Partial Resilient Leader-Follower Consensus in Time-Varying Graphs

Existing approaches typically require robustness conditions of the entire network to guarantee resilient consensus. However, the behavior of such systems when these conditions are not fully met remains unexplored. T o address this gap, we introduce the notion of partial leader-follower consensus, in which a subset of non-adversarial followers successfully tracks the leader's reference state despite insufficient robustness. We propose a novel distributed algorithm -- the Bootstrap Percolation and Mean Subsequence Reduced (BP-MSR) algorithm -- and establish sufficient conditions for individual followers to achieve consensus via the BP-MSR algorithm in arbitrary time-varying graphs. We validate our findings through simulations, demonstrating that our method guarantees partial leader-follower consensus, even when standard resilient consensus algorithms fail.