Noise further expresses exponential decay for globally exponentially stable time-varying delayed neural networks

Robust exponential stability of discrete-time uncertain impulsive stochastic neural networks with delayed impulses

This paper is devoted to the study of the robust exponential stability (RES) of discrete-time uncertain impulsive stochastic neural networks (DTUISNNs) with delayed impulses. Using Lyapunov function methods and Razumikhin techniques, a number of sufficient conditions for mean square (RES-ms) robust exponential stability are derived. The obtained results show that the hybrid dynamic is RES-ms with regard to lower boundary of impulse interval if the discrete-time stochastic neural networks (DTSNNs) is RES-ms and that the impulsive effects are instable. Conversely, if DTSNNs is not RES-ms, impulsive effects can induce unstable neural networks (NNs) to stabilize again concerning an upper bound of the impulsive interval. The results obtained in this study have a broader scope of application than some previously existing findings. Two numerical examples were presented to verify the availability and advantages of the results.

Polynomial Noises for Nonlinear Systems with Nonlinear Impulses and Time-Varying Delays

It is known that random noises have a significant impact on differential systems. Recently, the influences of random noises for impulsive systems have been started. Nevertheless, the existing references on this issue ignore the significant phenomena of nonlinear impulses and time-varying delays. Therefore, we see the necessity to study the influences of random noises for impulsive systems with the above two factors. Stimulated by the above, a polynomial random noise is introduced to suppress the potential explosive behavior of the nonlinear impulsive differential system with time-varying delay. Fortunately, the stochastically controlled impulsive delay differential system admits a unique global solution, is bounded, and grows at most in the polynomial form.

MultiStep Ahead Forecasting for Hourly PM10 and PM2.5 Based on Two-Stage Decomposition Embedded Sample Entropy and Group Teacher Optimization Algorithm

The randomness, nonstationarity and irregularity of air pollutant data bring difficulties to forecasting. To improve the forecast accuracy, we propose a novel hybrid approach based on two-stage decomposition embedded sample entropy, group teaching optimization algorithm (GTOA), and extreme learning machine (ELM) to forecast the concentration of particulate matter (PM10 and PM2.5). First, the improvement complementary ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is employed to decompose the concentration data of PM10 and PM2.5 into a set of intrinsic mode functions (IMFs) with different frequencies. In addition, wavelet transform (WT) is utilized to decompose the IMFs with high frequency based on sample entropy values. Then the GTOA algorithm is used to optimize ELM. Furthermore, the GTOA-ELM is utilized to predict all the subseries. The final forecast result is obtained by ensemble of the forecast results of all subseries. To further prove the predictable performance of the hybrid approach on air pollutants, the hourly concentration data of PM2.5 and PM10 are used to make one-step-, two-step- and three-step-ahead predictions. The empirical results demonstrate that the hybrid ICEEMDAN-WT-GTOA-ELM approach has superior forecasting performance and stability over other methods. This novel method also provides an effective and efficient approach to make predictions for nonlinear, nonstationary and irregular data.

Closed-loop control of nonlinear neural networks: The estimate of control time and energy cost

This paper concentrates on an estimate of the upper bounds for control time and energy cost of a class of nonlinear neural networks (NNs). By constructing the appropriate closed-loop controller u^S and utilizing the inequality technique, sufficient conditions are proposed to guarantee achieving control target in finite time of the considered systems. Then, the estimate of the upper bounds for the control energy cost of the designed controller u^S is proposed. Our results provide a new controller which can ensure the realization of finite time control and energy consumption control for a class of nonlinear NNs. Meanwhile, the obtained results contribute to qualitative analysis of some nonlinear systems. Finally, numerical examples are presented to demonstrate the effectiveness of our theoretical results.

Synchronization stability of memristor-based complex-valued neural networks with time delays

This paper focuses on the dynamical property of a class of memristor-based complex-valued neural networks (MCVNNs) with time delays. By constructing the appropriate Lyapunov functional and utilizing the inequality technique, sufficient conditions are proposed to guarantee exponential synchronization of the coupled systems based on drive-response concept. The proposed results are very easy to verify, and they also extend some previous related works on memristor-based real-valued neural networks. Meanwhile, the obtained sufficient conditions of this paper may be conducive to qualitative analysis of some complex-valued nonlinear delayed systems. A numerical example is given to demonstrate the effectiveness of our theoretical results.