This paper considers the multi-dimensional consensus in networked systems, where some of the agents might be misbehaving (or faulty). Despite the influence of these misbehaviors, the benign agents aim to reach an agreement while avoiding being seriously influenced by the faulty ones. To this end, this paper first considers a general class of consensus algorithms, where each benign agent computes an "auxiliary point" based on the received values and moves its state toward this point. Concerning this generic form, we present conditions for achieving resilient consensus and obtain a lower bound on the exponential convergence rate. Assuming that the number of malicious agents is upper bounded, two specific resilient consensus algorithms are further developed based on the obtained conditions. Particularly, the first solution, based on Helly's Theorem, achieves the consensus within the convex hull formed by the benign agents' initial states, where the auxiliary point can be efficiently computed through linear programming. On the other hand, the second algorithm serves as a "built-in" security guarantee for standard average consensus algorithms, in the sense that its performance coincides exactly with that of the standard ones in the absence of faulty nodes while also resisting the serious influence of the misbehaving ones in adversarial environment. Some numerical examples are provided in the end to verify the theoretical results.
We study the problem of resilient average consensus for multi-agent systems with misbehaving nodes. To protect consensus valuefrom being influenced by misbehaving nodes, we address this problem by detecting misbehaviors, mitigating the corresponding adverse impact and achieving the resilient average consensus. In this paper, general types of misbehaviors are considered,including deception attacks, accidental faults and link failures. We characterize the adverse impact of misbehaving nodes in a distributed manner via two-hop communication information and develop a deterministic detection-compen…
Several algorithms in prior literature have been proposed which guarantee consensus of normally behaving agents in a network that may contain adversarially behaving agents. These algorithms guarantee that the consensus value lies within the convex hull of initial normal agents' states, with the exact consensus value possibly being unknown. In leader-follower consensus problems however, the objective is for normally behaving agents to track a reference state that may take on values outside of this convex hull. In this paper we present methods for agents in time-varying graphs with discrete-time…
The problem of consensus in the presence of adversarially behaving agents has been studied extensively in the literature. The proposed algorithms typically guarantee that the consensus value lies within the convex hull of initial normal agents' states. In leader-follower consensus problems however, the objective for normally behaving agents is to track a time-varying reference state that may take on values outside of this convex hull. In this paper we present a method for agents with discrete-time dynamics to resiliently track a set of leaders' common time-varying reference state despite a bou…
This paper considers a resilient high-dimensional constrained consensus problem and studies a resilient distributed algorithm for complete graphs. For convex constrained sets with a singleton intersection, a sufficient condition on feasibility redundancy and set regularity for reaching a desired consensus exponentially fast in the presence of Byzantine agents is derived, which can be directly applied to polyhedral sets. A necessary condition on feasibility redundancy for the resilient constrained consensus problem to be solvable is also provided.
This paper considers the resilient multi-dimensional consensus problem in networked systems, where some of the agents might be malicious (or faulty). We propose a multi-dimensional consensus algorithm, where at each time step each healthy agent computes a "safe kernel" based on the information from its neighbors, and modifies its own state towards a point inside the kernel. Assuming that the number of malicious agents is locally (or globally) upper bounded, sufficient conditions on the network topology are presented to guarantee that the benign agents exponentially reach an agreement within th…
In this paper, we study the relationship between resilience and accuracy in the resilient distributed multi-dimensional consensus problem. We consider a network of agents, each of which has a state in $\mathbb{R}^d$. Some agents in the network are adversarial and can change their states arbitrarily. The normal (non-adversarial) agents interact locally and update their states to achieve consensus at some point in the convex hull $\calC$ of their initial states. This objective is achievable if the number of adversaries in the neighborhood of normal agents is less than a specific value, which is …
The paper considers the problem of multi-agent consensus in the presence of adversarial agents which may try to prevent and introduce undesired influence on the coordination among the regular agents. To our setting, we extend the so-called mean subsequence reduced algorithms with the aim to reduce the amount of communication via two measures: The agents exchange information in the form of ternary data at each transmission and moreover keep the frequency of data exchange low by employing self- and event-triggered communication. We will observe that in hostile environments with adversaries, the …
In this paper, we study the resilient vector consensus problem in networks with adversarial agents and improve resilience guarantees of existing algorithms. A common approach to achieving resilient vector consensus is that every non-adversarial (or normal) agent in the network updates its state by moving towards a point in the convex hull of its \emph{normal} neighbors' states. Since an agent cannot distinguish between its normal and adversarial neighbors, computing such a point, often called as \emph{safe point}, is a challenging task. To compute a safe point, we propose to use the notion of …
