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The distributed Nash equilibrium (NE) seeking problem for multicoalition games has attracted increasing attention in recent years, but the research mainly focuses on the case without agreement demand within coalitions. This article considers a class of networked games among multiple coalitions where each coalition contains multiple agents that cooperate to minimize the sum of their costs, subject to the demand of reaching an agreement on their state values. Furthermore, the underlying network topology among the agents does not need to be balanced. To achieve the goal of NE seeking within such a context, two estimates are constructed for each agent, namely, an estimate of partial derivatives of the cost function and an estimate of global state values, based on which, an iterative state updating law is elaborately designed. Linear convergence of the proposed algorithm is demonstrated. It is shown that the consistency-constrained multicoalition games investigated in this article put the well-studied networked games among individual players and distributed optimization in a unified framework, and the proposed algorithm can easily degenerate into solutions to these problems.

This article investigates the event-triggered distributed average tracking (ETDAT) control problems for the Lipschitz-type nonlinear multiagent systems with bounded time-varying reference signals. By using the state-dependent gain design approach and event-triggered mechanism, two types of ETDAT algorithms called: 1) static and 2) adaptive-gain ETDAT algorithms are developed. It is the first time to introduce the event-triggered strategy into DAT control algorithms and investigate the ETDAT problem for multiagent systems with Lipschitz nonlinearities, which is more practical in real physical systems and can better meet the needs of practical engineering applications. Besides, the adaptive-gain ETDAT algorithms do not need any global information of the network topology and are fully distributed. Finally, a simulation example of the Watts-Strogatz small-world network is presented to illustrate the effectiveness of the adaptive-gain ETDAT algorithms.

This article considers the fully distributed leaderless synchronization in a complex network by only utilizing local neighboring information to design and tune the coupling strength of each node such that the synchronization problem can be solved without involving any global information of the network. For an undirected network, a fully distributed synchronization algorithm is presented to adjust the coupling strength of each node based on a simple adaptive law. When the topology of a network is directed, two different types of adaptive algorithms are developed to achieve synchronization in a fully distributed manner, where the coupling strength of each node is designed to be either the sum or product of two non-negative scalar functions. The fully distributed leaderless synchronization of a directed network is investigated in a leader-follower framework, where the leader subnetwork is analyzed by using the techniques from constrained Rayleigh quotients and the follower subnetwork is addressed by employing the properties of nonsingular M -matrices. Simulations are given to illustrate the theoretical results.

International audience; This work addresses the distributed consensus tracking problem for an extended class of high-order nonlinear multiagent networks with guaranteed performances over a directed graph. The adding one power integrator methodology is skillfully incorporated into the distributed protocol so as to tackle high powers in a distributed fashion. The distinguishing feature of the proposed design, besides guaranteeing closed-loop stability, is that some transient-state and steady-state metrics (e.g., maximum overshoot and convergence rate) can be preselected a priori by devising a novel performance function. More precisely, as opposed to conventional prescribed performance functions, a new asymmetry local tracking error-transformed variable is designed to circumvent the singularity problem and alleviate the computational burden caused by the conventional transformation function and its inverse function, and to solve the nondifferentiability issue that exists in most existing designs. Furthermore, the consensus tracking error is shown to converge to a residual set, whose size can be adjusted as small as desired through selecting proper parameters, while ensuring closed-loop stability and preassigned performances. One numerical and one practical example have been conducted to highlight the superiority of the proposed strategy.

This article investigates the distributed optimal cooperation problems for multiple high-order systems, in which the dynamics of each agent is allowed to be subject to unknown nonlinearities. To eliminate the effect caused by unknown nonlinearities, a nonlinearity estimator is developed based on agents' states, which successfully reconstructs the nonlinear dynamics if the unknown nonlinearities are bounded. And to minimize the sum of multiple local nonlinear cost functions with Lipschitz-type gradients, a couple of static and adaptive state-dependent algorithms are designed, respectively, where each agent may only have access to its own local cost function. It is challenging to solve such an optimal cooperation problem as the performance of the whole multiagent network is evaluated by the sum of all local performance functions. In order to fulfill the goal of cooperative optimization, a state-dependent distributed optimal cooperation algorithm is proposed first. By utilizing tools from the Lyapunov stability theory and convex optimization analysis, it is proven that the considered distributed optimal cooperation problem for high-order nonlinear systems can be solved by the proposed optimal cooperation algorithm if the state-dependent parameters are suitably selected. It is noted that the selections of the state-dependent parameters depend on some global information of the multiagent systems. Furthermore, by incorporating the proposed optimal cooperation algorithm with adaptive parameters strategy, the optimal cooperation problem is solved in a fully distributed manner. Finally, a numerical simulation is shown to verify the effectiveness of the proposed algorithms.

