  There has been a growing interest in realizing the resilient consensus of the
multi-agent system (MAS) under cyber-attacks, which aims to achieve the
consensus of normal agents (i.e., agents without attacks) in a network,
depending on the neighboring information. The literature has developed
mean-subsequence-reduced (MSR) algorithms for the MAS with F adversarial
attacks and has shown that the consensus is achieved for the normal agents when
the communication network is at least (2F+1)-robust. However, such a stringent
requirement on the communication network needs to be relaxed to enable more
practical applications. Our objective is, for the first time, to achieve less
stringent conditions on the network, while ensuring the resilient consensus for
the general linear MAS subject to control input constraints. In this work, we
propose a distributed resilient consensus framework, consisting of a
pre-designed consensus protocol and distributed model predictive control (DMPC)
optimization, which can help significantly reduce the requirement on the
network robustness and effectively handle the general linear constrained MAS
under adversarial attacks. By employing a novel distributed adversarial attack
detection mechanism based on the history information broadcast by neighbors and
a convex set (i.e., resilience set), we can evaluate the reliability of
communication links. Moreover, we show that the recursive feasibility of the
associated DMPC optimization problem can be guaranteed. The proposed consensus
protocol features the following properties: 1) by minimizing a group of control
variables, the consensus performance is optimized; 2) the resilient consensus
of the general linear constrained MAS subject to F-locally adversarial attacks
is achieved when the communication network is (F+1)-robust. Finally, numerical
simulation results are presented to verify the theoretical results.
