Complex sensitive motions have been observed in ocean mooring systems consisting of nonlinear mooring geometries. These physical systems can be modeled as a system of first-order nonlinear ordinary differential equations, taking into account geometric nonlinearities in the restoring force, quadratic viscous drag, and harmonic excitation. This study examines the controllability of these systems utilizing an embedded approach to noise filtering and online controllers. The system is controlled using small perturbations about a selected unstable cycle and control is instigated for periodic cycles of varying periodicities. The controller, when applied to the system with additive random noise in the excitation, has marginal success. However, the addition of an iterated Kalman filter applied to the system increases the regime under which the controller behaves under the influence of noise. Because the Kalman filter is applied about locally linear trajectories, the feedback of the nonlinearities through the filter has little effect on the overall filtering system.