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.

Fixed-time consensus control offers an explicit upper bound on the settling time that is independent of initial conditions, making it particularly valuable for time-critical applications. This survey reviews recent advances in this field, with emphasis on two primary directions: extending fixed-time consensus to broader classes of dynamical multiagent systems, and designing engineered protocols that enhance practical applicability. First, we examine fixed-time consensus results for general dynamical systems, including well-established methods for general linear multiagent systems and emerging approaches for specific classes of nonlinear systems, where a unified theoretical framework remains elusive. Notably, conventional fixed-time consensus protocols often induce excessively large initial control inputs and lack fully distributed settling-time estimation, motivating the development of protocols with engineered features. Second, we review recent advances in specialized consensus protocols that address these practical challenges, focusing primarily on finite-time consensus protocols with bounded control inputs and fully distributed fixed-time consensus protocols, while also covering recent efforts on event-triggered implementations and secure strategies under cyberthreats. The practical utility of these protocols is demonstrated through two case studies: position synchronization of brushless dc motor systems and frequency regulation in islanded microgrids. Finally, key challenges and promising directions for future research are discussed.

Abstract Event-triggered control (ETC) offers an efficient strategy for significantly reducing communication and computation resources in networked systems by triggering control updates only when necessary. This study provides an overview of recent advances in ETC. First, data-driven (or model-free) ETC, which has gained significant attention in recent years, is reviewed for linear systems with and without unknown disturbances. Second, co-design issues are deeply analyzed for both state feedback and dynamic output feedback control. Third, the separation principle is thoroughly examined in the context of event-triggered observer-based output feedback control. Fourth, some insightful discussions are made on the ideal execution property of event-triggered schemes, as well as the modeling of ETC under packet dropouts. Finally, several challenging issues for future research are outlined.

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.

In this paper, consensus tracking is investigated for multi-agent systems (MASs) with unknown disturbances. A K∞function-based control strategy is proposed to guarantee that the tracking errors between each follower and the leader are converged to a small neighborhood of zero in finite-time. To be more specific, by introducing an error auxiliary considering local interactions, a K∞function-based adaptive controller is designed such that the error auxiliary is constrained to an adjustable region. Then, through a matrix-based rigorous proof, practical consensus tracking is realized in finite-time for MASs. A distinguished feature of the K∞function-based control is its independence on the use of the bound information of unknown disturbances. Another advantage of the proposed controller is its capability of alleviating the input chattering issue. Finally, numerical examples are presented to validate the effectiveness of the K∞function-based controller.

This article addresses the problem of cooperative control of double-integrator type multirobot systems. Different from some conventional results with the control gain explicitly known, the control gain in this article is subject to uncertainty. Three different collective behaviors are explored, i.e., leaderless consensus, leader-following consensus, and formation control. For leaderless consensus, a sliding variable is constructed, based on which a novel continuous controller is designed such that the sliding surface is reached in finite-time and thus the state agreement of all agents is realized. For leader-following consensus, two different cases are investigated, i.e., the leader with constant velocity and with time-varying velocity. In both cases, sliding-mode based controllers are developed and corresponding stability conditions are established to ensure that the leader state is tracked by all followers. Finally, the theoretical results are applied to achieve formation control of nonholonomic mobile robots and corresponding experimental studies are conducted to demonstrate the effectiveness of the proposed controllers.

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.

This article addresses the problem of synchronization of impulsive networks with switching topologies. A new synchronization framework is established with an emphasis on settling time estimation. The impulsive networks consist of physical nodes and cyber modules. For physical nodes, states are changed impulsively at discrete time instants due to some switching phenomena or unexpected sudden noises. For cyber modules, two cases of switching scenarios are considered for information exchange patterns during specific time intervals. In the first case, cyber modules lose all the communication links with others, resulting in disconnected topologies. Then, a distributed controller is proposed for nodes without intrinsic nonlinear dynamics. A distinguished feature of this controller is its capability to estimate a bound for settling time, beyond which the synchronization with respect to a virtual target is guaranteed. In the second case, cyber modules lose some communication links but build other new ones with the help of a smart communication center to form connected topologies. A distributed controller is further designed for nodes in the presence of intrinsic nonlinear dynamics. Accordingly, a sufficient condition is derived to achieve synchronization with an estimated settling time bound. For both cases, the estimated bounds are able to reveal the relationship between the impulsive strength and the synchronization performance. Finally, numerical examples including a case study on a modified IEEE 34 bus test feeder are provided to demonstrate the effectiveness of the proposed controllers.

