TY - JOUR

T1 - Nonlinear full information and moving horizon estimation

T2 - Robust global asymptotic stability

AU - Knüfer, Sven

AU - Müller, Matthias A.

N1 - Funding Information: This work was supported by the German Research Foundation under Grant MU3929-2/1 , project number: 426459964 . The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Denis Efimov under the direction of Editor Daniel Liberzon.

PY - 2023/4

Y1 - 2023/4

N2 - In this paper, we propose time-discounted schemes for full information estimation (FIE) and moving horizon estimation (MHE) that are robustly globally asymptotically stable (RGAS). We consider general nonlinear system dynamics with nonlinear process and output disturbances that are a priori unknown. For FIE being RGAS, our only assumptions are that the system is time-discounted incrementally input–output-to-state-stable (i-IOSS) and that the time-discounted FIE cost function is compatible with the i-IOSS estimate. Since for i-IOSS systems such a compatible cost function can always be designed, we show that i-IOSS is sufficient for the existence of RGAS observers. Based on the stability result for FIE, we provide sufficient conditions such that the induced MHE scheme is RGAS as well for sufficiently large horizons. For both schemes, we can guarantee convergence of the estimation error in case the disturbances converge to zero without incorporating a priori knowledge. Finally, we present explicit converge rates and show how to verify that the MHE results approach the FIE results for increasing horizons.

AB - In this paper, we propose time-discounted schemes for full information estimation (FIE) and moving horizon estimation (MHE) that are robustly globally asymptotically stable (RGAS). We consider general nonlinear system dynamics with nonlinear process and output disturbances that are a priori unknown. For FIE being RGAS, our only assumptions are that the system is time-discounted incrementally input–output-to-state-stable (i-IOSS) and that the time-discounted FIE cost function is compatible with the i-IOSS estimate. Since for i-IOSS systems such a compatible cost function can always be designed, we show that i-IOSS is sufficient for the existence of RGAS observers. Based on the stability result for FIE, we provide sufficient conditions such that the induced MHE scheme is RGAS as well for sufficiently large horizons. For both schemes, we can guarantee convergence of the estimation error in case the disturbances converge to zero without incorporating a priori knowledge. Finally, we present explicit converge rates and show how to verify that the MHE results approach the FIE results for increasing horizons.

KW - Detectability

KW - Full information estimation

KW - Moving horizon estimation

KW - Nonlinear systems

KW - Robust stability

UR - http://www.scopus.com/inward/record.url?scp=85146716308&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2022.110603

DO - 10.1016/j.automatica.2022.110603

M3 - Article

AN - SCOPUS:85146716308

VL - 150

JO - AUTOMATICA

JF - AUTOMATICA

SN - 0005-1098

M1 - 110603

ER -