This paper investigates the second-order consensus issue for multi-agent systems subject to both limited communication resources and replay attacks. First, an asynchronous dynamic edge event-triggered (DEET) communication scheme is developed to reduce the utilization of network resources in the absence of attacks. Then, we further consider the case of replay attacks launched by multiple adversaries, under which the transmitted information is maliciously replaced by a previous unnecessary message. To overcome the impact caused by replay attacks, a modified DEET scheme and an effective attack-resilient consensus protocol are well constructed, both of which successfully guarantee second-order consensus in the presence of replay attacks. In addition, internal dynamic variables are utilized in the proposed DEET schemes such that the triggering time sequence does not exhibit Zeno behavior. Finally, one numerical example is provided to illustrate our theoretical analysis.

In this article, a periodic self-triggered impulsive (PSTI) control scheme is proposed to achieve synchronization of neural networks (NNs). Two kinds of impulsive gains with constant and random values are considered, and the corresponding synchronization criteria are obtained based on tools from impulsive control, event-driven control theory, and stability analysis. The designed triggering protocol is simpler, easier to implement, and more flexible compared with some previously reported algorithms as the protocol combines the advantages of the periodic sampling and event-driven control. In addition, the chaotic synchronization of NNs via the presented PSTI sampling is further applied to encrypt images. Several examples are also utilized to illustrate the validity of the presented synchronization algorithm of NNs based on PSTI control and its potential applications in image processing.

We aim to address the Nash equilibrium (NE) seeking problem for multiple players over Markovian switching communication networks in this article, where a new type of distributed synchronous discrete-time algorithm is proposed and utilized. Specifically, each player in the present game model is assumed to employ a gradient-like projection algorithm to choose its action based upon the estimated ones for all the others. Under the mild condition that the union network of all communication network candidates is connected, we show that the players' actions could converge to an arbitrarily small neighborhood of the NE in the mean-square sense by adjusting the algorithm parameters. It is further found that the unique NE is mean-square stable when it is not restricted by any constraint set. In addition, we show that the proposed distributed discrete-time NE seeking algorithm can be utilized to deal with the energy trading problem in microgrids where each microgrid is modeled as a rational player using a purchase price as its action to buy energy from other microgrids with surplus supplies. The energy market allocates the excess energy according to the principle of proportional distribution. Some numerical simulations are finally presented to verify the validity of the present discrete-time NE seeking algorithm in solving the energy trading problem.

This article deals with the distributed H∞ robust control problem for linear multiagent systems perturbed by external disturbances and norm-bounded uncertain parameters over the Markovian randomly switching communication topologies. To tackle this problem, the distributed observer-based controller is proposed, which requires the relative information between neighbors and the absolute information of a subset of the nodes, and thus is intrinsically distributed. It is of great interest to see that the distributed H∞ robust control problem governed by such a controller can be converted to the stabilization with H∞ disturbance attenuation problems of some decoupled linear systems, whose dimensions equal those of a single node. Then, the H∞ stochastic robust performance region is defined to indicate the robustness of this controller against the variation of communication topologies. It is theoretically shown that the distributed observer-based controller yields bounded and connected robust performance region. Finally, the theoretical results are verified by conducting numerical simulations and experiments.

This article investigates the distributed average tracking (DAT) problem for disturbed second-order multiagent systems, where a crowd of agents is required to track the average of the multiple time-varying signals. First, a new kind of distributed average estimator is developed for each agent to estimate the average of the multiple time-varying signals in finite time. The protocol possesses the distinguished feature of robustness to initialization errors, which can recover from network alterations. Then, an observer-based finite-time tracking protocol is proposed to make each agent exactly track the average of the multiple time-varying signals in finite time in the absence of velocity measurement. By carefully analyzing the dynamic properties of the tracking error system, a suitable Lyapunov function is constructed to estimate the settling time for convergence of the tracking error system theoretically. Furthermore, an adaptive DAT protocol is proposed, which is a fully distributed protocol because it can solve the DAT problem without using any global information. Finally, two simulation examples are provided to verify the effectiveness of the methods.