Max-Plus (A,B)-Invariant Spaces and Control of Timed Discrete-Event Systems
The concept of (A,B)-invariant subspace (or controlled invariant) of a linear dynamical system is extended to linear systems over the max-plus semiring. Although this extension presents several difficulties, which are similar to those encountered in the same kind of extension to linear dynamical sys...
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| Veröffentlicht in: | IEEE transactions on automatic control 2007-02, Vol.52 (2), p.229-241 |
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| container_title | IEEE transactions on automatic control |
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| creator | Katz, R.D. |
| description | The concept of (A,B)-invariant subspace (or controlled invariant) of a linear dynamical system is extended to linear systems over the max-plus semiring. Although this extension presents several difficulties, which are similar to those encountered in the same kind of extension to linear dynamical systems over rings, it appears capable of providing solutions to many control problems like in the cases of linear systems over fields or rings. Sufficient conditions are given for computing the maximal (A,B)-invariant subspace contained in a given space and the existence of linear state feedbacks is discussed. An application to the study of transportation networks which evolve according to a timetable is considered |
| doi_str_mv | 10.1109/TAC.2006.890478 |
| format | Article |
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Although this extension presents several difficulties, which are similar to those encountered in the same kind of extension to linear dynamical systems over rings, it appears capable of providing solutions to many control problems like in the cases of linear systems over fields or rings. Sufficient conditions are given for computing the maximal (A,B)-invariant subspace contained in a given space and the existence of linear state feedbacks is discussed. An application to the study of transportation networks which evolve according to a timetable is considered</description><subject>Algebra</subject><subject>Applied sciences</subject><subject>Automatic control</subject><subject>Computer science; control theory; systems</subject><subject>Control system synthesis</subject><subject>Control systems</subject><subject>Control theory. 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Systems</topic><topic>Discrete event systems</topic><topic>Discrete-event systems (DESs)</topic><topic>Dynamical systems</topic><topic>Exact sciences and technology</topic><topic>geometric control</topic><topic>invariant spaces</topic><topic>Invariants</topic><topic>Linear systems</topic><topic>Mathematical model</topic><topic>max-plus algebra</topic><topic>Solid modeling</topic><topic>State feedback</topic><topic>Subspaces</topic><topic>Sufficient conditions</topic><topic>Timetables</topic><topic>Transportation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Katz, R.D.</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>Katz, R.D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Max-Plus (A,B)-Invariant Spaces and Control of Timed Discrete-Event Systems</atitle><jtitle>IEEE transactions on automatic control</jtitle><stitle>TAC</stitle><date>2007-02-01</date><risdate>2007</risdate><volume>52</volume><issue>2</issue><spage>229</spage><epage>241</epage><pages>229-241</pages><issn>0018-9286</issn><eissn>1558-2523</eissn><coden>IETAA9</coden><abstract>The concept of (A,B)-invariant subspace (or controlled invariant) of a linear dynamical system is extended to linear systems over the max-plus semiring. 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| ispartof | IEEE transactions on automatic control, 2007-02, Vol.52 (2), p.229-241 |
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| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | Algebra Applied sciences Automatic control Computer science control theory systems Control system synthesis Control systems Control theory. Systems Discrete event systems Discrete-event systems (DESs) Dynamical systems Exact sciences and technology geometric control invariant spaces Invariants Linear systems Mathematical model max-plus algebra Solid modeling State feedback Subspaces Sufficient conditions Timetables Transportation |
| title | Max-Plus (A,B)-Invariant Spaces and Control of Timed Discrete-Event Systems |
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