Dynamic Resilient Network Games with Applications to Multi-Agent Consensus

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 number of connected components of the graph. The resilient graph game is then applied to a multi-agent consensus problem. We study how the attacks and the recovery on the edges affect the consensus process. Finally, we also provide numerical simulation to illustrate the results.Comment: 12 pages, 13 figure

Effects of Topology Knowledge and Relay Depth on Asynchronous Appoximate Consensus

Consider a point-to-point message-passing network. We are interested in the asynchronous crash-tolerant consensus problem in incomplete networks. We study the feasibility and efficiency of approximate consensus under different restrictions on topology knowledge and the relay depth, i.e., the maximum number of hops any message can be relayed. These two constraints are common in large-scale networks, and are used to avoid memory overload and network congestion respectively. Specifically, for positive integer values k and k\u27, we consider that each node knows all its neighbors of at most k-hop distance (k-hop topology knowledge), and the relay depth is k\u27. We consider both directed and undirected graphs. More concretely, we answer the following question in asynchronous systems: "What is a tight condition on the underlying communication graphs for achieving approximate consensus if each node has only a k-hop topology knowledge and relay depth k\u27?" To prove that the necessary conditions presented in the paper are also sufficient, we have developed algorithms that achieve consensus in graphs satisfying those conditions: - The first class of algorithms requires k-hop topology knowledge and relay depth k. Unlike prior algorithms, these algorithms do not flood the network, and each node does not need the full topology knowledge. We show how the convergence time and the message complexity of those algorithms is affected by k, providing the respective upper bounds. - The second set of algorithms requires only one-hop neighborhood knowledge, i.e., immediate incoming and outgoing neighbors, but needs to flood the network (i.e., relay depth is n, where n is the number of nodes). One result that may be of independent interest is a topology discovery mechanism to learn and "estimate" the topology in asynchronous directed networks with crash faults

Event-triggered Consensus Frameworks for Multi-agent Systems

Recently, distributed multi-agent systems (MAS) have been widely studied for a variety of engineering applications, including cooperative vehicular systems, sensor networks, and electrical power grids. To solve the allocated tasks in MASs, each agent autonomously determines the appropriate actions using information available locally and received from its neighbours. Many cooperative behaviours in MAS are based on a consensus algorithm. Consensus, by definition, is to distributively agree on a parameter of interest between the agents. Depending on the application, consensus has different configurations such as leader-following, formation, synchronization in robotic arms, and state estimation in sensor networks. Consensus in MASs requires local measurements and information exchanges between the neighbouring agents. Due to the energy restriction, hardware limitation, and bandwidth constraint, strategies that reduce the amount of measurements and information exchanges between the agents are of paramount interest. Event-triggering transmission schemes are among the most recent strategies that efficiently reduce the number of transmissions. This dissertation proposes a number of event-triggered consensus (ETC) implementations which are applicable to MASs. Different performance objectives and physical constraints, such as a desired convergence rate, robustness to uncertainty in control realization, information quantization, sampled-data processing, and resilience to denial of service (DoS) attacks are included in realization of the proposed algorithms. A novel convex optimization is proposed which simultaneously designs the control and event-triggering parameters in a unified framework. The optimization governs the trade-off between the consensus convergence rate and intensity of transmissions. This co-design optimization is extended to an advanced class of event-triggered schemes, known as the dynamic event-triggering (DET), which is able to substantially reduce the amount of transmissions. In the presence of DoS attacks, the co-design optimization simultaneously computes the control and DET parameters so that the number of transmissions is reduced and a desired level of resilience to DoS is guaranteed. In addition to consensus, a formation-containment implementation is proposed, where the amount of transmissions are reduced using the DET schemes. The performance of the proposed implementations are evaluated through simulation over several MASs. The experimental results demonstrate the effectiveness of the proposed implementations and verify their design flexibility