Neurodynamic Programming and Zero-Sum Games for Constrained Control Systems
In this paper, neural networks are used along with two-player policy iterations to solve for the feedback strategies of a continuous-time zero-sum game that appears in L 2 -gain optimal control, suboptimal H infin control, of nonlinear systems affine in input with the control policy having saturatio...
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| Veröffentlicht in: | IEEE transaction on neural networks and learning systems 2008-07, Vol.19 (7), p.1243-1252 |
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| container_title | IEEE transaction on neural networks and learning systems |
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| creator | Abu-Khalaf, M. Lewis, F.L. Jie Huang |
| description | In this paper, neural networks are used along with two-player policy iterations to solve for the feedback strategies of a continuous-time zero-sum game that appears in L 2 -gain optimal control, suboptimal H infin control, of nonlinear systems affine in input with the control policy having saturation constraints. The result is a closed-form representation, on a prescribed compact set chosen a priori, of the feedback strategies and the value function that solves the associated Hamilton-Jacobi-Isaacs (HJI) equation. The closed-loop stability, L 2 -gain disturbance attenuation of the neural network saturated control feedback strategy, and uniform convergence results are proven. Finally, this approach is applied to the rotational/translational actuator (RTAC) nonlinear benchmark problem under actuator saturation, offering guaranteed stability and disturbance attenuation. |
| doi_str_mv | 10.1109/TNN.2008.2000204 |
| format | Article |
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Finally, this approach is applied to the rotational/translational actuator (RTAC) nonlinear benchmark problem under actuator saturation, offering guaranteed stability and disturbance attenuation.</description><identifier>ISSN: 1045-9227</identifier><identifier>ISSN: 2162-237X</identifier><identifier>EISSN: 1941-0093</identifier><identifier>EISSN: 2162-2388</identifier><identifier>DOI: 10.1109/TNN.2008.2000204</identifier><identifier>CODEN: ITNNEP</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Actuator saturation ; Actuators ; Applied sciences ; Artificial intelligence ; Attenuation ; Computer science; control theory; systems ; Connectionism. Neural networks ; Control systems ; Control theory ; Disturbances ; Exact sciences and technology ; Feedback ; H_{\infty} control ; Mathematical analysis ; Neural networks ; Neurodynamics ; Neurofeedback ; Nonlinear control systems ; Nonlinear systems ; Optimal control ; Policies ; policy iterations ; Stability ; Strategy ; zero-sum games</subject><ispartof>IEEE transaction on neural networks and learning systems, 2008-07, Vol.19 (7), p.1243-1252</ispartof><rights>2009 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2008</rights><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c352t-fc238d85233264d0ccf8dc42fce151f35234a81ffb09915ddc7041c6970cfe463</citedby><cites>FETCH-LOGICAL-c352t-fc238d85233264d0ccf8dc42fce151f35234a81ffb09915ddc7041c6970cfe463</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/4488043$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,27923,27924,54757</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/4488043$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20494161$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Abu-Khalaf, M.</creatorcontrib><creatorcontrib>Lewis, F.L.</creatorcontrib><creatorcontrib>Jie Huang</creatorcontrib><title>Neurodynamic Programming and Zero-Sum Games for Constrained Control Systems</title><title>IEEE transaction on neural networks and learning systems</title><addtitle>TNN</addtitle><description>In this paper, neural networks are used along with two-player policy iterations to solve for the feedback strategies of a continuous-time zero-sum game that appears in L 2 -gain optimal control, suboptimal H infin control, of nonlinear systems affine in input with the control policy having saturation constraints. The result is a closed-form representation, on a prescribed compact set chosen a priori, of the feedback strategies and the value function that solves the associated Hamilton-Jacobi-Isaacs (HJI) equation. The closed-loop stability, L 2 -gain disturbance attenuation of the neural network saturated control feedback strategy, and uniform convergence results are proven. Finally, this approach is applied to the rotational/translational actuator (RTAC) nonlinear benchmark problem under actuator saturation, offering guaranteed stability and disturbance attenuation.