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为了校核三次Hermite配点算法程序的正确性,选用了一类典型的动力学系统——双积分系统的时间最优控制问题作为研究对象,通过将三次Hermite配点法和序列二次规划算法的复合算法应用于该系统的时间最优控制模型,得到了数值仿真结果。通过与该系统解析解的比较可以看出,三次Hermite配点算法对于求解动力学系统最优控制的两点边值问题具有良好的适应性。该方法可以进一步应用于航天器轨道动力学和优化的研究。
In order to check the correctness of the Hermite collocation algorithm procedure, a class of typical dynamic system - time optimal control problem of double integral system was chosen as the research object. Through the combination of the cubic Hermite collocation method and the sequence quadratic programming algorithm The algorithm is applied to the time optimal control model of the system, and the numerical simulation results are obtained. By comparing with the analytical solution of this system, we can see that the cubic Hermite collocation algorithm has good adaptability to the two-point boundary value problem of optimal control of dynamic system. The method can be further applied to the study of spacecraft orbit dynamics and optimization.