Abstract: Addressing the online trajectory-tracking problem for systems with strongly nonlinear dynamics and stringent real-time computational demands, this work presents an efficient control method capable of rapidly propagating nonlinear system states, with application to Earth–Moon emergency return trajectory tracking. The proposed method builds on a Nonlinear Model Predictive Control (NMPC) framework, leveraging its ability to reformulate long-horizon control tasks into a sequence of shortened receding-horizon optimization problems. This restructuring mitigates the computational burden associated with constraint handling and reduces the complexity of individual problem solutions, thereby lowering overall computational cost, improving dynamic responsiveness, and enhancing robustness in online optimization. A key contribution lies in the integration of Differential Algebra (DA) to construct a high-order polynomial map-based prediction model within the NMPC loop, replacing conventional numerical integration with efficient algebraic calculation. This enables rapid evaluation of nonlinear dynamics and significantly improves real-time performance. The method is validated in an Earth–Moon emergency return scenario, where it successfully tracks a large-impulse reference trajectory via continuous braking, achieving high-precision tracking of the Earth re-entry corridor. Numerical simulation demonstrates a fivefold improvement in computational efficiency compared to conventional NMPC implementations. Moreover, the method maintains high accuracy in the presence of initial state errors and persistent perturbations, confirming its strong robustness in challenging space mission applications.

Key words: nonlinear model predictive control, differential algebra, online control, tracking control, real-time optimization