Nonlinear observer design for two‐time‐scale systems

Duan, Zhaoyang; Kravaris, Costas

doi:10.1002/aic.16956

Cited by 9 publications

(4 citation statements)

References 48 publications

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“…We decompose two-time-scale systems described in Equation (1) into two separate reduced subsystems evolving in a fast and a slow timescales as illustrated in the previous section. The fast subsystem is described by Equation ( 3) and the slow subsystem is described by Equation (8).…”

Section: Proposed Implementation Algorithmsmentioning

confidence: 99%

“…Recently, in Reference 8, two alternative nonlinear observer design approaches, one full‐order, and one reduced‐order are designed for two‐time‐scale systems. The full‐order observer is designed based on linearization of the original model around its stable steady state, whereas, the reduced‐order observer is derived based on a lower‐dimensional model to reconstruct the slow states which are used to calculate an invariant manifold for the fast state estimation.…”

Section: Introductionmentioning

confidence: 99%

“…One directional communication from the slow subsystem moving horizon estimators (MHEs) to the fast subsystem MHE is established and sufficient conditions on the convergence of the estimation error of the DMHE are derived. However, both References 3, 8, considered two‐time‐scale systems that can be described in the standard singular perturbation form where the fast and the slow dynamics are associated with distinct process variables and can be separated explicitly. There are a wide range of applications where slow and fast dynamics cannot be separated explicitly.…”

Section: Introductionmentioning

confidence: 99%

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Subsystem decomposition and distributed state estimation of nonlinear processes with implicit time‐scale multiplicity

et al. 2022

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In this work, we propose a subsystem decomposition approach and a distributed estimation scheme for a class of implicit two-time-scale nonlinear systems. Taking the advantage of the time scale separation, these processes are decomposed into fast subsystem and slow subsystem according to the dynamics. In the proposed method, an approach that combines the approximate solutions obtained from both the fast and slow subsystems to form a composite solution of the original system is proposed. Also, based on the fast and slow subsystems, a distributed state estimation scheme is proposed to handle the implicit time-scale multiplicity. In the proposed design, an extended Kalman filter (EKF) is designed for the fast subsystem and a moving horizon estimator (MHE) is designed for the slow subsystem. In the design, the slow subsystem is only required to send information to the fast subsystem one-directionally. The fast subsystem estimator does not send out any information. The estimators use different sampling times, that is, fast sampling of the fast state variables is considered in the fast EKF and slow sampling of the slow state variables is considered in the slow MHE. Extensive simulations based on a chemical process are performed to illustrate the effectiveness and applicability of the proposed subsystem decomposition and composite estimation architecture.

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Section: Proposed Implementation Algorithmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Subsystem decomposition and distributed state estimation of nonlinear processes with implicit time‐scale multiplicity

et al. 2022

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show abstract

“…Recently, two alternative nonlinear observer design approaches, one full-order, and one reduced-order are designed for a two-time-scale system. The full-order observer is designed based on the linearized original model around its stable steady state, whereas, the reduced-order observer is derived based on a lower-dimensional model to reconstruct the slow states which are used to calculate an invariant manifold for the fast state estimation 10 . Within the singular perturbation framework, a nonlinear system was decomposed into a fast system and several slow subsystems, and DMHE is applied in 3 .…”

Section: Introductionmentioning

confidence: 99%

Subsystem decomposition and state estimation of nonlinear processes with implicit time-scale multiplicity

Debnath¹,

Sahoo²,

Decardi‐Nelson³

et al. 2021

Preprint

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In this work, we propose a subsystem decomposition approach and a distributed estimation scheme for a class of implicit two-time-scale nonlinear systems. Taking the advantage of the two-time-scale separation, these processes are decomposed into smaller subsystems such as fast subsystem and slow subsystem. In the proposed method, an approach, composite solution, combines the approximate solutions obtained from both fast and slow subsystems. Based on the fast and slow subsystems, a distributed state estimation scheme is proposed to handle the implicit time-scale multiplicity. In the proposed design, an extended Kalman filter (EKF) is designed for the fast subsystem and a moving horizon estimator (MHE) is designed for the slow subsystem. There is a communication between the estimators: the slow subsystem is only required to send information to the fast subsystem one-directionally. The fast subsystem estimator does not send out any information. The estimators use different sampling of the state measurements, i.e., fast sampling of the fast state variables is considered in the fast EKF and slow sampling of the slow state variables is considered in the slow MHE. Extensive simulations based on a chemical process are performed to illustrate the effectiveness and applicability of the proposed subsystem decomposition and composite state estimation architecture.

show abstract

Two-time-scale robust output feedback control for aircraft longitudinal dynamics via sliding mode control and high-gain observer

Raza¹,

Malik²,

Mazhar³

et al. 2022

Alexandria Engineering Journal

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Nonlinear observer design for two‐time‐scale systems

Cited by 9 publications

References 48 publications

Subsystem decomposition and distributed state estimation of nonlinear processes with implicit time‐scale multiplicity

Subsystem decomposition and distributed state estimation of nonlinear processes with implicit time‐scale multiplicity

Subsystem decomposition and state estimation of nonlinear processes with implicit time-scale multiplicity

Two-time-scale robust output feedback control for aircraft longitudinal dynamics via sliding mode control and high-gain observer

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