Distributed Continuous-Time Algorithm for Time-Varying Optimization With Affine Formation Constraints

• 成果类型: Article
• 署名作者: Wu, Chu; Fang, Hao; Zeng, Xianlin; Yang, Qingkai; Wei, Yue; Chen, Jie
• 署名单位: Beijing Institute of Technology; Peng Cheng Laboratory; Tongji University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3190054
• 发表日期: 2023
• 页码: 2615-2622
• 关键词: Cost function; stress; Laplace equations; Time-varying systems; COSTS; trajectory; STANDARDS; Affine formation; fixed-time estimator; gradient tracking; time-varying optimization

摘要

In this article, we investigate a continuous-time distributed optimization problem with time-varying cost functions and affine formation constraints, which are described by the stress matrices rather than the standard Laplacians. The objective is to minimize the sum of local time-varying cost functions, each of which is known by only one individual agent. The optimal solution is a time-varying affine transformation of a nominal configuration rather than some constants. To tackle the difficulty caused by the dynamic aspect of the local cost functions and handle affine formation constraints, the fixed-time distributed estimator and distributed gradient tracking technique are developed, respectively, to compensate the time variation of solution trajectory and calculate the weighted sum of local gradients to eliminate the tracking error. The time-varying optimal solution trajectory is thus accurately tracked with the proposed estimator-based gradient tracking algorithm. Using appropriately chosen coefficients, the tracking error is guaranteed to vanish at an exponential rate. The proposed estimator-based gradient tracking algorithm is further validated through numerical simulations.