基于QSS的自适应多步校正算法及其在柔性航天器动力学中的应用

量化状态系统（QSS）算法是一种基于状态变量离散化的数值积分方法，该方法与基于时间离散的传统方法显著不同，QSS通过计算状态变量每次跃迁所需的时间来推进下一步的积分。在求解非刚性常微分方程时，QSS算法比传统算法更具优势，但它不适合求解刚性问题。为此提出一种基于QSS的自适应多步校正算法（AMCQSS），该算法以QSS为基础、结合隐式多步法思想，在计算过程中可以自适应选择二步法或三步法，以有效提高求解刚性问题的精度和效率。通过对柔性航天器动力学的仿真求解，验证了算法的可行性。将该算法与ODE23tb、ODE15s、ODE45以及QSS等算法进行对比，结果表明AMCQSS算法既能保证求解的效率及精度，又具有较好的收敛性和稳定性。

QSS based adaptive multi-step correction algorithm and its application in flexible spacecraft dynamics

Quantized State System (QSS) is a new numerical integration method based on discretization of state variables. Different from traditional time discretization methods, QSS advances the next integration by calculating the time required for each transition of the state variables. Despite its advantages over traditional methods in solving non-stiff ordinary differential equations, it is not suitable for solving stiff problems. Therefore, an adaptive multi-step correction algorithm based on QSS (AMCQSS) is proposed, combining the ideas of the QSS method and the implicit multi-step method. The AMCQSS can adaptively choose two-step or three-step methods in the calculation process to effectively improve the accuracy and efficiency of solving stiff problems. The feasibility of this algorithm is verified by the simulation of flexible spacecraft dynamics. The comparison of performance between this algorithm and the previous methods of ODE23tb, ODE15s, ODE45 and QSS shows that the AMCQSS can ensure the solution efficiency and accuracy with good convergence and stability.