  Controlling large swarms of robotic agents presents many challenges
including, but not limited to, computational complexity due to a large number
of agents, uncertainty in the functionality of each agent in the swarm, and
uncertainty in the swarm's configuration. This work generalizes the swarm state
using Random Finite Set (RFS) theory and solves a centralized control problem
with a Quasi-Newton optimization through the use of Model Predictive Control
(MPC) to overcome the aforementioned challenges. This work uses the RFS
formulation to control the distribution of agents assuming an unknown or
unspecified number of agents. Computationally efficient solutions are also
obtained via the MPC version of the Iterative Linear Quadratic Regulator
(ILQR), a variant of Differential Dynamic Programming (DDP). Information
divergence is used to define the distance between the swarm RFS and the desired
swarm configuration through the use of the modified $L_2^2$ distance.
Simulation results using MPC and ILQR show that the swarm intensity converges
to the desired intensity. Additionally, the RFS control formulation is shown to
be very flexible in terms of the number of agents in the swarm and
configuration of the desired Gaussian mixtures. Lastly, the ILQR and the
Gaussian Mixture Probability Hypothesis Density filter are used in conjunction
to solve a spacecraft relative motion problem with imperfect information to
show the viability of centralized RFS control for this real-world scenario.
