Affiliation:
1. Leibniz University Hannover, Institute of Automatic Control , Appelstr. 11, 30167 Hannover , Germany
Abstract
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
∞ 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.
Reference30 articles.
1. H. Michalska and D. Q. Mayne, “Moving horizon observers and observer-based control,” IEEE Trans. Autom. Control, vol. 40, no. 6, pp. 995–1006, 1995. https://doi.org/10.1109/9.388677.
2. J. B. Rawlings, D. Q. Mayne, and M. M. Diehl, Model Predictive Control: Theory, Computation, and Design, 2nd ed. Santa Barbara, CA, USA, Nob Hill Publish., LLC, 2020, 3rd Printing.
3. A. Alessandri, M. Baglietto, and G. Battistelli, “Moving-horizon state estimation for nonlinear discrete-time systems: new stability results and approximation schemes,” Automatica, vol. 44, no. 7, pp. 1753–1765, 2008. https://doi.org/10.1016/j.automatica.2007.11.020.
4. C. V. Rao, J. B. Rawlings, and D. Q. Mayne, “Constrained state estimation for nonlinear discrete-time systems: stability and moving horizon approximations,” IEEE Trans. Autom. Control, vol. 48, no. 2, pp. 246–258, 2003. https://doi.org/10.1109/tac.2002.808470.
5. J. B. Rawlings and L. Ji, “Optimization-based state estimation: current status and some new results,” J. Process Control, vol. 22, no. 8, pp. 1439–1444, 2012. https://doi.org/10.1016/j.jprocont.2012.03.001.