Heath J. LeBlanc

Resilient Asymptotic Consensus in Robust Networks

This paper addresses the problem of resilient in-network consensus in the presence of misbehaving nodes. Secure and fault-tolerant consensus algorithms typically assume knowledge of nonlocal information; however, this assumption is not suitable for large-scale dynamic networks. To remedy this, we focus on local strategies that provide resilience to faults and compromised nodes. We design a consensus protocol based on local information that is resilient to worst-case security breaches, assuming the compromised nodes have full knowledge of the network and the intentions of the other nodes. We provide necessary and sufficient conditions for the normal nodes to reach asymptotic consensus despite the influence of the misbehaving nodes under different threat assumptions. We show that traditional metrics such as connectivity are not adequate to characterize the behavior of such algorithms, and develop a novel graph-theoretic property referred to as network robustness. Network robustness formalizes the notion of redundancy of direct information exchange between subsets of nodes in the network, and is a fundamental property for analyzing the behavior of certain distributed algorithms that use only local information.

Consensus of multi-agent networks in the presence of adversaries using only local information

This paper addresses the problem of resilient consensus in the presence of misbehaving nodes. Although it is typical to assume knowledge of at least some nonlocal information when studying secure and fault-tolerant consensus algorithms, this assumption is not suitable for large-scale dynamic networks. To remedy this, we emphasize the use of local strategies to deal with resilience to security breaches. We study a consensus protocol that uses only local information and we consider worst-case security breaches, where the compromised nodes have full knowledge of the network and the intentions of the other nodes. We provide necessary and sufficient conditions for the normal nodes to reach consensus despite the influence of the malicious nodes under different threat assumptions. These conditions are stated in terms of a novel graph-theoretic property referred to as network robustness.

Consensus in networked multi-agent systems with adversaries

In the past decade, numerous consensus protocols for networked multi-agent systems have been proposed. Although some forms of robustness of these algorithms have been studied, reaching consensus securely in networked multi-agent systems, in spite of intrusions caused by malicious agents, or adversaries, has been largely underexplored. In this work, we consider a general model for adversaries in Euclidean space and introduce a consensus problem for networked multi-agent systems similar to the Byzantine consensus problem in distributed computing. We present the Adversarially Robust Consensus Protocol (ARC-P), which combines ideas from consensus algorithms that are resilient to Byzantine faults and from linear consensus protocols used for control and coordination of dynamic agents. We show that ARC-P solves the consensus problem in complete networks whenever there are more cooperative agents than adversaries. Finally, we illustrate the resilience of ARC-P to adversaries through simulations and compare ARC-P with a linear consensus protocol for networked multi-agent systems.

Low complexity resilient consensus in networked multi-agent systems with adversaries

Recently, many applications have arisen in distributed control that require consensus protocols. Concurrently, we have seen a proliferation of malicious attacks on large-scale distributed systems. Hence, there is a need for (i) consensus problems that take into consideration the presence of adversaries and specify correct behavior through appropriate conditions on agreement and safety, and (ii) algorithms for distributed control applications that solve such consensus problems resiliently despite breaches in security. This paper addresses these issues by (i) defining the adversarial asymptotic agreement problem, which requires that the uncompromised agents asymptotically align their states while satisfying an invariant condition in the presence of adversaries, and (ii) by designing a low complexity consensus protocol, the Adversarial Robust Consensus Protocol (ARC-P), which combines ideas from distributed computing and cooperative control. Two types of omniscient adversaries are considered: (i) Byzantine agents can convey different state trajectories to different neighbors in the network, and (ii) malicious agents must convey the same information to each neighbor. For each type of adversary, sufficient conditions are provided that ensure ARC-P guarantees the agreement and safety conditions in static and switching network topologies, whenever the number of adversaries in the network is bounded by a constant. The conservativeness of the conditions is examined, and the conditions are compared to results in the literature.Recently, many applications have arisen in distributed control that require consensus protocols. Concurrently, we have seen a proliferation of malicious attacks on large-scale distributed systems. Hence, there is a need for (i) consensus problems that take into consideration the presence of adversaries and specify correct behavior through appropriate conditions on agreement and safety, and (ii) algorithms for distributed control applications that solve such consensus problems resiliently despite breaches in security. This paper addresses these issues by (i) defining the adversarial asymptotic agreement problem, which requires that the uncompromised agents asymptotically align their states while satisfying an invariant condition in the presence of adversaries, and (ii) by designing a low complexity consensus protocol, the Adversarial Robust Consensus Protocol (ARC-P), which combines ideas from distributed computing and cooperative control. Two types of omniscient adversaries are considered: (i) Byzantine agents can convey different state trajectories to different neighbors in the network, and (ii) malicious agents must convey the same information to each neighbor. For each type of adversary, sufficient conditions are provided that ensure ARC-P guarantees the agreement and safety conditions in static and switching network topologies, whenever the number of adversaries in the network is bounded by a constant. The conservativeness of the conditions is examined, and the conditions are compared to results in the literature.

