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BS Invariance Pressures for Control Systems

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Abstract

Three types of BS inner invariance pressures for control systems, as well as three versions of measure-theoretic BS inner invariance pressures, are introduced in this paper. We show that those BS inner invariance pressures are equivalent for the strongly invariant sets. Moreover, it is confirmed that they are the roots of Bowen’s equations for control systems. Then, we can further obtain an inverse variational principle for the measure-theoretic BS inner invariance pressure. Finally, a type of upper capacity BS invariance pressure and an explicit formula are presented for computing this invariance pressure of controlled invariant sets under some reasonable assumptions.

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Funding

The first author was supported by the National Natural Science Funds of China (No. 12201135) and Guangdong Basic and Applied Basic Research Foundation (2019A1515110932). The second author was supported by the National Natural Science Funds of China (No. 12171492). The third author was supported by the Science and Technology Development Fund of Macao SAR (Grant No. 0122/2020/A3) and MYRG2020-00224-FST from University of Macau.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou, 510006, People’s Republic of China

    Xingfu Zhong

  2. School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, People’s Republic of China

    Yu Huang

  3. Department of Mathematics, University of Macau, Macao, People’s Republic of China

    Hai-Wei Sun

Authors
  1. Xingfu Zhong
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  2. Yu Huang
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  3. Hai-Wei Sun
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Correspondence to Xingfu Zhong.

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Zhong, X., Huang, Y. & Sun, HW. BS Invariance Pressures for Control Systems. J Dyn Control Syst 29, 1449–1469 (2023). https://doi.org/10.1007/s10883-023-09643-3

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  • DOI: https://doi.org/10.1007/s10883-023-09643-3

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