This article addresses the time-varying distributed optimization problem (DOP) for networked multiagent systems (NMASs) operating over directed graphs, considering the impact of edge-based additive measurement noise (EBAMN). First, a finite-time stochastic stability framework is established to demonstrate the global stochastic practical finite-time attraction of the origin, enabling robust control design for stochastic nonlinear systems. The proposed method achieves faster convergence rates and provides bounded finite convergence time estimates, outperforming asymptotic methods. Second, a novel distributed optimization algorithm (DOA) is introduced, incorporating consensus-gain function, state-dependent optimization gains, and integral information of the gradient of local objective functions. Using the It $\mathrm {\hat {o}}$ lemma and Lyapunov theory, the continuous-time DOA guarantees the $p$ th moment convergence for all agents, ensures practical finite-time consensus in probability, and drives that states of NMASs converge to the time-varying optimal solution, even in the presence of EBAMN interferences. Furthermore, a new adaptive dynamic event-triggered mechanism (ETM) integrated with the DOA is proposed. This mechanism significantly enhances communication efficiency and reduces resource consumption throughout the process of tracking the optimal solution while preventing Zeno behavior. Finally, numerical simulations in multiuncrewed aerial vehicle (UAV) target tracking validate the effectiveness of the robust continuous-time DOA against random EBAMN.

This paper explores the observer-based event-triggered security control problem for linear systems. Initially, a distributed dynamic-memory event-triggered scheme (DMETS) is proposed based on observed system states. This scheme is designed using information from past transmitted data packages, with the flexibility to dynamically adjust the quantity of transmitted data packages. Subsequently, a comprehensive mathematical model of hybrid cyber-attacks is established, and an observer-based distributed feedback control approach is proposed by utilizing the memory states. Furthermore, the asymptotic stability criterion of system is established by using Lyapunov direct method, and the design approaches of controller and observer are provided. Finally, contrast illustrative examples are presented to validate the advantage of DMETS and the effectiveness of the distributed control method. Note to Practitioners—This paper is prompted by the challenges of excessive consumption of network resources and the need for enhanced security control in linear systems. The prevailing approach to addressing this issue involves designing appropriate data transmission schemes, specifically ETS. However, a common limitation among these existing ETSs is the inability to efficiently utilize past transmitted data or dynamically adjust the quantity of data utilized in response to changes in system states. To overcome this limitation, we propose a DMETS, which aims to integrate memory characteristics and facilitate dynamic adjustments in memory data quantities.

This paper investigates the dual-channel event-triggered quantitative load frequency control for discrete-time micro-grid system via a delay-square-dependent Lyapunov-Krasovskii functional approach. Firstly, a novel dual-channel dynamic event-triggered quantified control strategy has been proposed to enhance time-delay tolerance and the utilization of communication resources. Secondly, a discrete-time Lyapunov-Krasovskii functional incorporates the square of the delay is introduced to fully deploy the desired delay information about the system. Thirdly, improved stability criteria with strict dissipative performance indexes are established by employing the proposed delay-square-dependent Lyapunov-Krasovskii functional. Finally, two numerical examples are presented to illustrate the effectiveness and superiority of the proposed control strategy.Note to Practitioners—Micro-grid typically consist of distributed power resources, loads and energy storage devices, those are deployed spatially and remotely over some wireless and digital network mediums. The constrained resource issue, posed by finite bandwidth and processing capabilities of battery-powered system components. This paper aims at designing a reasonable control strategy to deal with issues such as band-limited channels and communication delays that undermine system stability in the process of network transmission. Specifically, we propose a dual-channel asynchronous dynamic event-triggered control strategy to save the limited channel bandwidth. To mitigate the impact of time delays, we comprehensively consider the state-dependent delays and control-related delays, further establishing a novel Lyapunov functional incorporating delay squared terms. The proposed control approach is validated to be capable of better reduce the consumption of bandwidth and achieve the desired stability through theoretical investigation and simulation cases.