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.

This article deals with the problem of leader-following consensus for multiple wheeled mobile robots. Under a directed graph, a distributed observer is proposed for each follower to estimate the leader state in a fixed time. Based on the observer and a constructed nonlinear manifold, a novel protocol is designed such that the estimated leader state is tracked in a fixed time. Moreover, a switching protocol together with a linear manifold is proposed to ensure that fixed-time leader-following consensus is realized for any initial conditions without causing singularity issues. In contrast to alternative fixed-time consensus protocols in some existing results, the protocol proposed in this article is designed by constructing the nonlinear or linear manifold, which builds a new framework for fixed-time leader-following consensus. Furthermore, the obtained upper bound of settling time is explicitly linked with a single parameter in the protocol, which facilitates the adjustment of the bound under different performance requirements. Finally, the proposed protocol is applied to formation control of wheeled mobile robots.

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.

This paper deals with the problem of distributed optimization for multiagent systems by using an edge-based fixed-time consensus approach. In the case of time-invariant cost functions, a new distributed protocol is proposed to achieve the state agreement in a fixed time while the sum of local convex functions known to individual agents is minimized. In the case of time-varying cost functions, based on the new distributed protocol in the case of time-invariant cost functions, a distributed protocol is provided by taking the Hessian matrix into account. In both cases, stability conditions are derived to ensure that the distributed optimization problem is solved under both fixed and switching communication topologies. A distinctive feature of the results in this paper is that an upper bound of settling time for consensus can be estimated without dependence on initial states of agents, and thus can be made arbitrarily small through adjusting system parameters. Therefore, the results in this paper can be applicable in an unknown environment such as drone rendezvous within a required time for military purpose while optimizing local objectives. Case studies of a power output agreement for battery packages are provided to demonstrate the effectiveness of the theoretical results.

This paper deals with the problem of distributed optimization of a multiagent system with network connectivity preservation. In order to realize cooperative interactions, a connected network is the prerequisite for high-quality information exchange among agents. However, sensing or communication capability is range-limited, so it is impractical to simply make an assumption that network connectivity is preserved by default. To address this concern, a class of generalized potentials including discontinuities caused by unexpected obstacles or noises are designed. For a class of quadratic cost functions, based on the potentials, a new distributed protocol is proposed to formally guarantee the network connectivity over time and to realize the state agreement in finite time while the sum of local functions known to individual agents is optimized. Since the right-hand side of the proposed protocol is discontinuous, some nonsmooth analysis tools are applied to analyze system performance. In some practical scenarios, where initial states are unavailable, a distributed protocol is further developed to realize the consensus in a prescribed finite time while solving the distributed optimization problem and maintaining network connectivity. Illustrative examples are provided to demonstrate the effectiveness of the proposed protocols.

This paper is concerned with the collective behaviors of robots beyond the nearest neighbor rules, i.e., dispersion and flocking, when robots interact with others by applying an acute angle test (AAT)-based interaction rule. Different from a conventional nearest neighbor rule or its variations, the AAT-based interaction rule allows interactions with some far-neighbors and excludes unnecessary nearest neighbors. The resulting dispersion and flocking hold the advantages of scalability, connectivity, robustness, and effective area coverage. For the dispersion, a spring-like controller is proposed to achieve collision-free coordination. With switching topology, a new fixed-time consensus-based energy function is developed to guarantee the system stability. An upper bound of settling time for energy consensus is obtained, and a uniform time interval is accordingly set so that energy distribution is conducted in a fair manner. For the flocking, based on a class of generalized potential functions taking nonsmooth switching into account, a new controller is proposed to ensure that the same velocity for all robots is eventually reached. A co-optimizing problem is further investigated to accomplish additional tasks, such as enhancing communication performance, while maintaining the collective behaviors of mobile robots. Simulation results are presented to show the effectiveness of the theoretical results.

