Compositional Quantification of Invariance Feedback Entropy for Networks of Uncertain Control Systems
Compositional Quantification of Invariance Feedback Entropy for Networks of Uncertain Control Systems
复制标题
不确定控制系统网络不变反馈熵的组合量化
DOI：
10.1109/lcsys.2020.2992884
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发表时间：
2020
影响因子：
3
通讯作者：
Majid Zamani
中科院分区：
文献类型：
--
作者：
Mahendra Singh Tomar;Majid Zamani
在不确定控制系统的背景下，不变反馈熵(IFE)的概念量化了任何控制器使状态空间的子集不变所需的状态信息。IFE还等价地量化反馈环路中从编码器到控制器的最小比特率，在该最小比特率之上，可以在数字无噪声信道上保持不变。在这封信中，我们考虑了用差分包含描述的离散时间不确定控制系统，建立了IFE的三个结果。首先，我们证明了离散时间不确定控制系统<；内嵌公式&><；tex数学符号=“LaTeX”>；$\Sigma$<；/内嵌公式>；/内嵌公式>；和一个非空集<；内嵌公式符号=“laex”>；$q$<；/内嵌公式>；的IFE是上界的文本数学符号=“LaTeX”&>；$\Sigma$<；/文本数学&>；/行内公式&>lt；以及<；行内公式&>；的任何有限分区的任何成员。其次，我们考虑两个不确定控制系统，它们除了转移函数外都是相同的，它们的行为除了转移函数外，都是相同的行内公式>；<；文本数学符号=“LaTeX”>；$\Sigma_{1}$<；/文本数学&>；<；/行内公式&>包含在<；行内公式&>；<；行内数学符号=“LaTeX”>；$\Sigma_{2}$<；/文本数学&>；<；/行内公式&>中。对于给定的状态空间的一个非空子集，我们证明了<；inline-form>；<；tex-ath notation=“LaTeX”>；$\Sigma_{2}$<；/tex-ath>；<；/inline-form>；的IFE大于或等于<；的IFE=“laex”>；$\Sigma_{1}$<；/tex-ath>；<；/inline-form>；第三，我们根据较小子系统的IFE建立了不确定控制子系统网络IFE的上界。此外，通过一个例子，我们证明了某些系统的上界是紧的。最后，为了说明结果的有效性，我们计算了一个描述圆形建筑中100个房间温度演变的不确定、线性、离散时间子系统网络的IFE的上界和下界。
In the context of uncertain control systems, the notion of invariance feedback entropy (IFE) quantifies the state information required by any controller to render a subset <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> of the state space invariant. IFE equivalently also quantifies the smallest bit rate, from the coder to the controller in the feedback loop, above which <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> can be made invariant over a digital noiseless channel. In this letter, we consider discrete-time uncertain control systems described by difference inclusions and establish three results for IFE. First, we show that the IFE of a discrete-time uncertain control system <inline-formula> <tex-math notation="LaTeX">$\Sigma $ </tex-math></inline-formula> and a nonempty set <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> is upper bounded by the largest possible IFE of <inline-formula> <tex-math notation="LaTeX">$\Sigma $ </tex-math></inline-formula> and any member of any finite partition of <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula>. Second, we consider two uncertain control systems, <inline-formula> <tex-math notation="LaTeX">$\Sigma _{1}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\Sigma _{2}$ </tex-math></inline-formula>, which are identical except for the transition function, such that the behavior of <inline-formula> <tex-math notation="LaTeX">$\Sigma _{1}$ </tex-math></inline-formula> is included within that of <inline-formula> <tex-math notation="LaTeX">$\Sigma _{2}$ </tex-math></inline-formula>. For a given nonempty subset of the state space, we show that the IFE of <inline-formula> <tex-math notation="LaTeX">$\Sigma _{2}$ </tex-math></inline-formula> is larger or equal to the IFE of <inline-formula> <tex-math notation="LaTeX">$\Sigma _{1}$ </tex-math></inline-formula>. Third, we establish an upper bound for the IFE of a network of uncertain control subsystems in terms of the IFEs of smaller subsystems. Further, via an example, we show that the upper bound is tight for some systems. Finally, to illustrate the effectiveness of the results, we compute an upper bound and a lower bound of the IFE of a network of uncertain, linear, discrete-time subsystems describing the evolution of temperature of 100 rooms in a circular building.
影响因子：
6.8
作者：
Mahendra Singh Tomar;M. Rungger;Majid Zamani
通讯作者：
Mahendra Singh Tomar;M. Rungger;Majid Zamani