Novel Switching Jumps Dependent Exponential Synchronization Criteria for Memristor-Based Neural Networks

Exponential State Estimation for Stochastically Disturbed Discrete-Time Memristive Neural Networks: Multiobjective Approach

The state estimation of the discrete-time memristive model is studied in this article. By applying the stochastic analysis technique, sufficient formulas are established to ensure the exponentially mean-square stability of the error model. Moreover, the derived control gain matrix can be calculated via the linear matrix inequality (LMI). It should be mentioned that, by extending the derived conclusion to a multiobjective optimization problem, the maximum bound of the active function and the minimum bound of the disturbance attenuation are derived. The corresponding simulation figures are provided in the end.

New Criteria on Global Stabilization of Delayed Memristive Neural Networks With Inertial Item

In this paper, we are concerned with global stabilization for a kind of delayed memristive neural network with an inertial term. By building a new Lyapunov functional and designing a feedback controller, we obtain some new results on global stabilization of the addressed delayed memristive inertial neural networks (MINNs). An adaptive control strategy is also designed to realize the global stabilization. Compared with the reduced-order method used in the existing literature, we consider the stabilization directly from the MINNs themselves without a reduced-order method. In addition, the new results proposed here are shown as algebraic criteria, which are easy to test. At last, some simulations are given to show the validity of the derived criteria.

Quasi-Synchronization of Delayed Memristive Neural Networks via Region-Partitioning-Dependent Intermittent Control

This paper aims at investigating the master-slave quasi-synchronization of delayed memristive neural networks (MNNs) by proposing a region-partitioning-dependent intermittent control. The proposed method is described by three partitions of non-negative real region and an auxiliary positive definite function. Whether the control input is imposed on the slave system or not is decided by the dynamical relationships among the three subregions and the auxiliary function. From these ingredients, several succinct criteria with the associated co-design procedure are presented such that the synchronization error converges to a predetermined level. The proposed intermittent control scheme is also applied to the event-triggered control, and an intermittent event-triggered mechanism is devised to investigate the quasi-synchronization of MNNs correspondingly. Such mechanism eliminates the events in rest time, and then it reduces the amount of samplings. Finally, two illustrative examples are presented to verify the effectiveness of our theoretical results.

Cluster Synchronization for Neutral Stochastic Delay Networks via Intermittent Adaptive Control

This paper studies the problem of cluster synchronization at exponential rates in both the mean square and almost sure senses for neutral stochastic coupled neural networks with time-varying delay via a periodically intermittent pinning adaptive control strategy. The network topology can be symmetric or asymmetric, with each network node being described by neutral stochastic delayed neural networks. When considering the exponential stabilization in the mean square sense for neutral stochastic delay system, the delay integral inequality approach is used to circumvent the obstacle arising from the coexistence of random disturbance, neutral item, and time-varying delay. The almost surely exponential stabilization is also analyzed with the nonnegative semimartingale convergence theorem. Sufficient criteria on cluster synchronization at exponential rates in both the mean square and almost sure senses of the underlying networks under the designed control scheme are derived. The effectiveness of the obtained theoretical results is illustrated by two examples.

Finite-Time Decentralized Control of IT2 T-S Fuzzy Interconnected Systems With Discontinuous Interconnections

This paper investigates the finite-time decentralized control problem for interconnected systems with discontinuous interconnections. By using the interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy model, a unified IT2 T-S fuzzy interconnected system is provided, in which the global system is described as a fuzzy blending of local subsystems under IF-THEN rules. In addition, based on the differential inclusion theory, the solutions of such discontinuous system are defined in the sense of Filippov. In order to stabilize the considered system in finite time, several decentralized discontinuous state feedback controllers are proposed. Furthermore, by the finite-time stabilization theory and generalized Lyapunov functional method, decentralized control is carried out and several sufficient criteria are derived to ensure the finite-time stabilization of the concerned system. Correspondingly, the settling times for stabilization are given. Finally, the proposed methodology is illustrated by an example.

