Resilient Extremum Seeking Control for Cyber-Physical Systems Under Denial-of-Service Attacks

Abstract

Extremum seeking control (ESC) relies on deliberately injected excitation to extract optimization information from measured outputs, making its networked implementation particularly vulnerable to denial-of-service (DoS) attacks. This paper develops a resilient discrete-time ESC architecture for cyber-physical systems subject to DoS attacks. By holding the most recently successfully transmitted signals during DoS intervals, the proposed mechanism yields averaged error dynamics with an exponentially contracting mode under successful communication and a neutral mode under attack. For deterministic DoS attacks, practical exponential convergence to the extremum is established under an average bound on the attack duration, with an explicit convergence rate depending on the fraction of time under attack. For probabilistic DoS attacks, almost-sure and in-probability convergence properties are established via stochastic averaging, with the attack success probability explicitly entering the convergence rate. A key finding is that a seemingly natural zero-input strategy can fundamentally compromise ESC: attacks synchronized with the dither generate an 𝒪(1/a) bias in the averaged dynamics, where a is the dither amplitude, and can displace the equilibrium from the true optimizer. Thus, under the proposed hold-based architecture, increasingly severe DoS attacks primarily slow the optimization process rather than destroy its stability, provided that communication is not permanently blocked. Numerical simulations illustrate the theoretical guarantees and the failure mechanism induced by dither-synchronized attacks.

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Cite

BibTeX RIS

BibTeX

@misc{teixeira2026resilient,
  title = {{Resilient Extremum Seeking Control for Cyber-Physical Systems Under Denial-of-Service Attacks}},
  author = {Filipe da Silva Bastos Teixeira and Pedro Henrique Silva Coutinho and Tiago Roux Oliveira and Miroslav Krstic},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14192},
  eprint = {2609.14192},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14192},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Resilient Extremum Seeking Control for Cyber-Physical Systems Under Denial-of-Service Attacks
AU  - Filipe da Silva Bastos Teixeira
AU  - Pedro Henrique Silva Coutinho
AU  - Tiago Roux Oliveira
AU  - Miroslav Krstic
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.14192
UR  - https://arxiv.org/abs/2609.14192
AB  - Extremum seeking control (ESC) relies on deliberately injected excitation to extract optimization information from measured outputs, making its networked implementation particularly vulnerable to denial-of-service (DoS) attacks. This paper develops a resilient discrete-time ESC architecture for cyber-physical systems subject to DoS attacks. By holding the most recently successfully transmitted signals during DoS intervals, the proposed mechanism yields averaged error dynamics with an exponentially contracting mode under successful communication and a neutral mode under attack. For deterministic DoS attacks, practical exponential convergence to the extremum is established under an average bound on the attack duration, with an explicit convergence rate depending on the fraction of time under attack. For probabilistic DoS attacks, almost-sure and in-probability convergence properties are established via stochastic averaging, with the attack success probability explicitly entering the convergence rate. A key finding is that a seemingly natural zero-input strategy can fundamentally compromise ESC: attacks synchronized with the dither generate an 𝒪(1/a) bias in the averaged dynamics, where a is the dither amplitude, and can displace the equilibrium from the true optimizer. Thus, under the proposed hold-based architecture, increasingly severe DoS attacks primarily slow the optimization process rather than destroy its stability, provided that communication is not permanently blocked. Numerical simulations illustrate the theoretical guarantees and the failure mechanism induced by dither-synchronized attacks.
ER  -

Abstract

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