Global Mittag–Leffler projective synchronization of nonidentical fractional-order neural networks with delay via sliding mode control

Artificial neural networks: a practical review of applications involving fractional calculus

In this work, a bibliographic analysis on artificial neural networks (ANNs) using fractional calculus (FC) theory has been developed to summarize the main features and applications of the ANNs. ANN is a mathematical modeling tool used in several sciences and engineering fields. FC has been mainly applied on ANNs with three different objectives, such as systems stabilization, systems synchronization, and parameters training, using optimization algorithms. FC and some control strategies have been satisfactorily employed to attain the synchronization and stabilization of ANNs. To show this fact, in this manuscript are summarized, the architecture of the systems, the control strategies, and the fractional derivatives used in each research work, also, the achieved goals are presented. Regarding the parameters training using optimization algorithms issue, in this manuscript, the systems types, the fractional derivatives involved, and the optimization algorithm employed to train the ANN parameters are also presented. In most of the works found in the literature where ANNs and FC are involved, the authors focused on controlling the systems using synchronization and stabilization. Furthermore, recent applications of ANNs with FC in several fields such as medicine, cryptographic, image processing, robotic are reviewed in detail in this manuscript. Works with applications, such as chaos analysis, functions approximation, heat transfer process, periodicity, and dissipativity, also were included. Almost to the end of the paper, several future research topics arising on ANNs involved with FC are recommended to the researchers community. From the bibliographic review, we concluded that the Caputo derivative is the most utilized derivative for solving problems with ANNs because its initial values take the same form as the differential equations of integer-order.

Synchronization of discrete fractional-order complex networks with and without unknown topology

This paper studies the outer synchronization problem of discrete fractional complex networks (DFCNs) with and without the presence of unknown topology. A discrete complex network with a fractional difference is first established and analyzed. By constructing a suitable Lyapunov function and utilizing properties of the fractional difference, outer synchronization criteria for the DFCNs with and without unknown topology are established based on linear matrix inequalities. Meanwhile, the unknown parameters in the topology structure of the network can be identified by adaptive update laws. In the end, two numerical examples are given to exemplify the validity and applicability of the obtained results.

A dynamic general type-2 fuzzy system with optimized secondary membership for online frequency regulation

This study suggests a new control system for frequency regulation in AC microgrids. Unlike to the most studies, challenging conditions such as variation of wind speed, multiple load disturbance, unknown dynamics and variable solar radiation are taken to account. To cope with uncertainties, a novel dynamic general type-2 (GT2) fuzzy logic system (FLS) by an optimized secondary membership is suggested. The secondary membership and rule parameters of dynamic GT2-FLS are online tuned through the adaptive optimization rules. The optimization rules are determined such that the robustness and stability to be guaranteed. Also, a new compensator is presented to tackle with estimation error and perturbations. The simulations verify that schemed controller outperforms than conventional methods.

Synchronization in finite time for variable-order fractional complex dynamic networks with multi-weights and discontinuous nodes based on sliding mode control strategy

This paper is concerned with the global synchronization in finite time for variable-order fractional complex dynamic networks with multi-weights, where the dynamic nodes are modeled to be discontinuous, and subject to the local Hölder nonlinear growth in a neighborhood of continuous points. Firstly, an inequality with respect to variable-order fractional derivative for convex functions is proposed. On the basis of the proposed inequality, a global convergence principle in finite time for absolutely continuous functions is developed. Secondly, based on proposed convergence principle in finite time, a new sliding mode surface is presented, and an appropriate sliding mode control law is designed to drive the trajectory of the error system to the prescribed sliding mode surface in finite time and remain on it forever. In addition, on the basis of differential inclusions theory and Lur'e Postnikov-type convex Lyapunov function approach, the sufficient conditions with respect to the global stability in finite time are established in terms of linear matrix inequalities for the error system on designed sliding mode surface. Moreover, the upper bound of the settling time is explicitly evaluated. Finally, the effectiveness and correction of synchronization strategies are illustrated through two simulation experiments.