Distributed convex optimization based on zero‐gradient‐sum algorithm under switching topology

• Published in: IET control theory & applications Vol. 17; no. 12; pp. 1611 - 1624
• Main Authors: Tan, Manchun, Ren, Junwu, Ye, Lei, Xiang, Jianglian
• Format: Journal Article
• Language: English
• Published: Stevenage John Wiley & Sons, Inc 01.08.2023; Wiley
• Subjects: Algorithms; asymptotic stability; Communication; Communication networks; Communications networks; continuous time systems; Control algorithms; convergence; Convex analysis; Convexity; Cost analysis; distributed algorithms; Network topologies; Optimization algorithms; Stability analysis; Sums; Switching; Topology optimization
• ISSN: 1751-8644; 1751-8652; 1751-8652
• DOI: 10.1049/cth2.12497

This paper designs a finite‐time convergence protocol and an event‐triggered control protocol based on Zero‐Gradient‐Sum (ZGS) algorithm under stochastic switching undirected topology, respectively, which greatly expands the theory of continuous‐time distributed optimization algorithms. With finite‐time stability and Lyapunov stability analysis, it is illustrated that the proposed method can finite‐time converge to the optimal solution of distributed unconstrained convex optimization problem and overcome the disturbances of the switching communication networks. In addition, the event‐triggered mechanism can effectively reduce the network burden and communication cost as well as avoid Zeno behaviour. Finally, two numerical simulations verify the advantages and effectiveness of these methods. This paper designs a finite‐time convergence protocol and an event‐triggered control protocol based on Zero‐Gradient‐Sum (ZGS) algorithm under stochastic switching undirected topology, respectively, which greatly expands the theory of continuous‐time distributed optimization algorithms. With finite‐time stability and Lyapunov stability analysis, it is illustrated that the proposed method can converge to the optimal solution of distributed unconstrained convex optimization problem and overcome the disturbances of the switching communication networks.