Solving Specified-Time Distributed Optimization Problem via Sampled-Data-Based Algorithm

• Published in: IEEE transactions on network science and engineering Vol. 9; no. 4; pp. 2747 - 2758
• Main Authors: Zhou, Jialing, Lv, Yuezu, Wen, Changyun, Wen, Guanghui
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.07.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Communication; Convergence; Directed graph; distributed resource allocation; Eigenvalues and eigenfunctions; Energy sources; Initial conditions; Laplace equations; multi-agent network; Multiagent systems; Optimization; Resource allocation; Resource management; sampled-data communication; Settling; specified-time distributed optimization; Symmetric matrices; Topology
• ISSN: 2327-4697; 2334-329X
• DOI: 10.1109/TNSE.2022.3169151

Despite significant advances on distributed continuous-time optimization of multi-agent networks, there is still lack of an efficient algorithm to achieve the goal of distributed optimization at a pre-specified time, especially for the case with unbalanced directed topologies. Herein, a new out-degree based design structure is proposed for connected agents with directed topologies to collectively minimize the sum of individual objective functions and keep satisfying an equality constraint. With the designed algorithm, the settling time of distributed optimization can be exactly predefined. The specified selection of such a settling time is independent of not only the initial conditions of agents, but also the algorithm parameters and the communication topologies. Furthermore, the proposed algorithm can realize specified-time optimization by exchanging information among neighbors only at discrete sampling instants and thus reduces the communication burden. In addition, the equality constraint is always satisfied during the whole process, which makes the proposed algorithm applicable to online solving distributed optimization problems such as energy resource allocation. For the special case of undirected communication topologies, a reduced-order algorithm is also designed. Finally, the effectiveness of the theoretical analysis is justified by numerical simulations.