Group bounded consensus control of second-order multi-agent systems under unknown deception attacks

This paper investigates the group bounded consensus of the second-order multi-agent systems (MASs). Aiming at the issue that MASs are subjected to unknown deception attacks, the fuzzy logic systems are introduced to estimate the attacks. By virtue of the neighboring agents states information and the compensation function, pinning control protocols are designed to realize the group bounded consensus, where the compensation function is given by the fuzzy logic method. According to the graph theory, linear matrix inequality technique and Lyapunov function approach, the conditions for achieving the group consensus between two subgroups under attacks are put forward. Besides, the corresponding results are extended to the case of multiple subgroups. Meanwhile, a practical algorithm for group consensus is proposed and consensus error bound is calculated. Eventually, numerical examples are employed to validate that pinning control protocols are effective for second-order MASs.