Controlling noisy herds.

Controlling multi-agent systems is a persistent challenge in organismal, robotic, and social collectives, especially when agents exhibit stochastic indecisiveness - frequently switching between conflicting behavioral rules. Here, we investigate the control of such noisy indecisive collectives through the lens of century-old sheepdog trials, where small groups of sheep exhibit unpredictable switching between fleeing and following behaviors. Unlike cohesive large flocks, these small indecisive groups are difficult to control, yet skilled dog-handler teams excel at both herding and precisely splitting them (shedding) on demand. Using a stochastic model, we introduce two central parameters - pressure (stimulus intensity) and lightness (response isotropy) - to simulate and quantify herding and shedding dynamics. Light sheep rapidly reach stable herding states, while heavy sheep exhibit intermittent herding and orthogonal alignment to the dog. High response isotropy fosters group cohesion but complicates splitting tasks, highlighting the nuanced trade-offs in collective control of noisy herds. Surprisingly, we find that stochastic indecisiveness, typically perceived as a challenge, can be leveraged as a critical tool for efficient control, enabling controlled herding and splitting of noisy groups. Building on these insights, we develop the Indecisive Swarm Algorithm (ISA) for artificial agents and benchmark its performance against standard algorithms, including the Averaging-Based Swarm Algorithm (ASA) and the Leader-Follower Swarm Algorithm (LFSA). ISA minimizes control energy in trajectory-following tasks, outperforming alternatives under noisy conditions. By framing these results within a stochastic temporal network framework, we show that even with a probabilistic description of the future dynamics, network restructuring (temporality) enhances control efficiency in a specific class of control problems. These insights establish a scalable framework for controlling noisy, behavior-switching collectives, with applications in swarm robotics, cellular engineering, opinion dynamics, and temporal networks.