This article focuses on prescribed-time distributed robust Nash equilibrium seeking for monotone games impacted by unknown and time-varying disturbances. First, a regularization term with a prescribed-time decaying parameter is introduced to compensate for the absence of strong monotonicity in the merely monotone game. Based on the regularization technique, a new prescribed-time signum-based distributed Nash equilibrium seeking algorithm incorporating an integral sliding mode method, a leader-following consensus protocol, and a gradient algorithm is presented for monotone games with unknown but bounded disturbances. Then, to dispose of the unknown bounds of disturbances, a prescribed-time distributed adaptive integral sliding mode based Nash equilibrium seeking strategy is devised. On the basis of the proposed strategies, some sufficient conditions are obtained to guarantee that the players' actions are capable of converging to the least-norm Nash equilibrium of the monotone games in a prescribed time. In the end, numerical simulations on least-distance formation control of a network of players testify to the performance of the proposed seeking strategies.

Distributed control of networked Euler–Lagrange systems has broad applications in industrial engineering. However, challenges, such as multiple uncertainties and resource-constrained networks, remain urgent issues to be resolved. This article addresses the issue of distributed Nash equilibrium seeking for Euler–Lagrange systems subject to physical and cyber uncertainties and limited communication resources. Specifically, considering uncertain parameters and time-varying uncertainties imposed on communication links, a new distributed strategy integrating an optimizer, a state regulator, a consensus algorithm, and an adaptive law is proposed for Euler–Lagrange systems, in which gains for consensus modules adaptively adjust to cope with the compromised communication weights caused by cyber uncertainties. Moreover, a dynamic gradient-based event-triggered scheme is put forward to enable information exchanges among neighbors and control updates when the predetermined triggered conditions are met. It is shown by theoretical analysis that the proposed event-triggered strategy is effective for significantly reducing the numbers of information transmission and control updates nearly without degrading convergence performance. Furthermore, the Zeno phenomenon is theoretically precluded under the proposed event-triggered scheme. Finally, the efficacy of the proposed method is validated through simulation cases on robotic manipulators.

This paper considers a network of distributed energy resources (DERs) that intend to optimize their power generation in an open price-based energy management system. Specifically, in the considered problem, the cost function of each DER, depends on not only its own decision variable but also an aggregate of all DERs’ energy decision variables. The DERs are cooperative to minimize their total cost of power generations, thus forming a distributed aggregative optimization problem. In addition, it is considered that the DERs are allowed to frequently arrive in and leave the system, which brings great difficulties in the algorithm design and analysis. To address this problem, a novel distributed optimization algorithm is proposed, by integrating gradient descent algorithms with a multi-level storage-based consensus mechanism. In addition, the performance of the proposed algorithm is evaluated by the dynamic regret, which quantifies the sum of all DERs’ loss between the actual cost and real time optimal cost during its active period length. It is shown that the upper bound of the all active DERs’ dynamic regret over active period length grows sublinearly under diminishing stepsizes. Finally, a numerical simulation is provided to verify the effectiveness of the proposed method.

This paper addresses distributed formation tracking control for heterogeneous swarms consisting of quadrotor unmanned aerial vehicles (UAVs) and unmanned surface vehicles (USVs). A hierarchical control framework is proposed to coordinate overall swarm formation. At the upper layer, a position-based control strategy is designed for UAVs, in which a virtual leader is introduced to facilitate coordinated aerial formation. At the lower layer, a bearing-based control strategy is employed for USVs, with selected UAVs serving as mobile leaders to guide the USV formation. Within this framework, optimized formation controllers for both UAVs and USVs are developed by integrating the backstepping method with a reinforcement learning algorithm based on the actor-critic architecture. Lyapunov-based stability analysis demonstrates that the proposed scheme ensures the desired formation performance of the swarm. Compared with existing studies that primarily address homogeneous UAV or USV formations, the proposed method achieves optimized formation tracking control for more complex heterogeneous swarms, without requiring precise knowledge of their dynamic models. The effectiveness and robustness of the proposed approach are further validated through numerical simulations.

