallel structure. It is shown that, even with sparse data in a multidimensional measurement space, the algorithm provides smooth transitions from one observed value to another. The algorithmic form can be used for any regression problem in which an assumption of linearity is not justified.     

Artificial neural network based approach for dynamic parameter design

The Taguchi parameter design method has been recognized as an important tool for improving the quality of a product or a process. However, the statistical methods and optimization procedures proposed by Taguchi have much room for improvement. For instance, the two-step procedure proposed by Taguchi may fail to identify an optimum design condition if an adjustment parameter does not exist, the optimal setting of a design parameter is determined only among the levels included in the parameter design experiment, and, for the dynamic parameter design, the signal parameter is assumed to follow a uniform rather than a general distribution. This paper develops an artificial neural network based dynamic parameter design approach to overcome the shortcomings of the Taguchi and existing alternative approaches. First, an artificial neural network is trained to map the relationship between the characteristic, design, noise and signal parameters. Second, Latin hypercube samples of the signal and noise parameters are obtained and used to estimate the slope between the signal parameter and characteristic as well as the variance of the characteristic at each set of design parameter settings. Then, the dynamic parameter design problem is formulated as a nonlinear optimization problem and solved to find the optimal settings of the design parameters using sequential quadratic programming. The effectiveness of the proposed approach is illustrated with an example.     

Combining a neural network with a genetic algorithm for process parameter optimization

A neural-network model has been developed to predict the value of a critical strength parameter (internal bond) in a particleboard manufacturing process, based on process operating parameters and conditions. A genetic algorithm was then applied to the trained neural network model to determine the process parameter values that would result in desired levels of the strength parameter for given operating conditions. The integrated NN–GA system was successful in determining the process parameter values needed under different conditions, and at various stages in the process, to provide the desired level of internal bond. The NN–GA tool allows a manufacturer to quickly determine the values of critical process parameters needed to achieve acceptable levels of board strength, based on current operating conditions and the stage of manufacturing.     

Model-based recurrent neural network for modeling nonlinear dynamicsystems

A model-based recurrent neural network (MBRNN) is introduced for modeling dynamic systems. This network has a fixed structure that is defined according to the linearized state-space model of the plant. Therefore, the MBRNN has the ability to incorporate the analytical knowledge of the plant in its formulation. With its original topology intact, the MBRNN can then be trained to represent the plant nonlinearities through modifying its nodes' activation functions, which consist of contours of Gaussian radial basis functions (RBFs). Training in MBRNN involves adjusting the weights of the RBF's so as to modify the contours representing the activation functions. The performance of the MBRNN is demonstrated via several examples. The results indicate that it requires much shorter training than needed by ordinary recurrent networks. This efficiency in training is attributed to the MBRNN's fixed topology which is independent of training.     

Fuzzy neural network approaches for robotic gait synthesis

In this paper, a learning scheme using a fuzzy controller to generate walking gaits is developed. The learning scheme uses a fuzzy controller combined with a linearized inverse biped model. The controller provides the control signals at each control time instant. The algorithm used to train the controller is "backpropagation through time". The linearized inverse biped model provides the error signals for backpropagation through the controller at control time instants. Given prespecified constraints such as the step length, crossing clearance, and walking speed, the control scheme can generate the gait that satisfies these constraints. Simulation results are reported for a five-link biped robot.     

A novel neural network for nonlinear convex programming

In this paper, we present a neural network for solving the nonlinear convex programming problem in real time by means of the projection method. The main idea is to convert the convex programming problem into a variational inequality problem. Then a dynamical system and a convex energy function are constructed for resulting variational inequality problem. It is shown that the proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem. Compared with the existing neural networks for solving the nonlinear convex programming problem, the proposed neural network has no Lipschitz condition, no adjustable parameter, and its structure is simple. The validity and transient behavior of the proposed neural network are demonstrated by some simulation results.     

不确定非线性系统的直接自适应神经网络控制

为解决一类带干扰的不确定非线性系统中存在的两类未知项——未知函数和外界干扰,采用了直接自适应神经网络控制方法设计控制器。控制器设计中利用径向基函数神经网络良好的逼近性来近似未知函数,利用非线性衰减项来抑制干扰。所用方法结构简单、算法简洁,在一定条件下稳定性和收敛性能定性地得到保证。最后,仿真结果证明了该方法是正确的。     

Fuzzy data mining for time-series data

Time series analysis has always been an important and interesting research field due to its frequent appearance in different applications. In the past, many approaches based on regression, neural networks and other mathematical models were proposed to analyze the time series. In this paper, we attempt to use the data mining technique to analyze time series. Many previous studies on data mining have focused on handling binary-valued data. Time series data, however, are usually quantitative values. We thus extend our previous fuzzy mining approach for handling time-series data to find linguistic association rules. The proposed approach first uses a sliding window to generate continues subsequences from a given time series and then analyzes the fuzzy itemsets from these subsequences. Appropriate post-processing is then performed to remove redundant patterns. Experiments are also made to show the performance of the proposed mining algorithm. Since the final results are represented by linguistic rules, they will be friendlier to human than quantitative representation.     

