Design of a class of nonlinear controllers via state dependent Riccati equations
In this brief, infinite-horizon nonlinear regulation of second-order systems using the State Dependent Riccati Equation (SDRE) method is considered. By a convenient parametrization of the A(x) matrix, the state-dependent algebraic Riccati equation is solved analytically. As a result, the closed-loop...
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| Veröffentlicht in: | IEEE transactions on control systems technology 2004-01, Vol.12 (1), p.133-137 |
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| container_title | IEEE transactions on control systems technology |
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| creator | Erdem, E.B. Alleyne, A.G. |
| description | In this brief, infinite-horizon nonlinear regulation of second-order systems using the State Dependent Riccati Equation (SDRE) method is considered. By a convenient parametrization of the A(x) matrix, the state-dependent algebraic Riccati equation is solved analytically. As a result, the closed-loop system equations are obtained in analytical form. Global stability analysis is performed by a combination of Lyapunov analysis and LaSalle's Principle. Accordingly, a relatively straightforward condition for global asymptotic stability of the closed-loop system is derived. This is one of the first global results available for this class of systems controlled by SDRE methods. The stability results are demonstrated on an experimental magnetic levitation setup and are found to provide a great deal of flexibility in the control system design. |
| doi_str_mv | 10.1109/TCST.2003.819588 |
| format | Article |
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By a convenient parametrization of the A(x) matrix, the state-dependent algebraic Riccati equation is solved analytically. As a result, the closed-loop system equations are obtained in analytical form. Global stability analysis is performed by a combination of Lyapunov analysis and LaSalle's Principle. Accordingly, a relatively straightforward condition for global asymptotic stability of the closed-loop system is derived. This is one of the first global results available for this class of systems controlled by SDRE methods. 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By a convenient parametrization of the A(x) matrix, the state-dependent algebraic Riccati equation is solved analytically. As a result, the closed-loop system equations are obtained in analytical form. Global stability analysis is performed by a combination of Lyapunov analysis and LaSalle's Principle. Accordingly, a relatively straightforward condition for global asymptotic stability of the closed-loop system is derived. This is one of the first global results available for this class of systems controlled by SDRE methods. The stability results are demonstrated on an experimental magnetic levitation setup and are found to provide a great deal of flexibility in the control system design.</description><subject>Applied sciences</subject><subject>Asymptotic properties</subject><subject>Computer science; control theory; systems</subject><subject>Control</subject><subject>Control systems</subject><subject>Control systems design</subject><subject>Control theory. Systems</subject><subject>Error correction</subject><subject>Exact sciences and technology</subject><subject>Flexibility</subject><subject>Magnetic analysis</subject><subject>Mathematical analysis</subject><subject>Nonlinear control systems</subject><subject>Nonlinear equations</subject><subject>Nonlinear systems</subject><subject>Nonlinearity</subject><subject>Performance analysis</subject><subject>Riccati equation</subject><subject>Riccati equations</subject><subject>Sliding mode control</subject><subject>Stability</subject><subject>Stability analysis</subject><issn>1063-6536</issn><issn>1558-0865</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2004</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNqN0U1rHDEMBuChNNA06b3Qiyk0Oc1Gtse2fCybTwi0pNuz8Xo0xWFib-zZQP99Z9lAoIeQkwR6JBBv03zmsOAc7Nlq-Wu1EABygdwqxHfNIVcKW0Ct3s89aNlqJfWH5mOt9wC8U8IcNj_PqcY_ieWBeRZGX-uuTTmNMZEvLOQ0lTyOVCp7ip7VyU_EetpQ6ilN7C6G4KfI6HE7l5zqcXMw-LHSp-d61Py-vFgtr9vbH1c3y--3begMTq2xViLZfk2d7zofFFehR0PQBxLDYNbEufCdxjUQt1oF0aEWxhtphwG1lEfN6f7upuTHLdXJPcQaaBx9orytzgLXGjo0szx5VQpENMjlG6BQGrid4df_4H3eljS_6xClktYCzgj2KJRca6HBbUp88OWv4-B2kbldZG4XmdtHNq98e77ra_DjUHwKsb7sKSWkEnx2X_YuEtHLWGgEhfIfj5-ePw</recordid><startdate>200401</startdate><enddate>200401</enddate><creator>Erdem, E.B.</creator><creator>Alleyne, A.G.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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Systems</topic><topic>Error correction</topic><topic>Exact sciences and technology</topic><topic>Flexibility</topic><topic>Magnetic analysis</topic><topic>Mathematical analysis</topic><topic>Nonlinear control systems</topic><topic>Nonlinear equations</topic><topic>Nonlinear systems</topic><topic>Nonlinearity</topic><topic>Performance analysis</topic><topic>Riccati equation</topic><topic>Riccati equations</topic><topic>Sliding mode control</topic><topic>Stability</topic><topic>Stability analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Erdem, E.B.</creatorcontrib><creatorcontrib>Alleyne, A.G.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Aerospace Database</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><jtitle>IEEE transactions on control systems technology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Erdem, E.B.</au><au>Alleyne, A.G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Design of a class of nonlinear controllers via state dependent Riccati equations</atitle><jtitle>IEEE transactions on control systems technology</jtitle><stitle>TCST</stitle><date>2004-01</date><risdate>2004</risdate><volume>12</volume><issue>1</issue><spage>133</spage><epage>137</epage><pages>133-137</pages><issn>1063-6536</issn><eissn>1558-0865</eissn><coden>IETTE2</coden><abstract>In this brief, infinite-horizon nonlinear regulation of second-order systems using the State Dependent Riccati Equation (SDRE) method is considered. 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| ispartof | IEEE transactions on control systems technology, 2004-01, Vol.12 (1), p.133-137 |
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| source | IEEE Electronic Library (IEL) |
| subjects | Applied sciences Asymptotic properties Computer science control theory systems Control Control systems Control systems design Control theory. Systems Error correction Exact sciences and technology Flexibility Magnetic analysis Mathematical analysis Nonlinear control systems Nonlinear equations Nonlinear systems Nonlinearity Performance analysis Riccati equation Riccati equations Sliding mode control Stability Stability analysis |
| title | Design of a class of nonlinear controllers via state dependent Riccati equations |
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