Resilient continuous-time consensus in fractional robust networks

We study the continuous-time consensus problem in the presence of adversaries. The networked multi-agent system is modeled as a switched system, where the normal agents have integrator dynamics and the switching signal determines the topology of the network. We consider several models of omniscient adversaries under the assumption that at most a fraction of any normal agents neighbors may be adversaries. Under this assumption on the interaction between normal and adversary agents, we show that a novel graph theoretic metric, called fractional robustness, is useful for analyzing the network topologies under which the normal agents achieve consensus.

Resilient asymptotic consensus in asynchronous robust networks

In this paper, we study the problem of reaching consensus asymptotically in the presence of adversary nodes whenever the network is asynchronous under a local broadcast model of communication. The type of adversary considered is omniscient and may collude with other adversaries to achieve the goal of disrupting consensus among the normal nodes. The main limitation on the behavior of the adversary nodes is that whenever the adversary nodes communicate with neighbors, they must broadcast their messages so that all neighbors receive the same information. The asynchronous consensus algorithm studied here uses local strategies to ensure resilience against the adversary nodes. The class of topologies studied are those that are robust. Network robustness formalizes a notion of redundancy of direct information exchange between subsets of nodes in the network, and is an important property for analyzing the behavior of resilient distributed algorithms that use only local information.

A passivity approach for model-based compositional design of networked control systems

The integration of physical systems through computing and networking has become pervasive, a trend now known as cyber-physical systems (CPS). Functionality in CPS emerges from the interaction of networked computational and physical objects. System design and integration are particularly challenging because fundamentally different physical and computational design concerns intersect. The impact of these interactions is the loss of compositionality which creates tremendous challenges. The key idea in this article is to use passivity for decoupling the control design of networked systems from uncertainties such as time delays and packet loss, thus providing a fundamental simplification strategy that limits the complexity of interactions. The main contribution is the application of the approach to an experimental case study of a networked multi-robot system. We present a networked control architecture that ensures the overall system remains stable in spite of implementation uncertainties such as network delays and data dropouts, focusing on the technical details required for the implementation. We describe a prototype domain-specific modeling language and automated code generation tools for the design of networked control systems on top of passivity that facilitate effective system configuration, deployment, and testing. Finally, we present experimental evaluation results that show decoupling of interlayer interactions.

Resilient distributed parameter estimation in heterogeneous time-varying networks

In this paper, we study a lightweight algorithm for distributed parameter estimation in a heterogeneous network in the presence of adversary nodes. All nodes interact under a local broadcast model of communication in a time-varying network comprised of many inexpensive normal nodes, along with several more expensive, reliable nodes. Either the normal or reliable nodes may be tampered with and overtaken by an adversary, thus becoming an adversary node. The reliable nodes have an accurate estimate of their true parameters, whereas the inexpensive normal nodes communicate and take difference measurements with neighbors in the network in order to better estimate their parameters. The normal nodes are unsure, a priori, about which of their neighbors are normal, reliable, or adversary nodes. However, by sharing information on their local estimates with neighbors, we prove that the resilient iterative distributed estimation (RIDE) algorithm, which utilizes redundancy by removing extreme information, is able to drive the local estimates to their true parameters as long as each normal node is able to interact with a sufficient number of reliable nodes often enough and is not directly influenced by too many adversary nodes.

Algorithms for determining network robustness

In this paper, we study algorithms for determining the robustness of a network. Network robustness is a novel graph theoretic property that provides a measure of redundancy of directed edges between all pairs of nonempty, disjoint subsets of nodes in a graph. The robustness of a graph has been shown recently to be useful for characterizing the class of network topologies in which resilient distributed algorithms that use purely local strategies are able to succeed in the presence of adversary nodes. Therefore, network robustness is a critical property of resilient networked systems. While methods have been given to construct robust networks, algorithms for determining the robustness of a given network have not been explored. This paper introduces several algorithms for determining the robustness of a network, and includes centralized, decentralized, and distributed algorithms.

A Passivity-Based Approach to Group Coordination in Multi-agent Networks

Surveillance and convoy tracking applications often require groups of networked agents for redundancy and better coverage. Important goals upon deployment include the establishment of a formation around a target and synchronization of the output (e.g., velocity). Although there exist distributed algorithms using only local communication that achieve these goals, they typically ignore destabilizing effects resulting from implementation uncertainties, such as network delays and data loss. This paper resolves these issues by introducing a discrete-time distributed design framework that uses a compositional, passivity-based approach to ensure \(l_2^m\)-stability regardless of overlay network topology, in the presence of network delays and data loss. For the restricted case of a regular overlay network topology, this work shows that asymptotic formation establishment and output synchronization can be achieved. Finally, simulations of velocity-limited quadrotor unmanned air vehicles (UAVs) are presented to show the performance in the presence of time-varying network delays and varying amounts of data loss.