Many algorithms have been proposed in prior literature to guarantee resilient multi-agent consensus in the presence of adversarial attacks or faults. The majority of prior work present excellent results that focus on discrete-time or discretized continuous-time systems. Fewer authors have explored applying similar resilient techniques to continuous-time systems without discretization. These prior works typically consider asymptotic convergence and make assumptions such as continuity of adversarial signals, the existence of a dwell time between switching instances for the system dynamics, or th…
In this paper, we address the discrete-time dynamic average consensus (DAC) of a multi-agent system in the presence of adversarial attacks. The adversarial attack is considered to be of Byzantine type, which compromises the computation capabilities of the agent and sends arbitrary false data to its neighbours. We assume a few of the agents cannot be compromised by adversaries, which we term trusted agents. We first formally define resilient DAC in the presence of Byzantine adversaries. Then we propose our novel Resilient Dynamic Average Consensus (ResDAC) algorithm that ensures the trusted and…
In this paper, we study the problem of resilient consensus for a multi-agent network where some of the nodes might be adversarial, attempting to prevent consensus by transmitting faulty values. Our approach is based on that of the so-called weighted mean subsequence reduced (W-MSR) algorithm with a special emphasis on its use in agents capable to communicate with multi-hop neighbors. The MSR algorithm is a powerful tool for achieving resilient consensus under minimal requirements for network structures, characterized by the class of robust graphs. Our analysis highlights that through multi-hop…
A cyber security problem in a networked system formulated as a resilient graph problem based on a game-theoretic approach is considered. The connectivity of the underlying graph of the network system is reduced by an attacker who removes some of the edges whereas the defender attempts to recover them. Both players are subject to energy constraints so that their actions are restricted and cannot be performed continuously. For this two-stage game, which is played repeatedly over time, we characterize the optimal strategies for the attacker and the defender in terms of edge connectivity and the n…
This paper addresses novel consensus problems for multi-agent systems operating in an unreliable environment where adversaries are spreading. The dynamics of the adversarial spreading processes follows the susceptible-infected-recovered (SIR) model, where the infection induces faulty behaviors in the agents and affects their state values. Such a problem setting serves as a model of opinion dynamics in social networks where consensus is to be formed at the time of pandemic and infected individuals may deviate from their true opinions. To ensure resilient consensus among the noninfectious agents…
This paper addresses novel consensus problems in the presence of adversaries that can move within the network and induce faulty behaviors in the attacked agents. By adopting several mobile adversary models from the computer science literature, we develop protocols which can mitigate the influence of such malicious agents. The algorithms follow the class of mean subsequence reduced (MSR) algorithms, under which agents ignore the suspicious values received from neighbors during their state updates. Different from the static adversary models, even after the adversaries move away, the infected age…
A networked system can be made resilient against adversaries and attacks if the underlying network graph is structurally robust. For instance, to achieve distributed consensus in the presence of adversaries, the underlying network graph needs to satisfy certain robustness conditions. A typical approach to making networks structurally robust is to strategically add extra links between nodes, which might be prohibitively expensive. In this paper, we propose an alternative way of improving network's robustness, that is by considering heterogeneity of nodes. Nodes in a network can be of different …
In the face of an increasingly broad cyberattack surface, cyberattack-resilient load forecasting for electric utilities is both more necessary and more challenging than ever. In this paper, we propose an adversarial machine learning (AML) approach, which can respond to a wide range of attack behaviors without detecting outliers. It strikes a balance between enhancing a system's robustness against cyberattacks and maintaining a reasonable degree of forecasting accuracy when there is no attack. Attack models and configurations for the adversarial training were selected and evaluated to achieve t…
The University of Hong Kong（香港大学）；Shenzhen University（深圳大学）；Texas A&M University at Qatar（德州农工大学卡塔尔分校）
This paper studies the problem of cooperative control of heterogeneous multi-agent systems (MASs) against Byzantine attacks. The agent affected by Byzantine attacks sends different wrong values to all neighbors while applying wrong input signals for itself, which is aggressive and difficult to be defended. Inspired by the concept of Digital Twin, a new hierarchical protocol equipped with a virtual twin layer (TL) is proposed, which decouples the above problems into the defense scheme against Byzantine edge attacks on the TL and the defense scheme against Byzantine node attacks on the cyber-phy…
