  This paper proposes a new approach that enables multi-agent systems to
achieve resilient \textit{constrained} consensus in the presence of Byzantine
attacks, in contrast to existing literature that is only applicable to
\textit{unconstrained} resilient consensus problems. The key enabler for our
approach is a new device called a \textit{$(\gamma_i,\alpha_i)$-resilient
convex combination}, which allows normal agents in the network to utilize their
locally available information to automatically isolate the impact of the
Byzantine agents. Such a resilient convex combination is computable through
linear programming, whose complexity scales well with the size of the overall
system. By applying this new device to multi-agent systems, we introduce
network and constraint redundancy conditions under which resilient constrained
consensus can be achieved with an exponential convergence rate. We also provide
insights on the design of a network such that the redundancy conditions are
satisfied. Finally, numerical simulations and an example of safe multi-agent
learning are provided to demonstrate the effectiveness of the proposed results.
