  We propose distributed iterative algorithms for safe control design and
safety verification for networked multi-agent systems. These algorithms rely on
distributing a control barrier function (CBF) related quadratic programming
(QP) problem. The proposed distributed algorithm addresses infeasibility issues
of existing schemes by dynamically allocating auxiliary variables across
iterations. The resulting control input is guaranteed to be optimal, and
renders the system safe. Furthermore, a truncated algorithm is proposed to
facilitate computational implementation. The performance of the truncated
algorithm is evaluated using a distributed safety verification algorithm. The
algorithm quantifies safety for a multi-agent system probabilistically, using a
certain locally Lipschitz continuous feedback controller by means of CBFs. Both
upper and lower bounds on the probability of safety are obtained using the so
called scenario approach. Both the scenario sampling and safety verification
procedures are fully distributed. The efficacy of our algorithms is
demonstrated by an example on multi-robot collision avoidance.
