论文标题
关于动态遗憾与闭环稳定性之间的关系
On the relation between dynamic regret and closed-loop stability
论文作者
论文摘要
在这项工作中，我们研究了有限的动态遗憾与渐近稳定性的经典概念之间的关系，即先验不明的成本函数。特别是，我们表明，有界的动态遗憾意味着最佳稳态的渐近稳定性对于恒定的成本函数。对于渐近稳定的闭环，我们首先得出了实现有限动态遗憾的必要条件。然后，鉴于对系统和成本功能的一些其他假设，我们还提供了足够的条件，以确保有限的动态遗憾。我们的结果通过示例说明。
In this work, we study the relations between bounded dynamic regret and the classical notion of asymptotic stability for the case of a priori unknown and time-varying cost functions. In particular, we show that bounded dynamic regret implies asymptotic stability of the optimal steady state for a constant cost function. For the case of an asymptotically stable closed loop, we first derive a necessary condition for achieving bounded dynamic regret. Then, given some additional assumptions on the system and the cost functions, we also provide a sufficient condition ensuring bounded dynamic regret. Our results are illustrated by examples.
