Neural predictive control for high-spinning flight vehicles: A Fokker–Planck uncertainty control framework

To address the challenges posed by nonlinear coupled dynamics in the guidance and control of High-spinning Flight Vehicles (HFV), this study proposes a neural predictive control framework. By employing a closed-loop optimization mechanism based on a deviation-to-control command paradigm, the proposed approach effectively mitigates mapping inaccuracy and information loss inherent in traditional multi-stage conversion processes. Furthermore, a Bayesian Neural Network (BNN)-based probabilistic modeling approach is introduced to enable uncertainty-aware multimodal predictions of both impact point distributions and control correction effectiveness. A spatiotemporal entropy measurement framework is established by incorporating altitude sensitivity factor and time decay factor to construct a dynamic uncertainty representation model, which is further refined through a covariance fusion mechanism driven by the Fokker-Planck equation to optimize control decisions. This system effectively resolves core issues such as difficulties in control response limitation, sensitivity to time-varying control gains, and the coupling between control moment and range. Experimental results indicate that the proposed framework reduces the Circular Error Probable (CEP) from 75.12 m to 0.42 m, thereby providing a robust theoretical paradigm for the precision guidance of HFV.