论文标题
关于跟踪型最佳控制问题解决方案解决方案的不唯一性和不稳定性
On the Nonuniqueness and Instability of Solutions of Tracking-Type Optimal Control Problems
论文作者
论文摘要
我们研究跟踪类型的最佳控制问题，其中涉及非疗程，弱到弱的连续控制对状态映射，所需的状态$ y_d $以及所需的控制$ u_d $。事实证明，对于元组$（y_d，u_d）$的某些选择，这些问题总是无法解决，并且从某种意义上说，将解决方案集（解释为$（y_d，u_d）$的多价值函数）的意义上不承认连续选择。
We study tracking-type optimal control problems that involve a non-affine, weak-to-weak continuous control-to-state mapping, a desired state $y_d$, and a desired control $u_d$. It is proved that such problems are always nonuniquely solvable for certain choices of the tuple $(y_d, u_d)$ and instable in the sense that the set of solutions (interpreted as a multivalued function of $(y_d, u_d)$) does not admit a continuous selection.
