Adaptive modification of the delayed feedback control algorithm with a continuously varying time delay
We propose a simple adaptive delayed feedback control algorithm for stabilization of unstable periodic orbits with unknown periods. The state dependent time delay is varied continuously towards the period of controlled orbit according to a gradient-descent method realized through three simple ordina...
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| Veröffentlicht in: | Physics letters. A 2011-10, Vol.375 (44), p.3866-3871 |
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| container_title | Physics letters. A |
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| creator | Pyragas, V. Pyragas, K. |
| description | We propose a simple adaptive delayed feedback control algorithm for stabilization of unstable periodic orbits with unknown periods. The state dependent time delay is varied continuously towards the period of controlled orbit according to a gradient-descent method realized through three simple ordinary differential equations. We demonstrate the efficiency of the algorithm with the Rössler and Mackey–Glass chaotic systems. The stability of the controlled orbits is proven by computation of the Lyapunov exponents of linearized equations.
► A simple adaptive modification of the delayed feedback control algorithm is proposed. ► It enables the control of unstable periodic orbits with unknown periods. ► The delay time is varied continuously according to a gradient descend method. ► The algorithm is embodied by three simple ordinary differential equations. ► The validity of the algorithm is proven by computation of the Lyapunov exponents. |
| doi_str_mv | 10.1016/j.physleta.2011.08.072 |
| format | Article |
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► A simple adaptive modification of the delayed feedback control algorithm is proposed. ► It enables the control of unstable periodic orbits with unknown periods. ► The delay time is varied continuously according to a gradient descend method. ► The algorithm is embodied by three simple ordinary differential equations. ► The validity of the algorithm is proven by computation of the Lyapunov exponents.</description><identifier>ISSN: 0375-9601</identifier><identifier>EISSN: 1873-2429</identifier><identifier>DOI: 10.1016/j.physleta.2011.08.072</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Adaptive algorithms ; Adaptive control ; Adaptive control systems ; Algorithms ; Chaotic systems ; Delayed feedback control ; Differential equations ; Feedback control ; Lyapunov exponents ; Mathematical analysis ; Orbits ; Time delay ; Unstable periodic orbits</subject><ispartof>Physics letters. A, 2011-10, Vol.375 (44), p.3866-3871</ispartof><rights>2011 Elsevier B.V.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c344t-a1291b3b33ab2efbe9205b22a98bfd66a809d3a8c4ca50679a4dd74bf787197b3</citedby><cites>FETCH-LOGICAL-c344t-a1291b3b33ab2efbe9205b22a98bfd66a809d3a8c4ca50679a4dd74bf787197b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.physleta.2011.08.072$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>315,781,785,3551,27928,27929,45999</link.rule.ids></links><search><creatorcontrib>Pyragas, V.</creatorcontrib><creatorcontrib>Pyragas, K.</creatorcontrib><title>Adaptive modification of the delayed feedback control algorithm with a continuously varying time delay</title><title>Physics letters. A</title><description>We propose a simple adaptive delayed feedback control algorithm for stabilization of unstable periodic orbits with unknown periods. The state dependent time delay is varied continuously towards the period of controlled orbit according to a gradient-descent method realized through three simple ordinary differential equations. We demonstrate the efficiency of the algorithm with the Rössler and Mackey–Glass chaotic systems. The stability of the controlled orbits is proven by computation of the Lyapunov exponents of linearized equations.
