Stability of a nonlinear Moving Horizon Estimator with pre-estimation

Suwantong, Rata; Bertrand, Sylvain; Dumur, Didier; Beauvois, Dominique

doi:10.1109/acc.2014.6859072

Cited by 19 publications

(43 citation statements)

References 11 publications

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“…By introducing a nonlinear Luenberger observer into the MHO formulation , the MHO‐PE was first proposed for linear systems() and has been recently extended to nonlinear systems in the works of Polóni et al and Sunwantong et al); thus, we have

\begin{matrix} alignleft \\ align-1 \min_{{\hat{x}}_{i | k}} J_{k} ({\hat{x}}_{k - N | k}) & align-2 = {‖{\hat{x}}_{k - N | k} - {\bar{x}}_{k - N | k}‖}_{M}^{2} + \sum_{i = k - N}^{k} {‖y_{m, i} - ŷ_{i | k}‖}_{W}^{2} \\ align-1 s.t. {\hat{x}}_{i + 1 | k} & align-2 = f ({\hat{x}}_{i | k}, u_{m, i}) + L (y_{m, i} - ŷ_{i | k}), i = k - N, ⋯, k - 1, \\ align-1 ŷ_{i | k} & align-2 = h ({\hat{x}}_{i | k}), i = k - N, ⋯, k . \end{matrix}

On the one hand, the pre‐estimating Luenberger observer stabilizes the forward prediction by introducing feedback from output measurements, thus reducing the error accumulation in the forward prediction. On the other hand, observer gain L can be regarded as a parsimonious parameterization of the estimated disturbance sequence

ŵ_{k - N false| k}

, …,

…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

“…By introducing a nonlinear Luenberger observer into the MHO formulation (3), the MHO-PE was first proposed for linear systems 35,36 and has been recently extended to nonlinear systems in the works of Polóni et al 37 and Sunwantong et al 38 ; thus, we have min…”

Section: Preliminaries On Nonlinear Mhomentioning

confidence: 99%

“…respectively, for k > N. When k = N, the bounds on || w,k w k−N k || and || v,k v k−N k || are actually the second term on the right-hand side of (37) and (38), respectively. Following (32) and (35), the upper bound for ||ξ k || is…”

Section: Error Bounds Of State Estimatesmentioning

confidence: 99%

“…By avoiding the explicit calculation of disturbance estimates, the MHO‐PE has a computational complexity that scales significantly better with respect to the horizon length and the disturbance dimensions compared with the standard MHO. This idea has been recently extended to nonlinear systems in the works of Polóni et al and Sunwantong et al…”

Section: Introductionmentioning

confidence: 99%

“…By avoiding the explicit calculation of disturbance estimates, the MHO-PE has a computational complexity that scales significantly better with respect to the horizon length and the disturbance dimensions compared with the standard MHO. This idea has been recently extended to nonlinear systems in the works of Polóni et al 37 and Sunwantong et al 38 The aforementioned results on the MHO-PE all make use of exact solutions of the underlying optimization problem, which might not be computed within a short sampling interval. Hence, their real-time applicability is significantly limited.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Real‐time nonlinear moving horizon observer with pre‐estimation for aircraft sensor fault detection and estimation

Wan

Keviczky

2017

Intl J Robust & Nonlinear

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Summary This paper presents a real‐time nonlinear moving horizon observer (MHO) with pre‐estimation and its application to aircraft sensor fault detection and estimation. An MHO determines the state estimates by minimizing the output estimation errors online, considering a finite sequence of current and past measured data and the available system model. To achieve the real‐time implementability of such an online optimization–based observer, 2 particular strategies are adopted. First, a pre‐estimating observer is embedded to compensate for model uncertainties so that the calculation of disturbance estimates in a standard MHO can be avoided without losing much estimation performance. This strategy significantly reduces the online computational complexity. Second, a real‐time iteration scheme is proposed by performing only 1 iteration of sequential quadratic programming with local Gauss‐Newton approximation to the nonlinear optimization problem. Since existing stability analyses of real‐time moving horizon observers cannot address the incorporation of the pre‐estimating observer, a new stability analysis is performed in the presence of bounded disturbances and noises. Using a nonlinear passenger aircraft benchmark simulator, the simulation results show that the proposed approach achieves a good compromise between estimation performance and computational complexity compared with the extended Kalman filtering and 2 other moving horizon observers.

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