Trajectory-based Robustness Analysis for Nonlinear Systems
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912515272736768 |
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| author | Seiler, Peter Venkataraman, Raghu |
| author_facet | Seiler, Peter Venkataraman, Raghu |
| contents | This paper considers the robustness of an uncertain nonlinear system along a finite-horizon trajectory. The uncertain system is modeled as a connection of a nonlinear system and a perturbation. The analysis relies on three ingredients. First, the nonlinear system is approximated by a linear time-varying (LTV) system via linearization along a trajectory. This linearization introduces an additional forcing input due to the nominal trajectory. Second, the input/output behavior of the perturbation is described by time-domain, integral quadratic constraints (IQCs). Third, a dissipation inequality is formulated to bound the worst-case deviation of an output signal due to the uncertainty. These steps yield a differential linear matrix inequality (DLMI) condition to bound the worst-case performance. The robustness condition is then converted to an equivalent condition in terms of a Riccati Differential Equation. This yields a computational method that avoids heuristics often used to solve DLMIs, e.g. time gridding. The approach is demonstrated by a two-link robotic arm example. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2302_05604 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Trajectory-based Robustness Analysis for Nonlinear Systems Seiler, Peter Venkataraman, Raghu Systems and Control This paper considers the robustness of an uncertain nonlinear system along a finite-horizon trajectory. The uncertain system is modeled as a connection of a nonlinear system and a perturbation. The analysis relies on three ingredients. First, the nonlinear system is approximated by a linear time-varying (LTV) system via linearization along a trajectory. This linearization introduces an additional forcing input due to the nominal trajectory. Second, the input/output behavior of the perturbation is described by time-domain, integral quadratic constraints (IQCs). Third, a dissipation inequality is formulated to bound the worst-case deviation of an output signal due to the uncertainty. These steps yield a differential linear matrix inequality (DLMI) condition to bound the worst-case performance. The robustness condition is then converted to an equivalent condition in terms of a Riccati Differential Equation. This yields a computational method that avoids heuristics often used to solve DLMIs, e.g. time gridding. The approach is demonstrated by a two-link robotic arm example. |
| title | Trajectory-based Robustness Analysis for Nonlinear Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2302.05604 |