A Note on Observers for Discrete-Time Lipschitz Nonlinear Systems

Abstract-In this paper, a Moving Horizon Estimator with pre-estimation (MHE-PE) is proposed for discrete-time nonlinear systems under bounded noise. While the classical Moving Horizon Estimator (MHE) compensates for model errors by estimating the process noise sequence over the horizon via optimization, the MHE-PE does it using an auxiliary estimator. The MHE-PE is shown to require significantly less computation time compared to the MHE, while providing the same order of magnitude of estimation errors. The stability of the estimation errors of the MHE-PE is also proven and an upper bound on its estimation errors is derived. Performances of the MHE-PE is illustrated via a simulation example of pressure estimation in a gas-phase reversible reaction.

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“…where L = 0.0026 0.7046 T has been computed using proposition 3 in [11]. The values of L x f = 1, δ = 1, µ = 5·10 −4 are chosen.…”

Section: Numerical Examplementioning

confidence: 99%

Stability of a nonlinear Moving Horizon Estimator with pre-estimation

Suwantong

Bertrand

Dumur

et al. 2014

2014 American Control Conference

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“…Assumption 1: ∆(·) is one-sided Lipschitz (Zhang et al 2012) in e k , i.e. there exists ρ ∈ R such that, for an arbitrary e k ∈ R n :…”

Section: Observer Design With Unmeasurable Premise Variablesmentioning

confidence: 99%

“…Assumption 2: ∆(·) is quadratic inner-bounded (Zhang et al 2012) in e k−1 , i.e. for an arbitrary e k−1 ∈ R n , there exist σ, ϕ ∈ R such that:…”

Section: Observer Design With Unmeasurable Premise Variablesmentioning

confidence: 99%

“…The discussion in Zhang et al (2012) has shown that, under the setting of Lipschitz nonlinearities, it is difficult to design observers in the case of Lipschitz constant bigger than one. This fact has motivated the observer design for one-sided Lipschitz systems, with the aim of reducing the conservatism of the results.…”

Section: Observer Design With Unmeasurable Premise Variablesmentioning

confidence: 99%

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Robust unknown input observer for state and fault estimation in discrete-time Takagi–Sugeno systems

Rotondo

Witczak

Puig

et al. 2016

International Journal of Systems Science

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In this paper, a robust unknown input observer (UIO) for the joint state and fault estimation in discrete-time Takagi-Sugeno (TS) systems is presented. The proposed robust UIO, by applying the H∞ framework, leads to a less restrictive design procedure with respect to recent results found in the literature. The resulting design procedure aims at achieving a prescribed attenuation level with respect to the exogenous disturbances, while obtaining at the same time the convergence of the observer with a desired bound on the decay rate. An extension to the case of unmeasurable premise variables is also provided. Since the design conditions reduce to a set of linear matrix inequalities (LMIs), that can be solved efficiently using the available software, an evident advantage of the proposed approach is its simplicity. The final part of the paper presents an academic example and a real application to a multi-tank system, which exhibit clearly the performance and effectiveness of the proposed strategy.

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“…For such systems, less conservative designs on both full-order and reduced-order observers have been considered by Zhang et al 18,19 where the Riccati equation and the LMI approaches were, respectively, introduced. In the discrete-time case, the state estimation issue was investigated in Zhang et al 20 Moreover, the observer design for such systems with unknown inputs was addressed in Zhang et al 21 However, it should be noted that most of the above-mentioned references are focused on the observer deign issue. A more challenging problem is the observer-based stabilization or output feedback control for one-sided Lipschitz systems.…”

Section: Introductionmentioning

confidence: 99%

Observer-based stabilization of one-sided Lipschitz systems with application to flexible link manipulator

Zhang

Song

et al. 2015

Advances in Mechanical Engineering

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This article is concerned with the observer-based output feedback stabilization problem for a class of nonlinear systems that satisfies the one-sided Lipschitz and the quadratically inner-bounded conditions. The system model under consideration encompasses the classical Lipschitz nonlinear system as a special case. For such a system, we design the output feedback controller via constructing a full-order Luenberger-type state observer. Sufficient conditions that guarantee the existence of observer-based output feedback are established in the form of linear matrix inequalities, which are readily solved by the available numerical software. Moreover, the proposed observer-based output feedback designs are applied to a flexible link manipulator system. Finally, simulation study on the manipulator system is given to demonstrate the effectiveness of the developed control design.

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A Note on Observers for Discrete-Time Lipschitz Nonlinear Systems

Cited by 93 publications

References 24 publications

Stability of a nonlinear Moving Horizon Estimator with pre-estimation

Stability of a nonlinear Moving Horizon Estimator with pre-estimation

Robust unknown input observer for state and fault estimation in discrete-time Takagi–Sugeno systems

Observer-based stabilization of one-sided Lipschitz systems with application to flexible link manipulator

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