Event-Based Synchronization Control for Memristive Neural Networks With Time-Varying Delay

In this paper, we investigate the global synchronization control problem for memristive neural networks (MNNs) with time-varying delay. A novel event-triggered controller is introduced with the linear diffusive term and discontinuous sign term. In order to greatly reduce the computation cost of the controller under certain event-triggering condition, two event-based control schemes are proposed with static event-triggering condition and dynamic event-triggering condition. Some sufficient conditions are derived by these control schemes to ensure the response MNN to be synchronized with the driving one. Furthermore, under certain event-triggering conditions, a positive lower bound is achieved for the interexecution time to guarantee that Zeno behavior cannot be executed. Finally, numerical simulations are provided to substantiate the effectiveness of the proposed theoretical results.

Hybrid Regularized Echo State Network for Multivariate Chaotic Time Series Prediction

Multivariate chaotic time series prediction is a hot research topic, the goal of which is to predict the future of the time series based on past observations. Echo state networks (ESNs) have recently been widely used in time series prediction, but there may be an ill-posed problem for a large number of unknown output weights. To solve this problem, we propose a hybrid regularized ESN, which employs a sparse regression with the L₁/2 regularization and the L₂ regularization to compute the output weights. The L₁/2 penalty shows many attractive properties, such as unbiasedness and sparsity. The L₂ penalty presents appealing ability on shrinking the amplitude of the output weights. After the output weights are calculated, the input weights, internal weights, and output weights are fine-tuning by a Hessian-free optimization method-conjugate gradient backpropagation algorithm. The fine-tuning helps to bubble up the input information toward the output layer. Besides, the largest Lyapunov exponent is used to calculate the predictable horizon of a chaotic time series. Experimental results on benchmark and real-world datasets show that our proposed method is superior to other ESN-based models, as sparser, smaller-absolute-value, and more informative output weights are obtained. All of the predictions within the predictable horizon of the proposed model are accurate.

Exponential Stabilization of Fuzzy Memristive Neural Networks With Hybrid Unbounded Time-Varying Delays

This paper is concerned with exponential stabilization for a class of Takagi-Sugeno fuzzy memristive neural networks (FMNNs) with unbounded discrete and distributed time-varying delays. Under the framework of Filippov solutions, algebraic criteria are established to guarantee exponential stabilization of the addressed FMNNs with hybrid unbounded time delays via designing a fuzzy state feedback controller by exploiting inequality techniques, calculus theorems, and theories of fuzzy sets. The obtained results in this paper enhance and generalize some existing ones. Meanwhile, a general theoretical framework is proposed to investigate the dynamical behaviors of various neural networks with mixed infinite time delays. Finally, two simulation examples are performed to illustrate the validity of the derived outcomes.

Reduced-Order Filtering of Delayed Static Neural Networks With Markovian Jumping Parameters

The reduced-order filtering problems are investigated in this paper for static neural networks with Markovian jumping parameters and mode-dependent time-varying delays. By fully making use of integral inequalities, the designs of reduced-order and filters are discussed. The proper gain matrices of filters and the optimal performance indices are efficiently obtained by resolving corresponding convex optimization problems with the constraints of linear matrix inequalities. It is verified that the computational complexity for the reduced-order filter design is significantly reduced when compared with the full-order one. Furthermore, the nonfragile reduced-order filtering problems are also resolved in this paper. Two examples with simulation results are presented to demonstrate the feasibility and application of the established results.

Event-Triggered Stabilization of Neural Networks With Time-Varying Switching Gains and Input Saturation

This paper investigates the event-triggered stabilization of neural networks (NNs) subject to input saturation. The main core lies in the design of a novel controller with time-varying switching gains and the associated switching event-triggered condition (ETC). The ETC is essentially a switching between the aperiodic sampling and continuous event trigger. The control gains of the designed controller are composed of an exponentially decaying term and two gain matrices. The two gain matrices are required to be switched when the switching between the aperiodic sampling and continuous event trigger is met. By employing the generalized sector condition and switching Lyapunov function, several sufficient conditions that ensure the local exponential stability of the NNs are formulated in terms of linear matrix inequalities (LMIs). Both the exponentially decaying term and switching gains improve the feasible region of LMIs, and then they are helpful to enlarge the set of admissible initial conditions, the threshold in ETC, and the average waiting time. Together with several optimization problems, two numerical examples are employed to validate the effectiveness of our results.