Complex Laplacian based algorithm for output synchronization of multi-agent systems using internal model principle

Optimal topology design and distributed formation control of multiagent systems with complex‐weights directed networks

“…(i) Contrary to the previous works [8][9][10][11][12][13][14][15][16] where a stabilizing matrix is needed to stabilizing the overall system, the results derived in this article do not require any calculation of stabilizing gains. (ii) Compared with the previous works, [8][9][10][11][12][13][14][15][16] the choice of complex weights is unique, and given a formation basis we may choose a unique set of complex weights that satisfy associated conditions. (iii) Early studies on the distributed formation control problem via complex Laplacian have mainly focused on MAS with first-and second-order dynamics.…”

“…This scheme can be roughly categorized into three classes, namely, behavioral, virtual structure/leader, and leader-follower approaches. Leader-follower approach [7][8][9][10][11][12][13][14][15][16] is a special kind of formation control in MAS, where some agents are designed as leaders that drive the group, whereas the others can be designed as followers, which track the leaders.…”

“…[3][4][5][6][7] Complex Laplacian has been applied to MAS very recently. [8][9][10][11][12][13][14][15][16] Compared with the existing approaches for formation control, the main motivation for the use of the complex Laplacian-based approach is given below. 8 • This approach leads to simple linear control laws, which can guarantee control goals, while neither integrant distances nor nonlinear gradient control laws [17][18][19] cannot.…”

“…A control scheme to synchronize motion was proposed in the work of Lin et al 11 for MAS with the reference generated by a virtual exosystem having its dynamics. In the works of Japtap et al 12 and Wang et al, 13 a distributed control strategy for formation shape control of autonomous robots under complex-weighted switching topologies was developed. The problem of fault detection and tolerant control for MAS under complex-weighted networks was discussed in the works of Ghasemi et al [14][15][16] It is worth noting that the aforementioned studies [8][9][10][11][12][13][14][15][16] require a stabilize matrix such that the overall system is asymptotically stable and the choice of complex weights is not unique.…”

“…(iii) Early studies on the distributed formation control problem via complex Laplacian have mainly focused on MAS with first-and second-order dynamics. [8][9][10][11][12][13][14][15][16] However, in many practical applications, a wide class of systems and vehicles cannot be modeled exactly by first-and second-order kinematics. Therefore, it is necessary to extend the coordination problem via complex Laplacian to a general linear MAS.…”