Global stability in switched recurrent neural networks with time-varying delay via nonlinear measure

In this paper, based on switched systems and recurrent neural networks (RNNs) with time-varying delay, the model of switched RNNs is formulated. Global asymptotical stability (GAS) and global robust stability (GRS) for such switched neural networks are studied by employing nonlinear measure and linear matrix inequality (LMI) techniques. Some new sufficient conditions are obtained to ensure GAS or GRS of the unique equilibrium of the proposed switched system. Furthermore, the proposed LMI results are computationally efficient as it can be solved numerically with standard commercial software. Finally, three examples are provided to illustrate the usefulness of the results.     

Delay-independent exponential stability of stochastic Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms

Different from the approaches used in the earlier papers, in this paper, the Halanay inequality technique, in combination with the Lyapunov method, is exploited to establish a delay-independent sufficient condition for the exponential stability of stochastic Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms. Moreover, for the deterministic delayed Cohen–Grossberg neural networks, with or without reaction–diffusion terms, sufficient criteria for their global exponential stability are also obtained. The proposed results improve and extend those in the earlier literature and are easier to verify. An example is also given to illustrate the correctness of our results.     

Generalized LMI-based approach to global asymptotic stability of cellular neural networks with delay

A global asymptotic stability problem of cellular neural networks with delay is investigated. A new stability condition is presented based on the Lyapunov-Krasovskii method, which is dependent on the amount of delay. A result is given in the form of a linear matrix inequality, and the admitted upper bound of the delay can be easily obtained. The time delay dependent and independent results can be obtained, which include some previously published results. A numerical example is given to show the effectiveness of the main results.     

On the use of neural networks for identification of linear and nonlinear systems

A procedure based on neural networks for the classification of linear and nonlinear systems is presented, using excitation and response data under swept sine excitation. Special attention is paid to the classification and identification of linear and bilinear systems, the latter being considered since they exhibit typical characteristics of cracked systems. The computer simulations show that: (1) using the procedure presented in this paper the trained classification network can reliably classify a linear system and different nonlinear systems; (2) the output of the trained identification neural network for a linear system and a bilinear system can be used as a quantitative indicator of characteristics of bilinear systems having different stiffness ratios (k _(x>0)/k _(x<0)) with respect to the bilinear system used in the training stage; (3) for two-degree-of-freedom systems, the trained network can not only determine the existence of a bilinear stiffness and the magnitude of its stiffness ratio, but also specify which stiffness is bilinear, i.e. indicate its position. These results provide a possibility of using the trained neural networks to detect and locate structural cracks which have the characteristics of bilinear systems.Visiting scholar, from People's Republic of China.     

On delay-dependent robust exponential stability of stochastic neural networks with mixed time delays and Markovian switching

This paper deals with the global exponential stability analysis problem for a general class of uncertain stochastic neural networks with mixed time delays and Markovian switching. The mixed time delays under consideration comprise both the discrete time-varying delays and the distributed time-delays. The main purpose of this paper is to establish easily verifiable conditions under which the delayed stochastic neural network is robustly exponentially stable in the mean square in the presence of parameters uncertainties, mixed time delays, and Markovian switching. By employing new Lyapunov–Krasovskii functionals and conducting stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the criteria for the robust exponential stability, which can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox. The criteria derived are dependent on both the discrete time delay and distributed time delay, and, are therefore, less conservative. A simple example is provided to demonstrate the effectiveness and applicability of the proposed testing criteria. This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, the National Natural Science Foundation of China under Grant 60774073, the Natural Science Foundation of Jiangsu Province of China under Grant BK2007075, the Natural Science Foundation of Jiangsu Education Committee of China under Grant 06KJD110206, the Scientific Innovation Fund of Yangzhou University of China under Grant 2006CXJ002, and the Alexander von Humboldt Foundation of Germany.     

GLOBAL ASYMPTOTIC STABILITY CONDITIONS OF DELAYED NEURAL NETWORKS

1　IntroductionandProblemEductionRecently,thestudiesofthestabilityforcellularneuralnetworks (CNNs)anddelayedcellularneuralnetworks (DCNNs)haveattractedattentionsofresearchersandseveralimportantresultshavebeenobtained .MostpapersdealtwithcompletelystableCNNsandDCNNsthataresuitableforimageprocessingapplications.CNNshavebeenwidelyappliedtoimageprocessing ,toprocessmovingimages,onemustintroducedelaysinthesignalstransmittedamongthecells.Buttimedelaysmayleadtoanoscillationphenomenonand ,furt…     

