In this article, we investigate a Euclidean-distance-based distributed constrained optimal formation matching (EDCOFM) problem for open large-scale multiagent systems (OLSMASs), where the number of agents is large and variable. To address the open property of the multiagent system, we introduce the concept of a depository, which can provide additional agents or store redundant agents. When the number of agents is sufficient to achieve the formation configuration, a distributed formation matching algorithm for a large-scale multiagent system (DFMA-LSMAS) is proposed to search for the optimal location of the formation configuration within a designed constraint and the optimal matching relationship. Notably, the framework is applicable to open multiagent systems. When the number of agents is smaller than the requirement to achieve the formation configuration, and more than one agent needs to be provided from the depository, an unmatched phenomenon occurs, which results in the failure of the proposed algorithm. To address this, a disturbance-based approach is proposed to eliminate the phenomenon without impacting the optimal solution. When the number of agents is larger than the requirement to achieve the formation configuration, and some agents have to leave the system, a fair competition mechanism is proposed to selectthe remainder and their optimal matching relationship. This mechanism avoids multiple competitions in a centralized manner. Finally, several simulation results are provided to verify the proposed algorithms.

When employing evolutionary algorithms (EAs) to solve multimodal optimization problems (MMOPs), effectively utilizing diversity information is crucial to prevent the population from converging to a single peak. This requires balancing diversity and objective value—a challenge that inherently constitutes a penalty problem. Although some implicit penalty methods have been proposed to address this issue, most lack flexibility in penalty formulation. In this study, we present a novel explicit penalty method (EPM) designed to effectively leverage diversity information for multimodal optimization. First, the diversity of a solution is quantified by its distance to the nearest neighbor with a better objective value. Then, an explicit penalty function is formulated by integrating diversity and objective value. This function facilitates the capture of multiple peaks and balances the search among them. If a reasonable number of peaks are identified, a local search is applied to each for refinement; otherwise, a global search is conducted across the decision space. Through this adaptive process, EPM locates multiple optima both efficiently and accurately. Extensive experiments demonstrate that EPM outperforms several multimodal optimization methods, including 11 popular approaches, eight recent state-of-the-art algorithms, and an IEEE CEC competition winner. Moreover, even when integrated with classic differential evolution (DE), EPM exhibits highly competitive performance.

This paper addresses the problem of quasi-synchronization for a class of heterogeneous fractional-order dynamical networks with time-varying couplings. Our proposed approach, called delay-dependent hybrid impulsive control, considers the network’s topology and utilizes Lyapunov functions for synchronization analysis. We employ a graph-theoretic method to construct these Lyapunov functions, including a novel time-varying graph-theoretic Lyapunov function (TGLF) that changes with the network’s structure and state variables. However, applying fractional derivatives to the TGLF poses challenges, as the general Leibniz formula and chain rule do not apply. To overcome this obstacle, we establish a new fractional derivative rule for time-varying-coefficient convex functions. We also introduce a new lemma for a fractional-order delayed impulsive differential inequality to analyze the quasi-stability and instability of impulse-free systems. By combining the TGLF and the fractional-order delayed impulsive differential inequality, we derive criteria for quasi-synchronization and estimate the allowable error bounds. Finally, we provide numerical examples to demonstrate the effectiveness of our proposed approach.Note to Practitioners—Most quasi-synchronization results of complex dynamical networks are mainly supported by the traditional quadratic Lyapunov function or the graph-theoretic Lyapunov function. However, these functions are only effective for networks with fixed couplings, which limits the application scope of the Lyapunov method. Aiming at the case of time-varying couplings, this paper proposes a novel time-varying graph-theoretic Lyapunov function that changes with the network’s structure and state variables. By applying the new fractional derivative rule of this function, we shall obtain quasi-synchronization criteria of heterogeneous fractional-order complex dynamical networks with time-varying couplings by using delay-dependent hybrid impulsive control. To verify the application of theoretical results, a generalization of the fractional-order power system is provided, and we realize its quasi-synchronization theoretically and numerically.