In the evolving landscape of modern power systems, islanded microgrids have contributed a significant role, offering superior resilience, power quality, and the efficient harnessing of distributed generators (DGs). The dynamic nature of such systems necessitates advanced control techniques to ensure stability and optimal operation. This article provides a brief review of recent advances in distributed accelerated (including finite-time, fixed-time, and prescribed-time) control strategies, with a particular focus on their use in the distributed secondary control of islanded ac microgrids. The spotlight is on the application of these distributed accelerated secondary control techniques in managing DGs. We investigate the fundamental principles of these techniques, their evolution over time, and pivotal technological advancements. A comparative analysis underscores the strengths and potential limitations of these control methodologies in context to DGs. Finally, we list some opportunities that these advanced control techniques offer in addressing challenges associated with the control of DGs in islanded microgrids, thereby paving the path for future research.

This article is concerned with fully distributed Nash equilibrium seeking in networked games under both undirected and directed communication graphs. New fully Nash equilibrium seeking strategies incorporating gradient-based optimization algorithms, consensus algorithms, and double-layer adaptive control laws are presented. In particular, the double-layer adaptive control laws are introduced to ensure that the control gains are not overlarge and free of dependence on any global information. This is achieved by adding a damping term to the adaptive parameter design such that the continuous increase in control gains is avoided. Theoretical analyses are conducted to prove that players' actions can be convergent to the Nash equilibrium under the proposed strategies. Moreover, it is shown that the developed strategies can be extended to accommodate the players with heterogeneous linear dynamics. Finally, numerical examples are provided to illustrate the effectiveness of the proposed methods.

This article proposes an online data-based inverse reinforcement learning (IRL) scheme to solve optimal control problem for nonlinear systems with control constraints, in which the unknown reward functions are recovered based on the systems’ demonstrated state and input data. To deal with control constraint, we introduce a saturation function to formulate the original constrained optimal control problem into a new unconstrained optimal control problem. Then a data-based identifier using neural network (NN) approximation technique is designed to estimate the system’s dynamics. Subsequently, we develop a data-based IRL approach to learn the unknown reward function and establish the weight tuning law of the value function and reward function using demonstrated state and input data. The proof of the uniform boundedness of the weight estimation error is presented. A simulation example is provided to verify the effectiveness of the proposed approach.

In this paper, we consider the prescribed-time distributed Nash equilibrium (PTDNE) seeking problem in noncooperative monotone games under directed graphs. For the purpose of compensating for the absence of strong monotoncity condition, a time-varying decay regularization term is implemented in the merely monotone game. By using the regularization scheme, a new prescribed-time distributed algorithm is established for seeking the least-norm Nash equilibrium in monotone games, where the leader-following consensus protocol and gradient play are incorporated. Based on the proposed strategies, some sufficient conditions on time-varying parameters are provided through Lyapunov function analysis, under which the players’ actions are capable of converging to the least-norm one of the Nash equilibria in a prescribed time. Finally, numerical simulations on a network of players demonstrate the benefits of the proposed algorithm in achieving convergence at any arbitrary time.

This paper examines the distributed energy management and control of microgrids. First, a non-cooperative game-theoretic model is constructed to analyze the strategic behaviors in distributed microgrids with constraints, ultimately using Nash equilibrium to characterize the generation solutions. Subsequently, to reduce the consumption of communication resources, an event-triggered mechanism is introduced. This mechanism allows bus i to intermittently detect event-triggering conditions within constant sampling moments and use this information to determine when to pass its state information to its neighbors. Finally, a simulation study is conducted to validate the efficacy of the proposed algorithm.