Design of sampled data state estimator for Markovian jumping neural networks with leakage time-varying delays and discontinuous Lyapunov functional approach

This paper is concerned with the sampled-data state estimation problem for neural networks with both Markovian jumping parameters and leakage time-varying delays. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled-data estimator is constructed. In order to make full use of the sawtooth structure characteristic of the sampling input delay, a discontinuous Lyapunov functional is proposed based on the extended Wirtinger inequality. A less conservative delay dependent stability criterion is derived via constructing a new triple-integral Lyapunov–Krasovskii functional and the famous Jenson integral inequality. Based on the Lyapunov–Krasovskii functional approach, a state estimator of the considered neural networks has been achieved by solving some linear matrix inequalities, which can be easily facilitated by using the standard numerical software. Finally, two numerical examples are provided to show the effectiveness of the proposed methods.     

Forward kinematics analysis of the 6-3 SPM by using neural networks

A feed-forward neural network has been trained using backpropagation algorithm to solve the forward kinematics problem of the 6-3 Stewart Platform Mechanism (SPM). The forward kinematics problem of the SPM does not have a unique solution since it involves solving a polynomial of order 16. Purely translational, purely rotational and general spatial data sets have been used in training and testing, and then an optimization procedure has been applied to fine-tune the solution. The method yields results fast and accurate enough such that it can be used instead of a gyro and a position sensor for real time control of the mechanism.     

Investigation of the adaptive features of a real-time nonlinear freeway traffic state estimator

This paper reports on real-data testing results for a real-time nonlinear freeway traffic state estimator with particular focus on its adaptive features. The pursued general approach to the real-time adaptive estimation of the complete traffic state in freeway stretches is based on stochastic nonlinear macroscopic traffic flow modeling and extended Kalman filtering that are outlined in the paper. One major innovative aspect of the estimator is the on-line estimation of important model parameters (free speed, critical density, and capacity) simultaneously with the estimation of traffic flow variables (flows, mean speeds, and densities), which leads to three significant advantages of the traffic state estimator: (1) avoidance of off-line model calibration; (2) automatic adaptation to changing external conditions (e.g. weather and light conditions); (3) enabling of incident alarms. The purpose of the reported real-data testing is, first, to demonstrate advantage (1) by investigating some basic properties of the estimator and, second, to explore some adaptive capabilities of the estimator that enable the other two advantages. The achieved testing results are quite satisfactory and promising for subsequent work.     

Design method of multiple time-delay controller for active structural vibration control

An optimal control method for seismic-excited building structures with multiple time delays is investigated in this paper. The system state equation with multiple time delays is discretized and transformed into a standard discrete form without any explicit time delay by a particular augmenting for state variables. A time-delay controller is then designed based on this standard equation using the discrete optimal control method. Effectiveness of the proposed controller is demonstrated by numerical simulations. Simulation results indicate that a very small time delay may result in the instability of the control system if it is not compensated in the control design. Time delay may be compensated effectively by the proposed controller, in the mean time, an effective control may be obtained. The proposed controller is valid for both small and large time delays.     

Improving the neural network method for finite element model updating using homogenous distribution of design points

In developing a neural network technique for a finite element model updating, researchers have been shown that the number of training samples and their quality, significantly affect the accuracy of the NN predication. In this study, based on the genetic algorithm (GA) method, we reduce the number of analyses required to develop the training pairs and reduce the amount of time for training the NN. In the other words, a uniform distribution of design points inside the design space will be obtained by means of this approach. To validate the efficiency of GA sample selection, random generation (RG) method is used for comparison. Two comparisons are made based on a numerical and experimental example. One is updated from 10 degrees of freedom lumped parameters system and the other is updated from a free–free beam using test data. The results indicate that the GA sample selection can reduce the number of training samples without affecting the accuracy of the NN predication. In our present study, also, the advantages of using frequency response function (FRF) data as input to the NN are kept and the drawback of having too many frequency points is overcome by the application of principal component analyses (PCA).     

Adaptive neural network control for coordinated motion of a dual-arm space robot system with uncertain parameters

Control of coordinated motion between the base attitude and the arm joints of a free-floating dual-arm space robot with uncertain parameters is discussed. By combining the relation of system linear momentum conversation with the Lagrangian approach, the dynamic equation of a robot is established. Based on the above results, the free-floating dual-arm space robot system is modeled with RBF neural networks, the GL matrix and its product operator. With all uncertain inertial system parameters, an adaptive RBF neural network control scheme is developed for coordinated motion between the base attitude and the arm joints. The proposed scheme does not need linear parameterization of the dynamic equation of the system and any accurate prior-knowledge of the actual inertial parameters. Also it does not need to train the neural network offline so that it would present real-time and online applications. A planar free-floating dual-arm space robot is simulated to show feasibility of the proposed scheme.     

