Novel closed-loop controllers for fractional nonlinear quadratic systems
A novel closed-loop optimal controller for fractional nonlinear quadratic optimal control problems is introduced. By using a new idea, the optimality conditions for the fractional nonlinear problems are derived. The linearized Riccati fractional order differential equation is derived and a new solut...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-12-01
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| Series: | Mathematical Modelling and Control |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mmc.2023028?viewType=HTML |
| _version_ | 1827392007229669376 |
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| author | Iman Malmir |
| author_facet | Iman Malmir |
| author_sort | Iman Malmir |
| collection | DOAJ |
| description | A novel closed-loop optimal controller for fractional nonlinear quadratic optimal control problems is introduced. By using a new idea, the optimality conditions for the fractional nonlinear problems are derived. The linearized Riccati fractional order differential equation is derived and a new solution method is given for the first time, which can be applied to integer order nonlinear optimal control problems. The proposed closed-loop controller is applied to illustrative examples. Novel unprecedented processes of designing a variable linear controller and of finding the optimal performance index for integer order nonlinear systems are presented. |
| first_indexed | 2024-03-08T17:23:41Z |
| format | Article |
| id | doaj.art-5c5c946afdfa4487afa738caa5f50deb |
| institution | Directory Open Access Journal |
| issn | 2767-8946 |
| language | English |
| last_indexed | 2024-03-08T17:23:41Z |
| publishDate | 2023-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Modelling and Control |
| spelling | doaj.art-5c5c946afdfa4487afa738caa5f50deb2024-01-03T01:32:45ZengAIMS PressMathematical Modelling and Control2767-89462023-12-013434535410.3934/mmc.2023028Novel closed-loop controllers for fractional nonlinear quadratic systemsIman Malmir 0Aerospace and Mechanical Engineering Group, Ronin Institute, Montclair, NJ 07043, USAA novel closed-loop optimal controller for fractional nonlinear quadratic optimal control problems is introduced. By using a new idea, the optimality conditions for the fractional nonlinear problems are derived. The linearized Riccati fractional order differential equation is derived and a new solution method is given for the first time, which can be applied to integer order nonlinear optimal control problems. The proposed closed-loop controller is applied to illustrative examples. Novel unprecedented processes of designing a variable linear controller and of finding the optimal performance index for integer order nonlinear systems are presented.https://www.aimspress.com/article/doi/10.3934/mmc.2023028?viewType=HTMLfractional nonlinear optimal controlclosed-loop controllerfractional riccati equation for nonlinear systemsfractional nonlinear systemlinear controller for nonlinear systemshighly nonlinear system |
| spellingShingle | Iman Malmir Novel closed-loop controllers for fractional nonlinear quadratic systems Mathematical Modelling and Control fractional nonlinear optimal control closed-loop controller fractional riccati equation for nonlinear systems fractional nonlinear system linear controller for nonlinear systems highly nonlinear system |
| title | Novel closed-loop controllers for fractional nonlinear quadratic systems |
| title_full | Novel closed-loop controllers for fractional nonlinear quadratic systems |
| title_fullStr | Novel closed-loop controllers for fractional nonlinear quadratic systems |
| title_full_unstemmed | Novel closed-loop controllers for fractional nonlinear quadratic systems |
| title_short | Novel closed-loop controllers for fractional nonlinear quadratic systems |
| title_sort | novel closed loop controllers for fractional nonlinear quadratic systems |
| topic | fractional nonlinear optimal control closed-loop controller fractional riccati equation for nonlinear systems fractional nonlinear system linear controller for nonlinear systems highly nonlinear system |
| url | https://www.aimspress.com/article/doi/10.3934/mmc.2023028?viewType=HTML |
| work_keys_str_mv | AT imanmalmir novelclosedloopcontrollersforfractionalnonlinearquadraticsystems |