► A simple adaptive modification of the delayed feedback control algorithm is proposed. ► It enables the control of unstable periodic orbits with unknown periods. ► The delay time is varied continuously according to a gradient descend method. ► The algorithm is embodied by three simple ordinary differential equations. ► The validity of the algorithm is proven by computation of the Lyapunov exponents.</description><subject>Adaptive algorithms</subject><subject>Adaptive control</subject><subject>Adaptive control systems</subject><subject>Algorithms</subject><subject>Chaotic systems</subject><subject>Delayed feedback control</subject><subject>Differential equations</subject><subject>Feedback control</subject><subject>Lyapunov exponents</subject><subject>Mathematical analysis</subject><subject>Orbits</subject><subject>Time delay</subject><subject>Unstable periodic orbits</subject><issn>0375-9601</issn><issn>1873-2429</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNqFkEtPHDEQhC0UJDbAX0C-5TSDH7Mz9i0I5YGElEs4W227zXqZGW9s70b77xlYcs6l-9BVpeqPkBvOWs54f7ttd5tjGbFCKxjnLVMtG8QZWXE1yEZ0Qn8iKyaHdaN7xi_I51K2jC1Oplck3HnY1XhAOiUfQ3RQY5ppCrRukHoc4YieBkRvwb1Ql-aa00hhfE451s1E_y6Twvshzvu0L-ORHiAf4_xMa5w-Mq7IeYCx4PXHviRP37_9vv_ZPP768XB_99g42XW1AS40t9JKCVZgsKgFW1shQCsbfN-DYtpLUK5zsGb9oKHzfuhsGNTA9WDlJflyyt3l9GePpZopFofjCDMu3YwWvZRrpdSi7E9Kl1MpGYPZ5TgtxQ1n5o2r2Zp_XM0bV8OUWbguxq8nIy5_HCJmU1zE2aGPGV01PsX_RbwC0ZiHgg</recordid><startdate>20111024</startdate><enddate>20111024</enddate><creator>Pyragas, V.</creator><creator>Pyragas, K.</creator><general>Elsevier B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7QQ</scope><scope>7U5</scope><scope>8FD</scope><scope>JG9</scope><scope>L7M</scope></search><sort><creationdate>20111024</creationdate><title>Adaptive modification of the delayed feedback control algorithm with a continuously varying time delay</title><author>Pyragas, V. ; Pyragas, K.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c344t-a1291b3b33ab2efbe9205b22a98bfd66a809d3a8c4ca50679a4dd74bf787197b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Adaptive algorithms</topic><topic>Adaptive control</topic><topic>Adaptive control systems</topic><topic>Algorithms</topic><topic>Chaotic systems</topic><topic>Delayed feedback control</topic><topic>Differential equations</topic><topic>Feedback control</topic><topic>Lyapunov exponents</topic><topic>Mathematical analysis</topic><topic>Orbits</topic><topic>Time delay</topic><topic>Unstable periodic orbits</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Pyragas, V.</creatorcontrib><creatorcontrib>Pyragas, K.</creatorcontrib><collection>CrossRef</collection><collection>Ceramic Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Materials Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Physics letters. A</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Pyragas, V.</au><au>Pyragas, K.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Adaptive modification of the delayed feedback control algorithm with a continuously varying time delay</atitle><jtitle>Physics letters. A</jtitle><date>2011-10-24</date><risdate>2011</risdate><volume>375</volume><issue>44</issue><spage>3866</spage><epage>3871</epage><pages>3866-3871</pages><issn>0375-9601</issn><eissn>1873-2429</eissn><abstract>We propose a simple adaptive delayed feedback control algorithm for stabilization of unstable periodic orbits with unknown periods. The state dependent time delay is varied continuously towards the period of controlled orbit according to a gradient-descent method realized through three simple ordinary differential equations. We demonstrate the efficiency of the algorithm with the Rössler and Mackey–Glass chaotic systems. The stability of the controlled orbits is proven by computation of the Lyapunov exponents of linearized equations.
► A simple adaptive modification of the delayed feedback control algorithm is proposed. ► It enables the control of unstable periodic orbits with unknown periods. ► The delay time is varied continuously according to a gradient descend method. ► The algorithm is embodied by three simple ordinary differential equations. ► The validity of the algorithm is proven by computation of the Lyapunov exponents.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.physleta.2011.08.072</doi><tpages>6</tpages></addata></record> |
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| subjects | Adaptive algorithms Adaptive control Adaptive control systems Algorithms Chaotic systems Delayed feedback control Differential equations Feedback control Lyapunov exponents Mathematical analysis Orbits Time delay Unstable periodic orbits |
| title | Adaptive modification of the delayed feedback control algorithm with a continuously varying time delay |
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