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<p>We provide three types of invariance pressure for <i>uncertain</i> control systems, namely, invariance pressure, strong invariance pressure, and invariance feedback pressure. The first two respectively extend the corresponding pressures for <i>deterministic</i> control systems proposed by Colonius, Cossich, and Santana (2018) and by Nie, Wang, and Huang (2022); and the third generalizes invariance feedback entropy of <i>uncertain</i> control systems presented by Tomar, Rungger, and Zamani (2020), by adding potentials on the control range. Then we prove that (1) an explicit formula for invariance pressure of a controlled invariant set with respect to a potential by the logarithm of the spectral radius of the admissible weighted matrix determined by this potential under some suitable conditions; (2) an explicit formula for pressure of invariant quasi-partitions by maximum mean weight over all irreducible periodic sequences; (3) the invariance feedback pressure of a controlled invariant set is equal to the pressure of an atom partition under some technical assumptions; (4) lower and upper bounds for pressure of invariant quasi-partitions w.r.t. a potential by the logarithm of the spectral radius of the weighted adjacency matrix determined by this potential; (5) a variational principle for strong invariance pressure.</p>

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Invariance Pressures for Uncertain Control Systems

  • 期刊论文

  • 发表日期：

    2025年12月15日

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  • Xingfu Zhong,
  • Yu Huang

摘要

We provide three types of invariance pressure for uncertain control systems, namely, invariance pressure, strong invariance pressure, and invariance feedback pressure. The first two respectively extend the corresponding pressures for deterministic control systems proposed by Colonius, Cossich, and Santana (2018) and by Nie, Wang, and Huang (2022); and the third generalizes invariance feedback entropy of uncertain control systems presented by Tomar, Rungger, and Zamani (2020), by adding potentials on the control range. Then we prove that (1) an explicit formula for invariance pressure of a controlled invariant set with respect to a potential by the logarithm of the spectral radius of the admissible weighted matrix determined by this potential under some suitable conditions; (2) an explicit formula for pressure of invariant quasi-partitions by maximum mean weight over all irreducible periodic sequences; (3) the invariance feedback pressure of a controlled invariant set is equal to the pressure of an atom partition under some technical assumptions; (4) lower and upper bounds for pressure of invariant quasi-partitions w.r.t. a potential by the logarithm of the spectral radius of the weighted adjacency matrix determined by this potential; (5) a variational principle for strong invariance pressure.