Based on the hybrid-index model, this article investigates the asymptotic feedback set stabilization of Boolean control networks (BCNs) with random impulsive disturbances. In this model, it is assumed that the sequence of intervals between adjacent impulsive instants is independent and identically distributed. This assumption ensures that the subsequence of solutions sampled at impulsive moments is a Markov chain. Based on this assumption and the semi-tensor product (STP), random impulsive BCNs (RI-BCNs) can be converted into impulsive-interval driven probabilistic BCNs (ID-PBCNs), and the input-state transition probability matrix (IS-TPM) is constructed, the calculations of convergent target set in the hybrid domain and the time domain are discussed, and the necessary and sufficient conditions for asymptotic feedback set stabilizability are obtained. On this basis, we propose a design algorithm of state feedback controllers to stabilize RI-BCNs asymptotically with respect to a target set by using state-space partition, which enables the system to converge to a given set with the least number of impulsive intervals. Finally, the effectiveness of the obtained results is verified by simulations.

The phase information of the optical wave plays a vital role in processing wave-related signals. In deep learning fields, complex-valued neural networks are put forward on the concept of complex amplitudes for full utilization of phase information. To build a complex-valued neural network, the common way is to exploit Fourier Transform of the observed signal to extract amplitude and phase information. However, this will lead to spectrum waste for a real-valued signal by introducing negative frequencies that have no physical meaning. To this end, we attempt to use Hilbert Transform as an alternative to yield a single sideband spectrum and avoid negative frequencies from interacting with positive ones. On the other hand, Fourier transform is a global analysis thus it tells nothing about the time domain. As our key insight, we further explore the usage of instantaneous frequency calculated by Hilbert Transform and propose a new method of constructing complex input from a time–frequency angle. Simple pixel-wise classification experiments are carried out on two hyperspectral datasets and MNIST dataset. Experimental results have demonstrated that Hilbert Transform with instantaneous frequency performs better by a large margin than Fourier Transform owing to the additional time information.

In cognitive science, the bottleneck of information processing capabilities promotes humans to selectively focus on part of the visible information while ignoring the rest. This is usually called the attention mechanism. Among different attention mechanisms, spectrum attention focuses on assigning every frequency channel obtained by DCT an appropriate weight to achieve adaptive filtering and sends the reweighting frequency components into a real-valued neural network. However, DCT is a real-valued transformation for signal processing thus phase information tends to be omitted. Here we consider a departure from these conventions and propose a spectrum attention complex neural network assisted by DFT, to make a holistic frequency analysis in a completely complex domain. Our proposed network demonstrates outstanding performance on a one-dimensional hyperspectral dataset and MNIST dataset, compared to both traditional complex neural networks and DCT based frequency attention methods.

The issue of finite-time synchronization (FTS) of complex dynamical networks (CDNs) is investigated in this article. A new control strategy coupling weak finite-time control and finite times of impulsive control is proposed to realize the FTS of CDNs, where the impulses are synchronizing and restricted by maximal impulsive interval (MII), differing from the existing results. In this framework, several global and local FTS criteria are established by using the concept of impulsive degree. The times of impulsive control in the controllers and the settling time, which are all dependent on initial values, are derived optimally. A technical lemma is developed, reflecting the core idea of this article. A simulation example is given to demonstrate the main results finally.

This article presents a self-triggered impulsive framework for group consensus of multiagent systems (MASs). Two types of self-triggered delayed impulsive control schemes are proposed to regulate impulsive protocols with sensing and actuation delays, respectively. Here, the Lyapunov-based and comparison-system-based approaches are constructed to achieve the iterative updates of impulse sequences with flexibility, especially the upper bound or average interval of impulsive periods is not restricted explicitly. In addition, several sufficient criteria for multigroup consensus of MASs with sensing and actuation delays are presented, where the correlation inequalities between trigger parameters, time delays, and control strengths are established to promote the co-design of impulsive controller and self-triggering algorithm. The Zeno behavior could be successfully eliminated. It is shown that the presented self-triggered schemes do not necessitate continuous or periodic event-detections and the interaction for neighboring agents works in an impulsive manner, which significantly saves the resource consumption of communication and control. Finally, two numerical examples illustrate the effectiveness of the proposed schemes.