Fixed-time cooperative control is currently a hot research topic in multiagent systems since it can provide a guaranteed settling time, which does not depend on initial conditions. Compared with asymptotic cooperative control algorithms, fixed-time cooperative control algorithms can achieve better closed-loop performance and disturbance rejection properties. Different from finite-time control, fixed-time cooperative control produces the faster rate of convergence and provides an explicit estimation of the settling time independent of initial conditions, which is desirable for multiagent systems. This paper aims at presenting an overview of recent advances in fixed-time cooperative control of multiagent systems. Some fundamental concepts about finite- and fixed-time stability and stabilization are first recalled with insight understanding. Then, recent results in finite- and fixed-time cooperative control are reviewed in detail and categorized according to different agent dynamics. Finally, this paper raises several challenging issues that need to be addressed in the near future.

In this paper, we study the fixed-time cooperative tracking control problem for multi-robot systems with doubleintegrator dynamics. First, a novel distributed observer is proposed for each follower to estimate the leader state in a fixed time, then a local tracking controller based on sliding mode technique is proposed such that the estimated leader state is tracked in a fixed time. Both cases of a stationary leader and a dynamic leader are investigated. Since nonholonomic dynamics can better describe the mobile robots in reality, we further extend the results to achieve fixed-time cooperative tracking for multi-robot systems with nonholonomic dynamics. Different from the conventional finite-time cooperative tracking strategies, the fixed-time approach in this work guarantees that an upper bound of settling time can be prescribed without dependence on initial states of robots, which provides additional system information in advance. Finally, numerical simulations are given to demonstrate the effectiveness of the theoretical results.

Suppose a disaster happens, and several groups of robots are dispatched from distant control stations. To enable rescue staff to make collective decisions, reliable and robust connections need to be established among stations. Motivated by this scenario, a two-stage robot deployment strategy is proposed for wireless robotic networks (WRNs). In the first stage, robots in distant groups are merged into one group that covers a desirable area. Since connectivity alone cannot guarantee a high communication quality, in the second stage, the flow between any two stations is further optimized in terms of expected number of transmissions per successfully delivered packet. In both stages, a distributed collision-free controller is proposed to regulate the interactive force among robots. The stability issues of WRNs, where the proposed controller together with a class of interaction models based on an acute angle test is implemented for robots, are analyzed under both fixed and switching topology. In order to efficiently switch the neighbor set for each robot, a new energy function is constructed taking finite-time consensus into account. To guarantee that energy agreement is achieved before the next topology change, a fixed-time consensus approach is further proposed and an upper bound of the settling time for the energy agreement is obtained. Numerical simulations are provided to demonstrate the effectiveness of the two-stage deployment strategy.

In this paper, we treat mobility as a network control primitive in wireless robotic networks (WRNs), which consist of a number of mobile robots. The aim is to achieve better communication performance by making use of the mobility of the robots. In the literature, it has been shown that for a graph-based connectivity model, an equal-space configuration of robot nodes is optimal in terms of energy efficiency. To be more realistic, we adopt a signal to interference plus noise ratio (SINR)-based physical model in this work. With this model, we show that the equal-space configuration of robots is no longer optimal from the perspective of network interference. Instead, an equal-SINR configuration of robots is demonstrated to be optimal for a unicast topology in WRNs. Based on our network interference reduction method, a distributed mobility control algorithm is proposed to achieve the equal-SINR configuration. Simulation results verify that the proposed algorithm can drive robots to the desired positions where the network interference is minimized.