The performance of deep learning (DL)-based methods for predicting remaining useful life (RUL) may be limited in practice due to the scarcity of representative time-to-failure (TTF) data. To overcome this challenge, generating physically plausible synthetic data is a promising approach. In this study, a novel hybrid framework is proposed that combines a controlled physics-informed data generation approach with a DL-based prediction model for prognostics. The framework introduces a new controlled physics-informed generative adversarial network (CPI-GAN) that generates diverse and physically interpretable synthetic degradation trajectories. The generator includes five basic physics constraints that serve as controllable settings. The regularization term, which is a physics-informed loss function with a penalty, ensures that the synthetic data’s changing health state trend complies with the underlying physical laws. The synthetic data is then fed to the DL-based prediction model to estimate RUL. The framework's effectiveness is evaluated using the New Commercial Modular Aero-Propulsion System Simulation (N-CMAPSS), a turbofan engine prognostics dataset with limited TTF trajectories. The experimental results demonstrate that the proposed framework can generate synthetic TTF trajectories that are consistent with underlying degradation trends and significantly improve RUL prediction accuracy.