Equi-invariability, bounded invariance complexity and L-stability for control systems

Zhong, Xingfu; Chen, Zhijing; Yu, Huan

doi:10.1007/s11425-020-1693-7

Cited by 9 publications

(1 citation statement)

References 26 publications

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“…For better understanding of invariance entropy, various notions relating to invariance entropy have been proposed by several groups of researchers from different views, such as invariance pressure [15,16,17,18,19,20], measure-theoretic versions of invariance entropy [21,22,23,24], dimension types of invariance entropy [25], complexity of invariance entropy [26,27,28]. Note that Kawan and Yüksel [29] introduced a notion of stabilization entropy which is a variant of invariance entropy.…”

Section: Introductionmentioning

confidence: 99%

Invariance entropy for uncertain control systems

Zhong¹,

Huang²,

Zou³

2022

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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 quasiinvariant-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.

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