In this paper, the discrete-time stochastic extremum seeking method with binary-valued measurements is developed. In this case, the exact measurement of an objective function value cannot be obtained; instead, only real-time information indicating whether this function value is smaller than a fixed threshold is available. With this kind of coarse measurement, an online stochastic extremum seeking algorithm is proposed, and a rigorous convergence analysis is provided. Furthermore, the proposed scheme is extended to solve the distributed optimization problem in terms of both the coarse measurements of local objective functions and the coarse information exchanged among agents. It is demonstrated that agents can cooperatively find the optimal solution by utilizing the binary-valued measurements of their local objective functions and the signs of relative state estimates of their neighbors, rather than relying on exact relative state estimates. Finally, some numerical examples are provided to illustrate the effectiveness of our algorithms. (c) 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Publication:

AUTOMATICA

http://dx.doi.org/10.1016/j.automatica.2025.112664

Author:

Yanlong Zhao

State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

E-mail addresses: ylzhao@amss.ac.cn