Resilient Multiscale Coordination Control against Adversarial Nodes

Abstract

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.Energies 2018, 11, 1844 2 of 17 be specialized to obtain standard consensus, cluster or group consensus [9], in which different subnetworks are allowed to achieve different consistent values, bipartite consensus [10] and sign consensus [11] by adopting appropriate scales.Multiscale consensus has been explored for fixed strongly connected topology in [8] as well as switching topologies in [12], where the autonomous agents are described by continuous-time single integrators. Some scaled consensus protocols are proposed to solve the finite-time coordination control for continuous-time multi-vehicle systems in [13] and for discrete-time ones in [14]. In the recent work [15], multiscale consensus has been further characterized by sufficient and necessary conditions accommodating signal processing delays and signal transmission delays. All the aforementioned work assumes that all agents in the communication networks are cooperative. However, the performance of such systems deteriorates when one or more agents are compromised, potentially preventing the team of cooperative agents from achieving their goal. To the best of our knowledge, the problem of multiscale consensus in the presence of adversaries has not been addressed due to its complexity.Large-scale cyber-physical systems are susceptible to adversarial or non-cooperative nodes due to malicious attacks (for instance, an attacker taking control of the communication module of certain agents trying to manipulate the entire network) or platform-level failures (for instance, a faulty robot sharing an incorrect location due to a defective Global Positioning Sy...

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