This article presents a novel event-triggered sliding-mode control (ET-SMC) strategy for impulsive nonlinear systems (INS) in the presence of matched disturbances. Most of the existing sliding mode control (SMC) strategies work well when the system continually converges toward a predefined sliding surface, but have been proven to be inapplicable for discontinuous systems subjected to impulsive disturbances. Consequently, it becomes crucial and imperative to develop SMC strategies tailored for discontinuous dynamics affected by impulsive phenomena. Leveraging the event-triggering mechanism with a time-varying threshold and incorporating piecewise Lyapunov function techniques, we propose a novel ET-SMC strategy. It is proved that the proposed control strategy can effectively avoid Zeno behavior and ensure the finite-time stability (FTS) of the considered system via finite-time control theory and innovative impulsive estimation schemes. Furthermore, our results quantitatively measure changes in convergence rate under varying impulsive conditions, which provides valuable insights for performance analysis and the design of SMC strategies in such scenarios. As a specific application, we apply the proposed ET-SMC strategy to coupled reaction-diffusion neural networks (RDNNs) in the presence of both cyber-attacks and matched disturbances. Finally, we present several simulation examples to illustrate the effectiveness and practical applicability of the analytical methods presented in this article.

In islanded AC microgrids, achieving optimal power distribution across distributed generators (DGs) and restoring frequency post-primary control under limited communication resources is paramount for ensuring stability and flexibility. In this paper, we develop a distributed adaptive secondary control strategy tailored for islanded AC microgrids. This strategy facilitates effective active power sharing and frequency regulation using solely local network information. A unique adaptive edge-based event-triggered transmission mechanism is also proposed, obviating Zeno behavior, to reduce communication overhead. It requires only the degree information of a single node in the DG network topology. Contrasting most existing research that necessitates global network topology details, like the Laplacian matrix, this work establishes a fully distributed control performance criterion that operates devoid of global data. The effectiveness of the proposed control approach is validated using a modified IEEE 34-bus test system.

This study addresses the frequency control problem in multiarea power systems through the design of a decentralized periodic event-triggered scheme (DPETS). Initially, a unified discrete-time multiarea model is developed for power systems by adopting the general discretization method. Subsequently, a discrete-type DPETS is designed, relying solely on the locally available area control error to determine the time instants for transmitting the control signal to the equivalent generating unit. Furthermore, the ultimate boundedness of power systems under time-varying load demand disturbance is demonstrated by constructing novel discrete-time Lyapunov-Krasovskii functionals, leading to a rigorous bound of ultimate states. Finally, a case study involving three-area interconnected power systems is presented to validate the feasibility of the designed control strategy.

This brief tackles the finite-time consensus and distributed optimization issues in multi-agent systems (MASs) affected by time-varying delays (TDs). It centers on scenarios where the agents' communication network topology is characterized by a switching undirected graph. Distributed time-varying optimization involves a collective effort by multiple agents to collaboratively minimize the aggregate of local objective functions that change over time. This process is subject to time-dependent equality constraints and relies solely on information available at the local level and from neighboring agents. First, a finite-time multi-parameter smooth distributed algorithm with input TDs is proposed to solve the optimization problem of MASs with arbitrary switching topologies. Secondly, combined with the Lyapunov stability theory, the states of each agent can achieve consensus and asymptotically track the optimal solution trajectory within a finite-time is proved. At last, an illustrative simulation example of target tracking with MASs is given to verify the effectiveness and applicability of the theoretical results.

This paper focuses on distributed sliding-mode consensus tracking control of fuzzy multi-agent systems (MASs) under time-varying transmission delays and hybrid cyber-attacks, including deception and denial-of-service (DoS) attacks. Impulsive and switching signals are adopted to describe the dynamic process of the fuzzy MAS subject to hybrid cyber-attacks. In order to address the hybrid cyber-attacks, a novel integral-type sliding surface function grounded on lumped consensus tracking errors is presented, and a resilient control scheme based on this surface is designed accordingly. By adopting the analysis method of hybrid systems and finite-time control theory, sufficient conditions are deduced to guarantee that the tracking error dynamics can achieve the intended sliding surface in a finite time and remain on the surface thereafter. Meanwhile, the quantitative relationships between the influence of hybrid cyber attacks on the convergence rate of the control strategy are clearly revealed. Moreover, the stabilities of the corresponding sliding mode dynamics are investigated. Finally, the example of cooperative fuzzy robot manipulators is used to illustrate the effectiveness and validity of the proposed theoretical results.

