Robust Stability of Recurrent Neural Networks With Time-Varying Delays and Input Perturbation

Mittag-Leffler stability and application of delayed fractional-order competitive neural networks

In the article, the Mittag-Leffler stability and application of delayed fractional-order competitive neural networks (FOCNNs) are developed. By virtue of the operator pair, the conditions of the coexistence of equilibrium points (EPs) are discussed and analyzed for delayed FOCNNs, in which the derived conditions of coexistence improve the existing results. In particular, these conditions are simplified in FOCNNs with stepped activations. Furthermore, the Mittag-Leffler stability of delayed FOCNNs is established by using the principle of comparison, which enriches the methodologies of fractional-order neural networks. The results on the obtained stability can be used to design the horizontal line detection of images, which improves the practicability of image detection results. Two simulations are displayed to validate the superiority of the obtained results.

Unified analysis on multistablity of fraction-order multidimensional-valued memristive neural networks

This article provides a unified analysis of the multistability of fraction-order multidimensional-valued memristive neural networks (FOMVMNNs) with unbounded time-varying delays. Firstly, based on the knowledge of fractional differentiation and memristors, a unified model is established. This model is a unified form of real-valued, complex-valued, and quaternion-valued systems. Then, based on a unified method, the number of equilibrium points for FOMVMNNs is discussed. The sufficient conditions for determining the number of equilibrium points have been obtained. By using 1-norm to construct Lyapunov functions, the unified criteria for multistability of FOMVMNNs are obtained, these criteria are less conservative and easier to verify. Moreover, the attraction basins of the stable equilibrium points are estimated. Finally, two numerical simulation examples are provided to verify the correctness of the results.

Neuroadaptive Fault-Tolerant Control Embedded With Diversified Activating Functions With Application to Auto-Driving Vehicles Under Fading Actuation

This article presents a neuroadaptive fault-tolerant control method for path tracking of multiinput multioutput (MIMO) systems in the presence of modeling uncertainties and external disturbances. In dealing with modeling uncertainties, neural networks (NNs) with diversified activation/basis functions are considered, with which we establish a set of control algorithms that are robust against uncertainties, adaptive to unknown parameters, and tolerant to actuation faults. This is the first work that explicitly takes into account the neural weights uncertainties and activating function uncertainties in multiple layered neural networks in control design. In addition, we apply the developed control algorithms to unmanned ground vehicles (UGVs) with actuator failures. With the aid of Lyapunov stability theory, it is shown that the proposed control is able to drive the vehicle along the desired path with high precision and all the internal signals are uniformly ultimately bounded (UUB) and continuous. Both theoretical analysis and numerical simulation confirm the effectiveness of the designed strategy.

Multistability and Stabilization of Fractional-Order Competitive Neural Networks With Unbounded Time-Varying Delays

This article investigates the multistability and stabilization of fractional-order competitive neural networks (FOCNNs) with unbounded time-varying delays. By utilizing the monotone operator, several sufficient conditions of the coexistence of equilibrium points (EPs) are obtained for FOCNNs with concave-convex activation functions. And then, the multiple μ -stability of delayed FOCNNs is derived by the analytical method. Meanwhile, several comparisons with existing work are shown, which implies that the derived results cover the inverse-power stability and Mittag-Leffler stability as special cases. Moreover, the criteria on the stabilization of FOCNNs with uncertainty are established by designing a controller. Compared with the results of fractional-order neural networks, the obtained results in this article enrich and improve the previous results. Finally, three numerical examples are provided to show the effectiveness of the presented results.