Stability Properties of the Discrete-Time Extended Kalman Filter

Rapp, Knut; Nyman, Per-Ole

doi:10.1016/s1474-6670(17)31420-9

Cited by 14 publications

(9 citation statements)

References 6 publications

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“…See [199] for λ > 0 and [63] for λ = 0. However, the trajectory of Π depends on that of x itself and the assumption (52) cannot be in general checked "a priori", introducing therefore a loop in the stability analysis (the same issue appears in the discretetime context [67,220,198]). An exception is [114], where an infinitesimal observability assumption is made on the plant, and not along the estimate.…”

Section: Extended Kalman Filtermentioning

confidence: 99%

Observer design for continuous-time dynamical systems

Bernard

Andrieu

Astolfi

2022

Annual Reviews in Control

106

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We review the main design techniques of state observer design for continuous-time dynamical systems, namely algorithms which reconstruct online the full information of a dynamical process on the basis of partially measured data. Starting from necessary conditions for the existence of such asymptotic observers, we classify the available methods depending on the detectability/observability assumptions they require. We show how each class of observer relies on transforming the system dynamics in a particular normal form which allows the design of an observer, and how each observability condition guarantees the invertibility of its associated transformation and the convergence of the observer. Finally, some implementation aspects and open problems are briefly discussed.

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Section: Extended Kalman Filtermentioning

confidence: 99%

Observer design for continuous-time dynamical systems

Bernard

Andrieu

Astolfi

2022

Annual Reviews in Control

106

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“…where Q and R commonly denote the covariance of the noise in Kalman filter, and they can also be used as parameters for strategy design in noiseless environment. The application of state estimation in noiseless environment is discussed in Rapp and Nyman (2004) and Dutta et al (2019). In principle, they can be selected as any positive definite matrices.…”

Section: Problem Formulationmentioning

confidence: 99%

Discrete-time resilient-distributed secondary control strategy against unbounded attacks in polymorphic microgrid

et al. 2022

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This study proposes a polymorphic cooperative control system for microgrid consisting of a service layer, a control layer, a data layer, and a power layer to apply a resilient-distributed secondary control strategy to distributed generators (DGs) from different manufacturers more conveniently. Due to the improvement of network openness, external cyberattacks are more likely to tamper with the neighbor information transmitted in the cooperative control system. In this study, a discrete-time resilient-distributed secondary control strategy is designed to resist potential unbounded false data injection (FDI) attacks, which introduces a virtual network layer interconnecting the control network layer to form a layered network. The strategy can maintain the stability of voltage and frequency under unbounded attacks and then greatly suppress the state estimation difference of voltage and frequency. Meanwhile, the unbounded attack depending on voltage and frequency estimation difference is suppressed to a nearly bounded attack. Finally, a microgrid consisting of six inverter-based DGs is taken as an example to validate the effectiveness of the strategy against unbounded attacks.

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“…It is obtained by copying the dynamics (1) and using a gain P (∂h/∂x) R −1 , that mimics the Kalman-Bucy filter gain for linear systems ( [15], [16]), where the linear dynamics matrices are simply replaced by the linearized pair (∂f /∂x, ∂h/∂x) around the only available estimate (x, u). Unfortunately, apart from specific triangular structures [10], [17], only local convergence of the estimation error x − x can be ensured, under the additional ad-hoc assumption that there exist p, p > 0 such that (see [3], [5], [24], [25], [28])…”

Section: Consider a Plantmentioning

confidence: 99%

“…Unfortunately, the linearization is carried out along the estimated trajectory, which introduces a loop in the analysis and only local convergence can be proved. More importantly, the stability analysis is performed under an ad-hoc lower/upper-boundedness assumption on the Riccati solution that depends on the estimate itself and thus cannot be verified [3], [5], [24], [25], [28]. Very few exceptions exist in the particular context of uniformly observable systems in triangular form [10], [17].…”

Section: Introductionmentioning

confidence: 99%

On the Semi-Global Stability of an EK-Like Filter

Bernard

Mimmo²,

Marconi³

2021

IEEE Control Syst. Lett.

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This paper proposes to apply the Kalmanlike observer paradigm to general nonlinear systems by linearization along the estimated trajectory, similarly to an Extended Kalman Filter. The main difference is that the quadratic Riccati equation is replaced by a linear Lyapunov equation which can be solved and explicitly related to a determinability Gramian. This allows to show by Lyapunov analysis and without any ad-hoc assumption on the Riccati solution, that the resulting observer, called Extended Kalman-like Filter, can be made semi-globally convergent if the input is actively used to a) stabilize the (unknown) true trajectory, b) sufficiently excite the determinability of the linearized systems along the (known) estimated trajectory. A class of systems where this compromise can be reached is provided.

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Stability Properties of the Discrete-Time Extended Kalman Filter

Cited by 14 publications

References 6 publications

Observer design for continuous-time dynamical systems

Observer design for continuous-time dynamical systems

Discrete-time resilient-distributed secondary control strategy against unbounded attacks in polymorphic microgrid

On the Semi-Global Stability of an EK-Like Filter

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