A bounded-error approach to piecewise affine system identification
This paper proposes a three-stage procedure for parametric identification of piecewise affine autoregressive exogenous (PWARX) models. The first stage simultaneously classifies the data points and estimates the number of submodels and the corresponding parameters by solving the partition into a mini...
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| Veröffentlicht in: | IEEE transactions on automatic control 2005-10, Vol.50 (10), p.1567-1580 |
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| creator | Bemporad, A. Garulli, A. Paoletti, S. Vicino, A. |
| description | This paper proposes a three-stage procedure for parametric identification of piecewise affine autoregressive exogenous (PWARX) models. The first stage simultaneously classifies the data points and estimates the number of submodels and the corresponding parameters by solving the partition into a minimum number of feasible subsystems (MIN PFS) problem for a suitable set of linear complementary inequalities derived from data. Second, a refinement procedure reduces misclassifications and improves parameter estimates. The third stage determines a polyhedral partition of the regressor set via two-class or multiclass linear separation techniques. As a main feature, the algorithm imposes that the identification error is bounded by a quantity /spl delta/. Such a bound is a useful tuning parameter to trade off between quality of fit and model complexity. The performance of the proposed PWA system identification procedure is demonstrated via numerical examples and on experimental data from an electronic component placement process in a pick-and-place machine. |
| doi_str_mv | 10.1109/TAC.2005.856667 |
| format | Article |
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The first stage simultaneously classifies the data points and estimates the number of submodels and the corresponding parameters by solving the partition into a minimum number of feasible subsystems (MIN PFS) problem for a suitable set of linear complementary inequalities derived from data. Second, a refinement procedure reduces misclassifications and improves parameter estimates. The third stage determines a polyhedral partition of the regressor set via two-class or multiclass linear separation techniques. As a main feature, the algorithm imposes that the identification error is bounded by a quantity /spl delta/. Such a bound is a useful tuning parameter to trade off between quality of fit and model complexity. The performance of the proposed PWA system identification procedure is demonstrated via numerical examples and on experimental data from an electronic component placement process in a pick-and-place machine.</description><subject>Bounded error</subject><subject>Contracts</subject><subject>Electronic components</subject><subject>MIN PFS problem</subject><subject>Neural networks</subject><subject>Nonlinear dynamical systems</subject><subject>nonlinear identification</subject><subject>Parameter estimation</subject><subject>Partitioning algorithms</subject><subject>piecewise affine autoregressive exogenous models</subject><subject>Region 3</subject><subject>State estimation</subject><subject>Studies</subject><subject>System identification</subject><subject>Time series analysis</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2005</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNqFkE1LAzEQhoMoWKtnD14WD962zfcmx1r8goKXeg7Z7ART2t012UX896asIHjxNAzzvMPMg9A1wQtCsF5uV-sFxVgslJBSVidoRoRQJRWUnaIZxkSVmip5ji5S2uVWck5m6H5V1N3YNtCUEGMXC9v3sbPuvRi6og_g4DMkKKz3oYUifaUBDkVooB2CD84OoWsv0Zm3-wRXP3WO3h4ftuvncvP69LJebUrHRTWUmjnNsKxrhq2QNbWa1w0G0ijOGu8aLqmjlkPlvLMeO-bzwHquhK64bCybo7tpbz7wY4Q0mENIDvZ720I3JkOVYkwq-T9Yaa0oZhm8_QPuujG2-Qlz3KVoFpah5QS52KUUwZs-hoONX4ZgczRvsnlzNG8m8zlxMyUCAPzSgkgqFPsGtzR-2w</recordid><startdate>200510</startdate><enddate>200510</enddate><creator>Bemporad, A.</creator><creator>Garulli, A.</creator><creator>Paoletti, S.</creator><creator>Vicino, A.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</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>H8D</scope></search><sort><creationdate>200510</creationdate><title>A bounded-error approach to piecewise affine system identification</title><author>Bemporad, A. ; Garulli, A. ; Paoletti, S. ; Vicino, A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c457t-93c9306bb30a56b2a94bd0e1d843dfcd462c2a4e7cfcaf0c3f843af4859746da3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2005</creationdate><topic>Bounded error</topic><topic>Contracts</topic><topic>Electronic components</topic><topic>MIN PFS problem</topic><topic>Neural networks</topic><topic>Nonlinear dynamical systems</topic><topic>nonlinear identification</topic><topic>Parameter estimation</topic><topic>Partitioning algorithms</topic><topic>piecewise affine autoregressive exogenous models</topic><topic>Region 3</topic><topic>State estimation</topic><topic>Studies</topic><topic>System identification</topic><topic>Time series analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bemporad, A.</creatorcontrib><creatorcontrib>Garulli, A.</creatorcontrib><creatorcontrib>Paoletti, S.</creatorcontrib><creatorcontrib>Vicino, A.</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>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>Aerospace Database</collection><jtitle>IEEE transactions on automatic control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Bemporad, A.</au><au>Garulli, A.</au><au>Paoletti, S.</au><au>Vicino, A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A bounded-error approach to piecewise affine system identification</atitle><jtitle>IEEE transactions on automatic control</jtitle><stitle>TAC</stitle><date>2005-10</date><risdate>2005</risdate><volume>50</volume><issue>10</issue><spage>1567</spage><epage>1580</epage><pages>1567-1580</pages><issn>0018-9286</issn><eissn>1558-2523</eissn><coden>IETAA9</coden><abstract>This paper proposes a three-stage procedure for parametric identification of piecewise affine autoregressive exogenous (PWARX) models. The first stage simultaneously classifies the data points and estimates the number of submodels and the corresponding parameters by solving the partition into a minimum number of feasible subsystems (MIN PFS) problem for a suitable set of linear complementary inequalities derived from data. Second, a refinement procedure reduces misclassifications and improves parameter estimates. The third stage determines a polyhedral partition of the regressor set via two-class or multiclass linear separation techniques. As a main feature, the algorithm imposes that the identification error is bounded by a quantity /spl delta/. Such a bound is a useful tuning parameter to trade off between quality of fit and model complexity. 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| subjects | Bounded error Contracts Electronic components MIN PFS problem Neural networks Nonlinear dynamical systems nonlinear identification Parameter estimation Partitioning algorithms piecewise affine autoregressive exogenous models Region 3 State estimation Studies System identification Time series analysis |
| title | A bounded-error approach to piecewise affine system identification |
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