Input-to-State Stability and Inverse Optimality of Linear Time-Varying-Delay Predictor Feedbacks
For linear systems with time-varying input delay and additive disturbances we show that the basic predictor feedback control law is inverse optimal, with respect to a meaningful differential game problem, and establish its robustness to constant multiplicative perturbations appearing at the system i...
Gespeichert in:
| Veröffentlicht in: | IEEE transactions on automatic control 2018-01, Vol.63 (1), p.233-240 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 240 |
|---|---|
| container_issue | 1 |
| container_start_page | 233 |
| container_title | IEEE transactions on automatic control |
| container_volume | 63 |
| creator | Xiushan Cai Bekiaris-Liberis, Nikolaos Krstic, Miroslav |
| description | For linear systems with time-varying input delay and additive disturbances we show that the basic predictor feedback control law is inverse optimal, with respect to a meaningful differential game problem, and establish its robustness to constant multiplicative perturbations appearing at the system input. Both of these properties of the basic predictor feedback controller have not been established so far, even for the constant-delay case. We then show that the basic predictor feedback controller, when applied through a low-pass filter, is again inverse optimal and study its input-to-state stability as well as its robustness, to the low-pass filter time constant properties. All of the stability and inverse optimality proofs are based on the infinite-dimensional backstepping transformation, which allows us to construct appropriate Lyapunov functionals. A numerical example is also provided. |
| doi_str_mv | 10.1109/TAC.2017.2722104 |
| format | Article |
| fullrecord | <record><control><sourceid>crossref_RIE</sourceid><recordid>TN_cdi_ieee_primary_7964747</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>7964747</ieee_id><sourcerecordid>10_1109_TAC_2017_2722104</sourcerecordid><originalsourceid>FETCH-LOGICAL-c263t-bde691d6f68d65f0a4defa24ed43856bf32d77e4ba8e5f30c38dc554d51601563</originalsourceid><addsrcrecordid>eNo9kE9LAzEQxYMoWKt3wUu-QGr-b_ZYqq2FQgWr1zW7mUi03S1JFPbbu7XFyzzm8d4w_BC6ZXTCGC3vN9PZhFNWTHjBOaPyDI2YUoZwxcU5GlHKDCm50ZfoKqXPYdVSshF6X7b770xyR16yzYCHWYdtyD22rcPL9gdiArze57Czf3bn8Sq0YCPehB2QNxv70H6QB9jaHj9HcKHJXcRzAFfb5itdowtvtwluTjpGr_PHzeyJrNaL5Wy6Ig3XIpPagS6Z014bp5WnVjrwlktwUhilay-4KwqQtTWgvKCNMK5RSjrFNGVKizGix7tN7FKK4Kt9HH6OfcVodSBUDYSqA6HqRGio3B0rAQD-40WpZSEL8QtU62MF</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Input-to-State Stability and Inverse Optimality of Linear Time-Varying-Delay Predictor Feedbacks</title><source>IEEE Electronic Library (IEL)</source><creator>Xiushan Cai ; Bekiaris-Liberis, Nikolaos ; Krstic, Miroslav</creator><creatorcontrib>Xiushan Cai ; Bekiaris-Liberis, Nikolaos ; Krstic, Miroslav</creatorcontrib><description>For linear systems with time-varying input delay and additive disturbances we show that the basic predictor feedback control law is inverse optimal, with respect to a meaningful differential game problem, and establish its robustness to constant multiplicative perturbations appearing at the system input. Both of these properties of the basic predictor feedback controller have not been established so far, even for the constant-delay case. We then show that the basic predictor feedback controller, when applied through a low-pass filter, is again inverse optimal and study its input-to-state stability as well as its robustness, to the low-pass filter time constant properties. All of the stability and inverse optimality proofs are based on the infinite-dimensional backstepping transformation, which allows us to construct appropriate Lyapunov functionals. A numerical example is also provided.