In this paper, we investigate the distributed resilient control problem of voltage and frequency restoration in AC microgrids (MGs) subject to false data injection (FDI) attacks under event-triggered communication. To solve the problem, new distributed dynamic event-triggered$k$-step attack observers are primarily designed for the accurate estimation of attacks while avoiding continuous communication. Based on the observer state, cooperative resilient controllers for voltage and frequency restoration are proposed, and the convergence of the voltage and frequency of the AC MGs as well as the exclusion of Zeno behavior are proved theoretically. Different from the existing event-triggered resilient control methods in AC MGs subject to unknown bounded FDI attacks, the developed distributed dynamic event-triggered based$k$-step attack observers and cooperative resilient controllers can guarantee accurate observation and compensation for FDI attacks. Finally, experimental tests are carried out to validate the effectiveness of the proposed control method, which demonstrates great resilience in maintaining stable operations under FDI attacks and represents a dramatic reduction in communication costs.

This paper proposes a privacy-preserving distributed collaboration (PPDC) scheme for connected autonomous vehicles (CAVs) to cross signal-free intersections based on the cloud, while securing the private data of the vehicles. Firstly, this paper converts the cooperation problem into a multi-objective problem that aims to improve the efficiency of traffic and fuel economy. Secondly, to prevent the privacy of the transmitted data of vehicles from being inferred by untrusted cloud servers or external attackers, an affine masking-based privacy strategy is designed. Specifically, the vehicle first uploads the encrypted state data to the cloud with the affine masking method. Then the cloud returns the control input by solving the newly constructed optimization problem, which is different but equivalent to the original problem. Then the vehicle calculates the real control input by the inverse affine masking mechanism. Simulation examples show that the proposed PPDC scheme can guarantee collision avoidance and the privacy protection of transmitted data of CAVs, improve traffic efficiency as well as fuel economy, and avoid extensive computation burden.

Mobile Edge Computing (MEC), as a promising key technology, provides tremendous support for latency-sensitive applications in Internet of Vehicles (IoV). In this paper, we focus on the MEC-assisted computation offloading problem for mixed traffic scenarios that autonomous and human-driven connected vehicles coexist. With the objective of minimizing system average latency, a priority-based serial and parallel joint offloading scheme is designed and formulate the optimization problem as a Markov decision process (MDP). Then, we propose an adaptive offloading strategy based on deep reinforcement learning. Simulation results compared to contrast algorithm and baseline schemes demonstrate the superiority of the proposed priority-based offloading scheme, effectively reducing the system average latency and ensuring the latency requirements of latency-sensitive tasks.

Passive localization is commonly achieved through the direction finding and positioning technique, which uses a airborne or ground multi-station angle measuring system to intersect pointing lines for fast and omnidirectional positioning. However, as the number of targets increases, so does the occurrence of false points. This poses a challenge to the positioning performance of system, requiring the prompt elimination of false points. To address the issue, we propose a high detection rate passive localization method based on density peak clustering (DPC). In this method, a suitable non-ideal location model is established, and improved density peak clustering is utilized to achieve data association and target localization. Simulation results confirm the proposed positioning method’s superior performance and adaptation to the non-ideal conditions of multi-target localization.

The optimization of power control for base station (BS) and user equipment (UE) is crucial to enhance network performance in the dynamic landscape of wireless communication. With the advent of Sixth Generation (6G) communication systems, the demand for real-time communication has surged, leading to a pressing need to develop power optimization strategies that can tackle network latency. We propose a joint power optimization method for both BS and user UE based on the Age of Information (AoI), and address the challenge of power allocation in multi-user communication systems. We begin by modeling a single BS and studying the impact of its power on the AoI. Next, we design a UE power allocation algorithm that considers limited conditions. To achieve this, we transform the problem into a Markov decision problem and solve for the optimal solution using a deep learning algorithm. Our proposed method provides an effective approach to optimize power allocation in multi-user communication systems. The simulation results demonstrate that our proposed algorithm can effectively minimize AoI and achieve on-demand power allocation. Compared to the mean algorithm for power allocation, our proposed algorithm has better performance.

