Aiguo Song

Delay-Derivative-Dependent Stability for Delayed Neural Networks With Unbound Distributed Delay

In this brief, based on Lyapunov-Krasovskii functional approach and appropriate integral inequality, a new sufficient condition is derived to guarantee the global stability for delayed neural networks with unbounded distributed delay, in which the improved delay-partitioning technique and general convex combination are employed. The LMI-based criterion heavily depends on both the upper and lower bounds on time delay and its derivative, which is different from the existent ones and has wider application fields than some present results. Finally, three numerical examples can illustrate the efficiency of the new method based on the reduced conservatism which can be achieved by thinning the delay interval.

Combined Convex Technique on Delay-Dependent Stability for Delayed Neural Networks

In this brief, by employing an improved Lyapunov-Krasovskii functional (LKF) and combining the reciprocal convex technique with the convex one, a new sufficient condition is derived to guarantee a class of delayed neural networks (DNNs) to be globally asymptotically stable. Since some previously ignored terms can be considered during the estimation of the derivative of LKF, a less conservative stability criterion is derived in the forms of linear matrix inequalities, whose solvability heavily depends on the information of addressed DNNs. Finally, we demonstrate by two numerical examples that our results reduce the conservatism more efficiently than some currently used methods.

Synchronization control for arrays of coupled discrete-time delayed Cohen-Grossberg neural networks

This paper investigates the global exponential synchronization for an array of coupled discrete-time Cohen-Grossberg neural networks (CGNNs) with time-varying delay, in which both the constant coupling and delayed one are considered. Through constructing an improved Lyapunov-Krasovskii functional, the delay-dependent sufficient condition is obtained to guarantee the global synchronization based on linear matrix inequality (LMI) approach. The criterion is presented in terms of LMIs and its feasibility can be easily checked by resorting to Matlab LMI Toolbox. Moreover, the addressed system can include some famous neural network models as its special cases, which can help extend those present results. Finally, the effectiveness of the proposed method can be further illustrated with the help of two numerical examples.

Letters: Robust stability of stochastic Cohen-Grossberg neural networks with mixed time-varying delays

In the paper, the problem of robust exponential stability analysis is investigated for stochastic Cohen-Grossberg neural networks with both interval time-varying and distributed time-varying delays. By employing an augmented Lyapunov-Krasovskii functional, together with the LMI approach and definition on convex set, two delay-dependent conditions guaranteeing the robust exponential stability (in the mean square sense) of addressed system are presented. Additionally, the activation functions are of more general descriptions and the derivative of time-varying delay being less than 1 is released, which generalize and further improve those earlier methods. Numerical examples are provided to demonstrate the effectiveness of proposed stability conditions.

Iterative GDHP-based approximate optimal tracking control for a class of discrete-time nonlinear systems

In this paper, an iterative globalized dual heuristic programming (GDHP) method is developed to deal with the approximate optimal tracking control for a class of discrete-time nonlinear systems. The optimal tracking control problem is formulated by solving the discrete-time Hamilton-Jacobi-Bellman (DTHJB) equation. Then, it is approximately solved by the developed iterative GDHP-based algorithm with convergence analysis. The iterative GDHP algorithm is implemented by constructing three neural networks to approximate the error system dynamics, the cost function with its derivative, and the control policy in each iteration, respectively. The information of the cost function and its derivative is provided during iteration calculation. Two simulation examples are investigated to verify the performance of the proposed approximate optimal tracking control approach.

Letters: Fuzzy MSD based feature extraction method for face recognition

To improve the recognition performance of maximum scatter difference (MSD), a fuzzy MSD method is proposed in this paper. In the existing MSD model, the class mean vector in the expressions of within-class scatter matrix and between-class scatter matrix is estimated by class sample average. Obviously, the class sample average is not sufficient to provide an accurate estimate of the class mean using a few of the given samples, because there will be some outliers in the sample set under the non-ideal conditions such as variations of expression, illumination, pose, and so on. As a result, the recognition performance of traditional MSD model will decrease. To address this problem, inspired by existing fuzzy application, the fuzzy theory is incorporated into traditional maximum scatter difference algorithm. In this method, applying fuzzy K-nearest neighbor (FKNN), the membership degree matrix of training samples is calculated, which is used to get fuzzy means of each class and the average of fuzzy means is then applied to the definition of within-class scatter matrix and between class scatter difference matrix, respectively. The results of experiments conducted on ORL, YALE and FERET face database indicate the effectiveness of the proposed approach.

