Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/79728
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dc.contributorDepartment of Applied Mathematicsen_US
dc.creatorJing, GSen_US
dc.creatorZhang, GFen_US
dc.creatorLee, HWJen_US
dc.creatorWang, Len_US
dc.date.accessioned2018-12-21T07:13:12Z-
dc.date.available2018-12-21T07:13:12Z-
dc.identifier.issn0363-0129en_US
dc.identifier.urihttp://hdl.handle.net/10397/79728-
dc.language.isoenen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.rights© 2018 Society for Industrial and Applied Mathematicsen_US
dc.rightsPosted with permission of the publisher.en_US
dc.rightsThe following publication Jing, G., Zhang, G., Lee, H. W. J., & Wang, L. (2018). Weak Rigidity Theory and Its Application to Formation Stabilization. SIAM Journal on Control and Optimization, 56(3), 2248-2273 is available at https://doi.org/10.1137/17M1122049.en_US
dc.subjectGraph rigidityen_US
dc.subjectRigid formationen_US
dc.subjectMultiagent systemsen_US
dc.subjectMatrix completionen_US
dc.titleWeak rigidity theory and its application to formation stabilizationen_US
dc.typeJournal/Magazine Articleen_US
dc.identifier.spage2248en_US
dc.identifier.epage2273en_US
dc.identifier.volume56en_US
dc.identifier.issue3en_US
dc.identifier.doi10.1137/17M1122049en_US
dcterms.abstractThis paper introduces the notion of weak rigidity to characterize a framework by pairwise inner products of interagent displacements. Compared to distance-based rigidity, weak rigidity requires fewer constrained edges in the graph to determine a geometric shape in an arbitrarily dimensional space. A necessary and sufficient graphical condition for infinitesimal weak rigidity of planar frameworks is derived. As an application of the proposed weak rigidity theory, a gradient-based control law and a nongradient-based control law are designed for a group of single-integrator modeled agents to stabilize a desired formation shape, respectively. Using the gradient control law, we prove that an infinitesimally weakly rigid formation is locally exponentially stable. In particular, if the number of agents is one greater than the dimension of the space, a minimally infinitesimally weakly rigid formation is almost globally asymptotically stable. In the literature of rigid formation, the sensing graph is always required to be rigid. Using the nongradient control law based on weak rigidity theory, it is not necessary for the sensing graph to be rigid for local exponential stability of the formation. A numerical simulation is performed for illustrating the effectiveness of our main results.en_US
dcterms.accessRightsopen accessen_US
dcterms.bibliographicCitationSIAM journal on control and optimization, 2018, v. 56, no. 3, p. 2248-2273en_US
dcterms.isPartOfSIAM journal on control and optimizationen_US
dcterms.issued2018-
dc.identifier.isiWOS:000437010100024-
dc.identifier.eissn1095-7138en_US
dc.description.validate201812 bcrcen_US
dc.description.oaVersion of Recorden_US
dc.identifier.FolderNumbera0850-n37-
dc.identifier.SubFormID1768-
dc.description.fundingSourceRGCen_US
dc.description.fundingText531213 and 15206915en_US
dc.description.pubStatusPublisheden_US
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