倒向微分方程在一类奇异最优控制中的应用

Solution to Singular Optimal Control by Canonical Backward Differential Equation

利用Krotov方法把一类奇异最优控制问题转化为一族球约束的全局优化问题,然后引入一族初值连续依赖于时间参量的倒向微分方程,给出相应的全局优化问题的解析解,用以构造最优控制的解析表达式.

A singular optimal control problem is solved by Krotov Extension method and Canonical backward differential flows. By using Krotov equivalent transformation, the cost functional of the problem is converted to a class of global optimization problems which are solved by a class of backward differential equations with initial values relying on the time point continuously.