This article investigates the problem of exponential bipartite synchronization of fractional-order multilayer signed networks via hybrid impulsive control. First, the mathematical model of the networks is established by integrating the fractional dynamics of nodes, the multilayer network edges, and the positive and negative weights (antagonistic relationship), which is more pluralistic and practical. Second, a hybrid impulsive controller is designed, which is composed of the feedback control part and the impulsive control part to realize the exponential bipartite synchronization objective. Both positive and negative impulsive effects are considered and the ranges of the impulsive control gain related to the order of Caputo fractional derivative are discussed. In addition, some sufficient conditions for exponential bipartite synchronization of fractional-order multilayer signed networks are obtained by using the signed graph theory, Lyapunov method, and average impulsive interval method. Furthermore, in order to illustrate the practicability of the theoretical results, fractional-order coupled Chua's circuits model and fractional-order power systems built on multilayer signed networks are established and the exponential bipartite synchronization issues are analyzed. Numerical examples and simulations are provided to show the effectiveness of the obtained results.

The article investigates the practical finite-time stability (PFTS) issue of continuous-time nonlinear systems with disturbance. Some extended Lyapunov results for semi-global/global PFTS, including attraction domain and settling time estimation are obtained based on a relaxed Lyapunov condition. Especially, for systems with stabilizing delayed impulses, a new scheme of delayed impulsive control involving a finite number of impulses is proposed to realize semi-global and/or global PFTS, where the minimum number of impulses can be explicitly designed in terms of initial states. Optimal delayed impulsive control design is provided in different situations to yield the minimum settling time estimation. Several numerical examples illustrate the validity of the obtained results finally.

This article investigates the hybrid event-triggered and impulsive consensus problems for leaderless and leader-following multiagent systems (MASs) with switching topologies. Based on the state information of neighboring agents at event-triggered moments and impulsive instants, a hybrid event-triggered and impulsive control strategy (HETICS) is designed to reduce the communication frequency between neighboring agents and to ensure consensus of leaderless and leader-following MASs. By utilizing the Lyapunov direct method, some consensus criteria are obtained for leaderless and leader-following MASs with switching topologies. It is shown that the HETICS excludes the Zeno behavior. Several numerical examples and simulations are given to illustrate the effectiveness of the proposed consensus strategy and a comparison with previous consensus control methods is given.

In this article, the sampled-data-based event-triggered synchronization control for fractional and impulsive complex networks (CNs) with time-varying delay is investigated and a class of more general network structure based on the switching topologies at impulsive instants is considered. First, a class of novel fractional-order integral inequalities is produced to obtain depend-delay synchronization criteria and estimate Lyapunov–Krasovskii functions. Then, a sampled-data-based event-triggered control is designed, which can ensure synchronization of fractional and impulsive CNs (FICNs) with time-varying delay. Next, by using the Lyapunov direct method, some criteria are obtained to guarantee the synchronization of FICNs. Numerical simulations are given to demonstrate that the designed sampled-data-based event-triggered synchronization strategy can effectively not only achieve synchronization of FICNs but reduce the frequency of controller update compared to the previous related works.

Recent IoT applications gradually adapt more complicated end systems with commodity software. Ensuring the runtime integrity of these software is a challenging task for the remote controller or cloud services. Popular enforcement is the runtime remote attestation which requires the end system (prover) to generate evidence for its runtime behavior and a remote trusted verifier to attest the evidence. Control-flow attestation is a kind of runtime attestation that provides diagnoses towards the remote control-flow hijacking at the prover. Most of these attestation approaches focus on small or embedded software. The recent advance to attesting complicated software depends on the source code and CFG traversing to measure the checkpoint-separated subpaths, which may be unavailable for commodity software and cause possible context missing between consecutive subpaths in the measurements.

