Invariance Feedback Entropy of Uncertain Control Systems
Invariance Feedback Entropy of Uncertain Control Systems
复制标题
DOI：
10.1109/tac.2020.3038702
复制
发表时间：
2017-06
影响因子：
6.8
通讯作者：
Mahendra Singh Tomar;M. Rungger;Majid Zamani
中科院分区：
文献类型：
--
作者：
Mahendra Singh Tomar;M. Rungger;Majid Zamani
我们引入了一个新的概念不变性反馈熵量化的状态信息，所需的任何控制器，强制执行一个给定的状态空间的子集是不变的。我们建立了一些基本性质，例如，我们提供的条件，确保不变性反馈熵是有限的，并显示为确定性的情况下，我们恢复了众所周知的概念熵确定性控制系统。我们证明了数据速率定理，这表明，不变性熵是一个严格的下限的数据速率的任何编码器控制器，实现在闭环中的不变性。分析了不确定线性控制系统，给出了不变性反馈熵的一个普适下界。下界取决于系统矩阵的行列式的绝对值和涉及不变集和不确定性集的体积的比率。此外，我们推导出任何静态的，无记忆编码器控制器的数据速率的下限。这两个下限是密切相关的，并且对于某些情况，有可能将由于对静态编码器控制器的限制而导致的性能损失限制在1比特/时间单位。我们在整篇文章中提供了各种例子来说明和讨论不同的定义和结果。
We introduce a novel notion of invariance feedback entropy to quantify the state information that is required by any controller that enforces a given subset of the state space to be invariant. We establish a number of elementary properties, e.g., we provide conditions that ensure that the invariance feedback entropy is finite and show for the deterministic case that we recover the well-known notion of entropy for deterministic control systems. We prove the data rate theorem, which shows that the invariance entropy is a tight lower bound of the data rate of any coder controller that achieves invariance in the closed loop. We analyze uncertain linear control systems and derive a universal lower bound of the invariance feedback entropy. The lower bound depends on the absolute value of the determinant of the system matrix and a ratio involving the volume of the invariant set and the set of uncertainties. Furthermore, we derive a lower bound of the data rate of any static, memoryless coder controller. Both lower bounds are intimately related and for certain cases it is possible to bound the performance loss due to the restriction to static coder controllers by 1 bit/time unit. We provide various examples throughout the article to illustrate and discuss different definitions and results.