Limited availability of representative time-to-failure (TTF) trajectories either limits the performance of deep learning (DL)-based approaches on remaining useful life (RUL) prediction in practice or even precludes their application. Generating synthetic data that is physically plausible is a promising way to tackle this challenge. In this study, a novel hybrid framework combining the controlled physics-informed data generation approach with a deep learning-based prediction model for prognostics is proposed. In the proposed framework, a new controlled physics-informed generative adversarial network (CPI-GAN) is developed to generate synthetic degradation trajectories that are physically interpretable and diverse. Five basic physics constraints are proposed as the controllable settings in the generator. A physics-informed loss function with penalty is designed as the regularization term, which ensures that the changing trend of system health state recorded in the synthetic data is consistent with the underlying physical laws. Then, the generated synthetic data is used as input of the DL-based prediction model to obtain the RUL estimations. The proposed framework is evaluated based on new Commercial Modular Aero-Propulsion System Simulation (N-CMAPSS), a turbofan engine prognostics dataset where a limited availability of TTF trajectories is assumed. The experimental results demonstrate that the proposed framework is able to generate synthetic TTF trajectories that are consistent with underlying degradation trends. The generated trajectories enable to significantly improve the accuracy of RUL predictions.