Adaptive tracking control for a class of continuous-time uncertain nonlinear systems using the approximate solution of HJB equation

Abstract In this paper, an adaptive tracking control scheme is designed for a class of continuous-time uncertain nonlinear systems based on the approximate solution of the Hamilton–Jacobi–Bellman (HJB) equation. Considering matched uncertainties, the tracking control of the continuous-time uncertain nonlinear system can be transformed to the optimal tracking control of the associated nominal system. By building the nominal error system and modifying its cost function, the solution of the relevant HJB equation can be contributed to the adaptive tracking control of the continuous-time uncertain nonlinear system. In view of the complexity on solving the HJB equation, its approximate solution is pursued by the policy iteration algorithm under the adaptive dynamic programming (ADP) framework, where a critic neural network is constructed to approximate the optimal cost function, and an action network is used to directly calculate the approximate optimal control law, which constitutes the tracking control law for the original uncertain system together with the steady control law. The weight convergence of the critic network and the stability of the closed-loop system are provided as the theoretical guarantee based on the Lyapunov theory. Two simulation examples are studied to verify the theoretical results and the effectiveness of the proposed tracking control scheme.

Decentralized adaptive optimal stabilization of nonlinear systems with matched interconnections

In this paper, we investigate the decentralized feedback stabilization and adaptive dynamic programming (ADP)-based optimization for the class of nonlinear systems with matched interconnections. The decentralized control law of the overall system is designed by integrating all controllers of the isolated subsystems, and it satisfies the optimality on the basis of optimal control laws of all the subsystems. For solving the optimal control problems of these isolated subsystems, the policy iteration algorithm is used to approximately solve the Hamilton–Jacobi–Bellman equations in the framework of ADP with the neural network implementation, where a set of critic neural networks is constructed to estimate the optimal cost functions, and the approximate optimal control laws can be obtained after the learning of critic neural networks. The weight estimation errors of the critic networks and the stability of all isolated subsystems are proved based on the Lyapunov theory. Finally, the performance of the proposed decentralized optimal control strategy is verified by simulation results.

Enhanced Logical Stochastic Resonance in Synthetic Genetic Networks

In this brief, the concept of logical stochastic resonance is applied to implement the Set-Reset latch in a synthetic gene network derived from a bacteriophage λ. Clear Set-Reset latch operation is obtained when the network is only subjected to periodic forcing. The correct probability of obtaining the desired logic operation first increases to unity and then decreases as the amplitude of the periodic forcing increases. In addition, the output logic operation can be easily morphed by tuning the frequency and the amplitude of the periodic forcing. At the same time, we indicate that adding moderate periodic forcing to the background Gaussian noise may increase the length of the optimal plateau of getting the desired logic operation in genetic regulatory network. We also point out that robust Set-Reset latch operation can be obtained using the interplay of periodic forcing and background noise when the noise strength is lower than what is required.

Parameter-induced logical stochastic resonance

In this paper, we discuss how to get adaptive logical stochastic resonance (LSR) by modulating the parameters of nonlinear system. The effects of linear and nonlinear coefficients of a quartic-bistable system on the system?s response to feeble input signals in noisy background are investigated. Genetic Algorithm is applied to search for the optimal system parameters in the given noise. The success probability of obtaining desired logic output is used as the fitness function. Experimental results show that the system can achieve robust logic operation in a wide range of noise intensity by adjusting the parameters. The study might provide an example of the application of parameter-induced LSR in engineering practice.