A continuous-time consensus algorithm using neurodynamic system for distributed time-varying optimization with inequality constraints. Issue 13 (September 2021)

• Record Type: Journal Article
• Authors: He, Shuang; He, Xing; Huang, Tingwen
• Is Part Of: Journal of the Franklin Institute. Volume 358:Issue 13(2021)
• Page Start: 6741
• Page End: 6758
• Publication Date: 2021-09
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2021.07.007
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: In this paper, a distributed time-varying convex optimization problem with inequality constraints is discussed based on neurodynamic system. The goal is to minimize the sum of agents' local time-varying objective functions subject to some time-varying inequality constraints, each of which is known only to an individual agent. Here, the optimal solution is time-varying instead of constant. Under an undirected and connected graph, a distributed continuous-time consensus algorithm is designed by using neurodynamic system, signum functions and log-barrier penalty functions. The proposed algorithm can be understood through two parts: one part is used to reach consensus and the other is used to achieve gradient descent to track the optimal solution. Theoretical studies indicate that all agents will achieve consensus and the proposed algorithm can track the optimal solution of the time-varying convex problem. Two numerical examples are provided to validate the theoretical results.