论文标题
最佳控制问题的放松方法
Relaxation methods for optimal control problems
论文作者
论文摘要
我们考虑了一个非线性最佳控制问题，其动力学是由涉及最大单调映射$ a的差分包含描述的动力学，\ Mathbb {r}^n \ rightArrow2^{\ mathbb {r}^n} $。我们不认为$ d（a）= \ mathbb {r}^n $，以这种方式并入我们的框架中具有单方面约束的系统。我们提出了两种放松方法。第一个是从存在理论中减少方法的产物，而第二种方法则采用了年轻措施。我们表明，这两种放松方法是等效的且可以接受的。
We consider a nonlinear optimal control problem with dynamics described by a differential inclusion involving a maximal monotone map $A:\mathbb{R}^N\rightarrow2^{\mathbb{R}^N}$. We do not assume that $D(A)=\mathbb{R}^N$, incorporating in this way systems with unilateral constraints in our framework. We present two relaxation methods. The first one is an outgrowth of the reduction method from the existence theory, while the second method uses Young measures. We show that the two relaxation methods are equivalent and admissible.