Nash equilibrium, as an essential strategic profile in game theory, is of both practical relevance and theoretical significance due to its wide penetration into various fields, such as smart grids, wireless communication networks, and networked mobile vehicles. In particular, distributed Nash equilibrium seeking strategies have recently attracted increasing attention because they show remarkable advantages in relaxing the requirement of a central node for information broadcasting or full observation of players’ actions. This article aims to provide a survey of distributed Nash equilibrium seeking in games with partial decision information, in which players can only exchange information with their neighbors and their objective functions may explicitly depend on all players’ actions. First, fundamental problem descriptions on distributed Nash equilibrium seeking are presented. Second, related results on distributed Nash equilibrium seeking in general multiplayer games, aggregative games, and multicluster games are reviewed, respectively, where representative continuous- and discrete-time methods are explained in detail. Third, two practical applications, including collaborative control for a network of mobile sensors and energy consumption control in smart grids, are provided to demonstrate the applicability of distributed Nash equilibrium seeking strategies. Finally, some promising directions are suggested for future research.

Fixed-time and prescribed-time consensus control can bring an explicit estimate of the settling time without dependence on initial conditions, which is important in providing control engineersa priorisystem information. This article aims at presenting a survey of recent trends and methodologies of fixed-time and prescribed-time consensus control in multiagent systems. First, some typical fixed-time consensus results are reviewed. Despite the advantage in deriving a fixed settling time bound, fixed-time consensus controllers usually result in a conservative estimate of the bound and a large magnitude of initial control input, which in turn show the necessity of designing prescribed-time consensus controllers. Second, characteristics and controller design of (practical, respectively) prescribed-time consensus are provided in detail. Particularly, representative time-varying function-based controllers are presented, by which (practical, respectively) consensus can be achieved in prescribed time. Third, applications of fixed-time and prescribed-time consensus control in mobile robots and smart grids are illustrated in case studies. Finally, several challenging issues in prescribed-time consensus control are discussed for future research.

In practical applications, decision makers with heterogeneous dynamics may be engaged in the same decision-making process. This motivates us to study distributed Nash equilibrium seeking for games in which players are mixed-order (first- and second-order) integrators influenced by unknown dynamics and external disturbances in this article. To solve this problem, we employ an adaptive neural network to manage unknown dynamics and disturbances, based on which a distributed Nash equilibrium seeking algorithm is developed by further adapting concepts from gradient-based optimization and multiagent consensus. By constructing appropriate Lyapunov functions, we analytically prove the convergence of the reported method. Theoretical investigations suggest that players’ actions would be steered to an arbitrarily small neighborhood of the Nash equilibrium, which is also testified by simulations.

In this paper, we consider the problem of resilient economic dispatch for power grid under denial-of-service (DoS) attacks. By introducing a resilient distributed economic dispatch algorithm, the minimum of the generation cost can be found while balancing the supply and demand. The global information is estimated by the resilient consensus protocol in a distributed fashion and the optimal solution of the economic dispatch problem is searched by the saddle point dynamics. It is shown that the developed resilient algorithm can ensure the exponential convergence of the closed-loop systems by using the Lyapunov stability theory. Finally, an illustrative example based on the IEEE 9-bus attacked by multi-channels DoS is provided to verify the effectiveness of the proposed method.

This paper studies the leader following consensus of cloud-based multi-agent systems under switching topologies. Firstly, a cloud-based control framework is proposed, in which each agent can upload and download data from the cloud through communication channels and communication tolopolgies among neighbors are switching. Based on the proposed cloud control framework and switching topology model, a cloud-based distributed consensus protocol is proposed. By using switching theory approach, sufficient conditions are provided to ensure that consensus tracking can be achieved. Moreover, the existence of controller gain matrices can be guaranteed by solving LMI. Finally, a simulation example is given to verify the theoretical results.

