Optimal mass transport and kernel density estimation for state-dependent networked dynamic systems

Abstract: State-dependent networked dynamical systems are ones where the interconnections between agents change as a function of the states of the agents. Such systems are highly nonlinear, and a cohesive strategy for their control is lacking in the literature. In this paper, we present two techniques pertaining to the density control of such systems. Agent states are initially distributed according to some density, and a feedback law is designed to move the agents to a target density profile. We use optimal mass transport to design a feedforward control law propelling the agents towards this target density. Kernel density estimation, with constraints imposed by the state-dependent dynamics, is then used to allow each agent to estimate the local density of the agents.