Direct Data-Driven State-Feedback Control of Linear Parameter-Varying Systems
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| Format: | Preprint |
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2022
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| _version_ | 1866912456562966528 |
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| author | Verhoek, Chris Tóth, Roland Abbas, Hossam S. |
| author_facet | Verhoek, Chris Tóth, Roland Abbas, Hossam S. |
| contents | The framework of linear parameter-varying (LPV) systems has shown to be a powerful tool for the design of controllers for complex nonlinear systems using linear tools. In this work, we derive novel methods that allow to synthesize LPV state-feedback controllers directly from only a single sequence of data and guarantee stability and performance of the closed-loop system. We show that if the measured open-loop data from the system satisfies a persistency of excitation condition, then the full open-loop and closed-loop input-scheduling-state behavior can be represented using only the data. With this representation we formulate data-driven analysis and synthesis problems, where the latter yields controllers that guarantee stability and performance in terms of infinite horizon quadratic cost, generalized $\mathcal{H}_2$-norm and $\ell_2$-gain of the closed-loop system. The controllers are synthesized by solving a semi-definite program. Additionally, we provide a synthesis method to handle noisy measurement data. Competitive performance of the proposed data-driven synthesis methods is demonstrated w.r.t. model-based synthesis in multiple simulation studies, including a nonlinear unbalanced disc system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_17182 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Direct Data-Driven State-Feedback Control of Linear Parameter-Varying Systems Verhoek, Chris Tóth, Roland Abbas, Hossam S. Systems and Control The framework of linear parameter-varying (LPV) systems has shown to be a powerful tool for the design of controllers for complex nonlinear systems using linear tools. In this work, we derive novel methods that allow to synthesize LPV state-feedback controllers directly from only a single sequence of data and guarantee stability and performance of the closed-loop system. We show that if the measured open-loop data from the system satisfies a persistency of excitation condition, then the full open-loop and closed-loop input-scheduling-state behavior can be represented using only the data. With this representation we formulate data-driven analysis and synthesis problems, where the latter yields controllers that guarantee stability and performance in terms of infinite horizon quadratic cost, generalized $\mathcal{H}_2$-norm and $\ell_2$-gain of the closed-loop system. The controllers are synthesized by solving a semi-definite program. Additionally, we provide a synthesis method to handle noisy measurement data. Competitive performance of the proposed data-driven synthesis methods is demonstrated w.r.t. model-based synthesis in multiple simulation studies, including a nonlinear unbalanced disc system. |
| title | Direct Data-Driven State-Feedback Control of Linear Parameter-Varying Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2211.17182 |