• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.7
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• pp.729-739
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• 1990

This paper deals with the fault detection problem in uncertain linear/non-linear systems having both undermodelling and noise. A robust fault detection method is presented which accounts for the effects of noise, model mismatch and nonlinearities. The basic idea is to embed the unmodelled dynamics in a stochastic process and to use the nominal model with a predetermined fixed denominator. This allows the input /output relationship to be represented as a linear function of the system parameters and also facilitate the quatification of the effect of noise, model mismatch and linearization errors on parameter estimation by the Bayesian method. Comparisons are made via simulations with traditional fault detection methods which do not account for model mismatch or linearization errors. The new method suggested in this paper is shown to have a marked improvement over traditional methods on a number of simulations, which is a consequence of the fact that the new method explicitly for the effects of undermodelling and linearization errors.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.38 no.11
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• pp.905-912
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• 1989

An adaptive control scheme is presented for uncertain systems whose uncertainties are upper-bounded by a linear combination of unknown constants and known continuous functions. The state of the closed-loop system is proven to be ultimately bounded. The proposed method modifies the method of Corless and Leitmann in the following two respects. First, the linear region of the saturation function in controller is fixed. Second, the intergration from in parameter estimator is replaced by a low pass filter form. These modifications prevent performance degradation and destabilization of the control system more effectively. The norm of the system states can be made sufficiently small by an appropriate choice of design parameters in the control law. The applicability of the proposed scheme is demonstrated in the position control of a simple pendulum via simulation.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.34.1-34
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• 2001

We deal with robust control problem for singularly perturbed linear systems with norm-bounded structured uncertainty under state constraints. We assume that the norm-bounded uncertainty is composed of repeated scalar-block and full-block forms. In the structured uncertainty, repeated scalar block forms account for uncertain physical parameter value and full-block forms may be some unknown nonlinear dynamics. In order deal with uncertainty and state constraints, we use LMI(Linear Matrix Inequality). The original problem is decomposed into two well behaved reduced order problems. Shinc two LMI problems are completely independent, each solution can be computed simultaneously and work in parallel.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.48 no.5
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• pp.59-65
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• 2011

In this paper, we present a reduced-order parameter-dependent robust $H_{\infty}$ filter design method for discrete-time singular systems with polytopic uncertainties. A BRL(bounded real lemma) for parameter-dependent singular systems is derived from a parameter-dependent Lyapunov function. On the basis of the obtained BRL, low order robust $H_{\infty}$ filter design method is presented by polytopic approach, new reduced-order method, and LMI(linear matrix inequality) technique. Finally, a numerical example is presented to illustrated the feasibility of the proposed method.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.39 no.6
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• pp.20-26
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• 2002

This paper deals with the guaranteed cost control problems for a class of discrete-time linear uncertain systems with time-varying delay. The uncertain systems under consideration depend on time-varying norm-bounded parameter uncertainties. We address the existence condition and the design method of the memoryless state feedback control law such that the closed loop system not only is quadratically stable but also guarantees an adequate level of performance for all admissible uncertainties. Through some changes of variables and Schur complement, It is shown that the sufficient condition can be rewritten as an LMI(linear matrix inequality) form in terms of all variables.

• International Journal of Control, Automation, and Systems
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• v.4 no.6
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• pp.689-696
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• 2006

This paper presents a new algorithm for the closed-loop $H_{\infty}$ composite control of weakly coupled bilinear systems with time-varying parameter uncertainties and exogenous disturbance using the successive Galerkin approximation(SGA). By using weak coupling theory, the robust $H_{\infty}$ control can be obtained from two reduced-order robust $H_{\infty}$ control problems in parallel. The $H_{\infty}$ control theory guarantees robust closed-loop performance but the resulting problem is difficult to solve for uncertain bilinear systems. In order to overcome the difficulties inherent in the $H_{\infty}$ control problem, two $H_{\infty}$ control laws are constructed in terms of the approximated solution to two independent Hamilton-Jacobi-Isaac equations using the SGA method. One of the purposes of this paper is to design a closed-loop parallel robust $H_{\infty}$ control law for the weakly coupled bilinear systems with parameter uncertainties using the SGA method. The other is to reduce the computational complexity when the SGA method is applied to the high order systems.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.40 no.4
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• pp.251-263
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• 2003

This paper presents matrix inequality conditions for Η$_2$control and Η$_2$controller design method of linear time-invariant descriptor systems with parameter uncertainties in continuous and discrete time cases, respectively. First, the necessary and sufficient condition for Η$_2$control and Η$_2$ controller design method are expressed in terms of LMI(linear matrix inequality) with no equality constraints in continuous time case. Next, the sufficient condition for Hi control and Η$_2$controller design method are proposed by matrix inequality approach in discrete time case. Based on these conditions, we develop the robust Η$_2$controller design method for parameter uncertain descriptor systems and give a numerical example in each case.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.876-881
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• 2004

Finite element model updating is an inverse problem to identify and correct uncertain modeling parameters that leads to better predictions of the dynamic behavior of a target structure. Unlike other inverse problems, the restrictions on selecting parameters all: very high since the updated model should maintains its physical meaning. That is, only the regions with modeling errors should be parameterized. And the variations of the parameters should be kept small while the updated results give acceptable correlations with experimental data. To avoid an ill-conditioned numerical problem, the number of parameters should be kept as small as possible. Thus it is very difficult to select an adequate set of updating parameters which meet all these requirements. In this paper, the importance of updating parameter selection is illustrated through a case study, and an automated procedure to guide the parameter selection is suggested based on simple observations. The effectiveness of the suggested procedure is tested with two example problems, ones is a simulated case study and the other is a real engineering structure.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.139-142
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• 1997

In this paper, a robust controller is proposed to achieve an accurate tracking for an uncertain nonlinear plant with actuator dynamics. The extent of parameter uncertainty can be quantified by using linear parameterization technique. A switching controller is proposed to guarantee the global asymptotic stability of the plant. In order to eliminate the chattering caused by the switching controller, a smoothing controller is designed using the boundary layer technique around the sliding surface and guarantees the uniform ultimate boundedness of the tracking error.

• Proceedings of the KIEE Conference
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• 2003.11b
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• pp.15-18
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• 2003

This paper presents an adaptive control scheme for parking or regulating a nonholonomic mobile robot of an unicycle type with parameter uncertainty. The kinematics can be described with Brockett's nonholonomic integrator. The control law is designed in cylindrical coordinates together with the estimation law for the uncertain parameters such that the controlled signals converge to zero while guaranteeing the boundedness of the estimation errors. The effectiveness of the proposed scheme is demonstrated using simulations.