Adversarial Robustness for Matrix Control Barrier Functions in Sampled-Data Systems

Abstract: This paper presents novel theoretical results to guarantee multi-agent set invariance using Matrix Control Barrier Functions in sampled-data systems. More specifically, the paper presents conditions under which heterogeneous control-affine agents applying zero-order-hold control inputs can compute control inputs to render safe sets defined by matrix inequalities forward invariant. It then introduces methods to guarantee set invariance while accounting for the presence of adversarial agents seeking to drive the system state to unsafe sets. Finally, the paper presents theoretical extensions of these set invariance results to systems having high relative degree with respect to the matrix-valued safe set function.