LAUSR

Existing resilient consensus algorithms are mainly developed based on the mean subsequence reduced (MSR) method, which relies on the assumption that there exist at most $f$ malicious agents in the entire network or each neighborhood (i.e., $f$-total or $f$-local model). However, in some practical cases, it may be impossible to estimate an appropriate upper bound on the number of malicious agents. This paper proposes a novel method, called trusted-region subsequence reduction (TSR), for designing resilient consensus algorithm without the $f$-total/local model assumption. The main idea of the TSR method is to filter out the received information beyond a dynamic trusted region, determined by the current relative positions of the neighboring trusted nodes. Based on the TSR method, we design a sampled-data resilient consensus algorithm for double-integrator multi-agent networks. A necessary and sufficient graph-theoretic condition is obtained to achieve resilient consensus. Finally, simulations are conducted to illustrate the effectiveness of the proposed algorithm and the faster convergence rate of the TSR-based algorithm than the classical MSR-based algorithm.