This paper proposes a novel Hamiltonian servo system, a combined modeling framework for control and estimation of a large team/fleet of autonomous robotic vehicles. The Hamiltonian servo framework represents high-dimensional, nonlinear and non-Gaussian generalization of the classical Kalman servo system. After defining the Kalman servo as a motivation, we define the affine Hamiltonian neural network for adaptive nonlinear control of a team of UGVs in continuous time. We then define a high-dimensional Bayesian particle filter for estimation of a team of UGVs in discrete time. Finally, we formulate a hybrid Hamiltonian servo system by combining the continuous-time control and the discrete-time estimation into a coherent framework that works like a predictor-corrector system.