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Event-Based Boundary Control of a Linear 2\times 2 Hyperbolic System via Backstepping Approach
In this paper, we introduce an event-based boundary control for a 2\times 2 coupled linear hyperbolic system. We use a well-established backstepping controller which stabilizes the system along with a dynamic triggering condition which determines when the controller must be updated. The main contri...
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| Published in: | IEEE transactions on automatic control 2018-08, Vol.63 (8), p.2686-2693 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c1084-771ba738ffc21aa88073d02ea207c47944395a9a3c40a5dfbab0c87771bf1fb3 |
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| cites | cdi_FETCH-LOGICAL-c1084-771ba738ffc21aa88073d02ea207c47944395a9a3c40a5dfbab0c87771bf1fb3 |
| container_end_page | 2693 |
| container_issue | 8 |
| container_start_page | 2686 |
| container_title | IEEE transactions on automatic control |
| container_volume | 63 |
| creator | Espitia, Nicolas Girard, Antoine Marchand, Nicolas Prieur, Christophe |
| description | In this paper, we introduce an event-based boundary control for a 2\times 2 coupled linear hyperbolic system. We use a well-established backstepping controller which stabilizes the system along with a dynamic triggering condition which determines when the controller must be updated. The main contributions rely on the definition of an event-based controller under which global exponential stability of the system is achieved and, furthermore, the existence of a minimal dwell-time between two triggering times is guaranteed. The well-posedness of the system under the event-based controller is stated. A simulation example is presented to illustrate the results. |
| doi_str_mv | 10.1109/TAC.2017.2774011 |
| format | article |
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A simulation example is presented to illustrate the results.</description><subject>Backstepping</subject><subject>Backstepping control design</subject><subject>Boundary conditions</subject><subject>dynamic triggering condition</subject><subject>Electronic mail</subject><subject>event-based control</subject><subject>Kernel</subject><subject>linear hyperbolic systems</subject><subject>Lyapunov methods</subject><subject>Stability analysis</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNo9kF1LwzAUhoMoOKf3gjf5A50nH13Sy61MJxS8cJdiOU0TjW5NSepg_96ODa8OL7zPC-ch5J7BjDEoHjeLcsaBqRlXSgJjF2TC8lxnPOfikkwAmM4KrufX5Cal7zHOpWQT8rHa227IlphsS5fht2sxHmgZuiGGLQ2OIq18ZzFS_j74nU2U0_Wht7EJW2_o2yENdkf3HukSzc8Y-t53n3TR9zGg-bolVw63yd6d75Rsnlabcp1Vr88v5aLKDAMtM6VYg0po5wxniFqDEi1wixyUkaqQUhQ5FiiMBMxb12ADRqsj5phrxJTAadbEkFK0ru6j342f1Azqo5561FMf9dRnPSPycEK8tfa_rsey4lL8Af49YNA</recordid><startdate>201808</startdate><enddate>201808</enddate><creator>Espitia, Nicolas</creator><creator>Girard, Antoine</creator><creator>Marchand, Nicolas</creator><creator>Prieur, Christophe</creator><general>IEEE</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-4456-2019</orcidid><orcidid>https://orcid.org/0000-0002-4075-9041</orcidid><orcidid>https://orcid.org/0000-0001-8241-0633</orcidid></search><sort><creationdate>201808</creationdate><title>Event-Based Boundary Control of a Linear 2\times 2 Hyperbolic System via Backstepping Approach</title><author>Espitia, Nicolas ; Girard, Antoine ; Marchand, Nicolas ; Prieur, Christophe</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c1084-771ba738ffc21aa88073d02ea207c47944395a9a3c40a5dfbab0c87771bf1fb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Backstepping</topic><topic>Backstepping control design</topic><topic>Boundary conditions</topic><topic>dynamic triggering condition</topic><topic>Electronic mail</topic><topic>event-based control</topic><topic>Kernel</topic><topic>linear hyperbolic systems</topic><topic>Lyapunov methods</topic><topic>Stability analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Espitia, Nicolas</creatorcontrib><creatorcontrib>Girard, Antoine</creatorcontrib><creatorcontrib>Marchand, Nicolas</creatorcontrib><creatorcontrib>Prieur, Christophe</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005–Present</collection><collection>IEEE All-Society Periodicals Package (ASPP) Online</collection><collection>IEEE Xplore</collection><collection>CrossRef</collection><jtitle>IEEE transactions on automatic control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Espitia, Nicolas</au><au>Girard, Antoine</au><au>Marchand, Nicolas</au><au>Prieur, Christophe</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Event-Based Boundary Control of a Linear 2\times 2 Hyperbolic System via Backstepping Approach</atitle><jtitle>IEEE transactions on automatic control</jtitle><stitle>TAC</stitle><date>2018-08</date><risdate>2018</risdate><volume>63</volume><issue>8</issue><spage>2686</spage><epage>2693</epage><pages>2686-2693</pages><issn>0018-9286</issn><eissn>1558-2523</eissn><coden>IETAA9</coden><abstract>In this paper, we introduce an event-based boundary control for a <inline-formula><tex-math notation="LaTeX"> 2\times 2</tex-math></inline-formula> coupled linear hyperbolic system. 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| ispartof | IEEE transactions on automatic control, 2018-08, Vol.63 (8), p.2686-2693 |
| issn | 0018-9286 1558-2523 |
| language | eng |
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| source | IEEE Xplore (Online service) |
| subjects | Backstepping Backstepping control design Boundary conditions dynamic triggering condition Electronic mail event-based control Kernel linear hyperbolic systems Lyapunov methods Stability analysis |
| title | Event-Based Boundary Control of a Linear 2\times 2 Hyperbolic System via Backstepping Approach |
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