A new optimal control approach to uncertain Euler-Lagrange equations: $ H_\infty $ disturbance estimator and generalized $ H_2 $ tracking controller
This paper proposed a new optimal control method for uncertain Euler-Lagrange systems, focusing on estimating model uncertainties and improving tracking performance. More precisely, a linearization of the nonlinear equation was achieved through the inverse dynamic control (IDC) and an $ H_\infty $ o...
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241642 |
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| author | Taewan Kim Jung Hoon Kim |
| author_facet | Taewan Kim Jung Hoon Kim |
| author_sort | Taewan Kim |
| collection | DOAJ |
| description | This paper proposed a new optimal control method for uncertain Euler-Lagrange systems, focusing on estimating model uncertainties and improving tracking performance. More precisely, a linearization of the nonlinear equation was achieved through the inverse dynamic control (IDC) and an $ H_\infty $ optimal estimator was designed to address model uncertainties arising in this process. Subsequently, a generalized $ H_2 $ optimal tracking controller was obtained to minimize the effect of the estimation error on the tracking error in terms of the induced norm from $ L_2 $ to $ L_\infty $. Necessary and sufficient conditions for the existences of these two optimal estimator and controller were characterized through the linear matrix inequality (LMI) approach, and their synthesis procedures can be operated in an independent fashion. To put it another way, this developed approach allowed us to minimize not only the modeling error between the real Euler-Lagrange equations and their nominal models occurring from the IDC approach but also the maximum magnitude of the tracking error by solving some LMIs. Finally, the effectiveness of both the $ H_\infty $ optimal disturbance estimator and the generalized $ H_2 $ tracking controller were demonstrated through some comparative simulation and experiment results of a robot manipulator, which was one of the most representative examples of Euler-Lagrange equations. |
| format | Article |
| id | doaj-art-2189b2a67951451a88131c0ed1acd822 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
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| series | AIMS Mathematics |
| spelling | doaj-art-2189b2a67951451a88131c0ed1acd8222025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912344663448710.3934/math.20241642A new optimal control approach to uncertain Euler-Lagrange equations: $ H_\infty $ disturbance estimator and generalized $ H_2 $ tracking controllerTaewan Kim0Jung Hoon Kim1Department of Electrical Engineering, Pohang University of Science and Technology (POSTECH), Pohang 37673, Republic of KoreaDepartment of Electrical Engineering, Pohang University of Science and Technology (POSTECH), Pohang 37673, Republic of KoreaThis paper proposed a new optimal control method for uncertain Euler-Lagrange systems, focusing on estimating model uncertainties and improving tracking performance. More precisely, a linearization of the nonlinear equation was achieved through the inverse dynamic control (IDC) and an $ H_\infty $ optimal estimator was designed to address model uncertainties arising in this process. Subsequently, a generalized $ H_2 $ optimal tracking controller was obtained to minimize the effect of the estimation error on the tracking error in terms of the induced norm from $ L_2 $ to $ L_\infty $. Necessary and sufficient conditions for the existences of these two optimal estimator and controller were characterized through the linear matrix inequality (LMI) approach, and their synthesis procedures can be operated in an independent fashion. To put it another way, this developed approach allowed us to minimize not only the modeling error between the real Euler-Lagrange equations and their nominal models occurring from the IDC approach but also the maximum magnitude of the tracking error by solving some LMIs. Finally, the effectiveness of both the $ H_\infty $ optimal disturbance estimator and the generalized $ H_2 $ tracking controller were demonstrated through some comparative simulation and experiment results of a robot manipulator, which was one of the most representative examples of Euler-Lagrange equations.https://www.aimspress.com/article/doi/10.3934/math.20241642euler-lagrange equationsinverse dynamic control$ h_\infty $ optimal estimatorgeneralized $ h_2 $ optimal controllerlinear matrix inequalities |
| spellingShingle | Taewan Kim Jung Hoon Kim A new optimal control approach to uncertain Euler-Lagrange equations: $ H_\infty $ disturbance estimator and generalized $ H_2 $ tracking controller AIMS Mathematics euler-lagrange equations inverse dynamic control $ h_\infty $ optimal estimator generalized $ h_2 $ optimal controller linear matrix inequalities |
| title | A new optimal control approach to uncertain Euler-Lagrange equations: $ H_\infty $ disturbance estimator and generalized $ H_2 $ tracking controller |
| title_full | A new optimal control approach to uncertain Euler-Lagrange equations: $ H_\infty $ disturbance estimator and generalized $ H_2 $ tracking controller |
| title_fullStr | A new optimal control approach to uncertain Euler-Lagrange equations: $ H_\infty $ disturbance estimator and generalized $ H_2 $ tracking controller |
| title_full_unstemmed | A new optimal control approach to uncertain Euler-Lagrange equations: $ H_\infty $ disturbance estimator and generalized $ H_2 $ tracking controller |
| title_short | A new optimal control approach to uncertain Euler-Lagrange equations: $ H_\infty $ disturbance estimator and generalized $ H_2 $ tracking controller |
| title_sort | new optimal control approach to uncertain euler lagrange equations h infty disturbance estimator and generalized h 2 tracking controller |
| topic | euler-lagrange equations inverse dynamic control $ h_\infty $ optimal estimator generalized $ h_2 $ optimal controller linear matrix inequalities |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241642 |
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