Data‐Driven Distributed Safe Control Design for Multi‐Agent Systems

ABSTRACT This paper presents a data‐driven control barrier function (CBF) technique for ensuring safe control of multi‐agent systems (MASs) with uncertain linear dynamics. A data‐driven quadratic programming (QP) optimization is first developed for CBF‐based safe control of single‐agent systems using a nonlinear controller. This approach is then extended to the distributed safe control of MASs. To bypass system identification, the closed‐loop dynamics are represented using collected data, and the safety constraints are imposed on this closed‐loop representation. This data‐efficient representation is subsequently integrated into QP optimizations, resulting in data‐driven QP formulations that learn the closed‐loop systems and their corresponding controllers, ensuring the safety of the MASs. As a result, the presented CBF‐based approach designs a safe controller based solely on input, state, and state‐derivative measurements without requiring knowledge of the underlying dynamics of the agents. Furthermore, for the special case of linear controllers, we show that the need for state‐derivative measurements can be eliminated. We also show that the sample complexity of learning closed‐loop dynamics is less than that of its model‐based counterpart, which relies on open‐loop system identification. The simulation results for a safe formation control problem demonstrate the efficacy of the proposed approach for the MASs.