论文标题
不确定控制系统的不变性熵
Invariance entropy for uncertain control systems
论文作者
论文摘要
我们引入了一个不确定控制系统的不变性熵概念，大概是由控件形成的“树”的“分支”的指数增长率，对于实现状态空间的受控子集的不变性是必不可少的。该熵扩展了Colonius和Kawan（2009）引入的确定性控制系统的不变性熵。我们表明，由Tomar，Rungger和Zamani（2020）提出的不变性反馈熵是由我们的不变性熵从下面界定的。我们概括了Tomar，Kawan和Zamani（2020）获得的不变分区的熵的公式，从而将其计算为准易变分区。此外，我们还通过光谱半径的邻接矩阵和加权的邻接矩阵来得出了准不变部分的熵和上限。有了一些合理的假设，我们获得了用于计算不确定控制系统的不变性熵的明确公式，以及有限控制不变集的不变性反馈熵。
We introduce a notion of invariance entropy for uncertain control systems, which is, roughly speaking, the exponential growth rate of "branches" of "trees" that are formed by controls and are necessary to achieve invariance of controlled invariant subsets of the state space. This entropy extends the invariance entropy for deterministic control systems introduced by Colonius and Kawan (2009). We show that invariance feedback entropy, proposed by Tomar, Rungger, and Zamani (2020), is bounded from below by our invariance entropy. We generalize the formula for the calculation of entropy of invariant partitions obtained by Tomar, Kawan, and Zamani (2020) to quasi-invariant-partitions. Moreover, we also derive lower and upper bounds for entropy of a quasi-invariant-partition by spectral radii of its adjacency matrix and weighted adjacency matrix. With some reasonable assumptions, we obtain explicit formulas for computing invariance entropy for uncertain control systems and invariance feedback entropy for finite controlled invariant sets.
