Uncertain Neural Networks Research Articles

Robustly Exponential Stability Analysis for Discrete-Time Stochastic Neural Networks with Interval Time-Varying Delays

This paper deals with the problems of the global exponential stability and stabilization for a class of uncertain discrete-time stochastic neural networks with interval time-varying delay. By using the linear matrix inequality method and the free-weighting matrix technique, we construct a new Lyapunov–Krasovskii functional and establish new sufficient conditions to guarantee that the uncertain discrete-time stochastic neural networks with interval time-varying delay are globally exponential stable in the mean square. Furthermore, we extend our consideration to the stabilization problem for a class of discrete-time stochastic neural networks. Based on the state feedback control law, some novel delay-dependent criteria of the robust exponential stabilization for a class of discrete-time stochastic neural networks with interval time-varying delay are established. The controller gains are designed to ensure the global robust exponential stability of the closed-loop systems. Finally, numerical examples illustrate the effectiveness of the theoretical results we have obtained.

Robust stability analysis for uncertain recurrent neural networks with leakage delay based on delay-partitioning approach

This paper focuses on the issue of robust stability analysis for recurrent neural networks (RNNs) with leakage delay. By constructing a novel Lyapunov–Krasovskii functional together with the reciprocally convex approach and the free-weighting matrix technique, some less conservative stability criteria in terms of linear matrix inequalities for RNNs are derived. The new contribution of this paper is that a novel delay-partitioning method is proposed, and some new zero equalities are introduced. Finally, several examples are given to demonstrate the effectiveness of the proposed methods. The simulated results reveal that the leakage delay has great influence on the dynamical systems, and it cannot be neglected.

Complete delay-decomposing approach to exponential stability for uncertain cellular neural networks with discrete and distributed time-varying delays

This paper considers the problem of exponential stability of uncertain cellular neural networks with discrete and distribute time-varying delays. Some new delay-dependent stability condition are derived in terms of linear matrix inequality. We divide delay interval into multiple segments and employ the free-weighting matrices method to obtained some less conservative criteria. Finally, numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

Robust finite time stabilization analysis for uncertain neural networks with leakage delay and probabilistic time-varying delays

This paper investigates the problem of robust finite time stabilization for a uncertain neural networks with leakage delay and probabilistic time-varying delays. By introducing a stochastic variable which satisfies Bernoulli distribution, the information of probabilistic time-varying delay is equivalently transformed into the deterministic time-varying delay with stochastic parameters. The main objective of this paper is to design a memoryless state feedback control such that the resulting proposed system is robustly finite time stable with admissible uncertainties. Based on a suitable Lyapunov–Krasovskii functional, model transformation technique and Wirtinger-based double integral inequality, the general framework is obtained in terms of linear matrix inequalities to determine the finite time stability and to achieve the control design. Finally, three numerical examples are presented to validate the effectiveness and less conservatism of the proposed method.

Finite-time stabilization of uncertain neural networks with distributed time-varying delays

In this paper, the problem of finite-time stabilization for a class of uncertain neural networks with distributed time-varying delays is investigated. Based on the Lyapunov stability theory and integral inequality technique, some sufficient LMI conditions are derived to ensure the finite-time stability of considered neural networks. In addition, the upper bound of the settling time for stabilization is estimated. Numerical simulations are carried out to demonstrate the effectiveness of the obtained results.

Delay-partitioning approach design for stochastic stability analysis of uncertain neutral-type neural networks with Markovian jumping parameters

This paper investigates the problem of stability analysis for uncertain neutral-type neural networks with Markovian jumping parameters and interval time-varying delays. By separating the delay interval into multiple subintervals, a Lyapunov–Krasovskii methodology is established, which contains triple and quadruple integrals. The time-varying delay is considered to locate into any subintervals, which is different from existing delay-partitioning methods. Based on the proposed delay-partitioning approach, a stability criterion is derived to reduce the conservatism. Numerical examples show the effectiveness of the proposed methods.

Global exponential stability of uncertain neural networks with discontinuous Lurie-type activation and mixed delays

This paper deals with the problem of the global exponential stability of a class of uncertain neural networks with discontinuous Lurie-type activation and mixed delays. By establishing a new sufficient condition, we first prove the existence of the equilibrium point by using the Leray–Schauder alternative theorem. Then, by employing a new Lyapunov functional, we obtain the global exponential stability of the equilibrium point of the uncertain neural network. In the end, some comparisons and numerical examples are given to show the improvement of the conclusions in this paper.