This article is concerned with attack-resilient event-triggered$H_{\infty }$filtering for a class of networked nonlinear systems described by an interval type-2 (IT2) fuzzy model. Suppose that data transmission from the plant to the filter is completed through a wireless sensor network subject to denial-of-service attacks (DoS). In order to save the limited network bandwidth and resist the effects of DoS attacks, a resilient event-triggered communication scheme is devised. Then, an attack-resilient IT2 filter model is introduced to estimate system states of the nonlinear plant. Based on a piecewise Lyapunov–Krasovskii functional, sufficient conditions are obtained to ensure that the filtering error system is exponentially stable and satisfies a certain$H_{\infty }$performance level. Moreover, explicit expressions for the attack-resilient filter gain parameters and event-triggering parameters can be derived if a set of linear matrix inequalities are feasible. Finally, a practical example is provided to demonstrate the effectiveness of the proposed theoretical results.

In this article, a source–grid–load-collabora tion-based control framework is proposed to improve the power quality of active distribution networks (ADNs) with high penetration of low-carbon energy. First, hybrid dynamics of ADNs are characterized by addressing the voltage regulation and operation economics in each operation mode, and the mode switching control is designed in line with the operation principle of the on-load tap changer, where voltage security events are used to build the event-triggered functions. Second, multiobjective optimization is formulated with consideration of the system-wide operation cost and distribution circuit loss of the ADN in a relatively slow time scale, while in the fast time scale, all the inverter-based distributed generators, energy storages, and static var compensator devices are coordinated at the source–load side, through which multiple voltage issues, including voltage profile issue and voltage increment issue, can be addressed in a fully distributed manner. Finally, simulation results validate the effectiveness and robustness of the proposed method based on the modified IEEE 33-bus system.

This article is concerned with the distributed secondary frequency and voltage control for islanded microgrids. First, the distributed secondary control problem is formulated by taking both communication delays and switching topologies into account. Second, by using an Artstein model reduction method, a novel delay-compensated distributed control scheme is proposed to restore frequencies of each distributed generator (DG) to a reference level in finite time, while achieving active power sharing in prescribed finite-time regardless of initial deviations generated from primary control. Third, a distributed finite-time controller is developed to regulate voltages of all DGs to a reference level. Fourth, the proposed idea is also applied to deal with the finite-time consensus for first-order multiagent systems. Finally, case studies are carried out, demonstrating the effectiveness, the robustness against load changes, and the plug-and-play capability of the proposed controllers.

An event-triggered mechanism is of great efficiency in reducing unnecessary sensor samplings/transmissions and, thus, resource consumption such as sensor power and network bandwidth, which makes distributed event-triggered estimation a promising resource-aware solution for sensor network-based monitoring systems. This paper provides a survey of recent advances in distributed event-triggered estimation for dynamical systems operating over resource-constrained sensor networks. Local estimates of an unavailable state signal are calculated in a distributed and collaborative fashion based on only invoked sensor data. First, several fundamental issues associated with the design of distributed estimators are discussed in detail, such as estimator structures, communication constraints, and design methods. Second, an emphasis is laid on recent developments of distributed event-triggered estimation that has received considerable attention in the past few years. Then, the principle of an event-triggered mechanism is outlined and recent results in this subject are sorted out in accordance with different event-triggering conditions. Third, applications of distributed event-triggered estimation in practical sensor network-based monitoring systems including distributed grid-connected generation systems and target tracking systems are provided. Finally, several challenging issues worthy of further research are envisioned.

This article is concerned with designing resilient state feedback controllers for a class of networked control systems under denial-of-service (DoS) attacks. The sensor samples system states periodically. The DoS attacks usually prevent those sampled signals from being transmitted through a communication network. A logic processor embedded in the controller is introduced to not only receive sampled signals but also capture information on the duration time of each DoS attack. Note that the duration time of DoS attacks is usually both lower and upper bounded. Then the closed-loop system is modeled as an aperiodic sampled-data system closely related to both lower and upper bounds of duration time of DoS attacks. By introducing a novel looped functional, which caters for the N -order canonical Bessel-Legendre inequalities, some N -dependent stability criteria are presented for the resultant closed-loop system. It is worth pointing out that a number of identity formulas are uncovered, which enable us to apply the notable free-weighting matrix approach to derive less conservative stability criteria. A linear-matrix-inequality-based criterion is provided to design stabilizing state-feedback controllers against DoS attacks. A satellite control system is given to demonstrate the effectiveness of the proposed method.

