  Control barrier functions (CBFs) have recently become a powerful method for
rendering desired safe sets forward invariant in single- and multi-agent
systems. In the multi-agent case, prior literature has considered scenarios
where all agents cooperate to ensure that the corresponding set remains
invariant. However, these works do not consider scenarios where a subset of the
agents are behaving adversarially with the intent to violate safety bounds. In
addition, prior results on multi-agent CBFs typically assume that control
inputs are continuous and do not consider sampled-data dynamics. This paper
presents a framework for normally-behaving agents in a multi-agent system with
heterogeneous control-affine, sampled-data dynamics to render a safe set
forward invariant in the presence of adversarial agents. The proposed approach
considers several aspects of practical control systems including input
constraints, clock asynchrony and disturbances, and distributed calculation of
control inputs. Our approach also considers functions describing safe sets
having high relative degree with respect to system dynamics. The efficacy of
these results are demonstrated through simulations.

Optimization and Control