Finite-Time Consensus of Opinion Dynamics and its Applications to Distributed Optimization Over Digraph

Abstract

In this paper, some efficient criteria for finite-time consensus of a class of nonsmooth opinion dynamics over a digraph are established. The lower and upper bounds on the finite settling time are obtained based respectively on the maximal and minimal cut capacity of the digraph. By using tools of the nonsmooth theory and algebraic graph theory, the Carathéodory and Filippov solutions of nonsmooth opinion dynamics are analyzed and compared in detail. In the sense of Filippov solutions, the dynamic consensus is demonstrated without a leader and the finite-time bipartite consensus is also investigated in a signed digraph correspondingly. To achieve a predetermined consensus, a leader agent is introduced to the considered agent networks. As an application, the nonsmooth compartmental dynamics in the presence of a leader is embedded in the proposed continuous-time protocol to solve the distributed optimization problems over an unbalanced digraph. The convergence to the optimal solution by using the proposed distributed algorithm is guaranteed with appropriately selected parameters. To verify the effectiveness of the proposed protocols, three numerical examples are performed.

Distributed Adaptive Optimization for Generalized Linear Multiagent Systems

“…In [11], edge-based fixed-time consensus algorithms have been established. More results can be found in [12][13][14][15].…”

“…For ( ), we have similar results. Compared with the adaptive law in [14,15], the advantage of the adaptive law introducing the damping term is that the adaptive control gains and the amplitude of the control inputs are smaller; this makes our algorithm more robust.…”

Data Driven Distributed Bipartite Consensus Tracking for Nonlinear Multiagent Systems via Iterative Learning Control

“…where ∆e(l, k + 1)=e(l, k + 1) − e(l − 1, k + 1). According to (13) and (14), (15) can be rewritten as following.…”

Event-triggered finite-time consensus control under uncertain disturbances with fully continuous communication and chattering free

“…Further, the work in Zhang et al (2019a) applied finite-time consensus approach in formation control problem of multi-UAV system with time delay and input saturation. In addition, finite-time consensus governed by general linear dynamics and high-order dynamics have also been extensively investigated, see for instance (Liu and Geng, 2015; Shi et al, 2018, 2019; Wang and Song, 2018; Zhang et al, 2019c). Although the aforementioned finite-time consensus algorithms have solved consensus problem in different scenarios, one of the common disadvantages lies in the above literatures is that the agents need to continuously update their control input through frequent communication with their neighbors, which as a consequence produces great energy consumption and seems to be unrealistic due to the energy and computation limitation of small intelligent agents.…”