Resilient consensus of second-order agent networks: Asynchronous update rules with delays

Abstract

We study the problem of resilient consensus of sampled-data multi-agent networks with double-integrator dynamics. The term resilient points to algorithms considering the presence of attacks by faulty/malicious agents in the network. Each normal agent updates its state based on a predetermined control law using its neighbors' information which may be delayed while misbehaving agents make updates arbitrarily and might threaten the consensus within the network. Assuming that the maximum number of malicious agents in the system is known, we focus on algorithms where each normal agent ignores large and small position values among its neighbors to avoid being influenced by malicious agents. The malicious agents are assumed to be omniscient in that they know the updating times and delays and can collude with each other. We deal with both synchronous and partially asynchronous cases with delayed information and derive topological conditions in terms of graph robustness.

A New Approach for Distributed Hypothesis Testing with Extensions to Byzantine-Resilience

“…Pick any agent i ∈ L m (θ , θ), and notice that it has a neighbor j (say) from the set (m−1) q=0 L q (θ , θ) at some time-step τ ∈ [(m − 1)T, mT ). The induction hypothesis coupled with (35) implies that c j,τ (θ) ≤ τ , and hence c i,τ +1 (θ) ≤ c j,τ (θ) + 1 ≤ τ + 1 based on (31). Appealing to (35) then reveals that c i,mT (θ) ≤ mT , thus completing the induction step.…”

“…We prove part (i) by inducting on the value of c i,t (θ). For the base case, suppose c i,t (θ) = 1 for some agent i ∈ V \ {v θ } at some time-step t. Based on (31), notice that this can happen if and only if v θ ∈ N i [t − 1]; the claim in part (i) then follows readily for the base case. Fix an integer m ≥ 2, and suppose that the assertion of part (i) holds for any agent i ∈ V \ {v θ } and at any time-step t, whenever c i,t (θ) ∈ {1, .…”

“…Finally, we emphasize that the non-adversarial agents are unaware of the identities of the adversaries in their neighborhood. As is fairly standard in the distributed fault-tolerant literature [29][30][31][32][33][34][35][36], we only assume that non-adversarial agents know the upper bound f on the number of adversaries in their neighborhood. The adversarial set will be denoted by A ⊂ V, and the remaining agents R = V \ A will be called the regular agents.…”

Robust Cooperative Guidance Law for Simultaneous Arrival

“…estimates; 8 end 9 Define R i (t k ) as the set of in-neighbors of ith interceptor whose time-to-go estimate is retained at time-step t k ; 10 The time-varying communication weights are defined as…”

“…The unknown dynamics caused by faulty interceptors make the cooperative guidance design for the normal interceptors difficult. Inspired by the time-to-go approximate model in [4] and the notion of network robustness [9]- [11], we integrate a local filtering algorithm with other cooperative guidance law and present a useful robust cooperative guidance law (RCGL). If the misbehavior of faulty interceptors can be characterized by a threat model (each faulty interceptor sends the same value to all of its out-neighbors at each time-step), the RCGL can reduce the variance of impact times between normal interceptors without identifying faulty interceptors.…”