This article studies the nonfragile sampled-data filtering problems for Takagi-Sugeno fuzzy systems with uncertainties and delays. By introducing two delay-product-type terms and other augmented terms, a novel Lyapunov-Krasovskii functional containing more detailed information of time delays is constructed. With the help of some new bounding inequalities, improved stability results for the addressed systems are established. Besides, a resilient sampled-data controller is devised with less cost. Furthermore, the efficiency of the obtained criteria is illustrated by a numerical example.

In this paper, the robust stabilization issues on uncertain system with H∞performance are investigated by applying impulsive time related control algorithm. A hybrid control scheme is novelly proposed using proportional impulsive plus integral mechanism. This impulse-time-dependent (ITD) feedback controller employs the proportional control action Kpat impulse instants for stabilizing. Then, intermittently the integral control strategy KI(t) is implemented between impulsive time intervals for improving the state convergence. Sufficient conditions are derived to ensure the closed-loop performance. In addition, a memory controller KDis introduced to tackle the stabilization problem of system with signal transmission delay. Furthermore, a distributed time-varying delay δk(t) is defined in the impulsive control-based system. Considering discrete and distributed time-varying delays concurrently, the ITD stability criteria are deduced to guarantee the H∞performance on uncertain system with exogenous disturbance. Numerical examples are conducted to show the expected stabilization and state convergence response with disturbance attenuation of this development.

The stability of delayed Markovian generalized neural networks is studied where the transition rates of the modes are partly unknown. The partly unknown transition rates generalize the traditional works that are with all known transition rates. Then, a Lyapunov-Krasovskii functional (LKF) with a delay-product-type (DPT) term is constructed. The DPT term is not only simple but also fully utilizes the information of time delay. Based on the new DPT LKF, stability criteria are presented, which are with lower computational complexity and less conservative. In the end, the validity and superiorities of the analytical results are verified by several examples.

This paper studies the problem of synchronization for a class of stochastic complex dynamical networks. It designs for the first time a distributed impulsive protocol based on pinning control that involves a constant signal transmission delay to tackle synchronization issues of such networks. Novel criteria on network synchronization are established by employing a time-dependent Lyapunov functional and a mathematical induction approach, where information on the state variables themselves and their neighbors is sufficiently utilized. Moreover, it is shown that the frequency of impulsive occurrence, impulsive input delays, stochastic perturbations, and the feedback control strength can significantly affect the synchronization performance. Numerical simulations are given to illustrate the effectiveness of the derived theoretical results.

This paper investigates the exponential synchronization of reaction-diffusion neural networks with time-varying delays subject to Dirichlet boundary conditions. A novel type of pinning impulsive controllers is proposed to synchronize the reaction-diffusion neural networks with time-varying delays. By applying the Lyapunov functional method, sufficient verifiable conditions are constructed for the exponential synchronization of delayed reaction-diffusion neural networks with large and small delay sizes. It is shown that synchronization can be realized by pinning impulsive control of a small portion of neurons of the network; the technique used in this paper is also applicable to reaction-diffusion networks with Neumann boundary conditions. Numerical examples are presented to demonstrate the effectiveness of the theoretical results.

In this paper, we investigate the synchronization of non-autonomous chaotic systems with time-varying delay via delayed feedback control. Using a combination of Riccati differential equation approach, Lyapunov-Krasovskii functional, inequality techniques, some new sufficient conditions for exponentially stability of the error system are formulated in form of a solution to the standard Riccati differential equation. The designed controller ensures that the synchronization of non-autonomous chaotic systems are proposed via delayed feedback control. Numerical simulations are presented to illustrate the effectiveness of these synchronization criteria.

TCP has been the dominant congestion control protocol in the Internet. Although it is well known that TCP combined with intermediate systems with active queue management (AQM) schemes can not guarantee asymptotical stability when the feedback delay or the link capacity is large, the asymptotical stability may not be necessary for network achieving good performance in terms of resource utilization, flow throughput and queueing delay. Practical bounds are important performance index for congestion control protocols and AQM schemes. How to derive practical bounds for realistic systems with heterogeneous flows, various delays and multiple bottlenecks is an important and challenging open issue. In this paper, we study the boundedness of generalized TCP and AQM systems considering the heterogeneity of flows and the impact of multiple bottlenecks. We derive the uniform bounds and uniform ultimate bounds of flow window size, which reveal how the system and flow parameters affect the system performance. Extensive simulation results have been given to verify the correctness of the bounds.

