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Summary: This paper considers the resilient interval consensus problems for continuous‐time time‐varying multi‐agent systems when a normal agent is surrounded by no more than r misbehaving agents. Each normal agent individually proposes a constraint interval which specifies their acceptable consensus range and misbehaving agents are anonymous and exert different arbitrary rules posing threats to the global performance of the systems. On the basis of our purely distributed resilient interval consensus strategy, we showed that if the network is (2r + 1)‐robust and the interval intersection is nonempty, the normal agents are able to reach an agreement with the final consensus equilibrium in the interval intersection. A numerical example is presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a novel finite-time median-related group consensus problem, where the finial consensus value can be identified as a desired function of the median of initial states instead of the much studied average value. The underlying communication topology is modelled by a weighted dynamical directed network. A distributed control protocol is firstly introduced to ensure that the agents can reach a median-related consensus in finite time in a collaboration network, meaning that all edge-weights of the communication network are non-negative. We then generalise the results to cooperation–competition networks, where the communication network is divided into predetermined collaboration subnetworks allowing possibly negative weights. Effective group control protocols are designed to guarantee the median-related group consensus in finite time. Finally, numerical simulations are presented to illustrate the availability of our theoretical results. [ABSTRACT FROM AUTHOR]

Abstract This letter considers the resilient consensus problem for switched multi-agent systems composed of continuous-time and discrete-time subsystems. We propose a switched filtering strategy for cooperative nodes based upon available local information, withstanding the threat of non-cooperative nodes. We provide conditions that guarantee resilient consensus in the presence of locally bounded Byzantine nodes in directed networks under arbitrary switching. Resilient scaled consensus and resilient scaled formation generation problems for switched multi-agent systems are solved as generalizations. Simulations are also provided to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this study, the author studies fixed‐time group consensus problem in networks of dynamic agents with intrinsic non‐linear dynamics and bounded uncertainties. Three types of distributed control protocols are proposed to achieve fixed‐time group consensus when the subgroups are connected and have inter‐group common influence. By using Lyapunov theory, algebraic graph theory, and fixed‐time stability, some conditions are derived to select the controller gains to ensure the convergence in a prescribed time regardless of the initial conditions. Numerical examples are worked out to illustrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the problem of resilient consensus in continuous-time multiagent systems against potential malicious agents. Network topology conditions have been developed to ensure asymptotic consensus of cooperative agents in the network under multi-hop communication and path-dependent heterogeneous delays. We develop two new distributed protocols based on the idea of weighted mean subsequence reduced algorithm to address scalar resilient consensus and vector resilient consensus problems in path-weighted directed networks leveraging on the capability of multi-hop communication. Our frameworks are flexible in that both linear and general nonlinear network coupling functions are featured. Resilient consensus problem for dynamical agents with higher-order integrators is solved as a byproduct. We illustrate the error introduced by the resilience mechanisms when the network is free of malicious agents through numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, group consensus problems in fixed directed networks of dynamic agents are investigated. Group consensus means that the agents in each group share a consistent value while there is no agreement between any two groups. Based on algebraic graph theory, sufficient conditions guaranteeing group consensus under the proposed control protocol in the presence of random noises and communication delays are derived. The analysis uses a stability result of Mao for stochastic differential delay equations, which ensures the consensus can be achieved almost surely and exponentially fast. Numerical examples are provided to demonstrate the availability of the obtained results as well as the effect of time delay/noise intensity. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate average consensus problem in continuous-time multi-agent systems with uncertain topologies as well as multiple time-varying communication delays. The network of dynamic agents is directed and both fixed and switching topologies are considered. By using the linear matrix inequality method, we prove that all the nodes in the network can achieve average consensus asymptotically for appropriate delays and uncertainties if the network topology is weakly connected and balanced. Feasible linear matrix inequalities are established to determine the maximal allowable upper bounds of multiple delays. Numerical examples are presented to illustrate the availability of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the group consensus problem for generic linear multi-agent systems under directed information flow. External adapted inputs are introduced to realize the intra-group synchronization as well as the inter-group separation. Without imposing complicated algebraic criteria or restrictive graphic conditions on the interaction topology, we show that the group consensus can be achieved by designing appropriate gains given any magnitude of the coupling strengths among the agents. Numerical examples are presented to illustrate the availability of our results. [ABSTRACT FROM AUTHOR]