This article addresses the problem of distributed resilient finite-time control of multiple heterogeneous battery energy storage systems (BESSs) in a microgrid subject to denial-of-service (DoS) attacks. Note that DoS attacks may block information transmission among BESSs by preventing the BESS from sending data, compromising the devices and jamming a communication network. A distributed secure control framework is presented, where an acknowledgment (ACK)-based attack detection strategy and a communication recovery mechanism are introduced to mitigate the impact of DoS attacks by repairing the paralyzed topology graphs caused by DoS attacks back into the initial connected graph. Under this framework, a distributed resilient finite-time secondary control scheme is proposed such that frequency regulation, active power sharing, and energy level balancing of BESSs can be achieved simultaneously in a finite time; meanwhile, operational constraints can be satisfied at any control transient time. Moreover, based on theoretical analysis, the impact of the duration time of DoS attacks on the convergence time of the control algorithm can be explicitly revealed. Finally, validity and effectiveness of the proposed control scheme are demonstrated by case studies on a modified IEEE 57-bus testing system.

Fault-tolerant cooperative control of multiagent systems has attracted ever-increasing attention in recent years due to the fact that multiple agents can provide much more redundancy than a single agent system, thereby making the fault tolerant cooperative control design more flexible. However, multiagent systems may bring severe challenges that do not exist in single-agent systems. This article aims at presenting a survey of trends and methodologies of fault tolerant cooperative control in multiagent systems. Depending on the countermeasure against the faults, the existing fault-tolerant cooperative control methodologies are first classified into four categories: Individual methodologies, cooperative methodologies, topology reconfiguration-based methodologies, and composition reconfiguration-based methodologies. Then the characteristics and implementation schemes of four categories of methodologies are discussed in detail. Furthermore, the applicability of fault tolerant cooperative control in smart grids is outlined. Finally, several challenging issues are envisioned for future research.

Distributed coordination control is the current trend in networked systems and finds prosperous applications across a variety of fields, such as smart grids and intelligent transportation systems. One fundamental issue in coordinating and controlling a large group of distributed and networked agents is the influence of intermittent interagent interactions caused by constrained communication resources. Event-triggered communication scheduling stands out as a promising enabler to strike a balance between the desired control performance and the satisfactory resource efficiency. What distinguishes dynamic event-triggered scheduling from traditional static event-triggered scheduling is that the triggering mechanism can be dynamically adjusted over time in accordance with both available system information and additional dynamic variables. This article provides an up-to-date overview of dynamic event-triggered distributed coordination control. The motivation of dynamic event-triggered scheduling is first introduced in the context of distributed coordination control. Then some techniques of dynamic event-triggered distributed coordination control are discussed in detail. Implementation and design issues are well addressed. Furthermore, this article exemplifies two applications of dynamic event-triggered distributed coordination control in the fields of microgrids and automated vehicles. Several challenges are suggested to direct the future research.

With the rapid development and widespread utilization of advanced communication, sensing, and computation technologies, increasing attention has been paid to develop new techniques of control and filtering for distributed networked systems. Note that the utilization of communication networks can improve efficiency, flexibility, and scalability in designing networked controllers and filters. However, communication networks usually suffer from communication resource constraints with detrimental consequences, such as long latency, increased packet dropout, reduced throughput, and so on. In order to address the challenges caused by limited communication resources, an event-triggered communication paradigm is an effective and promising technique that can significantly reduce computation/communication utilization while maintaining the desired estimation and the control performance. As a result, a variety of event-triggered control and filtering techniques for distributed networked systems have been proposed.

This paper is concerned with the distributed secondary control problem of multiple battery energy storage systems (BESSs) in an islanded microgrid, where the dynamics of each battery is heterogeneous. It is assumed that each battery can communicate with its neighbors via communication networks whose communication topologies are switching over time. A distributed finite-time secondary control scheme is proposed to ensure frequency regulation, active power sharing and energy level balancing of BESSs in a finite time, while operational constraints can be satisfied at any control transient time. Finally, validity and effectiveness of the proposed control scheme are demonstrated by case studies on a modified IEEE 57-bus testing system.

