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arXiv · 2305.06614

Robust stability of moving horizon estimation for continuous-time systems

Julian D. Schiller·Matthias A. Müller
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Abstract

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.

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Julian D. Schiller, Matthias A. Müller. 2023-05-11. Robust stability of moving horizon estimation for continuous-time systems. https://doi.org/10.1515/auto-2023-0087

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