Stochastic Hybrid Networks for Global Almost Sure Unanimous Decision Making

A stochastic, hybrid algorithm for global almost sure unanimous decision making in multiagent systems is introduced. Homogeneous agents communicate over an undirected connected graph to make a unanimous selection among a finite set of decision states. The agents have inertia corresponding to stable, linear, and continuous-time dynamics. The algorithm equips each agent with a logic variable and designs logic-variable reset rules to ensure eventual unanimity. These resets occur randomly in time. They are randomly assigned among those indices of the decision states that nearly minimize the value of a function that quantifies the mismatch between the average of the agent states, or a local estimate thereof, and the corresponding decision state. In order to satisfy regularity properties that confer robustness, the resulting update rule corresponds to an inclusion, i.e., a set-valued mapping. Global almost sure decision making is established using a classical Lyapunov function argument that has recently been extended to stochastic hybrid inclusions.