Resilience or recovery of multi-agent systems against attacks is believed to be one of the most important topics in control and management of complex systems. Previous studies have mainly focused on the random failure and intentional attack targeted on node degrees, whereas consensus recovery is much less investigated. In this paper, two kinds of targeted attacks are introduced and corresponding recovery strategies are proposed to address the consensus recovery of continuous-time nonlinear multi-agent systems under directed topologies against subsequent attacks. The cut-nodes and cut-edges are chosen as the targets of attack, and the multi-agent system becomes disconnected when they are deleted from the system. The neighbor nodes of the cut-node and end nodes of the cut-edge are used to recover the connectivity of the network. It is shown that our proposed strategies can significantly improve the convergence speed of reaching consensus of the resulting multi-agent systems. A cost function is also proposed to compare different recovery strategies. [ABSTRACT FROM AUTHOR]

Abstract: Understanding how interacting subsystems of an overall system lead to cluster/group consensus is a key issue in the investigation of multi-agent systems. In this Letter, we study the group consensus problem of discrete-time multi-agent systems with external stochastic inputs. Based on ergodicity theory and matrix analysis, group consensus criteria are obtained for multi-agent systems with switching topologies. Some numerical examples are provided to illustrate the effectiveness and feasibility of the theoretical results. [Copyright &y& Elsevier]

We addressL1group consensus problems of networked multi-agent systems with fixed directed information exchange in this article. A discrete-time protocol is designed to solve theL1group consensus problems via general stochastic inputs. Under some mild assumptions, we derive sufficient conditions to guarantee theL1group consensus based on algebraic graph theory and ergodicity theory for finite Markov chains. Moreover, the boundedness of the expected infinite sum of the inputs ensures the boundedness of the expected trajectory. Numerical simulations instantiating the inputs as varied independent and identically distributed random processes as well as autoregressive processes are presented to demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM PUBLISHER]

In this article, we study finite-time state consensus problems for continuous multi-agent systems with nonlinear protocols. Building on the theory of finite-time Lyapunov stability, we propose sufficient criteria which guarantee the system to reach a consensus in finite time, provided that the underlying directed network contains a spanning tree. Novel finite-time consensus protocols are introduced as examples for applying the criteria. Simulations are also presented to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates resilient consensus problems over directed networks with state constraints. Cooperative agents in the network can potentially be influenced by uncooperative neighbors, who are knowledgeable, anonymous and able to spread misinformation. We formulate the resilient constrained consensus problem for high-dimensional multi-agent systems. A projection based resilient constrained consensus protocol is presented so that the agent's state will be pushed back to the constraint set when it approaches the boundary. We show that resilient constrained consensus can be reached for robust networks when the constraint sets are convex and share a non-empty overlap. The proposed algorithm is of low complexity, purely distributed, and can be performed in tandem with a max-consensus process to estimate the allowed number of uncooperative neighbors. [ABSTRACT FROM AUTHOR]

Multiscale consensus has been studied recently as a new concept in the field of multi-agent systems, which is able to accommodate many complicated coordination control tasks where values are measured in different scales due to, e.g., the constraints of physical environment. In this paper, we investigate the problem of resilient multiscale coordination control against a set of adversarial or non-cooperative nodes in directed networks. We design a multiscale filtering algorithm based upon local information which can withstand both faulty and Byzantine nodes. Building on the concept of network robustness, we establish necessary and sufficient conditions guaranteeing multiscale consensus with general time varying scales in the presence of globally bounded as well as locally bounded threats. In particular, for a network containing at most R faulty nodes, multiscale consensus is achieved if and only if the network is (R + 1 , R + 1) -robust. The counterpart when having at most R Byzantine nodes instead is that the induced subnetwork of cooperative nodes is R + 1 -robust. Conditions guaranteeing resilient consensus for time-dependent networks are developed. Moreover, multiscale formation generation problems are introduced and solved as the generalizations. Finally, some numerical examples including applications in modular microgrids and power systems are worked out to demonstrate the availability of our theoretical results. [ABSTRACT FROM AUTHOR]