• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.175-181
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• 2000

The purpose of this to measure, with explicit constants as small as possible, a priori error bounds for approximation by picewise polynomials. These constants play an important role in the numerical verification method of solutions for obstacle problems by using finite element methods .

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.64-69
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• 1993

In this paper we present the performance bounds of the optimal FIR filter in continuous time systems with modeling uncertainty. The performance measure bounds are calculated from the estimation error covariance bounds of the optimal FIR filter and the suboptimal FIR filter. Performance error bounds range are expressed by the upper bounds on the estimation error covariance difference between the real and nominal values in case of the systems with noise uncertainty or model uncertainty. The performance bounds of the systems are derived on the assumption that the system uncertainty and the estimation error covariance are imperfectly known a priori. The estimation error bounds of the optimal FIR filter is compared with those of the Kalman filter via a numerical example applied to the estimation of the motion of an aircraft carrier at sea, which shows the former has better performances than the latter.

• Journal of Institute of Control, Robotics and Systems
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• v.1 no.1
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• pp.20-24
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• 1995

In this paper we analyze the performance bounds of the optimal FIR filter in continuous time systems with modeling uncertainty. The performance bounds are presented by the estimation error convariance and they are here expressed by the upper bounds of the difference of the estimation error covariance between the real and nominal values in case of the system with model uncertainties whose upper bounds are imperfrctly known a priori. The performance bounds of the optimal FIR filter are compared with those of the Kalman filter via a numerical example applied to the estimation of the motion of an aircraft carrier at sea, which shows the former has better performances than the latter.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.399-416
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• 2013

The semilocal convergence of a third order iterative method used for solving nonlinear operator equations in Banach spaces is established by using recurrence relations under the assumption that the second Fr´echet derivative of the involved operator satisfies the ${\omega}$-continuity condition given by $||F^{\prime\prime}(x)-F^{\prime\prime}(y)||{\leq}{\omega}(||x-y||)$, $x,y{\in}{\Omega}$, where, ${\omega}(x)$ is a nondecreasing continuous real function for x > 0, such that ${\omega}(0){\geq}0$. This condition is milder than the usual Lipschitz/H$\ddot{o}$lder continuity condition on $F^{\prime\prime}$. A family of recurrence relations based on two constants depending on the involved operator is derived. An existence-uniqueness theorem is established to show that the R-order convergence of the method is (2+$p$), where $p{\in}(0,1]$. A priori error bounds for the method are also derived. Two numerical examples are worked out to demonstrate the efficacy of our approach and comparisons are elucidated with a known result.

• Proceedings of the KIEE Conference
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• 2001.07d
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• pp.2320-2322
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• 2001

This paper describes the design of a robust adaptive neural-net(NN) observer for uncertain nonlinear dynamical system. The Lyapunov synthesis approach is used to guarantee a uniform ultimate boundedness property of the state estimation error, as well as of all other signals in the closed-loop system. Especially, for reducing the dynamic oder of the observer, we propose a new method in which no strictly positive real(SPR) condition is needed with on-line estimation of weights of the NNs. No a priori knowledge of an upper bounds on the uncertain terms is required. The theoretical results are illustrated through a simulation example.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.12
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• pp.1670-1679
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• 1995

In this paper, an optimal variable structure controller with a multilayer neural inverse identifier is proposed. A multilayer neural network with error back propagation learning algorithm is used for construction the neural inverse identifier which is an observer of the external disturbances and the parameter variations of the system. The variable structure controller with the multilayer neural inverse identifier not only needs a small part of a priori knowledge of the bounds of external disturbances and parameter variations but also alleviates the chattering magnitude of the control input. Also, an optimal sliding line is designed by the optimal linear regulator technique and an integrator is introduced for solving the reaching phase problem. Computer simulation results show that the proposed approach gives the effective control results by reducing the chattering magnitude of control input.