</description><identifier>ISSN: 0018-9286</identifier><identifier>EISSN: 1558-2523</identifier><identifier>DOI: 10.1109/TAC.2017.2722104</identifier><identifier>CODEN: IETAA9</identifier><language>eng</language><publisher>IEEE</publisher><subject>Adaptive control ; Backstepping ; Delay systems ; Delays ; disturbance attenuation ; input-to-state stabilization ; inverse optimality ; linear predictor feedback ; Linear systems ; Numerical stability ; Robustness ; Stability criteria</subject><ispartof>IEEE transactions on automatic control, 2018-01, Vol.63 (1), p.233-240</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c263t-bde691d6f68d65f0a4defa24ed43856bf32d77e4ba8e5f30c38dc554d51601563</citedby><cites>FETCH-LOGICAL-c263t-bde691d6f68d65f0a4defa24ed43856bf32d77e4ba8e5f30c38dc554d51601563</cites><orcidid>0000-0001-9698-9148 ; 0000-0002-4223-2681 ; 0000-0002-5523-941X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/7964747$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,778,782,794,27907,27908,54741</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/7964747$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Xiushan Cai</creatorcontrib><creatorcontrib>Bekiaris-Liberis, Nikolaos</creatorcontrib><creatorcontrib>Krstic, Miroslav</creatorcontrib><title>Input-to-State Stability and Inverse Optimality of Linear Time-Varying-Delay Predictor Feedbacks</title><title>IEEE transactions on automatic control</title><addtitle>TAC</addtitle><description>For linear systems with time-varying input delay and additive disturbances we show that the basic predictor feedback control law is inverse optimal, with respect to a meaningful differential game problem, and establish its robustness to constant multiplicative perturbations appearing at the system input. Both of these properties of the basic predictor feedback controller have not been established so far, even for the constant-delay case. We then show that the basic predictor feedback controller, when applied through a low-pass filter, is again inverse optimal and study its input-to-state stability as well as its robustness, to the low-pass filter time constant properties. All of the stability and inverse optimality proofs are based on the infinite-dimensional backstepping transformation, which allows us to construct appropriate Lyapunov functionals. A numerical example is also provided.</description><subject>Adaptive control</subject><subject>Backstepping</subject><subject>Delay systems</subject><subject>Delays</subject><subject>disturbance attenuation</subject><subject>input-to-state stabilization</subject><subject>inverse optimality</subject><subject>linear predictor feedback</subject><subject>Linear systems</subject><subject>Numerical stability</subject><subject>Robustness</subject><subject>Stability criteria</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kE9LAzEQxYMoWKt3wUu-QGr-b_ZYqq2FQgWr1zW7mUi03S1JFPbbu7XFyzzm8d4w_BC6ZXTCGC3vN9PZhFNWTHjBOaPyDI2YUoZwxcU5GlHKDCm50ZfoKqXPYdVSshF6X7b770xyR16yzYCHWYdtyD22rcPL9gdiArze57Czf3bn8Sq0YCPehB2QNxv70H6QB9jaHj9HcKHJXcRzAFfb5itdowtvtwluTjpGr_PHzeyJrNaL5Wy6Ig3XIpPagS6Z014bp5WnVjrwlktwUhilay-4KwqQtTWgvKCNMK5RSjrFNGVKizGix7tN7FKK4Kt9HH6OfcVodSBUDYSqA6HqRGio3B0rAQD-40WpZSEL8QtU62MF</recordid><startdate>201801</startdate><enddate>201801</enddate><creator>Xiushan Cai</creator><creator>Bekiaris-Liberis, Nikolaos</creator><creator>Krstic, Miroslav</creator><general>IEEE</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-9698-9148</orcidid><orcidid>https://orcid.org/0000-0002-4223-2681</orcidid><orcidid>https://orcid.org/0000-0002-5523-941X</orcidid></search><sort><creationdate>201801</creationdate><title>Input-to-State Stability and Inverse Optimality of Linear Time-Varying-Delay Predictor Feedbacks</title><author>Xiushan Cai ; Bekiaris-Liberis, Nikolaos ; Krstic, Miroslav</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c263t-bde691d6f68d65f0a4defa24ed43856bf32d77e4ba8e5f30c38dc554d51601563</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Adaptive control</topic><topic>Backstepping</topic><topic>Delay systems</topic><topic>Delays</topic><topic>disturbance attenuation</topic><topic>input-to-state stabilization</topic><topic>inverse optimality</topic><topic>linear predictor feedback</topic><topic>Linear systems</topic><topic>Numerical stability</topic><topic>Robustness</topic><topic>Stability criteria</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Xiushan Cai</creatorcontrib><creatorcontrib>Bekiaris-Liberis, Nikolaos</creatorcontrib><creatorcontrib>Krstic, Miroslav</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><jtitle>IEEE transactions on automatic control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Xiushan Cai</au><au>Bekiaris-Liberis, Nikolaos</au><au>Krstic, Miroslav</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Input-to-State Stability and Inverse Optimality of Linear Time-Varying-Delay Predictor Feedbacks</atitle><jtitle>IEEE transactions on automatic control</jtitle><stitle>TAC</stitle><date>2018-01</date><risdate>2018</risdate><volume>63</volume><issue>1</issue><spage>233</spage><epage>240</epage><pages>233-240</pages><issn>0018-9286</issn><eissn>1558-2523</eissn><coden>IETAA9</coden><abstract>For linear systems with time-varying input delay and additive disturbances we show that the basic predictor feedback control law is inverse optimal, with respect to a meaningful differential game problem, and establish its robustness to constant multiplicative perturbations appearing at the system input. Both of these properties of the basic predictor feedback controller have not been established so far, even for the constant-delay case. We then show that the basic predictor feedback controller, when applied through a low-pass filter, is again inverse optimal and study its input-to-state stability as well as its robustness, to the low-pass filter time constant properties. All of the stability and inverse optimality proofs are based on the infinite-dimensional backstepping transformation, which allows us to construct appropriate Lyapunov functionals. A numerical example is also provided.</abstract><pub>IEEE</pub><doi>10.1109/TAC.2017.2722104</doi><tpages>8</tpages><orcidid>https://orcid.org/0000-0001-9698-9148</orcidid><orcidid>https://orcid.org/0000-0002-4223-2681</orcidid><orcidid>https://orcid.org/0000-0002-5523-941X</orcidid></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | ISSN: 0018-9286 |
| ispartof | IEEE transactions on automatic control, 2018-01, Vol.63 (1), p.233-240 |
| issn | 0018-9286 1558-2523 |
| language | eng |
| recordid | cdi_ieee_primary_7964747 |
| source | IEEE Electronic Library (IEL) |
| subjects | Adaptive control Backstepping Delay systems Delays disturbance attenuation input-to-state stabilization inverse optimality linear predictor feedback Linear systems Numerical stability Robustness Stability criteria |
| title | Input-to-State Stability and Inverse Optimality of Linear Time-Varying-Delay Predictor Feedbacks |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-17T04%3A43%3A19IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-crossref_RIE&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Input-to-State%20Stability%20and%20Inverse%20Optimality%20of%20Linear%20Time-Varying-Delay%20Predictor%20Feedbacks&rft.jtitle=IEEE%20transactions%20on%20automatic%20control&rft.au=Xiushan%20Cai&rft.date=2018-01&rft.volume=63&rft.issue=1&rft.spage=233&rft.epage=240&rft.pages=233-240&rft.issn=0018-9286&rft.eissn=1558-2523&rft.coden=IETAA9&rft_id=info:doi/10.1109/TAC.2017.2722104&rft_dat=%3Ccrossref_RIE%3E10_1109_TAC_2017_2722104%3C/crossref_RIE%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_ieee_id=7964747&rfr_iscdi=true |