• Journal of Institute of Control, Robotics and Systems
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• v.12 no.3
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• pp.201-207
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• 2006

A robust Kalman filtering method for uncertain stochastic systems is suggested by adopting a perturbation estimation process which is to reconstruct total uncertainty with respect to the nominal state transition equation. The predictor and corrector of discrete Kalman filter are reformulated with the perturbation estimator. Successively, the state and perturbation estimation error dynamics and the corresponding error covariance propagation equations are derived as well. Finally we have the recursive algorithm of Combined Kalman Filter-Perturbation Estimator (CKF). The proposed combined Kalman filter-perturbation estimator has the property of integrating innovations and the adaptation capability to system uncertainties. A numerical example is shown to demonstrate the effectiveness of the proposed scheme.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.38 no.1
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• pp.15-20
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• 2015

Control charts are generally used for process control, but the role of traditional control charts have been limited in case of a non-contaminated process. Traditional ${\bar{x}}$-s control chart has not been activated well for such a problem because of trying to control processes as center line and control limits changed by the contaminated value. This paper suggests modified ${\bar{x}}$-s control chart based on robust estimation. In this paper, we consider the trimmed mean of the sample means and the trimmed mean of the sample standard deviations. By comparing with ARL value, the responding results are decided. The comparison resultant results of traditional control chart and modified control chart are contrasted.

• Communications for Statistical Applications and Methods
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• v.11 no.1
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• pp.153-160
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• 2004

In recent years, the size of data set which we usually handle is enormous, so a lot of outliers could be included in data set. Therefore the robust procedures that automatically handle outliers become very importance issue. We consider the robust estimation problem of location parameter in the univariate case. In this paper, we propose a new method for defining robustness weights for the weighted mean based on the median distance of observations and compare its performance with several existing robust estimators by a simulation study. It turns out that the proposed method is very competitive.

• Journal of the Korean Statistical Society
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• v.20 no.2
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• pp.147-155
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• 1991

This paper treats a robust design criterion which minimizes the effects of outliers and model inadequacy, and investigates robust designs for some response surface designs. In order to develop a robust design criterion and robust design, the integrated mean squared error of *(equation omitted) over a region is utilized, where *(equation omitted). is the estimated response by the minimum bias estimation proposed by carson, Manson and Hader (1969) . According to the number of aberrant observations and their positions, the proposed criterion and designs are studied. Also further development of the proposed criterion is treated when outliers can occur in any position of a design.

• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.543-556
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• 2015

We present a survey of contributions that defined the nature and extent of robust statistics for the last 50 years. From the pioneering work of Tukey, Huber, and Hampel that focused on robust location parameter estimation, we presented various generalizations of these estimation procedures that cover a wide variety of models and data analysis methods. Among these extensions, we present linear models, clustered and dependent observations, times series data, binary and discrete data, models for spatial data, nonparametric methods, and forward search methods for outliers. We also present the current interest in robust statistics and conclude with suggestions on the possible future direction of this area for statistical science.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.130-130
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• 2000

This paper presents a robust fault diagnosis and fault tolerant control lot the actuator and sensor faults in the closed-loop systems affected by unknown inputs or disturbances. The fault diagnostic scheme is based on the residual set generation by using robust Parity space approach. Residual set is evaluated through the threshold test and then fault is isolated according to the decision logic table. Once the fault diagnosis module indicates which actuator or sensor is faulty, the fault magnitude is estimated by using the disturbance-decoupled optimal state estimation and a new additive control law is added to the nominal one to override the fault effect on the system. Simulation results show that the method has definite fault diagnosis and fault tolerant control ability against actuator and sensor faults.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.2
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• pp.95-101
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• 2001

Most robust control schemes for stabilizing the systems with uncertainties require that the systems are satisfied with matching conditions. This paper is proposed to robust control using the time delay estimation for the nonlinear single input systems not satisfying the matching conditions. Synthetic input concept is used to design the control law. The unmatched uncertainties considered in this paper are more general than other studies and they need not a special form or information about their bound. We applied the proposed method to a single pendulum with a motor system.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.5
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• pp.560-570
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• 1999

This paper formulates the suboptimal robust Kalman filtering problem into two coupled Linear Matrix Inequality (LMI) problems by applying Lyapunov theory to the augmented system which is composed of the state equation in the uncertain linear system and the estimation error dynamics. This formulations not only provide the sufficient conditions for the existence of the desired filter, but also construct the suboptimal robust Kalman filter. The proposed filter can guarantee the optimized upper bound of the estimation error variance for uncertain systems with parametric uncertainties in both the state and measurement matrices. In addition, this paper shows how the problem of finding the minimizing solution subject to Quadratic Matrix Inequality (QMI), which cannot be easily transformed into LMI using the usual Schur complement formula, can be successfully modified into a generic LMI problem.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.12
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• pp.1833-1844
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• 2004

A controller is proposed for the robust backstepping control of a class of nonlinear multiple-input multiple-output (MIMO) systems which can be converted to a strict feedback form. The proposed robust backstepping control scheme follows a systematic procedure for the design of control laws and uses time delay estimation (TDE) to estimate the uncertainties such as parameter variations, unknown disturbances, and unmodeled dynamics, etc. The proposed controller can be also applied to nonlinear MIMO systems with unmatched uncertainties. Stability analysis of the closed-loop system which contains the plant and the proposed controller is also studied and hereby a sufficient stability condition for the closed-loop system is proposed. The simulation results show that the control scheme works well with uncertainties and the proposed stability condition is valid. The controller is experimentally verified on a single-link flexible arm to show the effectiveness of the proposed scheme in the complicated systems with uncertainties.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.8
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• pp.923-931
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• 1999

In this paper, a modeling and a robust time-delay control for the reclaimer are investigated. Supplying the same amount of a raw material throughout the reclamation process from the raw yard to a sinter plant is important to keep the quality of the molten steel uniform in blast furnaces. As the actual parameter values of the reclaimer are not available, the boom rotational dynamics are modeled as a second order differential equation with unknown coefficients. The unknown parameters in the nominal model are estimated using a recursive estimation method. Another important factor in the control design of the reclaimer is the large time-delay in output measurement. Assuming a multiplicative uncertainty, that accounts for both the unstructured uncertainty neglected in the modeling and the structured uncertainty contained in the parameter estimation, a robust Smith predictor is designed. A robust stability criterion for the multiplicative uncertainty is also derived. Following the work of Goodwin et al. [4], a quantifying procedure of the multiplicative uncertainty bound, through experiments , is described. Experimental and simulation results are provided.