Stability analysis of reaction-diffusion uncertain memristive neural networks with time-varying delays and leakage term

In this paper, the stability problem is investigated for a class of reaction-diffusion uncertain memristive neural networks with time-varying delays and leakage term. To investigate the dynamic behavior of the memristive system, we turn to the qualitative analysis of a relevant differential inclusion under the framework of Filippov’s solution, which is easier to handle. By using Lyapunov stability theory, Jensen integral inequality, Schur complement Lemma, free-weighting matrix approach together with the linear matrix inequality (LMI) approach, the sufficient conditions are derived to ensure the stability of the considered systems. The easy-to-test stability criteria established in this paper depend on the leakage delay as well as the reaction-diffusion terms, which is more reasonable. Moreover, the existing stability criteria can be treated as a special case of this paper. Finally, two numerical examples are exploited to show the effectiveness of the derived LMI-based stability conditions.

Robust adaptive lag synchronization of uncertain fuzzy memristive neural networks with time-varying delays

This paper investigates the problem of robust adaptive lag synchronization of uncertain fuzzy memristive neural networks with time-varying delays. The memristive neural networks combining fuzzy model with uncertain parameters are described at length. Based on the Lyapunov functional method and novel update laws for parameter uncertainties and controller gain, some sufficient conditions which guarantee the slave systems robust adaptive lag synchronized with the master systems are obtained. Finally, two simulated examples are presented to show the effectiveness and applications of the obtained results.

Novel Robust Exponential Stability of Markovian Jumping Impulsive Delayed Neural Networks of Neutral-Type with Stochastic Perturbation

The robust exponential stability problem for a class of uncertain impulsive stochastic neural networks of neutral-type with Markovian parameters and mixed time-varying delays is investigated. By constructing a proper exponential-type Lyapunov-Krasovskii functional and employing Jensen integral inequality, free-weight matrix method, some novel delay-dependent stability criteria that ensure the robust exponential stability in mean square of the trivial solution of the considered networks are established in the form of linear matrix inequalities (LMIs). The proposed results do not require the derivatives of discrete and distributed time-varying delays to be 0 or smaller than 1. Moreover, the main contribution of the proposed approach compared with related methods lies in the use of three types of impulses. Finally, two numerical examples are worked out to verify the effectiveness and less conservativeness of our theoretical results over existing literature.

Robust stabilization of uncertain neural networks with additive time-varying delays∗∗This work was supported by SERB project DST, New Delhi, India under the F. No: YSS/2014/000447 dated 20.11.2015.

Abstract This study is mainly concerned with the problem of robust stabilization of neural networks with two additive time-varying delays via Wirtinger-based double integral inequality. The main purpose of this paper is to design a memoryless state feedback controller which ensuring that the global asymptotic stability of closed loop system. By constructing a suitable Lyapunov-Krosovskii functionals, utilizing Wirtinger-based double integral inequality, the sufficient criteria are derived in terms of linear matrix inequalities technique which ensuring the global asymptotic stability of the proposed neural networks with norm bounded uncertainties. The desired controllers can be calculated by solving the linear matrix inequalities with the help of some standard numerical packages. Finally, the numerical examples are given to demonstrate the effectiveness of the theoretical results.

Delay-range-dependent passivity analysis for uncertain stochastic neural networks with discrete and distributed time-varying delays

The purpose of this paper is to investigate the problem of passivity analysis for delayed uncertain stochastic neural networks (DUSNNs) with discrete and distributed time-varying delays. The novelty of this paper lies in the consideration of a new integral inequality proved to be less conservatism than celebrated Jensen׳s inequality and takes fully the relationship between the terms in the Leibniz–Newton formula within the framework of linear matrix inequalities (LMIs). By constructing a suitable Lyapunov–Krasovskii functional with triple integral terms and using Jensen׳s inequality, integral inequality technique and linear matrix inequality frame work, which guarantees stability for the passivity of addressed neural networks. This LMI can be easily solved via convex optimization techniques. Using several examples from the literature, it is shown that the proposed stabilization theorem is less conservative than previous results. Finally, the technique is applied to benchmark problem, showing how to derive efficient stability criteria for realistic problems, using the proposed technique.

The hybrid uncertain neural network method for mechanical reliability analysis

Concerning the issue of high-dimensions, hybrid uncertainties of randomness and intervals including implicit and highly nonlinear limit state function, reliability analysis based on the hybrid uncertainty reliability mode combining with back propagation neural network (HU-BP neural network) is proposed in this paper. Random variables and interval variables are as input layer of the neural network, after the training and approximation of the neural network, the response variables are obtained through the output layer. Reliability index is calculated by solving the optimization model of the most probable point (MPP) searching in the limit state band. Two numerical cases are used to demonstrate the method proposed in this paper, and finally the method is employed to solving an engineering problem of the aerospace friction plate. For this high nonlinear, small failure probability problem with interval variables, this method could achieve a good analysis result.

