Edge Convergence Problems on Signed Networks

A Comment on and Correction to: Opinion dynamics in the presence of increasing agreement pressure

“…In this technical note we correct and clarify a consensus result given in [1]. This correction is relevant not only to the general literature but in particular to [2], which uses the same proof technique as [1] and [3][4][5][6][7][8][9][10], which cite [1]. We show this proof method is incomplete due to the use of a lemma drawn from outside the consensus literature.…”

Leader-follower and leaderless bipartite formation-consensus over undirected coopetition networks and under proximity and collision-avoidance constraints

“…Definition 3 (Leader-follower bipartite consensus). Let x 0 ∈ R n be the position of the virtual leader ν 0 , whose dynamics are given in (5), provided to at least one follower. Then, the systems (1)-( 2) are said to achieve leader-follower bipartite position and velocity consensus if (4) and…”

“…Moreover, we recast the problem stated above into the space of the synchronization errors using the edge-based framework [9]. Thus, we first recall some facts on signed networks [1] and on the edge-based formulation for signed networks [5].…”

“…We propose a distributed bipartite formation control law that prevents inter-vehicle collisions and keeps vehicles in their sensors' range. We base our control law and analysis on the edge representation for signed networks [5]. This also allows to recast the bipartite formation-consensus problem into the space of the error coordinates.…”

“…A structurally balanced signed network can be transformed into an unsigned one using the gauge transformation-see[1,5].…”