约束线性系统关于非凸评价泛函的最优控制

Solution to a Non convex Linear Quadratic Optimal Control Problem with Constraint

摘要:

研究一类约束线性系统关于非凸评价泛函的最优控制问题，该最优控制问题的评价泛函的被积函数中含有关于控制变量的非凸二次函数．由Pontryagin极值原理建立球约束下非凸二次优化问题，并利用倒向微分流求解该问题，进而求解一组微分边值问题以得到原问题的最优控制．同时把数学过程转化为求解的算法，并给出了一个数值计算的例子．

Abstract:

It is studied how to solve the optimal control problem for a constrained linear system with a non convex cost functional. With Pontryagin’s maximum principle, a non convex quadratic programming is treated by a backward differential flow. Then the optimal control is obtained by solving a nonlinear differential boundary problem. An algorithm is given corresponding to the mathematical process. It follows by a numerical example.