• International Journal of Control, Automation, and Systems
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• v.6 no.3
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• pp.378-385
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• 2008

This paper aims to present a polynomial approach to the steady-state optimal filtering for delayed systems. The design of the steady-state filter involves solving one polynomial equation and one spectral factorization. The key problem in this paper is the derivation of spectral factorization for systems with delayed measurement, which is more difficult than the standard systems without delays. To get the spectral factorization, we apply the reorganized innovation approach. The calculation of spectral factorization comes down to two Riccati equations with the same dimension as the original systems.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.73-93
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• 2005

In this paper, we attempt to present a new numerical approach to solve non-linear backward stochastic differential equations. First, we present some definitions and theorems to obtain the conditions, from which we can approximate the non-linear term of the backward stochastic differential equation (BSDE) and we get a continuous piecewise linear BSDE correspond with the original BSDE. We use the relationship between backward stochastic differential equations and stochastic controls by interpreting BSDEs as some stochastic optimal control problems, to solve the approximated BSDE and we prove that the approximated solution converges to the exact solution of the original non-linear BSDE in two different cases.

• Proceedings of the KIEE Conference
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• 1997.07b
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• pp.414-417
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• 1997

We propose a decentralized $H_{\infty}$ state estimation method in the multisensor state estimation problem. The proposed method bounds the maximum energy gain from unknown external disturbances to the estimation errors in the suboptimal case. And we formulate the decentralized state estimation method in the general case of different global and local models using alternative gain equation of the $H_{\infty}$ state estimator which can calculate global state estimates from the the linear combination of local state estimates. In addition, the proposed update equation between global and local Riccati solutions can reduce unnecessary calculation burden efficiently.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.30B no.11
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• pp.93-101
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• 1993

The transfer function of vector-controlled induction motor is represented along with both unstructured and structured uncertainty such as the error of rotor time constant and current ripple. The low-pass-filter behavior of a magnetizing inductance gets rid of unstructured uncertainty in the transfer function. The robust controller to compensate variation of the transfer function is designed using simple P-I linear controllers. The coefficients of speed PI controller are determined from an overshoot and a rising time of system and the coefficients of model-following PI controller are obtained using the solution of Riccati equation of LQR control in the state space equation of the error system. Experimental results with the DSP-based model-following robust controller are shown a good robustness against the structured uncertainty of the motor.

• Wind and Structures
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• v.2 no.3
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• pp.189-200
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• 1999

In this paper, a new algorithm for active control design of structures is proposed and investigated. The algorithm preserves the decoupling property of the modal vibration equation and eliminates the spillover problem, which is the main shortcoming in the independent modal space control(IMSC) algorithm. With linear quadratic regulator(LQR) control law, the analytical solution of algebraic Riccati equation and the optimal actuator control force are obtained, and the control design procedure is significantly simplified. A numerical example for the control design of a tall building subjected to wind loads demonstrates the effectiveness of the proposed algorithm in reducing the acceleration and displacement responses of tall buildings under wind actions.

• Proceedings of the IEEK Conference
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• 2007.07a
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• pp.485-486
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• 2007

In this paper, we use Lyapunov equations and functions to consider the linear systems with perturbed system matrices. And we consider that what choice of Lyapunov function V would allow the largest perturbation and still guarantee that V is negative definite. We find that this is determined by testing for the existence of solutions to a related quadratic equation with matrix coefficients and unknowns the so-called matrix Riccati equation.

• International Journal of Aeronautical and Space Sciences
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• v.12 no.1
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• pp.43-56
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• 2011

An integrated system composed of guidance, navigation and control (GNC) system for autonomous proximity operations and the docking of two spacecraft was developed. The position maneuvers were determined through the integration of the state-dependent Riccati equation formulated from nonlinear relative motion dynamics and relative navigation using rendezvous laser vision (Lidar) and a vision sensor system. In the vision sensor system, a switch between sensors was made along the approach phase in order to provide continuously effective navigation. As an extension of the rendezvous laser vision system, an automated terminal guidance scheme based on the Clohessy-Wiltshire state transition matrix was used to formulate a "V-bar hopping approach" reference trajectory. A proximity operations strategy was then adapted from the approach strategy used with the automated transfer vehicle. The attitude maneuvers, determined from a linear quadratic Gaussian-type control including quaternion based attitude estimation using star trackers or a vision sensor system, provided precise attitude control and robustness under uncertainties in the moments of inertia and external disturbances. These functions were then integrated into an autonomous GNC system that can perform proximity operations and meet all conditions for successful docking. A six-degree of freedom simulation was used to demonstrate the effectiveness of the integrated system.

• Communications for Statistical Applications and Methods
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• v.28 no.5
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• pp.477-491
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• 2021

The Markov modulated Brownian motion is a substantial generalization of the classical Brownian Motion. On the other hand, the Markovian arrival process (MAP) is a point process whose family is dense for any stochastic point process and is used to approximate complex stochastic counting processes. In this paper, we consider a superposition of the Markov modulated Brownian motion (MMBM) and the Markovian arrival process of jumps which are distributed as the bilateral ph-type distribution, the class of which is also dense in the space of distribution functions defined on the whole real line. In the model, we assume that the inter-arrival times of the MAP depend on the underlying Markov process of the MMBM. One of the subjects of this paper is introducing how to obtain the first passage probabilities of the superposed process using a stochastic doubling algorithm designed for getting the minimal solution of a nonsymmetric algebraic Riccatti equation. The other is to provide eigenvalue and eigenvector results on the superposed process to make it possible to apply the GTH-like algorithm, which improves the accuracy of the doubling algorithm.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.60-63
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• 1996

This study deals with the nonlinear H$_{\infty}$ control problem of linear system using nonlinear weight. Generally the solvable condition of nonlinear H$_{\infty}$ control problem is given by the Hamilton Jacobi equality or inequality, but it is very difficult to solve. In this study, some constraints of nonlinear weight reduce the solvable condition to linear Riccati equation. Some examples of the control system design using nonlinear weight are shown.n.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.10
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• pp.874-881
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• 2001

By showing the existence of the ARE solution and the convergence property of the DRE solution, this paper proves that a Kalman filter for the linear system with the unobservable bias is stable. It is also shown that the Kalman filter has a biased steady state estimation error whose covariance is affected mainly by the unobservable bias. Finally, the results are illustrated through a 2nd order system example including the inertial navigation system.