Robust Sliding Mode Observer based Fault Estimation for Certain Class of Uncertain Nonlinear Systems

Zhang, Jian; Swain, Akshya; Nguang, Sing Kiong

doi:10.1002/asjc.987

Cited by 34 publications

(18 citation statements)

References 29 publications

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“…Then substituting (17) into the right side of (18), it can be computed out that Aer { +1 ( )} = Aer { ( )} − ( ) Aer {̇ * ( )} .…”

Section: Proof With Definition 6 and System Function (1) Let δ ( ) mentioning

confidence: 99%

“…Let Ξ{•} denote the expectation of the stochastic variable; combining with (17) and (20), one can obtain that…”

Section: Proof With Definition 6 and System Function (1) Let δ ( ) mentioning

confidence: 99%

“…Over the past decades, observer-based fault estimation [12,13] has received considerable attention both in academic research and in industrial application domains. It has made significant progress and covered a wide scope of research issues such as linear systems [14], nonlinear systems [15], time-delay systems [16], uncertain systems [17], multiagent systems [18] and fuzzy systems [19].…”

Section: Introductionmentioning

confidence: 99%

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Iterative Learning Fault Estimation Design for Nonlinear System with Random Trial Length

et al. 2017

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An iterative learning scheme-based fault estimation observer is designed for a class of nonlinear systems with randomly changed trial length. This is achieved by presenting a state observer for monitoring the system state and an iterative learning law for fault estimation in the presence of imprecise system model. An average factor is defined to deal with the lack and redundancy in tracking information caused by random trial length. Via the convergence analysis, sufficient design conditions are developed for estimation of fault signal. The observer gains and iterative learning law indexes are computed by solving the proposed conditions underconstraints. Numerical examples are presented to demonstrate the validity, the effectiveness, and the superiority of this method.

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“…Then substituting (17) into the right side of (18), it can be computed out that Aer { +1 ( )} = Aer { ( )} − ( ) Aer {̇ * ( )} .…”

Section: Proof With Definition 6 and System Function (1) Let δ ( ) mentioning

confidence: 99%

“…Let Ξ{•} denote the expectation of the stochastic variable; combining with (17) and (20), one can obtain that…”

Section: Proof With Definition 6 and System Function (1) Let δ ( ) mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Iterative Learning Fault Estimation Design for Nonlinear System with Random Trial Length

et al. 2017

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“…Next we define an augmented system with

e = ([], \begin{array}{c} center & e_{x} \\ center & e_{a} \end{array}), \overset{x}{true} = ([], \begin{array}{c} center & x \\ center & a \end{array}), \overset{M}{true} ((), \overset{true¯}{x}) = ([], \begin{array}{c} center & M_{x, 2} ((),, x, a) \\ center & 0 \\ center & M_{y, 2} ((),, x, a) \end{array}), L_{1} = ([], \begin{array}{c} center & L_{1, 1} \\ center & L_{1, 2} \end{array}), {\overset{true¯}{italicA}}_{1} = ([], \begin{array}{c} center & italicA & F_{x} \\ center & 0 & 0 \end{array})

and Ā 3 = [ C F y ]. The nonlinear term

\overset{M}{true} ((), \overset{true¯}{x})

is assumed to be Lipschitz and satisfies the following condition

(‖‖, \overset{M}{true} ((), x_{1}) - \overset{M}{true} ((), x_{2})) \leq γ (‖‖, x_{1} - x_{2})

for any vector x 1 , x 2 where, γ is the Lipschitz constant and γ > 0. Substituting into , and subtracting from the resultant yields the following error system

\overset{e}{true} = \underset{A_{o}}{\underset{true⏟}{((), {\overset{true¯}{A}}_{1} - L_{1} {(I_{p} + L_{2})}^{- 1} {\overset{true¯}{A}}_{3})}} e + L_{o} ((), \overset{M}{true} ((), \overset{true¯}{x}))

…”

Section: System Formulation and Fault Estimation Observermentioning

confidence: 99%

“…, and Zhang et al . developed FDI schemes for a class of nonlinear systems using sliding mode observers. However, those schemes are only applicable for systems where the faults enter via constant and known matrices.…”

Section: Introductionmentioning

confidence: 99%

A Robust Fault Estimation Scheme for a Class of Nonlinear Systems

Chua

Tan

Aldeen

et al. 2016

Asian Journal of Control

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This paper presents an observer‐based robust fault estimation scheme for a class of nonlinear systems. We consider the system where the fault enters both the state and output equations via unmeasurable nonlinear functions, for which currently no fault estimation scheme exists. The proposed scheme exploits the special structures and information embedded in the fault‐dependent nonlinear functions. We propose a design method to minimize the ℒ2 gain from the disturbances to the fault estimation, and provide conditions for the existence of such observers. The effectiveness of this scheme is demonstrated on a nonlinear single‐link flexible joint robot system with disturbances.

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Observer‐based Fault Estimators Using Iterative Learning Scheme for Linear Time‐delay Systems with Intermittent Faults

Zhang

Chai

et al. 2017

Asian Journal of Control

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This paper deals with the fault estimation problem for a class of linear time-delay systems with intermittent fault and measurement noise. Different from existing observer-based fault estimation schemes, in the proposed design, an iterative learning observer is constructed by using the integrated errors composed of state predictive error and tracking error in the previous iteration. First of all, Lyapunov function including the information of time delay is proposed to guarantee the convergence of system output. Subsequently, a novel fault estimation law based on iterative learning scheme is presented to estimate the size and shape of various fault signals. Upon system output convergence analysis, we proposed an optimal function to select appropriate learning gain matrixes such that tracking error converges to zero, simultaneously to ensure the robustness of the proposed iterative learning observer which is influenced by measurement noise. Note that, an improved sufficient condition for the existence of such an estimator is established in terms of the linear matrix inequality (LMI) by the Schur complements and Young relation. In addition, the results are both suit for the systems with time-varying delay and the systems with constant delay. Finally, three numerical examples are given to illustrate the effectiveness of the proposed methods and two comparability examples are provided to prove the superiority of the algorithm.

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Robust Sliding Mode Observer based Fault Estimation for Certain Class of Uncertain Nonlinear Systems

Cited by 34 publications

References 29 publications

Iterative Learning Fault Estimation Design for Nonlinear System with Random Trial Length

Iterative Learning Fault Estimation Design for Nonlinear System with Random Trial Length

A Robust Fault Estimation Scheme for a Class of Nonlinear Systems

Observer‐based Fault Estimators Using Iterative Learning Scheme for Linear Time‐delay Systems with Intermittent Faults

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