Algorithms for Leader Selection in Stochastically Forced Consensus Networks
We are interested in assigning a pre-specified number of nodes as leaders in order to minimize the mean-square deviation from consensus in stochastically forced networks. This problem arises in several applications including control of vehicular formations and localization in sensor networks. For ne...
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| Published in | IEEE transactions on automatic control Vol. 59; no. 7; pp. 1789 - 1802 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
IEEE
01.07.2014
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| Online Access | Get full text |
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| Abstract | We are interested in assigning a pre-specified number of nodes as leaders in order to minimize the mean-square deviation from consensus in stochastically forced networks. This problem arises in several applications including control of vehicular formations and localization in sensor networks. For networks with leaders subject to noise, we show that the Boolean constraints (which indicate whether a node is a leader) are the only source of nonconvexity. By relaxing these constraints to their convex hull we obtain a lower bound on the global optimal value. We also use a simple but efficient greedy algorithm to identify leaders and to compute an upper bound. For networks with leaders that perfectly follow their desired trajectories, we identify an additional source of nonconvexity in the form of a rank constraint. Removal of the rank constraint and relaxation of the Boolean constraints yields a semidefinite program for which we develop a customized algorithm well-suited for large networks. Several examples ranging from regular lattices to random graphs are provided to illustrate the effectiveness of the developed algorithms. |
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| AbstractList | We are interested in assigning a pre-specified number of nodes as leaders in order to minimize the mean-square deviation from consensus in stochastically forced networks. This problem arises in several applications including control of vehicular formations and localization in sensor networks. For networks with leaders subject to noise, we show that the Boolean constraints (which indicate whether a node is a leader) are the only source of nonconvexity. By relaxing these constraints to their convex hull we obtain a lower bound on the global optimal value. We also use a simple but efficient greedy algorithm to identify leaders and to compute an upper bound. For networks with leaders that perfectly follow their desired trajectories, we identify an additional source of nonconvexity in the form of a rank constraint. Removal of the rank constraint and relaxation of the Boolean constraints yields a semidefinite program for which we develop a customized algorithm well-suited for large networks. Several examples ranging from regular lattices to random graphs are provided to illustrate the effectiveness of the developed algorithms. |
| Author | Jovanovic, Mihailo R. Fardad, Makan Fu Lin |
| Author_xml | – sequence: 1 surname: Fu Lin fullname: Fu Lin email: fulin@mcs.anl.gov organization: Math. & Comput. Sci. Div., Argonne Nat. Lab., Argonne, IL, USA – sequence: 2 givenname: Makan surname: Fardad fullname: Fardad, Makan email: makan@syr.edu organization: Dept. of Electr. Eng. & Comput. Sci., Syracuse Univ., Syracuse, NY, USA – sequence: 3 givenname: Mihailo R. surname: Jovanovic fullname: Jovanovic, Mihailo R. email: mihailo@umn.edu organization: Dept. of Electr. & Comput. Eng., Univ. of Minnesota, Minneapolis, MN, USA |
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| SubjectTerms | Algorithms Automatic control Boolean algebra Convex functions Deviation Greedy algorithms Heuristic Laplace equations Linear programming Networks Position (location) Probability theory Randomness Trajectory Upper bound Vectors |
| Title | Algorithms for Leader Selection in Stochastically Forced Consensus Networks |
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