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Consensus tracking for multiagent systems with nonlinear dynamics.

Dong R - ScientificWorldJournal (2014)

Bottom Line: This paper concerns the problem of consensus tracking for multiagent systems with a dynamical leader.In particular, it proposes the corresponding explicit control laws for multiple first-order nonlinear systems, second-order nonlinear systems, and quite general nonlinear systems based on the leader-follower and the tree shaped network topologies.Several numerical simulations are given to verify the theoretical results.

View Article: PubMed Central - PubMed

Affiliation: The State Key Laboratory for Turbulence and Complex System, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China.

ABSTRACT
This paper concerns the problem of consensus tracking for multiagent systems with a dynamical leader. In particular, it proposes the corresponding explicit control laws for multiple first-order nonlinear systems, second-order nonlinear systems, and quite general nonlinear systems based on the leader-follower and the tree shaped network topologies. Several numerical simulations are given to verify the theoretical results.

Show MeSH
The undirected graph for a group of three followers with a leader. Here L0 denotes the leader and Fi, i = 1,2, 3, denote the followers. The direct arrows represent the information flow from the leader to the follower and the indirect edges represent the bidirectional information flow between followers.
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fig1: The undirected graph for a group of three followers with a leader. Here L0 denotes the leader and Fi, i = 1,2, 3, denote the followers. The direct arrows represent the information flow from the leader to the follower and the indirect edges represent the bidirectional information flow between followers.

Mentions: In this section, three numerical simulation examples are given to illustrate the theoretical results. Consider the first example, a network of three followers with a leader shown in Figure 1. Assume that the dynamics of the follower agents with n = 2 are described by the following equations:(52)f(t,xi)=(xi1sintxi2cos⁡t),f(t,xr)=(xr1sintxr2cos⁡t).The control input of the leader is given by ur = [1,1]T. Choose βi = 1 for i = 1,2, 3 and ω = 1.5. Note that . The initial values of the error between the multiple followers and the leader, which is described by , i = 1,2, 3, j = 1,2, are given as [0.1, −0.2,0.3, −0.1,0.4,0.2]T. Then the results of consensus tracking are shown in Figure 2, where x1 = [x11, x21, x31]T and x2 = [x12, x22, x32]T. Since as t moves on, consensus tracking is finally achieved.


Consensus tracking for multiagent systems with nonlinear dynamics.

Dong R - ScientificWorldJournal (2014)

The undirected graph for a group of three followers with a leader. Here L0 denotes the leader and Fi, i = 1,2, 3, denote the followers. The direct arrows represent the information flow from the leader to the follower and the indirect edges represent the bidirectional information flow between followers.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4150520&req=5

fig1: The undirected graph for a group of three followers with a leader. Here L0 denotes the leader and Fi, i = 1,2, 3, denote the followers. The direct arrows represent the information flow from the leader to the follower and the indirect edges represent the bidirectional information flow between followers.
Mentions: In this section, three numerical simulation examples are given to illustrate the theoretical results. Consider the first example, a network of three followers with a leader shown in Figure 1. Assume that the dynamics of the follower agents with n = 2 are described by the following equations:(52)f(t,xi)=(xi1sintxi2cos⁡t),f(t,xr)=(xr1sintxr2cos⁡t).The control input of the leader is given by ur = [1,1]T. Choose βi = 1 for i = 1,2, 3 and ω = 1.5. Note that . The initial values of the error between the multiple followers and the leader, which is described by , i = 1,2, 3, j = 1,2, are given as [0.1, −0.2,0.3, −0.1,0.4,0.2]T. Then the results of consensus tracking are shown in Figure 2, where x1 = [x11, x21, x31]T and x2 = [x12, x22, x32]T. Since as t moves on, consensus tracking is finally achieved.

Bottom Line: This paper concerns the problem of consensus tracking for multiagent systems with a dynamical leader.In particular, it proposes the corresponding explicit control laws for multiple first-order nonlinear systems, second-order nonlinear systems, and quite general nonlinear systems based on the leader-follower and the tree shaped network topologies.Several numerical simulations are given to verify the theoretical results.

View Article: PubMed Central - PubMed

Affiliation: The State Key Laboratory for Turbulence and Complex System, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China.

ABSTRACT
This paper concerns the problem of consensus tracking for multiagent systems with a dynamical leader. In particular, it proposes the corresponding explicit control laws for multiple first-order nonlinear systems, second-order nonlinear systems, and quite general nonlinear systems based on the leader-follower and the tree shaped network topologies. Several numerical simulations are given to verify the theoretical results.

Show MeSH