不确定性参数系统振动控制闭环特征值的上、下界估计

用凸模型理论讨论参数不确定性系统的振动控制问题。把不确定系统的振动控制转化为确定性问题来处理,然后讨论不确定参数对闭环特征值的影响,提出了闭环系统特征值上、下界的计算公式。     

Design and experimental validation of piecewise-linear state observers for flexible link mechanisms

The design of an observer estimating the state variables of a plant is an essential step towards the synthesis of high-performance model-based control schemes. In this paper, the problem of designing accurate state observers for flexible link mechanisms is tackled. The complexity of such a problem is considerable due to the nonlinear characteristics of flexible link mechanism dynamic models. Since nonlinear state observers have limited practical utility, in this work an investigation is made on the possibility of employing the Kalman filter theory together with suitable piecewise-linear truncated dynamic models. A general approach is developed and experimental results are given for the case of a four bar linkage with flexible links. Not only do these results confirm the theoretical and numerical results, but they also prove the practical effectiveness and efficiency of the proposed approach.     

Neural networks for computing in the elastoplastic analysis of structures

A neural network model is proposed and studied for the treatment of elastoplastic analysis problems. These problems are formulated as Q.P.P.s with inequality subsidiary conditions. In order to treat these conditions the Hopfield model is appropriately generalized and a neural model is proposed covering the case of inequalities. Finally, the parameter identification problem is formulated as a supervised learning problem. Numerical applications close the presentation of the theory and the advantages of the neural network approach are illustrated.

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Sommario Si propone un modello di rete neurale con l'obiettivo di usarlo per la trattazione di problemi di analisi elastoplastica, formulati come problemi di programmazione quadratica con disequazioni sussidiarie. Allo scopo di trattare queste condizioni si generalizza il modello di Hopfield e si propone un modello neurale che copre il caso di disequazioni. Inoltre il problema di identificazione parametrica viene formulato come un problema di apprendimento guidato. La presentazione della teoria è seguita da esempi di applicazioni numeriche e dalla illustrazione dei vantaggi dell'uso delle reti neurali.

     

An operative algebraic formulation for the unilaterally-constrained mechanical problem of smart tensegrities

Kinematics and statics of tensegrities are addressed by means of a novel algebraic formulation. The inequality constraints, associated to cable-type unilateral structural members, are explicitly enforced in the equilibrium and compatibility problems. Fundamental tensegrity properties (rigidity, pre-stressability, and stability) are focused by a novel structural perspective and algebraic criteria for their assessment are established. Some classical results are generalized to the case of tensegrity models involving both deformable and non-deformable structural members. An operative algorithm for the analysis of the large-displacement elastic tensegrity response is proposed, not limited by special requirements in terms of structural symmetries or member connectivity, and therefore resulting a general design tool. Exemplary applications highlight the effectiveness of the proposed approach for designing tensegrity structures endowed with smart global behavior related to the optimal tuning of structural stiffness.     

A non-linear method for the calculation of the loss tangent distribution function

A procedure to obtain the tangent distribution function from internal friction peaks in solids is described. The method was applied to simulated data in order to show that the distribution can reproduce accurately the internal friction data in transition region as well as in most of the terminal region. Finally, the procedure is applied to experimental data in glass transition peaks of polystyrene.     

Accuracy analysis of predicted velocity profiles of laminar duct flow with entropy generation method

The objective of this work is to estimate the accuracy of a predicted velocity profile which can be gained from experimental results, in comparison with the exact ones by the methodology of entropy generation. The analysis is concerned with the entropy generation rate in hydrodynamic, steady, laminar, and incompressible flow for Newtonian fluids in the insulated channels of arbitrary cross section. The entropy generation can be calculated from two local and overall techniques. Adaptation of the results of these techniques depends on the used velocity profile. Results express that in experimental works, whatever the values of local and overall entropy generation rates are close to each other, the results are more accuracy. In order to extent the subject, different geometries have been investigated. Also, the influence studied, and the distribution of volumetric geometries is drawn. of geometry on the entropy generation rate is local entropy generation rate for the selected geometries is drawn.     

Matrix perturbation method for the vibration problem of structures with interval parameters

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