On Achieving Size-Independent Stability Margin of Vehicular Lattice Formations With Distributed Control
We study the stability margin of a vehicular formation with distributed control, in which the control at each vehicle only depends on the information from its neighbors in an information graph. We consider a D-dimensional lattice as information graph, of which the 1-D platoon is a special case. The...
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description | We study the stability margin of a vehicular formation with distributed control, in which the control at each vehicle only depends on the information from its neighbors in an information graph. We consider a D-dimensional lattice as information graph, of which the 1-D platoon is a special case. The stability margin is measured by the real part of the least stable eigenvalue of the closed-loop state matrix, which quantifies the rate of decay of initial errors. In [1], it was shown that with symmetric control, in which two neighbors put equal weight on information received from each other, the stability margin of a 1-D vehicular platoon decays to 0 as 0(1/N 2 ), where N is the number of vehicles. Moreover, a perturbation analysis was used to show that with vanishingly small amount of asymmetry in the control gains, the stability margin scaling can be improved to 0(1/N). In this technical note, we show that, with judicious choice of nonvanishing asymmetry in control, the stability margin of the closed loop can be bounded away from zero uniformly in N. Asymmetry in control gains thus makes the control architecture highly scalable. The results are also generalized to D-dimensional lattice information graphs that were studied in [2], and the correspondingly stronger conclusions than those derived in [2] are obtained. In addition, we show that the size-independent stability margin can be achieved with relative position and relative velocity (RPRV) feedback as well as relative position and absolute velocity (RPAV) feedback, while the analysis in [1], [2] was only for the RPAV case. |
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We consider a D-dimensional lattice as information graph, of which the 1-D platoon is a special case. The stability margin is measured by the real part of the least stable eigenvalue of the closed-loop state matrix, which quantifies the rate of decay of initial errors. In [1], it was shown that with symmetric control, in which two neighbors put equal weight on information received from each other, the stability margin of a 1-D vehicular platoon decays to 0 as 0(1/N 2 ), where N is the number of vehicles. Moreover, a perturbation analysis was used to show that with vanishingly small amount of asymmetry in the control gains, the stability margin scaling can be improved to 0(1/N). In this technical note, we show that, with judicious choice of nonvanishing asymmetry in control, the stability margin of the closed loop can be bounded away from zero uniformly in N. Asymmetry in control gains thus makes the control architecture highly scalable. The results are also generalized to D-dimensional lattice information graphs that were studied in [2], and the correspondingly stronger conclusions than those derived in [2] are obtained. In addition, we show that the size-independent stability margin can be achieved with relative position and relative velocity (RPRV) feedback as well as relative position and absolute velocity (RPAV) feedback, while the analysis in [1], [2] was only for the RPAV case.</description><identifier>ISSN: 0018-9286</identifier><identifier>EISSN: 1558-2523</identifier><identifier>DOI: 10.1109/TAC.2012.2191179</identifier><identifier>CODEN: IETAA9</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Applied sciences ; Asymmetric control ; Asymmetry ; automated platoon ; Computer science; control theory; systems ; Computer systems and distributed systems. User interface ; Control system analysis ; Control systems ; Control theory ; Control theory. Systems ; distributed control ; Eigenvalues and eigenfunctions ; Exact sciences and technology ; Feedback ; Gain ; Graphs ; Lattices ; Modelling and identification ; multiagent system ; Numerical stability ; Robotics ; Software ; Stability ; Stability criteria ; stability margin ; Studies ; Vehicle dynamics ; Vehicles</subject><ispartof>IEEE transactions on automatic control, 2012-10, Vol.57 (10), p.2688-2694</ispartof><rights>2015 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Oct 2012</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c396t-6ae67cd6adfc199e4436bb8d3c945077792861d8afd3f4c0d1241353b57ac96f3</citedby><cites>FETCH-LOGICAL-c396t-6ae67cd6adfc199e4436bb8d3c945077792861d8afd3f4c0d1241353b57ac96f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/6170546$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/6170546$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=26443256$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>He Hao</creatorcontrib><creatorcontrib>Barooah, P.</creatorcontrib><title>On Achieving Size-Independent Stability Margin of Vehicular Lattice Formations With Distributed Control</title><title>IEEE transactions on automatic control</title><addtitle>TAC</addtitle><description>We study the stability margin of a vehicular formation with distributed control, in which the control at each vehicle only depends on the information from its neighbors in an information graph. We consider a D-dimensional lattice as information graph, of which the 1-D platoon is a special case. The stability margin is measured by the real part of the least stable eigenvalue of the closed-loop state matrix, which quantifies the rate of decay of initial errors. In [1], it was shown that with symmetric control, in which two neighbors put equal weight on information received from each other, the stability margin of a 1-D vehicular platoon decays to 0 as 0(1/N 2 ), where N is the number of vehicles. Moreover, a perturbation analysis was used to show that with vanishingly small amount of asymmetry in the control gains, the stability margin scaling can be improved to 0(1/N). In this technical note, we show that, with judicious choice of nonvanishing asymmetry in control, the stability margin of the closed loop can be bounded away from zero uniformly in N. Asymmetry in control gains thus makes the control architecture highly scalable. The results are also generalized to D-dimensional lattice information graphs that were studied in [2], and the correspondingly stronger conclusions than those derived in [2] are obtained. In addition, we show that the size-independent stability margin can be achieved with relative position and relative velocity (RPRV) feedback as well as relative position and absolute velocity (RPAV) feedback, while the analysis in [1], [2] was only for the RPAV case.