</description><subject>Actuator saturation</subject><subject>Actuators</subject><subject>Applied sciences</subject><subject>Artificial intelligence</subject><subject>Attenuation</subject><subject>Computer science; control theory; systems</subject><subject>Connectionism. Neural networks</subject><subject>Control systems</subject><subject>Control theory</subject><subject>Disturbances</subject><subject>Exact sciences and technology</subject><subject>Feedback</subject><subject>H_{\infty} control</subject><subject>Mathematical analysis</subject><subject>Neural networks</subject><subject>Neurodynamics</subject><subject>Neurofeedback</subject><subject>Nonlinear control systems</subject><subject>Nonlinear systems</subject><subject>Optimal control</subject><subject>Policies</subject><subject>policy iterations</subject><subject>Stability</subject><subject>Strategy</subject><subject>zero-sum games</subject><issn>1045-9227</issn><issn>2162-237X</issn><issn>1941-0093</issn><issn>2162-2388</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpdkE1LAzEQhhdRsFbvgpdFEE9bJx-7mxylaBVLFVovXkLMR9mym9Rk99B_b0qLBy8zA3nmJfNk2TWCCULAH1aLxQQDsH0BDPQkGyFOUQHAyWmagZYFx7g-zy5i3AAgWkI1yt4WZghe75zsGpV_BL8Osusat86l0_mXCb5YDl0-k52JufUhn3oX-yAbZ_R-7oNv8-Uu9qaLl9mZlW00V8c-zj6fn1bTl2L-PnudPs4LRUrcF1ZhwjQrMSG4ohqUskwriq0yqEQ2MYRKhqz9Bs5RqbWqgSJV8RqUNbQi4-z-kLsN_mcwsRddE5VpW-mMH6JgdTot3UsSefuP3PghuPQ5wRHGDCNaJwgOkAo-xmCs2Iamk2EnEIi9W5Hcir1bcXSbVu6OuTIq2dognWri315CkvoKJe7mwDXGmL9nShlLIeQXVWWA_g</recordid><startdate>20080701</startdate><enddate>20080701</enddate><creator>Abu-Khalaf, M.</creator><creator>Lewis, F.L.</creator><creator>Jie Huang</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7QF</scope><scope>7QO</scope><scope>7QP</scope><scope>7QQ</scope><scope>7QR</scope><scope>7SC</scope><scope>7SE</scope><scope>7SP</scope><scope>7SR</scope><scope>7TA</scope><scope>7TB</scope><scope>7TK</scope><scope>7U5</scope><scope>8BQ</scope><scope>8FD</scope><scope>F28</scope><scope>FR3</scope><scope>H8D</scope><scope>JG9</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>P64</scope></search><sort><creationdate>20080701</creationdate><title>Neurodynamic Programming and Zero-Sum Games for Constrained Control Systems</title><author>Abu-Khalaf, M. ; Lewis, F.L. ; Jie Huang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c352t-fc238d85233264d0ccf8dc42fce151f35234a81ffb09915ddc7041c6970cfe463</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Actuator saturation</topic><topic>Actuators</topic><topic>Applied sciences</topic><topic>Artificial intelligence</topic><topic>Attenuation</topic><topic>Computer science; control theory; systems</topic><topic>Connectionism. Neural networks</topic><topic>Control systems</topic><topic>Control theory</topic><topic>Disturbances</topic><topic>Exact sciences and technology</topic><topic>Feedback</topic><topic>H_{\infty} control</topic><topic>Mathematical analysis</topic><topic>Neural networks</topic><topic>Neurodynamics</topic><topic>Neurofeedback</topic><topic>Nonlinear control systems</topic><topic>Nonlinear systems</topic><topic>Optimal control</topic><topic>Policies</topic><topic>policy iterations</topic><topic>Stability</topic><topic>Strategy</topic><topic>zero-sum games</topic><toplevel>online_resources</toplevel><creatorcontrib>Abu-Khalaf, M.</creatorcontrib><creatorcontrib>Lewis, F.L.</creatorcontrib><creatorcontrib>Jie Huang</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>Aluminium Industry Abstracts</collection><collection>Biotechnology Research Abstracts</collection><collection>Calcium & Calcified Tissue Abstracts</collection><collection>Ceramic Abstracts</collection><collection>Chemoreception Abstracts</collection><collection>Computer and Information Systems Abstracts</collection><collection>Corrosion Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Engineered Materials Abstracts</collection><collection>Materials Business File</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Neurosciences Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Materials Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</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>Biotechnology and BioEngineering Abstracts</collection><jtitle>IEEE transaction on neural networks and learning systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Abu-Khalaf, M.</au><au>Lewis, F.L.</au><au>Jie Huang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Neurodynamic Programming and Zero-Sum Games for Constrained Control Systems</atitle><jtitle>IEEE transaction on neural networks and learning systems</jtitle><stitle>TNN</stitle><date>2008-07-01</date><risdate>2008</risdate><volume>19</volume><issue>7</issue><spage>1243</spage><epage>1252</epage><pages>1243-1252</pages><issn>1045-9227</issn><issn>2162-237X</issn><eissn>1941-0093</eissn><eissn>2162-2388</eissn><coden>ITNNEP</coden><abstract>In this paper, neural networks are used along with two-player policy iterations to solve for the feedback strategies of a continuous-time zero-sum game that appears in L 2 -gain optimal control, suboptimal H infin control, of nonlinear systems affine in input with the control policy having saturation constraints. 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| subjects | Actuator saturation Actuators Applied sciences Artificial intelligence Attenuation Computer science control theory systems Connectionism. Neural networks Control systems Control theory Disturbances Exact sciences and technology Feedback H_{\infty} control Mathematical analysis Neural networks Neurodynamics Neurofeedback Nonlinear control systems Nonlinear systems Optimal control Policies policy iterations Stability Strategy zero-sum games |
| title | Neurodynamic Programming and Zero-Sum Games for Constrained Control Systems |
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