Probabilistic formulation of estimation problems for a class of Hamilton-Jacobi equations
This article presents a method for deriving the probability distribution of the solution to a Hamilton-Jacobi partial differential equation for which the value conditions are random. The derivations lead to analytical or semi-analytical expressions of the probability distribution function at any poi...
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| creator | Hofleitner, A. Claudel, C. Bayen, A. M. |
| description | This article presents a method for deriving the probability distribution of the solution to a Hamilton-Jacobi partial differential equation for which the value conditions are random. The derivations lead to analytical or semi-analytical expressions of the probability distribution function at any point in the domain in which the solution is defined. The characterization of the distribution of the solution at any point is a first step towards the estimation of the parameters defining the random value conditions. This work has important applications for estimation in flow networks in which value conditions are noisy. In particular, we illustrate our derivations on a road segment with random capacity reductions. |
| doi_str_mv | 10.1109/CDC.2012.6426316 |
| format | Conference Proceeding |
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In particular, we illustrate our derivations on a road segment with random capacity reductions.</description><subject>Boundary conditions</subject><subject>Equations</subject><subject>Estimation</subject><subject>Noise measurement</subject><subject>Probabilistic logic</subject><subject>Probability distribution</subject><subject>Random variables</subject><issn>0191-2216</issn><isbn>9781467320658</isbn><isbn>146732065X</isbn><isbn>1467320633</isbn><isbn>1467320668</isbn><isbn>9781467320634</isbn><isbn>9781467320665</isbn><isbn>9781467320641</isbn><isbn>1467320641</isbn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2012</creationdate><recordtype>conference_proceeding</recordtype><sourceid>6IE</sourceid><sourceid>RIE</sourceid><recordid>eNo1kE9PwzAMxYMAiW3sjsQlX6DDTpp_R1QYA02CAxw4TUmaSkHtMpruwLenY-Pk96yfrWcTcoOwQARzVz1UCwbIFrJkkqM8I1MspeIMJOfnZG6U_vdCX5AJoMGCMZRXZJrzFwBokHJCPt_65KyLbcxD9LRJfbdv7RDTlqaGhrHZHd1u5NrQ5QNCLfWtzfmArGwX2yFtixfrk4s0fO__BvI1uWxsm8P8VGfkY_n4Xq2K9evTc3W_LiIqMRReY1AMnHQCvLDMNBJCKZTFUSpwoa6NLmvWBM2s48KgkMwYJX09XsYDn5Hb494YQtjs-jFw_7M5vYX_AjiLVK0</recordid><startdate>201212</startdate><enddate>201212</enddate><creator>Hofleitner, A.</creator><creator>Claudel, C.</creator><creator>Bayen, A. 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M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-i175t-c81e720b6b50c5a29f60e457a129f70bedd984d2fe82ab35915629976cd6583e3</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Boundary conditions</topic><topic>Equations</topic><topic>Estimation</topic><topic>Noise measurement</topic><topic>Probabilistic logic</topic><topic>Probability distribution</topic><topic>Random variables</topic><toplevel>online_resources</toplevel><creatorcontrib>Hofleitner, A.</creatorcontrib><creatorcontrib>Claudel, C.</creatorcontrib><creatorcontrib>Bayen, A. M.</creatorcontrib><collection>IEEE Electronic Library (IEL) Conference Proceedings</collection><collection>IEEE Proceedings Order Plan (POP) 1998-present by volume</collection><collection>IEEE Xplore All Conference Proceedings</collection><collection>IEEE Electronic Library (IEL)</collection><collection>IEEE Proceedings Order Plans (POP) 1998-present</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Hofleitner, A.</au><au>Claudel, C.</au><au>Bayen, A. M.</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>Probabilistic formulation of estimation problems for a class of Hamilton-Jacobi equations</atitle><btitle>2012 IEEE 51st IEEE Conference on Decision and Control (CDC)</btitle><stitle>CDC</stitle><date>2012-12</date><risdate>2012</risdate><spage>3531</spage><epage>3537</epage><pages>3531-3537</pages><issn>0191-2216</issn><isbn>9781467320658</isbn><isbn>146732065X</isbn><eisbn>1467320633</eisbn><eisbn>1467320668</eisbn><eisbn>9781467320634</eisbn><eisbn>9781467320665</eisbn><eisbn>9781467320641</eisbn><eisbn>1467320641</eisbn><abstract>This article presents a method for deriving the probability distribution of the solution to a Hamilton-Jacobi partial differential equation for which the value conditions are random. The derivations lead to analytical or semi-analytical expressions of the probability distribution function at any point in the domain in which the solution is defined. The characterization of the distribution of the solution at any point is a first step towards the estimation of the parameters defining the random value conditions. This work has important applications for estimation in flow networks in which value conditions are noisy. In particular, we illustrate our derivations on a road segment with random capacity reductions.</abstract><pub>IEEE</pub><doi>10.1109/CDC.2012.6426316</doi><tpages>7</tpages></addata></record> |
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| language | eng |
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| source | IEEE Electronic Library (IEL) Conference Proceedings |
| subjects | Boundary conditions Equations Estimation Noise measurement Probabilistic logic Probability distribution Random variables |
| title | Probabilistic formulation of estimation problems for a class of Hamilton-Jacobi equations |
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