</description><subject>Applied sciences</subject><subject>Asymmetric control</subject><subject>Asymmetry</subject><subject>automated platoon</subject><subject>Computer science; control theory; systems</subject><subject>Computer systems and distributed systems. User interface</subject><subject>Control system analysis</subject><subject>Control systems</subject><subject>Control theory</subject><subject>Control theory. Systems</subject><subject>distributed control</subject><subject>Eigenvalues and eigenfunctions</subject><subject>Exact sciences and technology</subject><subject>Feedback</subject><subject>Gain</subject><subject>Graphs</subject><subject>Lattices</subject><subject>Modelling and identification</subject><subject>multiagent system</subject><subject>Numerical stability</subject><subject>Robotics</subject><subject>Software</subject><subject>Stability</subject><subject>Stability criteria</subject><subject>stability margin</subject><subject>Studies</subject><subject>Vehicle dynamics</subject><subject>Vehicles</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpdkEtrGzEQgEVJoc7jXuhFUAK5rKPRa1dH4zZtwCGHpOlx0Wq1tsJaciRtIfn1lbHJIZcZhvlmmPkQ-gpkDkDU9eNiOacE6JyCAqjVJzQDIZqKCspO0IwQaCpFG_kFnab0XErJOczQ-t7jhdk4-8_5NX5wb7a69b3d2RJ8xg9Zd250-RXf6bh2HocBP9mNM9OoI17pnJ2x-CbErc4u-IT_urzBP1zK0XVTtj1eBp9jGM_R50GPyV4c8xn6c_Pzcfm7Wt3_ul0uVpVhSuZKaitr00vdDwaUspwz2XVNz4zigtR1vX8B-kYPPRu4IT1QDkywTtTaKDmwM3R12LuL4WWyKbdbl4wdR-1tmFILTArgjChV0O8f0OcwRV-ua4E0RKiGcVoocqBMDClFO7S76LY6vhao3Ztvi_l2b749mi8jl8fFOhk9DlF749L7HC3mGRWycN8OnLPWvrcl1ERwyf4DfdaLxA</recordid><startdate>20121001</startdate><enddate>20121001</enddate><creator>He Hao</creator><creator>Barooah, P.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>F28</scope></search><sort><creationdate>20121001</creationdate><title>On Achieving Size-Independent Stability Margin of Vehicular Lattice Formations With Distributed Control</title><author>He Hao ; Barooah, P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c396t-6ae67cd6adfc199e4436bb8d3c945077792861d8afd3f4c0d1241353b57ac96f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Applied sciences</topic><topic>Asymmetric control</topic><topic>Asymmetry</topic><topic>automated platoon</topic><topic>Computer science; control theory; systems</topic><topic>Computer systems and distributed systems. User interface</topic><topic>Control system analysis</topic><topic>Control systems</topic><topic>Control theory</topic><topic>Control theory. Systems</topic><topic>distributed control</topic><topic>Eigenvalues and eigenfunctions</topic><topic>Exact sciences and technology</topic><topic>Feedback</topic><topic>Gain</topic><topic>Graphs</topic><topic>Lattices</topic><topic>Modelling and identification</topic><topic>multiagent system</topic><topic>Numerical stability</topic><topic>Robotics</topic><topic>Software</topic><topic>Stability</topic><topic>Stability criteria</topic><topic>stability margin</topic><topic>Studies</topic><topic>Vehicle dynamics</topic><topic>Vehicles</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>He Hao</creatorcontrib><creatorcontrib>Barooah, P.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><jtitle>IEEE transactions on automatic control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>He Hao</au><au>Barooah, P.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Achieving Size-Independent Stability Margin of Vehicular Lattice Formations With Distributed Control</atitle><jtitle>IEEE transactions on automatic control</jtitle><stitle>TAC</stitle><date>2012-10-01</date><risdate>2012</risdate><volume>57</volume><issue>10</issue><spage>2688</spage><epage>2694</epage><pages>2688-2694</pages><issn>0018-9286</issn><eissn>1558-2523</eissn><coden>IETAA9</coden><abstract>We study the stability margin of a vehicular formation with distributed control, in which the control at each vehicle only depends on the information from its neighbors in an information graph. We consider a D-dimensional lattice as information graph, of which the 1-D platoon is a special case. The stability margin is measured by the real part of the least stable eigenvalue of the closed-loop state matrix, which quantifies the rate of decay of initial errors. In [1], it was shown that with symmetric control, in which two neighbors put equal weight on information received from each other, the stability margin of a 1-D vehicular platoon decays to 0 as 0(1/N 2 ), where N is the number of vehicles. Moreover, a perturbation analysis was used to show that with vanishingly small amount of asymmetry in the control gains, the stability margin scaling can be improved to 0(1/N). In this technical note, we show that, with judicious choice of nonvanishing asymmetry in control, the stability margin of the closed loop can be bounded away from zero uniformly in N. Asymmetry in control gains thus makes the control architecture highly scalable. The results are also generalized to D-dimensional lattice information graphs that were studied in [2], and the correspondingly stronger conclusions than those derived in [2] are obtained. In addition, we show that the size-independent stability margin can be achieved with relative position and relative velocity (RPRV) feedback as well as relative position and absolute velocity (RPAV) feedback, while the analysis in [1], [2] was only for the RPAV case.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TAC.2012.2191179</doi><tpages>7</tpages><oa>free_for_read</oa></addata></record> |
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subjects | Applied sciences Asymmetric control Asymmetry automated platoon Computer science control theory systems Computer systems and distributed systems. User interface Control system analysis Control systems Control theory Control theory. Systems distributed control Eigenvalues and eigenfunctions Exact sciences and technology Feedback Gain Graphs Lattices Modelling and identification multiagent system Numerical stability Robotics Software Stability Stability criteria stability margin Studies Vehicle dynamics Vehicles |
title | On Achieving Size-Independent Stability Margin of Vehicular Lattice Formations With Distributed Control |
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