Secure model predictive static programming with initial value generator for online computational guidance of near-space vehicles

Abstract

For online trajectory programming of near-space vehicles with limited computation resources, conventional model predictive static programming approaches have two main challenges. Firstly, an inadequate initial control guess can lead to trajectory divergence or slow convergence, resulting in mission failure. Secondly, Euler discretization is a small-step local algorithm by point-to-point recursion. To ensure high precision solution, more discretization points are required, leading to low computation efficiency and accuracy; meanwhile conventional methods cannot guarantee that the problems are solved within the constraints and feasible domains, potentially affecting the solution stability. To solve the first problem, a variable coefficient near-optimal initial value generator is developed to provide an initial control guess that approximates the optimal trajectory, preventing divergence in subsequent iterations. To address the second problem, the trust-region constrained model predictive static programming is proposed with flipped-Radau pseudospectrum. This method reduces the number of discretization points and optimizes the performance index directly, thereby enhancing efficiency; meanwhile the trust region improves accuracy and ensures the updated trajectory remains close to the reference trajectory. Finally, the combination of above approaches enhances the calculating efficiency and precision significantly for online trajectory programming. Applied to a near-space vehicle, the proposed method reduces optimization time by 25 % for rapid and high-precision solutions, and improves terminal position accuracy from 43 m to 1 m with flipped-Radau pseudospectrum.