Design of non-fragile state estimators for discrete time-delayed neural networks with parameter uncertainties

This paper is concerned with the problem of designing a non-fragile state estimator for a class of uncertain discrete-time neural networks with time-delays. The norm-bounded parameter uncertainties enter into all the system matrices, and the network output is of a general type that contains both linear and nonlinear parts. The additive variation of the estimator gain is taken into account that reflects the possible implementation error of the neuron state estimator. The aim of the addressed problem is to design a state estimator such that the estimation performance is non-fragile against the gain variations and also robust against the parameter uncertainties. Sufficient conditions are presented to guarantee the existence of the desired non-fragile state estimators by using the Lyapunov stability theory and the explicit expression of the desired estimators is given in terms of the solution to a linear matrix inequality. Finally, a numerical example is given to demonstrate the effectiveness of the proposed design approach.

Novel results on robust finite-time passivity for discrete-time delayed neural networks

This paper presents some novel results on robust finite-time passivity for a class of uncertain discrete-time neural networks (DNNs) with time varying delays. Using the Lyapunov theory together with the zero inequalities, convex combination and reciprocally convex combination approaches, we propose the sufficient conditions for finite-time boundedness and finite-time passivity of DNN for all admissible uncertainties. The results are achieved by using a new Lyapunov-Krasovskii functional (LKF) with novel triple summation terms, several delay-dependent criteria for the DNN are derived in terms of linear matrix inequalities (LMIs) which can be easily verified via the LMI toolbox. Finally, numerical example with simulation scheme have been presented to illustrate the applicability and usefulness of the obtained results.

Matrix measure based dissipativity analysis for inertial delayed uncertain neural networks

The present paper is devoted to investigating the global dissipativity for inertial neural networks with time-varying delays and parameter uncertainties. By virtue of a suitable substitution, the original system is transformed to the first order differential system. By means of matrix measure, generalized Halanay inequality, and matrix-norm inequality, several sufficient criteria for the global dissipativity of the addressed neural networks are proposed. Meanwhile, the specific estimations of positive invariant sets and globally attractive sets are obtained. Finally, two examples are provided to validate our theoretical results.

Adaptive Synchronization for a Class of Uncertain Fractional-Order Neural Networks

In this paper, synchronization for a class of uncertain fractional-order neural networks subject to external disturbances and disturbed system parameters is studied. Based on the fractional-order extension of the Lyapunov stability criterion, an adaptive synchronization controller is designed, and fractional-order adaptation law is proposed to update the controller parameter online. The proposed controller can guarantee that the synchronization errors between two uncertain fractional-order neural networks converge to zero asymptotically. By using some proposed lemmas, the quadratic Lyapunov functions are employed in the stability analysis. Finally, numerical simulations are presented to confirm the effectiveness of the proposed method.

New passivity criteria for memristive uncertain neural networks with leakage and time-varying delays

In this paper, the problem of passivity analysis is studied for memristor-based uncertain neural networks with leakage and time-varying delays. By combining differential inclusions with set-valued maps, the system of memristive neural networks is changed into the conventional one. By adding a triple quadratic integral and relaxing the requirement for the positive definiteness of some matrices, a proper Lyapunov–Krasovskii functional is constructed. Based on the establishment of the novel Lyapunov–Krasovskii functional, the new passivity criteria are derived by mainly applying Wirtinger-based double integral inequality, S-procedure and so on. Moreover, the conservatism of passivity conditions can be reduced. Finally, four numerical examples are given to show the effectiveness and less conservatism of the proposed criteria.

Passivity analysis of uncertain stochastic neural networks with time-varying delays and Markovian jumping parameters

This paper investigates the problem of robust passivity of uncertain stochastic neural networks with time-varying delays and Markovian jumping parameters. To reflect most of the dynamical behaviors of the system, both parameter uncertainties and stochastic disturbances are considered; stochastic disturbances are given in the form of a Brownian motion. By utilizing the Lyapunov functional method, the Itô differential rule, and matrix analysis techniques, we establish a sufficient criterion such that, for all admissible parameter uncertainties and stochastic disturbances, the stochastic neural network is robustly passive in the sense of expectation. A delay-dependent stability condition is formulated, in which the restriction of the derivative of the time-varying delay should be less than 1 is removed. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.

Stability and passivity analysis for uncertain discrete-time neural networks with time-varying delay

In this paper, the problem of stability and passivity analysis for uncertain discrete-time neural networks with time-varying delay is investigated. By constructing a new Lyapunov–Krasovskii functional and employing a novel summation inequality which is a discrete-time counterpart of the Wirtinger-based integral inequality, a less conservative robust stability criterion is derived in terms of linear matrix inequalities. Furthermore, a new sufficient condition is established to assure the considered neural networks to be passive. Several numerical examples are provided to demonstrate the effectiveness of the proposed method.