A Class of Distributed Online Aggregative Optimization in Unknown Dynamic Environment

Chengqian Yang, Shuang Wang, Shuang Zhang, Shiwei Lin and Bomin Huang ()
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Chengqian Yang: School of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Shuang Wang: School of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Shuang Zhang: College of Computer Engineering, Jimei University, Xiamen 361021, China
Shiwei Lin: College of Computer Engineering, Jimei University, Xiamen 361021, China
Bomin Huang: College of Computer Engineering, Jimei University, Xiamen 361021, China

Mathematics, 2024, vol. 12, issue 16, 1-15

Abstract: This paper considers a class of distributed online aggregative optimization problems over an undirected and connected network. It takes into account an unknown dynamic environment and some aggregation functions, which is different from the problem formulation of the existing approach, making the aggregative optimization problem more challenging. A distributed online optimization algorithm is designed for the considered problem via the mirror descent algorithm and the distributed average tracking method. In particular, the dynamic environment and the gradient are estimated by the averaged tracking methods, and then an online optimization algorithm is designed via a dynamic mirror descent method. It is shown that the dynamic regret is bounded in the order of O ( T ) . Finally, the effectiveness of the designed algorithm is verified by some simulations of cooperative control of a multi-robot system.

Keywords: online optimization; aggregated terms; distributed algorithm; dynamic environment (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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