This article presents a novel degradation modeling and prognostic method for a class of closed-loop feedback systems with degrading actuators. Toward this end, we first present a degradation modeling framework by integrating the stochastic degradation process model of the actuator and the state transition model of the system. This takes into consideration the mutual effects between the component-level degradation and system-level state. Then, the particle filter algorithm is utilized to jointly estimate the hidden degradation state of the actuator and the system state through indirect observations. Further, a time-varying nonlinear diffusion process equipped with two-stage parameters updating procedure is used to learn the evolving progression of the hidden degradation state. As such, a residual-threshold-based remaining useful life (RUL) prediction method is presented by simulating future system states and degradation trajectories based on the learned degradation process. As the application of the predicted RUL, a fault tolerant control method is presented by adjusting the controller parameter so as to extend the life of the system. Finally, a simulation study is conducted using a closed-loop control system in an inertial platform to verify the proposed method. The results indicate that the proposed method can reduce prognosis error, improve robustness, and extend the lifetime of the system.