时间最短控制问题求解的分级优化策略

针对时间最短控制问题的求解,单纯地使用罚函数策略求解存在诸多不便,为此提出分级优化的策略,并结合罚函数策略实施。首先在某个终端时间的情况下构造终端状态自由的最优控制问题,为一级优化;在一级优化结果的基础上结合罚函数策略构造新的目标函数,并据此调整终端时刻,为二级优化。反复依次执行一级优化、二级优化,最终使得状态约束恰好得到满足。分级优化把复杂问题转化为一系列简单的问题,采用经典的优化算法即可实现。实例研究显示了分级优化策略是可行的,能以足够的精度满足边值约束,计算结果也更加精确。

Graded Optimization Strategy for Time-Optimal Control Problems

The essential of time-optimal control problems is to determine the critical time when restrictions of states are just satisfied.There is some inconvenience in using the penalty function strategy for those problems.A new strategy,named as graded optimization,was developed in combination with penalty function strategy.The first optimization is to construct optimal control problem with free final states under a given final time.The second optimization,whose objective function is constructed using penalty function,is to adjust the final time according to the results of the first optimization.By repeating the first and second optimization,the restrictions of states will finally be just satisfied.The proposed strategy(divides) a complex problem into a series of simple problems that can be solved by classic optimization(methods.) Case studies show that the graded optimization is feasible,and it provides enough accuracy for(states) requirements and more accurate results.