Robust stability of moving horizon estimation for continuous-time systems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2023
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| _version_ | 1866909088808435712 |
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| author | Schiller, Julian D. Müller, Matthias A. |
| author_facet | Schiller, Julian D. Müller, Matthias A. |
| contents | We consider a moving horizon estimation (MHE) scheme involving a discounted least squares objective for general nonlinear continuous-time systems. Provided that the system is detectable (incrementally integral input/output-to-state stable, i-iIOSS), we show that there exists a sufficiently long estimation horizon that guarantees robust global exponential stability of the estimation error in a time-discounted $L^2$-to-$L^\infty$ sense. In addition, we show that i-iIOSS Lyapunov functions can be efficiently constructed by verifying certain linear matrix inequality conditions. In combination, we propose a flexible Lyapunov-based MHE framework in continuous time, which particularly offers more tuning possibilities than its discrete-time analog, and provide sufficient conditions for stability that can be easily verified in practice. Our results are illustrated by a numerical example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06614 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Robust stability of moving horizon estimation for continuous-time systems Schiller, Julian D. Müller, Matthias A. Systems and Control We consider a moving horizon estimation (MHE) scheme involving a discounted least squares objective for general nonlinear continuous-time systems. Provided that the system is detectable (incrementally integral input/output-to-state stable, i-iIOSS), we show that there exists a sufficiently long estimation horizon that guarantees robust global exponential stability of the estimation error in a time-discounted $L^2$-to-$L^\infty$ sense. In addition, we show that i-iIOSS Lyapunov functions can be efficiently constructed by verifying certain linear matrix inequality conditions. In combination, we propose a flexible Lyapunov-based MHE framework in continuous time, which particularly offers more tuning possibilities than its discrete-time analog, and provide sufficient conditions for stability that can be easily verified in practice. Our results are illustrated by a numerical example. |
| title | Robust stability of moving horizon estimation for continuous-time systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2305.06614 |