广义LQ最优控制问题的极小化序列

Minimizing sequence to generalized LQ optimal control problem

将经典LQ问题的评价泛函中关于控制变量的二次型推广为一类偶次多项式,证明了这类广义LQ无约束最优控制问题的一个等价扩张逼近可由一列半径递增的球约束最优控制问题加以实现.进而利用P0ntryagin极值原理建立相应的球约束最优控制问题的二次规划,并通过Canonical倒向微分流及不动点定理,求解常微分方程边值问题,得到球约束最优控制问题的最优值.随着约束球半径趋于无穷大,形成原广义LQ最优控制问题的一个极小化序列,从而得到原问题的最优值.

This paper is devoted to solving a generalized LQ optimal control prob- lem. An equivalent extension to the original problem is derived by a sequence of op- timal control problems with ball constraints. Accordingly, a sequence of quadratic optimization problems is obtained by the Pontryagin principle. Then, the canonical backward differential flow and the fixed point theory are applied to deal with a differential boundary problem in solving the optimal control problem with ball constraints. Finally, by amplifying the radii of constraints, a minimizing sequence to .the generalized LQ optimal control problem is obtained by an example.