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Peer-reviewedCC BY 4.0Axioms

Distributed Stochastic Extremum Seeking for Optimal Resource Allocation over Networks with Time Delays

  • Pei-Pei Zhang1,2
  • Bao-Ting Zhang3
  • Na Li1
  1. 1School of Data and Computer Science, Shandong Women’s University, Jinan 250300, China
  2. 2School of Mathematics, Sichuan University, Chengdu 610064, China
  3. 3Advanced Technology Research Institute, Beijing Institute of Technology, Jinan 250307, China
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Abstract

This paper investigates optimal resource allocation in multi-agent networks subject to simultaneous measurement and communication delays. We propose a distributed stochastic extremum seeking (SES) algorithm for connected undirected graphs with heterogeneous constant communication delays. The algorithm uses only delayed pointwise measurements of the local objective values; neither gradient nor Hessian information is fed to the controller. It combines a proportional–integral (PI) consensus protocol, which enforces the supply–demand balance, with a one-stage sequential predictor that compensates for the measurement delays. The convergence analysis is developed for local objectives of quadratic type; this restriction, which is required by the stochastic-averaging argument, is stated explicitly and discussed. Using stochastic averaging theory and Lyapunov–Krasovskii functionals for delay systems, we prove that, for every finite initial history, the estimates converge almost surely to an arbitrarily small neighborhood of the optimum for every fixed tolerance, and we derive an explicit admissible range for the constant communication delays together with a sequential procedure for selecting the design parameters. Two case studies, namely a three-generator microgrid and a six-generator microgrid, are used to illustrate the theoretical results.

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Cite

BibTeXRIS
BibTeX
@article{zhang2026distributed,
  title = {{Distributed Stochastic Extremum Seeking for Optimal Resource Allocation over Networks with Time Delays}},
  author = {Pei-Pei Zhang and Bao-Ting Zhang and Na Li},
  journal = {Axioms},
  year = {2026},
  month = oct,
  doi = {10.3390/axioms15110805},
  url = {https://www.mdpi.com/2075-1680/15/11/805},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Distributed Stochastic Extremum Seeking for Optimal Resource Allocation over Networks with Time Delays
AU  - Pei-Pei Zhang
AU  - Bao-Ting Zhang
AU  - Na Li
PY  - 2026
DA  - 2026/10/29
JO  - Axioms
DO  - 10.3390/axioms15110805
UR  - https://www.mdpi.com/2075-1680/15/11/805
AB  - This paper investigates optimal resource allocation in multi-agent networks subject to simultaneous measurement and communication delays. We propose a distributed stochastic extremum seeking (SES) algorithm for connected undirected graphs with heterogeneous constant communication delays. The algorithm uses only delayed pointwise measurements of the local objective values; neither gradient nor Hessian information is fed to the controller. It combines a proportional–integral (PI) consensus protocol, which enforces the supply–demand balance, with a one-stage sequential predictor that compensates for the measurement delays. The convergence analysis is developed for local objectives of quadratic type; this restriction, which is required by the stochastic-averaging argument, is stated explicitly and discussed. Using stochastic averaging theory and Lyapunov–Krasovskii functionals for delay systems, we prove that, for every finite initial history, the estimates converge almost surely to an arbitrarily small neighborhood of the optimum for every fixed tolerance, and we derive an explicit admissible range for the constant communication delays together with a sequential procedure for selecting the design parameters. Two case studies, namely a three-generator microgrid and a six-generator microgrid, are used to illustrate the theoretical results.
SN  - 2075-1680
ER  -