Almost Sure Resilient Consensus Under Stochastic Interaction:Links Failure and Noisy Channels

Abstract

The resilient consensus problem over a class of discrete-time linear multiagent systems is addressed. Because of external cyber-attacks, some agents are assumed to be malicious and not following a desired cooperative behavior. Thus, the objective consists in designing a control strategy for the healthy agents to reach consensus upon their state vectors, while due to interaction among the agents, the malicious agents try to prevent them to achieve consensus. Although this problem has been investigated by some researchers, under the existing approaches in the literature, achieving consensus is only guaranteed when the information exchange among the agents is deterministic. Based on this motivation, the main contribution of the paper is on almost sure resilient consensus control of a network of healthy agents in the presence of stochastic links failure and communication noises. We design a discrete-time protocol for the set of the healthy agents, and we show that under some probabilistic conditions on interaction among the agents, achieving almost sure consensus among the healthy agents can be guaranteed. The results also are verified by numerical examples.

Resilient tracking consensus over dynamic random graphs: A linear system approach

“…On top of these deterministic system dynamics, some randomness has also been incorporated recently in resilient consensus problems to reflect varied challenges in real-world complex systems. Randomized quantized states [8] and random faulty links [21] have been factored in under the framework of almost sure convergence. In [24], mean square convergence for a class of hybrid systems containing some randomly interacting agents as well as misbehaving ones has been examined.…”

“…The former considers agreement seeking in a situation where no leader is present, while the objective of the latter is for other agents to follow the trajectory of a leader. Leaderless and tracking consensus problems have been extensively studied in fixed networks [5,20,28], switching or time-varying networks [12,33], and random networks [21,24]. An overview of some classical control theory results on consensus problems can be found in the review paper [20], and more recent advances are reviewed in the works [2,4] from a broader perspective of system science.…”

Median-Based Resilient Consensus Over Time-Varying Random Networks

“…In the above notation, it is worth noting that j 1 and j 2 essentially depend on the node i and time t. Clearly, we have j 1 = j 2 if d i (t) is odd. Compared to the W-MSR algorithms [4]- [6], [13], we here involve the weighted median of neighbors' states instead of their (reduced) mean. Recall that the estimate of the number of total malicious agents in the neighborhood of each cooperative agent has to be shared among the network in order to implement a W-MSR type algorithm, which is often not realistic in practice.…”

“…We claim that the limit point z must be zero. In fact, if z > 0, we consider three sets of cooperative nodes partitioning C [13]:…”

“…under random link failure and channel noise [13] as well as hybrid random behavior [14]. In some real-world applications involving complicated environment such as smart homes, heuristic algorithms and metaheuristic algorithms have also been widely applied to tackle cooperative control problems in complex nonlinear systems against adversarial hazards or obstacles; see e.g.…”