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Distributed Control Design and Safety Verification for Multi-Agent Systems. (arXiv:2303.12610v1 [eess.SY])

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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, with probabilistically guaranteed
constraint satisfication, while generating a Lipschitz continuous control
input. We further develop a distributed safety verification algorithm to
quantify safety for a multi-agent system by means of CBFs in probability. 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.

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