Fuzzy nonlinear regression with fuzzified radial basis function network

A fuzzified radial basis function network (FRBFN) is a kind of fuzzy neural network that is obtained by direct fuzzification of the well known neural model RBFN. A FRBFN contains fuzzy weights and can handle fuzzy-in fuzzy-out data. This paper shows that a FRBFN can also be interpreted as a kind of fuzzy expert system. Hence it owns the advantages of simple structure and clear physical meaning. Some metrics for fuzzy numbers have been extended to the metrics for n-dimensional fuzzy vectors, which are applicable to computations in FRBFNs. The corresponding metric spaces for n-dimensional fuzzy vectors are proved to be complete. Further, FRBFNs are proved to be able to act as universal function approximators for any continuous fuzzy function defined on a compact set. This paper applies the proposed FRBFN to nonparametric fuzzy nonlinear regression problems for multidimensional LR-type fuzzy data. Fuzzy nonlinear regression with FRBFNs can be formulated as a nonlinear mathematical programming problem. Two training algorithms are proposed to quickly solve the two types of problems under different criteria and constraint conditions, namely, the two-stage and BP (Back-Propagation) training algorithms. Simulation studies are carried out to verify the feasibility and demonstrate the advantages of the proposed approaches.     

L-p Fuzzy ARTMAP neural network architecture

In this paper, an L-p based Fuzzy ARTMAP neural network is presented. The category choice of this network is based on the L-p norm. Geometrical properties of this architecture are presented. Comparisons between this category choice and the category choice of the Fuzzy ARTMAP are illustrated. And simulation results on the databases taken from the UCI repository are performed. It will be shown that using the L-p norm is geometrically more attractive. It will operate directly on the input patterns without the need for doing any preprocessing. It should be noted that the Fuzzy ARTMAP architecture requires two preprocessing steps: normalization and complement coding. Simulation results on different databases show the good generalization performance of the L-p Fuzzy ARTMAP compared to the performance of Fuzzy ARTMAP.     

Forecasting nonlinear time series with neural network sieve bootstrap

A new method to construct nonparametric prediction intervals for nonlinear time series data is proposed. Within the framework of the recently developed sieve bootstrap, the new approach employs neural network models to approximate the original nonlinear process. The method is flexible and easy to implement as a standard residual bootstrap scheme while retaining the advantage of being a nonparametric technique. It is model-free within a general class of nonlinear processes and avoids the specification of a finite dimensional model for the data generating process. The results of a Monte Carlo study are reported in order to investigate the finite sample performances of the proposed procedure.     

Estimating time-series leaf area index based on recurrent nonlinear autoregressive neural networks with exogenous inputs

The leaf area index (LAI) is a key parameter in many meteorological, environmental and agricultural models. At present, global LAI products from several sensors have been released. These single sensor-based LAI products are generally discontinuous in time and cannot characterize the status of natural vegetation growth very well. In this study, by fusing Moderate Resolution Imaging Spectroradiometer (MODIS) and Satellite Pour l'Observation de la Terre (SPOT) VEGETATION products, time-series LAIs were used to train recurrent nonlinear autoregressive neural networks with exogenous inputs (NARXNNs) for six typical vegetation types. The exogenous inputs included time-series reflectances in the red, near-infrared and shortwave infrared bands as well as the corresponding sun-viewing angles. These NARXNNs subsequently served to predict the time-series LAI. The validation results show that the predicted LAI of the NARXNN is not only more continuous and stable than the MODIS LAI as a function of time but is also much closer to the ground truth. Thus, the proposed method may be helpful for improving the quality of the MODIS LAI.     

Control-affine fuzzy neural network approach for nonlinear process control

An internal model control strategy employing a fuzzy neural network is proposed for SISO nonlinear process. The control-affine model is identified from both steady state and transient data using back-propagation. The inverse of the process is obtained through algebraic inversion of the process model. The resulting model is easier to interpret than models obtained from the standard neural network approaches. The proposed approach is applied to the tasks of modelling and control of a continuous stirred tank reactor and a pH neutralization process which are not inherently control-affine. The results show a significant performance improvement over a conventional PID controller. In addition, an additional neural network which models the discrepancy between a control-affine model and real process dynamics is added, and is shown to lead to further improvement in the closed-loop performance.