This article investigates the stability and stabilization problem for delay-dependent Takagi–Sugeno (T–S) fuzzy load-frequency control (LFC) power system with energy storage system (ESS). First, a unified T–S fuzzy LFC model is constructed for power system with ESS by further analyzing the nonlinear characteristics existing in turbine and governor dynamics. Second, a fuzzy proportional-integral control strategy is proposed to stabilize the T–S fuzzy power system. Then, based on existing approaches to handle quadratic function with respect to the time-varying delay, an improved quadratic function negative-determination lemma is proposed to achieve larger upper bound of time delay. Furthermore, delay-dependent stability criteria with less conservatism are established by means of Lyapunov stability theorem. Finally, some contrast illustrative examples are given to verify the advantage of the proposed methods.

This paper studies the secure sampled-data consensus of multi-agent systems (MASs) under asynchronous independent deception attacks and multiplicative control gain disturbances by developing the looped Lyapunov-Krasovskii functional (LKF) approach. Because of the openness and shareability of communication network, as well as the time delay in the process of data transmission, two independent deception attacks with asynchronous phenomenon are considered in the sensor-to-controller (SC) and controller-to-actuator (CA) channel of MAS communication network. Furthermore, a coupled memory-based sampled-data control scheme is proposed and fractional-delay states on sampling intervals are introduced to construct an improved delay-dependent looped LKF. Therefore, a relaxed condition with lower conservatism is established to asymptotically ensure the secure sampled-data consensus of MASs in mean square under our designed control protocol. Finally, a simulation test applied to unmanned surface vehicles is conducted to validated the performance of designed control strategy.

In this work, a novel dynamic-memory event-triggered$H_{\infty }$load frequency control (LFC) approach for the power system is proposed considering the existence of hybrid attacks. A dynamic-memory event-triggered mechanism (DMETM) is first presented under denial-of-service (DoS) attacks to reduce the occupation of network communication bandwidth. Different from the existing event-triggered mechanisms (ETMs), the superiority of DMETM is that not only the past transmitted packets can be utilized but also the amount of utilized packets can be adjusted according to the state error of the power system. Then, the general LFC model of the power system is reconstructed as a switched system on account of the existence of DoS attacks and deception attacks. Based on the reconstructed switched model, an exponentially mean-square stability criterion with an$H_{\infty }$performance index is derived by constructing appropriate Lyapunov–Krasovskii functionals (LKFs). Furthermore, the DMETM controllers and event-triggered weighting matrices can be obtained by solving the relevant linear matrix inequalities (LMIs). Finally, some illustrated examples are presented to demonstrate the feasibility and effectiveness of the approach proposed.

In this article, we focus on the event-triggered observer-based fuzzy positioning control and$L_{2}$-gain analysis of nonlinear unmanned marine vehicle (UMV) systems in network environments, which is subject to a hybrid attack consisting of denial-of-service attack and deception attack. First, based on the Tagaki-Sugeno fuzzy modeling method, a unified switched system model is established for the positioning control of nonlinear UMV systems with actuator saturation, multiplicative gain uncertainties, external disturbance, and hybrid attacks. Then, by resorting to introducing the integral-type state error, a novel adaptive memory-based event-triggered mechanism is proposed to lighten the communication load in UMV systems. Furthermore, a sufficient criterion is proposed to make the mean square exponential stability of UMV systems with a nonweighted$L_{2}$-gain level be guaranteed, and gain parameters of the designed controller and observer are also solved efficiently. Finally, the simulation example demonstrates the effectiveness of the proposed nonfragile control strategy.

