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.

Prescribed-time consensus tracking for second-order nonlinear multiagent systems (MASs) with the unknown nonlinear dynamics satisfying a time-varying Lipschitz growth rate is investigated in this article. A time-varying function is introduced as a part of the controller gains, and it plays an important role in overcoming the rapid growth of nonlinear terms and in ensuring that the consensus can be achieved in a preassigned time. An integral sliding-mode control protocol, which forces the system trajectory to move on to the defined sliding manifold at the initial moment, is proposed for solving the prescribed-time consensus tracking problem of leader-following MASs with disturbances. Furthermore, we propose a slightly different control law based on terminal sliding-mode control, and under such a controller, the trajectories of each follower reach the sliding manifold in an arbitrary assigned time$T_{1}$, and then in a specified time$T_{2}$, the position and velocity tracking errors for all followers converge to 0 at the same time instant. Based on the graph theory, state transformations, and Lyapunov theorem, we prove that the proposed solutions are feasible and, finally, three simulation examples are provided to verify the theoretical results.

This article focuses on the finite-time and prescribed-time cluster synchronization problems of switched complex networks with proportional delays. Considering that the matched controller often switches behind the switched systems, asynchronous switching law and switching parameters have been introduced to the complex dynamical networks. By applying the stability theory of dynamical systems and the average dwell time approach, some sufficient criteria in form of linear matrix inequalities have been developed to guarantee such networks finite/prescribed-time cluster synchronization under the pinning control scheme. Finally, one numerical example is presented to show the effectiveness of the theoretical results.

Cluster synchronization means that all multiagents are divided into different clusters according to the equations or roles of nodes in a complex network, and by designing an appropriate algorithm, each cluster can achieve synchronization to a certain value or an isolated node. However, the synchronization values between different clusters are different. With a feedback controller based on the calculation of the control input value and a trigger condition leading to the updating instants, this article introduces the trigger mechanism and designs a new data sampling strategy to achieve cluster synchronization of the coupled neural networks (CNNs), which reduces the number of updates of the controller, thereby reducing unnecessary waste of limited resources. In addition, an example proposes a synchronization algorithm and gives iterative procedures to calculate the trigger instants and prove the validity of the theoretical results.

In this article, the cluster synchronization problem for a class of the nonlinearly coupled delayed neural networks (NNs) in both finite- and fixed-time cases are investigated. Based on the Lyapunov stability theory and pinning control strategy, some criteria are provided to ensure the cluster synchronization of the nonlinearly coupled delayed NNs in both finite-and fixed-time aspects. Then, the settling time for stabilization that is dependent on the initial value and independent of the initial value is estimated, respectively. Finally, we illustrate the feasibility and practicality of the results via a numerical example.

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.

This paper discusses the problem of adaptive exponential synchronization in mean square for a new neural network model with the following features: 1) the noise is characterized by the Lévy process and the parameters of the model change in line with the Markovian process; 2) the master system is also disturbed by the same Lévy noise; and 3) there are multiple slave systems, and the state matrix of each slave system is an affine function of the state matrices of all slave systems. Based on the Lyapunov functional theory, the generalized Itô's formula, -matrix method, and the adaptive control technique, some criteria are established to ensure the adaptive exponential synchronization in the mean square of the master system and each slave system. Moreover, the update law of the control gain and the dynamic variation of the parameters of the slave systems are provided. Finally, the effectiveness of the synchronization criteria proposed in this paper is verified by a practical example.

In this paper, the problem of adaptive synchronization is investigated for stochastic neural networks of neutral-type with Markovian switching parameters. Using the M-matrix approach and the stochastic analysis method, some sufficient conditions are obtained to ensure three kinds of adaptive synchronization for the stochastic neutral-type neural networks. These three kinds of adaptive synchronization include the almost sure asymptotical synchronization, exponential synchronization in p th moment and almost sure exponential synchronization. Some numerical examples are provided to illustrate the effectiveness and potential of the proposed design 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.

This brief investigates the problem of global exponential stability analysis for discrete recurrent neural networks with time-varying delays. In terms of linear matrix inequality (LMI) approach, a novel delay-dependent stability criterion is established for the considered recurrent neural networks via a new Lyapunov function. The obtained condition has less conservativeness and less number of variables than the existing ones. Numerical example is given to demonstrate the effectiveness of the proposed method.

In this paper, the design problem of /spl alpha/-robust H/sub /spl infin// state feedback controller for a class of linear parameter-varying (LPV) systems with time-delay is addressed. A sufficient condition for the existence of /spl alpha/-robust H/sub /spl infin//m state feedback controller is derived in terms of a new method and the corresponding design method of the controller is given. Furthermore, illustrative example is given to demonstrate the superiority of the presented method.

In this paper, the new absolute stability and stabilization conditions for a class of Lurie uncertain time-delay systems are proposed. Based on Lyapunov functions combined with linear matrix inequality (LMI) technology, the sufficient delay dependent absolute stability and stabilization conditions are derived for a class of Lurie uncertain time-delay systems with time-delay feedback either in states or nonlinear part through introducing a new state transformation. Finally, the absolute stability and stabilization conditions are illustrated by the detailed examples, and the result shows that there has been a distinct amelioration in conservation.

In this paper, the concepts of L-semi-regular set and L-semi-regular compactness are introduced whose characterizations by net, filter, and L-semi-regularization are obtained and who are many interesting properties are studied.