Iterative Learning Control of an Electrostatic Microbridge Actuator With Polytopic Uncertainty Models

Cichy, Błażej; Hladowski, Lukasz; Gałkowski, Krzysztof; Rauh, Andreas; Aschemann, Harald

doi:10.1109/tcst.2015.2394236

Cited by 11 publications

(8 citation statements)

References 13 publications

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“…Furthermore, the corresponding corollaries of the main results are provided for the non-differentiable time-delay case. Let us consider the nominal form of the closed-loop system (5) as…”

Section: Resultsmentioning

confidence: 99%

“…Therefore, we need to design the mixed H 1 and passivity-based reliable controller for the uncertain continuous time-varying delay systems in the presence of unknown actuator failures. For this purpose, we consider the following theorem for the uncertain closed-loop system (5). ; m/, l .l D 5; 6/, such that the following LMIs hold:…”

Section: Remark 32mentioning

confidence: 99%

“…Cichy et al. proposed a robust control design for an electrostatic micro‐bridge actuator by using an iterative learning control approach based on so‐called wave repetitive processes. Specifically, in most of the realistic systems, the existence of the uncertainty needs not to be always deterministic, but unfortunately, only a few results considered the uncertainty in random manner .…”

Section: Introductionmentioning

confidence: 99%

“…Based on Lyapunov function approach, the robust stabilization problem for a class of multi-agent systems with discontinuous observations and time-varying parameter uncertainties is studied in [4]. Cichy et al [5] proposed a robust control design for an electrostatic micro-bridge actuator by using an iterative learning control approach based on so-called wave repetitive processes. Specifically, in most of the realistic systems, the existence of the uncertainty needs not to be always deterministic, but unfortunately, only a few results considered the uncertainty in random manner [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

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Delay‐dependent fault‐tolerant controller for time‐delay systems with randomly occurring uncertainties

Sakthivel

Selvaraj

et al. 2017

Intl J Robust & Nonlinear

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Summary This paper addresses the passivity‐based H∞ control problem for a class of time‐varying delay systems subject to nonlinear actuator faults and randomly occurring uncertainties via fault‐tolerant controller. More precisely, the uncertainties are described in terms of stochastic variables, which satisfies Bernoulli distribution, and the existence of actuator faults are assumed not only linear but also nonlinear, which is a more general one. The main objective of this paper is to design a state feedback‐reliable controller such that the resulting closed‐loop time‐delay system is stochastically stable under a prescribed mixed H∞ and passivity performance level γ>0 in the presence of all admissible uncertainties and actuator faults. Based on Lyapunov stability method and some integral inequality techniques, a new set of sufficient conditions is obtained in terms of linear matrix inequality (LMI) constraints to ensure the asymptotic stability of the considered system. Moreover, the control design parameters can be computed by solving a set of LMI constraints. Finally, two examples including a quarter‐car model are provided to show the efficiency and usefulness of the proposed control scheme. Copyright © 2017 John Wiley & Sons, Ltd.

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“…Furthermore, the corresponding corollaries of the main results are provided for the non-differentiable time-delay case. Let us consider the nominal form of the closed-loop system (5) as…”

Section: Resultsmentioning

confidence: 99%

Section: Remark 32mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Delay‐dependent fault‐tolerant controller for time‐delay systems with randomly occurring uncertainties

Sakthivel

Selvaraj

et al. 2017

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…The essential difference of n-D systems from the classical (1-D) ones is that an information propagates in more than one independent directions. The class of n-D systems includes, e. g., repetitive processes [25,27], spatially invariant systems [10,11], positive n-D systems [20], or n-D systems of the fractional order [21], and iterative learning control [10,11,12]. The n-D systems approach is applied in control of ladder circuits [32,31], and in modelling of complex systems [5,6].…”

Section: Introductionmentioning

confidence: 99%

A fast numerical test of multivariate polynomial positiveness with applications

Augusta¹,

Augustová²

2018

Kybernetika

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A fast numerical test of multivariate polynomial positiveness with applications Kybernetika, Vol. 54 (2018) A FAST NUMERICAL TEST OF MULTIVARIATE POLYNOMIAL POSITIVENESS WITH APPLICATIONS Petr Augusta and Petra AugustováThe paper presents a simple method to check a positiveness of symmetric multivariate polynomials on the unit multi-circle. The method is based on the sampling polynomials using the fast Fourier transform. The algorithm is described and its possible applications are proposed. One of the aims of the paper is to show that presented algorithm is significantly faster than commonly used method based on the semi-definite programming expression.

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Fault Detection for Discrete‐Time Uncertain Systems with Polytopic Uncertainties: A Markov Approach

Wang

Gao

Miao

et al. 2018

Asian Journal of Control

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In this paper, the fault detection problem for a class of discrete-time polytopic uncertain systems is studied. Different from the traditional methods dealing with polytopic uncertainties, not only its values but also the probability distributions are considered. First of all, the above process about polytopic uncertainty is described by applying a Markov process. Then, the original system with polytopic uncertainties becomes to be a Markovian jump system (MJS) without any uncertainty. Accordingly, the fault detection problem is transformed to be a similar one but considered for an MJS. Particularly, the fault detection and isolation (FDI) filter is constructed to be mode-dependent and also said to be polytope-dependent. Since more information of uncertainty is considered, it is claimed that the obtained results are less conservative. Finally, a practical example is used to show the effectiveness and superiority of the proposed methods.

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Iterative Learning Control of an Electrostatic Microbridge Actuator With Polytopic Uncertainty Models

Cited by 11 publications

References 13 publications

Delay‐dependent fault‐tolerant controller for time‐delay systems with randomly occurring uncertainties

Delay‐dependent fault‐tolerant controller for time‐delay systems with randomly occurring uncertainties

A fast numerical test of multivariate polynomial positiveness with applications

Fault Detection for Discrete‐Time Uncertain Systems with Polytopic Uncertainties: A Markov Approach

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