Distributed optimization problem for second-order multi-agent networks with only position interaction

Distributed optimisation of second‐order multi‐agent systems by control algorithm using position‐only interaction with time‐varying delay

“…In this section, the optimisation problem and equivalent formulation are presented and some existing works are introduced. Based on the previous work [38], the distributed control algorithm for second-order MASs in the presence of communication delay is presented.…”

“…More recently, by removing the coupled term ∑ j ∈ N i a i j (x i (t) − x j (t)) in the distributed algorithm (6) and in the meanwhile, cutting down the need of the information of velocity states from neighbours (i.e. ∑ j ∈ N i a i j (v i (t) − v j (t)) in distributed algorithms of the works [34,36], a modified distributed optimisation algorithm is proposed in our work [38], which is rewritten as follows:…”

“…As discussed in [38], in the distributed control algorithm (8), although the information of the velocity states from neighbours in (6) and (7) is removed, it still ensures obtaining the optimisation (2) (referring to [38] for more details). However, in all aforementioned distributed control algorithms, the data transmission in the presence of the time delay is neglected.…”

“…Thereby, the second-order dynamic models have attracted a lot of attention from researchers. In recent years, some researchers have studied to solve distributed optimisation problem based on the second-order MASs and obtained some results [34][35][36][37][38]. In [34], a distributed algorithm for agents with second-order dynamics under the local directed communication topology has been investigated based on the Lyapunov analysis.…”

“…However, in practise, the relative velocity among agents is much more difficult to be obtained compared with the relative position. Therefore, the distributed optimisation secondorder algorithm is further modified in our previous work [38], which only utilises the position information of its neighbour under the undirected communication topology. However, as far as we know, all the existing works on distributed optimisation of secondorder MASs neglect the influence of time delay which is inevitable in the network.…”