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임윤식,이명규,안두수 成均館大學校 科學技術硏究所 1997 論文集 Vol.48 No.1
The orthogonal function has been widely employed to solve the control problems, whereas its application to solve the LQG prroblem has hardely been used. Chang & Lee suggested direct application of orthogonal function to Riccatti equation and covariance matrix Riccatti equation. But in this method, the dimension of the integration operational matrix enlarge as the order of the system or the number of expansion term increases. In this paper, in order to solving Riccatti equation and covariance matrix Riccatti equation, TPBVP and matrix fraction method are used. LQG controller is designed by applying block pulse function to this method.
임윤식,안비오,안두수 成均館大學校 科學技術硏究所 1996 論文集 Vol.47 No.1
This paper presents a method to design Kalman filter on continuous stochastic dynamical systems via BPF(block pulse functions). When we design Kalman filter , minimum error variance matrix is appeared as a form of nonlinear matrix differential equations. Such equations are very difficult to obtain the solutions. Therefore, in this paper, we simply obtain the solutions of nonlinear matrix differential equations from recursive algebraic equations using BPF. We believe that the presented method is very attractive and proper to the states estimation on continuous stochastic dynamical systems
블럭펄스 함수를 이용한 비선형 확률 시스템의 제어기 설계
임윤식,정제욱,안두수 成均館大學校 科學技術硏究所 1997 論文集 Vol.48 No.2
The purpose of this paper is to indicate how the available thoery of optimal control and estimation for the so called linear-quadratic-Gaussian(LQG) problem provides such a unified design procedure for the nonlinear system. In particular, we wish to stress the advantages of this method from the viewpoint of ease of computation, since the theory provides us with equation that can be readily solved by modern digital computers. This algorithm minimizes the effect for the initial error by adaptive analysis method via BPF and the each sampling interval of the nonlinear system is linearized using BPF's coefficients, the convergence of the estimated states can be improved.
월쉬 단일항 전개를 이용한 비선형 확률 시스템의 상태추정
林潤植(Yun-Sik Lim) 대한전기학회 2008 전기학회논문지 P Vol.57 No.2
The EKF(Extended Kalman filter) method which is the state estimation algorithm of nonlinear stochastic system depends on the initial error and the estimated states. Therefore, the divergence of the estimated state can be caused if the initial values of the estimated states are not chosen as approximate real state values. In this paper, the demerit of the existing EKF method is improved using the EKF algorithm transformated by STWS(Single Term Walsh Series). This method linearizes each sampling interval of continous-time system through the derivation of an algebraic iterative equation without discretizing continuous system by the characteristic of STWS, the convergence of the estimated states can be improved. The validity of the proposed method is checked through comparison with the existing EKF method in simulation.