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Research Papers

A Finite-Time Consensus Framework Over Time-Varying Graph Topologies With Temporal Constraints

[+] Author and Article Information
Zhen Kan

Department of Mechanical and
Industrial Engineering,
The University of Iowa,
Iowa City, IA 52242
e-mail: zhen-kan@uiowa.edu

Tansel Yucelen

Department of Mechanical Engineering,
University of South Florida,
Tampa, FL 33620
e-mail: yucelen@lacis.team

Emily Doucette

Munitions Directorate,
Air Force Research Laboratory,
Eglin Air Force Base,
Shalimar, FL 32579
e-mail: emily.doucette@eglin.af.mil

Eduardo Pasiliao

Munitions Directorate,
Air Force Research Laboratory,
Eglin Air Force Base,
Shalimar, FL 32579
e-mail: pasiliao@eglin.af.mil

1Corresponding author.

2Z. Kan and T. Yucelen contributed equally to this research.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 17, 2016; final manuscript received December 19, 2016; published online May 12, 2017. Assoc. Editor: Zongxuan Sun.

J. Dyn. Sys., Meas., Control 139(7), 071012 (May 12, 2017) (6 pages) Paper No: DS-16-1405; doi: 10.1115/1.4035612 History: Received August 17, 2016; Revised December 19, 2016

Finite-time consensus has attracted significant research interest due to its wide applications in multiagent systems. Various results have been developed to enable multiagent systems to complete desired tasks in finite-time. However, most existing results in the literature can only ensure finite-time consensus without considering temporal constraints, where the time used to achieve consensus cannot be preset arbitrarily and is generally determined by the system initial conditions, prohibiting its application in time-sensitive tasks. Motivated to achieve consensus within a desired time frame, user-specified finite-time consensus is developed in the present work for a multiagent system to ensure consensus at a prespecified time instant. The interaction among agents (e.g., communication and information exchange) is modeled as a time-varying graph, where each edge is associated with a time-varying weight representing the time-varying interaction between neighboring agents. Consensus over such time-varying graph is then proven based on a time transformation and is guaranteed to be completed within a prespecified time frame. To demonstrate the developed framework, finite-time rendezvous of a multiagent system is considered as an example application, where agents with limited communication capabilities are desired to meet at a common location at a preset time instant with constraints on preserving global network connectivity. A numerical simulation is provided to demonstrate the efficiency of the developed result.

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Figures

Grahic Jump Location
Fig. 1

The initial graph and trajectories of ten agents. The squares represent the initial positions of the agents and solid lines connecting agents indicate the interagent communication. The trajectory of each agent is represented by dots, which indicates that all agents converge to a common setpoint denoted by the circle.

Grahic Jump Location
Fig. 2

The evolution of interagent distance, which is maintained less than the communication radius R = 2.5 m, indicating that every existing communication link is preserved when performing rendezvous. Since all edges converge to 0 at tf = 10 s, the finite-time rendezvous is completed within the desired time frame.

Grahic Jump Location
Fig. 3

The control input of each agent, which indicates that the control input is bounded as ttf

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