Immersion of General Nonlinear Systems Into State-Affine Ones for the Design of Generalized Parameter Estimation-Based Observers: A Simple Algebraic Procedure
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929594776420352 |
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| author | Ortega, Romeo Bobtsov, Alexey Romero, Jose Guadalupe Fang, Leyan |
| author_facet | Ortega, Romeo Bobtsov, Alexey Romero, Jose Guadalupe Fang, Leyan |
| contents | Generalized parameter estimation-based observers have proven very successful to deal with systems described in state-affine form. In this paper, we enlarge the domain of applicability of this method proposing an algebraic procedure to immerse} an $n$-dimensional general nonlinear system into and $n_z$-dimensional system in state affine form, with $n_z>n$. First, we recall the necessary and sufficient condition for the solution of the general problem, which requires the solution of a partial differential equation that, moreover, has to satisfy a restrictive injectivity condition. Given the complexity of this task we propose an alternative simple algebraic method to identify the required dynamic extension and coordinate transformation, a procedure that, as shown in the paper, is rather natural for physical systems. We illustrate the method with some academic benchmark examples from observer theory literature -- that, in spite of their apparent simplicity, are difficult to solve with the existing methods -- as well as several practically relevant physical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10965 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Immersion of General Nonlinear Systems Into State-Affine Ones for the Design of Generalized Parameter Estimation-Based Observers: A Simple Algebraic Procedure Ortega, Romeo Bobtsov, Alexey Romero, Jose Guadalupe Fang, Leyan Systems and Control Generalized parameter estimation-based observers have proven very successful to deal with systems described in state-affine form. In this paper, we enlarge the domain of applicability of this method proposing an algebraic procedure to immerse} an $n$-dimensional general nonlinear system into and $n_z$-dimensional system in state affine form, with $n_z>n$. First, we recall the necessary and sufficient condition for the solution of the general problem, which requires the solution of a partial differential equation that, moreover, has to satisfy a restrictive injectivity condition. Given the complexity of this task we propose an alternative simple algebraic method to identify the required dynamic extension and coordinate transformation, a procedure that, as shown in the paper, is rather natural for physical systems. We illustrate the method with some academic benchmark examples from observer theory literature -- that, in spite of their apparent simplicity, are difficult to solve with the existing methods -- as well as several practically relevant physical examples. |
| title | Immersion of General Nonlinear Systems Into State-Affine Ones for the Design of Generalized Parameter Estimation-Based Observers: A Simple Algebraic Procedure |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2411.10965 |