A Cutting-Surface Consensus Approach for Distributed Robust Optimization of Multi-Agent Systems

• 成果类型: Article
• 署名作者: Fu, Jun; Wu, Xunhao
• 署名单位: Northeastern University - China
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3573763
• 发表日期: 2025
• 关键词: convex-optimization; algorithms; PROGRAMS; graphs

摘要

A novel and fully distributed optimization method is proposproed for the distributed robust convex program (DRCP) over a time-varying unbalanced directed network under the uniformly jointly strongly connected (UJSC) assumption. First, an approximated DRCP is introduced by discretizing the semi-infinite constraints into a finite number of inequality constraints to ensure tractability and restricting the right-hand side of the constraints with a positive parameter to ensure a feasible solution for DRCP can be obtained. This problem is iteratively solved by a distributed projected gradient algorithm proposed in this article, which is based on epigraphic reformulation and gradient projected operations. Second, a cutting-surface consensus approach is proposed for locating an approximately optimal consensus solution of the DRCP with guaranteed local feasibility for each agent. This approach is based on iteratively approximating the DRCP by successively reducing the restriction parameter of the right-hand constraints and adding the cutting surfaces into the existing finite set of constraints. Third, to ensure finite-time termination of the distributed optimization, a distributed termination algorithm is developed based on consensus and zeroth-order stopping conditions under UJSC graphs. Fourth, it is proved that the cutting-surface consensus approach terminates finitely and yields a feasible and approximate optimal solution for each agent. Finally, the effectiveness of the approach is illustrated through a numerical example.