This paper is concerned with active power sharing and frequency regulation in an islanded microgrid under event-triggered communication. A distributed secondary control scheme with a sampled-data-based event-triggered communication mechanism is proposed to achieve active power sharing and frequency regulation in a unified framework, where neighborhood sampled-data exchange occurs only when the predefined triggering condition is violated. Compared with traditional periodic communication mechanisms, the proposed event-triggered communication mechanism shows some prominent ability in reducing the number of communication among neighbors while guaranteeing the desired performance level of microgirds. By employing the Lyapunov-Kravovskii functional method, some sufficient conditions are derived to characterize the effects of control gains, system parameters, and sampling period on stability of microgrids. Finally, case studies on a modified IEEE 34-bus test system are conducted to evaluate the performance of the proposed distributed control scheme, showcasing its effectiveness, robustness against load changes, and plug-and-play ability.

Event-triggered consensus of multiagent systems (MASs) has attracted tremendous attention from both theoretical and practical perspectives due to the fact that it enables all agents eventually to reach an agreement upon a common quantity of interest while significantly alleviating utilization of communication and computation resources. This paper aims to provide an overview of recent advances in event-triggered consensus of MASs. First, a basic framework of multiagent event-triggered operational mechanisms is established. Second, representative results and methodologies reported in the literature are reviewed and some in-depth analysis is made on several event-triggered schemes, including event-based sampling schemes, model-based event-triggered schemes, sampled-data-based event-triggered schemes, and self-triggered sampling schemes. Third, two examples are outlined to show applicability of event-triggered consensus in power sharing of microgrids and formation control of multirobot systems, respectively. Finally, some challenging issues on event-triggered consensus are proposed for future research.

One of the fundamental and challenging issues in microgrids is to guarantee fairness of load sharing while realizing voltage regulation of distributed generations. In order to address this issue, a new multiobjective optimization problem with tunable weighting coefficients is first formulated for dc microgrids. Second, a new distributed control scheme, which only requires local communications among neighbors, is proposed to solve the optimization problem. It is theoretically proved that the distributed control scheme can exponentially achieve the global optimal outputs of voltages and currents at distributed generations. Compared with a centralized control scheme, the proposed distributed control scheme provides remarkable advantages in improving reliability and scalability of microgrids. Third, the distributed control scheme is extended to accommodate a constant communication delay. The effects of the communication delay on the stability of microgrids are explicitly characterized. Finally, the performance of the proposed control schemes is evaluated by a modified six-bus microgrid with dc-powered trolleybus systems in terms of their convergence, robustness to load variations, plug-and-play functionality, tradeoff ability, and effects of communication delays.

In this paper, the problem of network-based leader-following consensus is addressed for linear multi-agent systems with input saturation. First, a network-based consensus protocol with input saturation constraints is introduced to accommodate some network-induced effects such as delay, data quantization and time-varying sampling interval. Next, the Lyapunov-Krasovskii method is utilized to show the exponential convergence of the leader-following error system to a bounded set region under a delay-dependent stability condition, together with estimation of the region of initial conditions. Then with leveraging this stability condition, the gain matrix of the network-based consensus controller is designed for linear multi-agent systems.

This paper studies network-based practical leader-following consensus problem of heterogeneous multiagent systems with Lipschitz nonlinear dynamics under both fixed and switching topologies. Considering the effect of network-induced delay, a network-based leader-following consensus protocol with heterogeneous gain matrix is proposed for each follower agent. By employing Lyapunov-Krasovskii method, a sufficient condition for designing the network-based consensus controller gain is derived such that the leader-following consensus error exponentially converges to a bounded region under a fixed topology. Correspondingly, the proposed design approach is then extended to the case of switching topology. Two numerical examples with networked Chua's circuits are given to show the efficiency of the design method proposed in this paper.