A distributed coordination load frequency control (LFC) approach is proposed for interconnected power systems, and a detection and compensation mechanism targeting denial-of-service (DoS) attacks is designed in this work. Firstly, different from traditional LFC, a hybrid-type distributed control strategy is proposed, which takes full advantage of local control information and coordination control information. Then, for discovering DoS attacks timely, a feasible detection algorithm targeting DoS attacks is presented. Furthermore, in order to weaken the harm of cyber attacks, a triggered-type compensation mechanism for control data is proposed. By constructing appropriate Lyapunov–Krasovskii functionals, a stability criterion with an$H_{\infty }$performance index is developed. At last, the feasibility of detection and compensation mechanism targeting DoS attacks and the effectiveness of proposed control approach are demonstrated by presenting contrastive illustrative examples.

In this article, the consensus problem of nonlinear multiagent systems (MASs) with time-varying communication delays (TVCDs) is addressed by proposing a novel nonfragile memory-based sampled-data control approach. Different from the existing sampled-data control schemes, an improved memory-based proportional derivative like a sampled-data control scheme based on the information of neighbors is proposed. Besides, considering the inaccuracy and perturbation of controller, a nonfragile control method is also adopted to design the controller. Then, instead of the general quadratic type of the Lyapunov–Krasovskii functional, a delay-product-type quadratic is presented by taking full advantage of the information of TVCDs, and the positive definite constraint in the entire time domain is weakened to the sampled instants on account of adopting the two-sided looped-functional approach. Furthermore, less-conservative consensus criteria for MASs are developed. By solving linear matrix inequalities, the desired control gain matrices and larger sampled-data periods are achieved. Finally, illustrative examples are employed to demonstrate the effectiveness of the designed control strategy.

In this article, a novel co- design approach of observed-based fault detection filter (FDF) and dynamic event-triggered controller is proposed for multi-area wind power system under dual alterable aperiodic (DAA) denial-of-service (DoS) attacks. It is the first attempt to design an observed-based FDF for wind power system considering actuator fault signal. And a tolerable actuator fault threshold function is constructed to warn the occurrence of fault signal. Then, considering the bandwidth limitation of network communication, a novel dynamic event-triggered scheme is proposed to decrease the occupation of communication channel. Furthermore, the DAA DoS attacks presented in this work have different blocking effects on data transmission in different network channel. On account of the existence of aperiodic DoS attacks, the general load frequency control model for wind power system is reconstructed as a new switched system. Based on the reconstructed model, the stability with an$H_{\infty }$performance index is demonstrated by constructing appropriate polynomial Lyapunov-Krasovskii functionals. Besides, the FDF and dynamic event-triggered controller can be achieved by solving linear matrix inequalities. Finally, some contradistinctive case studies are given to illustrate the feasibility and effectiveness of the approaches proposed in this article.

In this article, a new event-triggered$H_{\infty }$load frequency control (LFC) approach with dynamic triggered algorithm (DTA) for multi-area nonlinear power systems (NPSs) based on non-fragile proportional integral control (NPI-control) strategy is addressed. Firstly, different from the existing linear single-area LFC model for power systems, an improved nonlinear multi-area model with the performance of large-scale adjustment frequency fluctuation is constructed by considering the phenomenon of overshoots and long-term oscillations. Due to the existence of control uncertainty, it is the first time that the NPI-control scheme is applied to LFC approach for NPSs. Then, the DTA is proposed to adjust the dynamic event-triggered parameters, which reduces the occupation of communication bandwidth and the data computation of NPSs. Furthermore, a modified quadratic form with time-varying matrix and two-side closed functional method are adopted to construct the relaxed Lyapunov-Krasovskii functional, where some slack matrices are unnecessarily positive definite. Based on Lyapunov method, some less-conservatism stability criteria are derived. Utilizing the linear matrix inequality toolbox, the allowable upper bound of time-varying delays and the NPI-controller are obtained. Finally, a numerical example is presented to demonstrate the availability of the approach developed in this work.