A robust estimation approach for uncertain systems with perturbed measurements

Bolajraf, M.; Rami, Mustapha Ait

doi:10.1002/rnc.3340

Cited by 27 publications

(13 citation statements)

References 21 publications

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“…Theorem 2. Given a RMES PMJLS (6) with u(t) = 0, a positive upper bounding observer (19) exists such that the augmented system (21) is positive and MES for any A 0i ∈ [A 0i , A 0i ] (RMES) if and only if there exist strictly positive vectors i ∈ R n , (n + p)-dimensional diagonal matrices Q i ≻ 0, matrices U i ∈ R (n+p)×n , and V i ∈ R (n+p)×p , i = 1, 2, … , s, satisfying…”

Section: Design Of Positive State-bounding Observermentioning

confidence: 99%

“…It is worth noting that the design of interval observers is highly relevant to the application of positive systems theory, based on which observer gains are determined to guarantee that the observer error dynamics are always positive . There have been several approaches in designing interval observers for systems with disturbances or uncertainties, time‐varying systems, delay systems, nonlinear systems, and discrete‐time systems . The techniques of interval observers can also been applied to tackle the problem of controller design, and with guaranteed interval estimates, the interval observers often simplify the control of transition processes .…”

Section: Introductionmentioning

confidence: 99%

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Descriptor state‐bounding observer design for positive Markov jump linear systems with sensor faults: Simultaneous state and faults estimation

Song

Lam

Chen

et al. 2020

Intl J Robust & Nonlinear

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Summary This article presents a descriptor observer design approach for positive Markov jump linear systems subject to interval parameter uncertainties and sensor faults. First, by taking the sensor fault term as an auxiliary state, an augmented descriptor system is constructed. A pair of positive observers with state‐bounding feature is then proposed, which enables simultaneous estimation of the system state and sensor faults. A necessary and sufficient condition on existence of the desired state‐bounding observer is derived by considering positivity and robust mean exponential stability of corresponding observer error dynamics. An iterative optimization algorithm is developed for the computation of the optimized observer matrices. Finally, a numerical example is presented to show the validity of the proposed methods.

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Section: Design Of Positive State-bounding Observermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Descriptor state‐bounding observer design for positive Markov jump linear systems with sensor faults: Simultaneous state and faults estimation

Song

Lam

Chen

et al. 2020

Intl J Robust & Nonlinear

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“…Moreover, as this weighting matrix is part of the arrival cost, then it helps to summarize the old data to obtain the moving horizon approximation. At time t, the arrival cost can be used to rewrite (13)…”

Section: The Arrival Cost In the  ∞ -Mhe And The Weighting Matrix π Kmentioning

confidence: 99%

“…7,8,10,11 Contributions addressing both uncertainty sources in the same statement of the problem are also available. 8,12,13 A literature review on state estimation for uncertain linear systems is found elsewhere. 14 The moving horizon estimator (MHE) has shown to be an effective estimation scheme able to handle constraints even in the nonlinear framework.…”

mentioning

confidence: 99%

A new approach to constrained state estimation for discrete‐time linear systems with unknown inputs

García-Tirado

Marquez-Ruiz

Castro

et al. 2017

Intl J Robust & Nonlinear

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SummaryThis paper addresses the problem of estimating the state for a class of uncertain discrete-time linear systems with constraints by using an optimization-based approach. The proposed scheme uses the moving horizon estimation philosophy together with the game theoretical approach to the  ∞ filtering to obtain a robust filter with constraint handling. The used approach is constructive since the proposed moving horizon estimator (MHE) results from an approximation of a type of full information estimator for uncertain discrete-time linear systems, named in short  ∞ -MHE and  ∞ -full information estimator, respectively. Sufficient conditions for the stability of the  ∞ -MHE are discussed for a class of uncertain discrete-time linear systems with constraints. Finally, since the  ∞ -MHE needs the solution of a complex minimax optimization problem at each sampling time, we propose an approximation to relax the optimization problem and hence to obtain a feasible numerical solution of the proposed filter. Simulation results show the effectiveness of the robust filter proposed.

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“…Regarding those unmeasurable states, we have to estimate them for the application purposes such as control design and fault diagnosis. As an important topic in the control field, the state estimation of a system has been attracting considerable attention [4], [7], [9].…”

Section: Introductionmentioning

confidence: 99%

Robust state estimation and fault detection combining unknown input observer and set-membership approach

Tan

Wang

et al. 2016

2016 3rd Conference on Control and Fault-Tolerant Systems (SysTol)

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Abstract-This paper aims to propose a new robust stateestimation and fault-detection method by combining the unknown input observer (UIO) and the set-membership estimator (SME). It is known that both the SUIO and the SME can be used to estimate the states of a system. The former aims to obtain a particular value by actively decoupling the effect of unknown inputs, while the latter can obtain state-estimation sets by prediction and correction based on the set theory. Instead of particular state values, the latter can obtain state-estimation sets guaranteeing to contain system states (i.e., robust state estimation). In this paper, we propose to use the framework of the UIO to actively decouple part of unknown inputs and then further employ the set-membership estimation method to estimate state sets and detect faults. The objective of the proposed method is to reduce the conservatism of robust stateestimation sets by using the UIO to remove the contribution of part of unknown inputs to the sizes of state-estimation sets. At the end of this paper, a numerical example is used to illustrate the effectiveness and advantages of the proposed approach.

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A robust estimation approach for uncertain systems with perturbed measurements

Cited by 27 publications

References 21 publications

Descriptor state‐bounding observer design for positive Markov jump linear systems with sensor faults: Simultaneous state and faults estimation

Descriptor state‐bounding observer design for positive Markov jump linear systems with sensor faults: Simultaneous state and faults estimation

A new approach to constrained state estimation for discrete‐time linear systems with unknown inputs

Robust state estimation and fault detection combining unknown input observer and set-membership approach

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