The threats on cyber-physical system have changed much into a level of sophistication that elude the traditional security and protection methods. This work addresses a proactive approaches to the cyber security of a formation flying UAVs. A resilient formation control of UAVs in the presence of non-cooperative (defective or malicious) UAVs is presented. Based on local information a resilient consensus in the presence of misbehaving nodes is dealt with fault-tolerant consensus algorithm. In the proposed framework, a graph-theoretic property of network robustness conveying the notion of a direct…
University of Notre Dame（圣母大学）；Stony Brook University（石溪大学）
Adversarial attacks during training can strongly influence the performance of multi-agent reinforcement learning algorithms. It is, thus, highly desirable to augment existing algorithms such that the impact of adversarial attacks on cooperative networks is eliminated, or at least bounded. In this work, we consider a fully decentralized network, where each agent receives a local reward and observes the global state and action. We propose a resilient consensus-based actor-critic algorithm, whereby each agent estimates the team-average reward and value function, and communicates the associated pa…
We tackle the problem of a set of agents achieving resilient consensus in the presence of attacked agents. We present a discrete-time reputation-based consensus algorithm for synchronous and asynchronous networks by developing a local strategy where, at each time, each agent assigns a reputation (between zero and one) to each neighbor. The reputation is then used to weigh the neighbors' values in the update of its state. Under mild assumptions, we show that: (i) the proposed method converges exponentially to the consensus of the regular agents; (ii) if a regular agent identifies a neighbor as …
An approach to resilient planning and control of autonomous vehicles in multi-vehicle traffic scenarios is proposed. The proposed method is based on model predictive control (MPC), where alternative predictions of the surrounding traffic are determined automatically such that they are intentionally adversarial to the ego vehicle. This provides robustness against the inherent uncertainty in traffic predictions. To reduce conservatism, an assumption that other agents are of no ill intent is formalized. Simulation results from highway driving scenarios show that the proposed method in real-time n…
In this paper, we consider a multi-agent resilient consensus problem, where some of the nodes may behave maliciously. The approach is to equip all nodes with a scheme to detect neighboring nodes when they behave in an abnormal fashion. To this end, the nodes exchange not only their own states but also information regarding their neighbor nodes. Such two-hop communication has long been studied in fault-tolerant algorithms in computer science. We propose two distributed schemes for detection of malicious nodes and resilient consensus with different requirements on resources for communication and…
Evolution of agents' dynamics of multiagent systems under consensus protocol in the face of jamming attacks is discussed, where centralized parties are able to influence the control signals of the agents. In this paper we focus on a game-theoretical approach of multiagent systems where the players have incomplete information on their opponents' strength. We consider repeated games with both simultaneous and sequential player actions where players update their beliefs of each other over time. The effect of the players' optimal strategies according to Bayesian Nash Equilibrium and Perfect Bayesi…
Networked microgrids with high penetration of distributed generators have ubiquitous remote information exchange, which may be exposed to various cyber security threats. This paper, for the first time, addresses a consensus problem in terms of frequency synchronisation in networked microgrids subject to multi-layer denial of service (DoS) attacks, which could simultaneously affect communication, measurement and control actuation channels. A unified notion of Persistency-of-Data-Flow (PoDF) is proposed to characterise the data unavailability in different information network links, and further q…
LEO satellite constellation coverage has served as the base platform for various space applications. However, the rapidly evolving security environment such as orbit debris and adversarial space threats are greatly endangering the security of satellite constellation and integrity of the satellite constellation coverage. As on-orbit repairs are challenging, a distributed and autonomous protection mechanism is necessary to ensure the adaptation and self-healing of the satellite constellation coverage from different attacks. To this end, we establish an integrative and distributed framework to en…
The University of Hong Kong（香港大学）；Shenzhen University（深圳大学）；China Academy of Space Technology（中国空间技术研究院）；University of Alberta（阿尔伯塔大学）；Texas A&M University at Qatar（德州农工大学卡塔尔分校）
This paper studies the leader-following consensuses of uncertain and nonlinear multi-agent systems against composite attacks (CAs), including Denial of Service (DoS) attacks and actuation attacks (AAs). A double-layer control framework is formulated, where a digital twin layer (TL) is added beside the traditional cyber-physical layer (CPL), inspired by the recent Digital Twin technology. Consequently, the resilient control task against CAs can be divided into two parts: One is distributed estimation against DoS attacks on the TL and the other is resilient decentralized tracking control against…
Recently, many cooperative distributed multi-agent reinforcement learning (MARL) algorithms have been proposed in the literature. In this work, we study the effect of adversarial attacks on a network that employs a consensus-based MARL algorithm. We show that an adversarial agent can persuade all the other agents in the network to implement policies that optimize an objective that it desires. In this sense, the standard consensus-based MARL algorithms are fragile to attacks.
