To evaluate the energy-saving effect of the controller, obtaining upper bounds on energy consumption and control time has become a worthwhile and meaningful issue to study. This article mainly discusses three contents about the Kuramoto oscillator network, including fixed-time synchronization (FxTS), prescribed-time synchronization (PTS), and energy consumption estimation. First, to reach FxTS, two sufficient conditions are proposed to guarantee that the Kuramoto oscillator network can reach fixed-time phase agreement and frequency synchronization. Unlike finite/fixed-time controllers, the prescribed-time controller in this article includes a time-varying function term, which is essential to ensure that the system achieves the prescribed-time phase agreement and frequency synchronization. At the same time, the setting-time for PTS is independent of the system initial values or controller parameters, which expands the application prospects of the system. Then, with limited setting-time as a premise, the energy consumed during the fixed/prescribed-time control process is obtained, which helps to evaluate the working time of the system. Finally, an example of a 5-node network is used to illustrate the effectiveness of FxTS and PTS in Kuramoto-oscillator networks.

With the popularity of the Internet of Things (IoT) and crowdsensing, sample data are more detailed and diverse. Users tend to avoid uploading personal data for privacy protection. Federated learning (FL) provides a new learning paradigm to complete training tasks without compromising user privacy. To deal with the challenge of malicious client attacks in FL systems, we present a robust framework for FL (RFFL) that can iteratively filter out malicious clients before federated aggregation, which results in defense capability against different types and levels of attacks. Then, we provide a convergence analysis of RFFL. Since client devices and edges distribute in different environments, which may cause client data heterogeneity, we offer an extension of RFFL (Ext. RFFL) to mitigate the effects of heterogeneity with no loss of defense capacity. Extensive experiments with real-world data sets demonstrate that our frameworks are competitive with benchmark algorithms in defending against various types and rates of attacks.

In this paper, the exponential stability in mean square for Markovian jumping systems (MJSs) is discussed. A new dynamic model, which involves parameters uncertainties, nonlinearities, and Lévy noises, is proposed. Moreover, an adaptive sliding mode controller is built to study the stability of such a complex model. First, an integral-type sliding mode surface (SMS) is established to obtain the sliding mode motion dynamics of MJSs. By the generalized Itô formula and the Lyapunov stability theory, some sufficient conditions are obtained to make sure the exponential stability in mean square for the sliding mode motion dynamics. Second, an adaptive sliding mode control law is provided to assure the reachability of the specified SMS. Furthermore, corresponding parameters of the sliding mode controller and the SMS can be got by solving the convex optimization problem. Finally, the validity of the stability results obtained is illustrated by a numerical simulation and a practical simulation.

This paper deals with two types of the stability problem for the delayed neural networks driven by fractional Brownian noise (FBN). The existence and the uniqueness of the solution to the main system with respect to FBN are proved via fixed point theory. Based on Hilbert-Schmidt operator theory and analytic semigroup principle, the mild solution of the stochastic neural networks is obtained. By applying the stochastic analytic technique and some well-known inequalities, the asymptotic stability criteria and the exponential stability condition are established. Both numerical example and practical application for synchronization control of multiagent system are provided to illustrate the effectiveness and potential of the proposed techniques.

In this brief, the analysis problem of the mode and delay-dependent adaptive exponential synchronization in th moment is considered for stochastic delayed neural networks with Markovian switching. By utilizing a new nonnegative function and the -matrix approach, several sufficient conditions to ensure the mode and delay-dependent adaptive exponential synchronization in th moment for stochastic delayed neural networks are derived. Via the adaptive feedback control techniques, some suitable parameters update laws are found. To illustrate the effectiveness of the -matrix-based synchronization conditions derived in this brief, a numerical example is provided finally.