State estimation of neural networks with time-varying delays and Markovian jumping parameter based on passivity theory

In this paper, the state estimation problem is investigated for neural networks with time-varying delays and Markovian jumping parameter based on passivity theory. The neural networks have a finite number of modes and the modes may jump from one to another according to a Markov chain. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time-delays, the dynamics of the estimation error is globally stable in the mean square and passive from the control input to the output error. Based on the new Lyapunov?CKrasovskii functional and passivity theory, delay-dependent conditions are obtained in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate effectiveness of the proposed method and results.     

Sampled-data state estimation for delayed neural networks with Markovian jumping parameters

This paper is concerned with the sampled-data state estimation problem for a class of delayed neural networks with Markovian jumping parameters. Unlike the classical state estimation problem, in our state estimation scheme, the sampled measurements are adopted to estimate the concerned neuron states. The neural network under consideration is assumed to have multiple modes that switch from one to another according to a given Markovian chain. By utilizing the input delay approach, the sampling period is converted into a time-varying yet bounded delay. Then a sufficient condition is given under which the resulting error dynamics of the neural networks is exponentially stable in the mean square. Based on that, a set of sampled-data estimators is designed in terms of the solution to a set of linear matrix inequalities (LMIs) which can be solved by using the available software. Finally, a numerical example is used to show the effectiveness of the estimation approach proposed in this paper.     

<Emphasis Type="Italic">p</Emphasis>th moment exponential synchronization for stochastic delayed Cohen–Grossberg neural networks with Markovian switching

This paper is a contribution to the analysis of the pth moment exponential synchronization problem for a class of stochastic delayed Cohen–Grossberg neural networks with Markovian switching. The jumping parameters are determined by a continuous-time, discrete-state Markov chain, and the delays are time-varying delays.     

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.     

Global exponential estimates for uncertain Markovian jump neural networks with reaction-diffusion terms

In this paper, the robust global exponential estimating problem is investigated for Markovian jumping reaction-diffusion delayed neural networks with polytopic uncertainties under Dirichlet boundary conditions. The information on transition rates of the Markov process is assumed to be partially known. By introducing a new inequality, some diffusion-dependent exponential stability criteria are derived in terms of relaxed linear matrix inequalities. Those criteria depend on decay rate, which may be freely selected in a range according to practical situations, rather than required to satisfy a transcendental equation. Estimates of the decay rate and the decay coefficient are presented by solving these established linear matrix inequalities. Numerical examples are provided to demonstrate the advantage and effectiveness of the proposed method.     

Exponential stability for switched Cohen–Grossberg neural networks with average dwell time

In this paper, uncertain switched Cohen–Grossberg neural networks with interval time-varying delay and distributed time-varying delay are proposed. Novel multiple Lyapunov functions are employed to investigate the stability of the switched neural networks under the switching rule with the average dwell time property. Sufficient conditions are obtained in terms of linear matrix inequalities (LMIs) which guarantee the exponential stability for the switched Cohen–Grossberg neural networks. Numerical examples are provided to illustrate the effectiveness of the proposed method.     

Exponential stability in the mean square for stochastic neural networks with mixed time-delays and Markovian jumping parameters

In this paper, the stability analysis problem is considered for a class of stochastic neural networks with mixed time-delays and Markovian jumping parameters. The mixed delays include discrete and distributed time-delays, and the jumping parameters are generated from a continuous-time discrete-state homogeneous Markov process. The aim of this paper is to establish some criteria under which the delayed stochastic neural networks are exponentially stable in the mean square. By constructing suitable Lyapunov functionals, several stability conditions are derived on the basis of inequality techniques and the stochastic analysis. An example is also provided in the end of this paper to demonstrate the usefulness of the proposed criteria.     

Robust observer for discrete-time Markovian jumping neural networks with mixed mode-dependent delays

The robust observer problem is considered in this paper for a class of discrete-time neural networks with Markovian jumping parameters and mode-dependent time delays which are in both discrete-time form and finite distributed form. The neural network switches from one mode to another controlled by a Markov chain with known transition probability. Time-delays considered in this paper are mode-dependent which may reflect a more realistic version of the neural network. By using the Lyapunov functional method and the techniques of linear matrix inequalities (LMIs), sufficient conditions are established in terms of LMIs that ensure the existence of the robust observer. The obtained conditions are easy to be verified via the LMI toolbox. An example is presented to show the effectiveness of the obtained results.     

Design of state estimator for uncertain neural networks via the integral-inequality method

The issue of state estimation is studied for a class of neural networks with norm-bounded parameter uncertainties and time-varying delay. Some new linear matrix inequality (LMI) representations of delay-dependent stability criteria are presented for the existence of the desired estimator for all admissible parametric uncertainties. The proposed method is based on the S-procedure and an extended integral inequality which can be deduced from the well-known Leibniz–Newton formula and Moon’s inequality. The results extend some models reported in the literature and improve conservativeness of those in the case that the derivative of the time-varying delay is assumed to be less than one. Two numerical examples are given to show the effectiveness and superiority of the results.     

