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This paper presents an adaptive hybrid feedback law designed to robustly steer a group of autonomous vehicles toward the source of an unknown but measurable signal, at the same time that an obstacle is avoided and a prescribed formation is maintained. The hybrid law overcomes the limitations imposed by the topological obstructions induced by the obstacle, which precludes the robust stabilization of the source of the signal by using smooth feedback. The control strategy implements a leader-follower approach, where the followers track, in a coordinated way, the position of the leader. 

Summary This paper introduces a new class of feedback‐based data‐driven extremum seeking algorithms for the solution of model‐free optimization problems in smooth continuous‐time dynamical systems. The novelty of the algorithms lies on the incorporation of memory to store recorded data that enables the use of information‐rich datasets during the optimization process, and allows to dispense with the time‐varying dither excitation signal needed by standard extremum seeking algorithms that rely on a persistence of excitation (PE) condition. The model‐free optimization dynamics are developed for single‐agent systems, as well as for multi‐agent systems with communication graphs that allow agents to share their state information while preserving the privacy of their individual data. In both cases, sufficient richness conditions on the recorded data, as well as suitable optimization dynamics modeled by ordinary differential equations are characterized in order to guarantee convergence to a neighborhood of the solution of the extremum seeking problems. The performance of the algorithms is illustrated via different numerical examples in the context of source‐seeking problems in multivehicle systems.