AIMD/RED (additive increase and multiplicative decrease/random early detection) systems with multiple- bottleneck links are becoming more and more common in the vast-scale Internet. In this paper, we develop a mathematical model of AIMD/RED systems with multiple bottlenecks and feedback delays, which can be brought into the frame of singularly perturbed systems. Stability properties of multiple- bottleneck systems are studied by applying the techniques for singularly perturbed systems. Delay-dependent LMI (Linear Matrix Inequalities) criteria for the stability of singularly perturbed AIMD/RED systems with multiple bottlenecks are obtained, and the existence of the sufficiently small parameters that guarantee the asymptotic stability of the system considered above is also demonstrated. Numerical results with Matlab and simulation results with NS-2 are given to validate the analytical results.

The Additive Increase and Multiplicative Decrease (AIMD) congestion control algorithm of TCP protocol deployed in the end systems and the Random Early Detection (RED) queue management scheme deployed in the intermediate systems contribute to Internet stability and integrity. Previous research based on the fluid-flow model analysis indicated that an AIMD/RED system may not be asymptotically stable when the feedback delays or the link capacity becomes large [3]. However, as long as the system operates near its desired equilibrium, small oscillations are acceptable and the network performance is still satisfactory. Deriving the bounds of these oscillations for the heterogeneous AIMD/RED system with time delays is non-trivial. In this paper, we study the practical stability of the AIMD/RED system with heterogeneous flows and feedback delays, and obtain theoretical bounds of the AIMD flow window size and the RED queue length, as functions of number of flows, link capacity, RED queue parameters, and AIMD parameters. Numerical results with Matlab and simulation results with NS-2 are given to validate the correctness of the theorems and demonstrate the tightness of the derived bounds. The analytical and simulation results provide important insights on which system parameters contribute to higher oscillations of the system and how to set system parameters to ensure system efficiency with bounded delay and loss.

This paper studies the problems of global exponential stability for impulsive high-order Hopfield-type neural networks (NNs) with time-varying delays. By employing the Lyapunov-Razumikhin technique, some criteria ensuring global exponential stability are derived. Our results are then used to obtain some sufficient conditions under which some NNs can be forced to converge by impulsive control. Numerical examples are also discussed to illustrate our results.

This correspondence is concerned with the robust stability for a class of impulsive switched systems under the LQ guaranteed cost control. Some results on robust stability for this class of impulsive switched systems are obtained. Sufficient conditions for the existence of a guaranteed cost control law are also given. Subject to these sufficient conditions, the closed-loop uncertain impulsive switched system under the guaranteed cost control law is robustly stable with a guaranteed cost value.

In this paper, we systematically study the stability of Additive Increase and Multiplicative Decrease (AIMD)/Random Early Detection (RED) system, considering heterogeneous flows and feedback delays. By applying the methods of Lyapunov functional and Lyapunov function with Lyapunov-Razumikhin condition to the fluid model of the generalized AIMD/RED system, we obtain sufficient conditions to guarantee local asymptotic stability of the system with heterogeneous feedback delays. Our study also reveals the relationship between the AIMD parameters and the average window size of competing AIMD flows. Consequently, the TCP-friendly condition is derived. Numerical results with Matlab and simulation results with NS-2 are given to validate the analytical results. The analysis and the stability conditions derived can be used as a guideline to set up the AIMD/RED system parameters in order to maintain network stability and integrity, and to enhance system performance.

This paper considers the problems of global exponential stability and exponential convergence rate for impulsive high-order Hopfield-type neural networks with time-varying delays. By using the method of Lyapunov functions, some sufficient conditions for ensuring global exponential stability of these networks are derived, and the estimated exponential convergence rate is also obtained. As an illustration, an numerical example is worked out using the results obtained.