Exponential state estimation for delayed recurrent neural networks with sampled-data

In this paper, the sampled-data state estimation problem is investigated for a class of recurrent neural networks with time-varying delay. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled-data estimator is constructed. By converting the sampling period into a bounded time-varying delay, the error dynamics of the considered neural network is derived in terms of a dynamic system with two different time-delays. Subsequently, by choosing an appropriate Lyapunov functional and using the Jensen??s inequality, a sufficient condition depending on the sampling period is obtained under which the resulting error system is exponentially stable. Then a sampled-data estimator is designed in terms of the solution to a set of linear matrix inequalities (LMIs) which can be solved by using available software. Finally, a numerical example is employed to demonstrate the effectiveness of the proposed sampled-data estimation approach.     

Switched exponential state estimation of neural networks based on passivity theory

In this paper, a new exponential state estimation method is proposed for switched Hopfield neural networks based on passivity theory. Through available output measurements, the main purpose is to estimate the neuron states such that the estimation error system is exponentially stable and passive from the control input to the output error. Based on augmented Lyapunov–Krasovskii functional, Jensen’s inequality, and linear matrix inequality (LMI), a new delay-dependent state estimator for switched Hopfield neural networks can be achieved by solving LMIs, which can be easily facilitated by using some standard numerical packages. The unknown gain matrix is determined by solving delay-dependent LMIs. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.     

Stability analysis of non-autonomous stochastic Cohen–Grossberg neural networks

This paper is concerned with pth moment exponential stability of stochastic Cohen–Grossberg neural networks (SCGNN) with time-varying connection matrix and delays. With the help of Lyapunov function, stochastic analysis technique and the generalized Halanay inequality, a set of novel sufficient conditions on pth moment exponential stability for SCGNN is given. These results are helpful to design exponentially stable non-autonomous Cohen–Grossberg neural networks when stochastic effects are taken into consideration in practice. This work was supported in part by the High-Tech Research and Development Program of China under Grant No. 2006AA04A104, the National Natural Science Foundation of China under Grant No. 50677014, China Postdoctoral Science Foundation under Grant No. 20070410300, the Hunan Provincial Natural Science Foundation of China under Grant No. 07JJ4001.     

Dynamic stability recognition of cylindrical shallow shells in Kelvin–Voigt viscoelastic medium under transverse white noise excitation

Nonlinear Dynamics - This paper investigates the problem of delay-dependent dissipativity for a class of Markovian jump neural networks with a time-varying delay. A generalized integral inequality...     

Neural networks based self-learning PID control of electronic throttle

An electronic throttle is a low-power DC servo drive which positions the throttle plate. Its application in modern automotive engines leads to improvements in vehicle drivability, fuel economy, and emissions. In this paper, a neural networks based self-learning proportional-integral-derivative (PID) controller is presented for electronic throttle. In the proposed self-learning PID controller, the controller parameters, K _P , K _I , and K _D are treated as neural networks weights and they are adjusted using a neural networks algorithm. The self-learning algorithm is operated iteratively and is developed using the Lyapunov method. Hence, the convergence of the learning algorithm is guaranteed. The neural networks based self-learning PID controller for electronic throttle is verified by computer simulations.     

State estimator for neural networks with sampled data using discontinuous Lyapunov functional approach

In this paper, the sampled-data state estimation problem is investigated for neural networks with 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. Based on the extended Wirtinger inequality, a discontinuous Lyapunov functional is introduced, which makes full use of the sawtooth structure characteristic of sampling input delay. New delay-dependent criteria are developed to estimate the neuron states through available output measurements such that the estimation error system is asymptotically stable. The criteria are formulated in terms of a set of linear matrix inequalities (LMIs), which can be checked efficiently by use of some standard numerical packages. Finally, a numerical example and its simulations are given to demonstrate the usefulness and effectiveness of the presented results.     

Exponential synchronization of Markovian jumping complex dynamical networks with randomly occurring parameter uncertainties

This paper investigates the mean-square exponential synchronization problem of complex dynamical networks with Markovian jumping and randomly occurring parameter uncertainties. The considered Markovian transition rates are assumed to be partially unknown. The parameter uncertainties are considered to be random occurrence and norm-bounded, and the randomly occurring parameter uncertainties obey certain Bernoulli-distributed white noise sequences. Based on the Lyapunov method and stochastic analysis, by designing mode-dependent feedback controller, some sufficient conditions are presented to ensure the mean-square exponential synchronization of Markovian jumping complex dynamical networks with partly unknown transition rates and randomly occurring parameter uncertainties. Numerical examples are given to demonstrate the validity of the theoretical results.     

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.     

Markovian risk process

A Markovian risk process is considered in this paper,which is the gener- alization of the classical risk model.It is proper that a risk process with large claims is modelled as the Markovian risk model.In such a model,the occurrence of claims is described by a point process {N(t)}_(t≥0) with N(t) being the number of jumps during the interval(0,t]for a Markov jump process.The ruin probabilityΨ(u)of a company facing such a risk model is mainly studied.An integral equation satisfied by the ruin probability functionΨ(u)is obtained and the bounds for the convergence rate of the ruin probabilityΨ(u)are given by using a generalized renewal technique developed in the paper.     

Projective synchronization of neural networks with mixed time-varying delays and parameter mismatch

In this paper, the projective synchronization of neural networks with mixed time-varying delays and parameter mismatch is discussed. Due to parameter mismatch and projective factor, complete projective synchronization cannot be achieved. Therefore, a new weak projective synchronization scheme is proposed to ensure that coupled neural networks are in a state of synchronization with an error level. Several criteria are derived and the error level is estimated by applying a generalized Halanay inequality and matrix measure. Finally, a numerical example is given to verify the efficiencies of theoretical results.