Density Control of Interacting Agent Systems

We consider the problem of controlling group behavior a large number dynamic systems that are constantly interacting with each other. These assumed to have identical dynamics (e.g., flocks birds, UAV swarms) and their can be modeled by distribution. Thus, this viewed as an optimal control over space distributions. propose novel algorithm compute feedback strategy so that, when adopted agents, distribution them would transformed from initial one target finite time window. Our method is built on transport theory but differs significantly existing work in area our models interactions among agents explicitly. From algorithmic point view, based generalized proximal gradient descent has convergence guarantee sublinear rate. further extend framework account for scenarios where multiple species. In linear quadratic setting, solution characterized system coupled Riccati equations which solved closed form. Finally, several numerical examples presented illustrate framework.