论文标题
关于可及性能的熵概念
On a notion of entropy for reachability properties
论文作者
论文摘要
在这项工作中，我们介绍了可及性熵的概念，以表征最小的数据速率，该数据速率足以实施到达时期规格。我们还定义了可以在有限时间内执行此规范的编码器控制器的数据速率。然后，我们建立了数据率定理，该定理指出可及性熵是数据速率的紧密下限，可以满足到达时期的满足。对于与反馈改进关系中的另一个系统相关的系统，我们表明前者的熵不会大于后者的熵。我们还提供了一个程序，以通过利用其有限的抽象来计算离散时间控制系统的可及性熵的上限。最后，我们提出了一些示例，以证明提出的结果的有效性。
In this work, we introduce a notion of reachability entropy to characterize the smallest data rate which is sufficient enough to enforce reach-while-stay specification. We also define data rates of coder-controllers that can enforce this specification in finite time. Then, we establish the data-rate theorem which states that the reachability entropy is a tight lower bound of the data rates that allow satisfaction of the reach-while-stay specification. For a system which is related to an another system under feedback refinement relation, we show that the entropy of the former will not be larger than that of the latter. We also provide a procedure to numerically compute an upper bound of the reachability entropy for discrete-time control systems by leveraging their finite abstractions. Finally, we present some examples to demonstrate the effectiveness of the proposed results.
