Inducing Optimality in Prescribed Performance Control for Uncertain Euler–Lagrange Systems
The goal of this paper is to find a stabilizing and optimal control policy for a class of systems dictated by Euler–Lagrange dynamics, that also satisfies predetermined response criteria. The proposed methodology builds upon two stages. Initially, a neural network is trained online via an iterative...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/13/21/11923 |
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| author | Christos Vlachos Ioanna Malli Charalampos P. Bechlioulis Kostas J. Kyriakopoulos |
| author_facet | Christos Vlachos Ioanna Malli Charalampos P. Bechlioulis Kostas J. Kyriakopoulos |
| author_sort | Christos Vlachos |
| collection | DOAJ |
| description | The goal of this paper is to find a stabilizing and optimal control policy for a class of systems dictated by Euler–Lagrange dynamics, that also satisfies predetermined response criteria. The proposed methodology builds upon two stages. Initially, a neural network is trained online via an iterative process to capture the system dynamics, which are assumed to be unknown. Subsequently, a successive approximation algorithm is applied, employing the acquired dynamics from the previous step, to find a near-optimal control law that takes into consideration prescribed performance specifications, such as convergence speed and steady-state error. In addition, we concurrently guarantee that the system evolves exclusively within the compact set for which sufficient approximation capabilities have been acquired. Finally, we validate our claims through various simulated studies that confirm the success of both the identification process and the minimization of the cost function. |
| first_indexed | 2024-03-11T11:33:42Z |
| format | Article |
| id | doaj.art-82d6c4da35814aa4bd2469735598b90a |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-11T11:33:42Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-82d6c4da35814aa4bd2469735598b90a2023-11-10T14:59:10ZengMDPI AGApplied Sciences2076-34172023-10-0113211192310.3390/app132111923Inducing Optimality in Prescribed Performance Control for Uncertain Euler–Lagrange SystemsChristos Vlachos0Ioanna Malli1Charalampos P. Bechlioulis2Kostas J. Kyriakopoulos3Department of Electrical and Computer Engineering, University of Patras, Rio, 26504 Patras, GreeceSchool of Mechanical Engineering, National Technical University of Athens, 15772 Athens, GreeceDepartment of Electrical and Computer Engineering, University of Patras, Rio, 26504 Patras, GreeceSchool of Mechanical Engineering, National Technical University of Athens, 15772 Athens, GreeceThe goal of this paper is to find a stabilizing and optimal control policy for a class of systems dictated by Euler–Lagrange dynamics, that also satisfies predetermined response criteria. The proposed methodology builds upon two stages. Initially, a neural network is trained online via an iterative process to capture the system dynamics, which are assumed to be unknown. Subsequently, a successive approximation algorithm is applied, employing the acquired dynamics from the previous step, to find a near-optimal control law that takes into consideration prescribed performance specifications, such as convergence speed and steady-state error. In addition, we concurrently guarantee that the system evolves exclusively within the compact set for which sufficient approximation capabilities have been acquired. Finally, we validate our claims through various simulated studies that confirm the success of both the identification process and the minimization of the cost function.https://www.mdpi.com/2076-3417/13/21/11923adaptive dynamic programmingoptimal controlEuler–Lagrange systemsprescribed performance controltracking differentiator |
| spellingShingle | Christos Vlachos Ioanna Malli Charalampos P. Bechlioulis Kostas J. Kyriakopoulos Inducing Optimality in Prescribed Performance Control for Uncertain Euler–Lagrange Systems Applied Sciences adaptive dynamic programming optimal control Euler–Lagrange systems prescribed performance control tracking differentiator |
| title | Inducing Optimality in Prescribed Performance Control for Uncertain Euler–Lagrange Systems |
| title_full | Inducing Optimality in Prescribed Performance Control for Uncertain Euler–Lagrange Systems |
| title_fullStr | Inducing Optimality in Prescribed Performance Control for Uncertain Euler–Lagrange Systems |
| title_full_unstemmed | Inducing Optimality in Prescribed Performance Control for Uncertain Euler–Lagrange Systems |
| title_short | Inducing Optimality in Prescribed Performance Control for Uncertain Euler–Lagrange Systems |
| title_sort | inducing optimality in prescribed performance control for uncertain euler lagrange systems |
| topic | adaptive dynamic programming optimal control Euler–Lagrange systems prescribed performance control tracking differentiator |
| url | https://www.mdpi.com/2076-3417/13/21/11923 |
| work_keys_str_mv | AT christosvlachos inducingoptimalityinprescribedperformancecontrolforuncertaineulerlagrangesystems AT ioannamalli inducingoptimalityinprescribedperformancecontrolforuncertaineulerlagrangesystems AT charalampospbechlioulis inducingoptimalityinprescribedperformancecontrolforuncertaineulerlagrangesystems AT kostasjkyriakopoulos inducingoptimalityinprescribedperformancecontrolforuncertaineulerlagrangesystems |