• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.83-92
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• 2012

In this paper, a generalized Shannon-McMillan theorem for the nonhomogeneous Markov chains indexed by an infinite tree which has a uniformly bounded degree is discussed by constructing a nonnegative martingale and analytical methods. As corollaries, some Shannon-Mcmillan theorems for the nonhomogeneous Markov chains indexed by a homogeneous tree and the nonhomogeneous Markov chain are obtained. Some results which have been obtained are extended.

• 대한수학회보
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• 제59권5호
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• pp.1305-1315
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• 2022

Let u be a function on a connected finite graph G = (V, E). We consider the mean field equation (1) $-{\Delta}u={\rho}\({\frac{he^u}{\int_Vhe^ud{\mu}}}-{\frac{1}{{\mid}V{\mid}}}\),$ where ∆ is 𝜇-Laplacian on the graph, 𝜌 ∈ ℝ\{0}, h : V → ℝ⁺ is a function satisfying min_x∈V h(x) > 0. Following Sun and Wang [15], we use the method of Brouwer degree to prove the existence of solutions to the mean field equation (1). Firstly, we prove the compactness result and conclude that every solution to the equation (1) is uniformly bounded. Then the Brouwer degree can be well defined. Secondly, we calculate the Brouwer degree for the equation (1), say $$d_{{\rho},h}=\{{-1,\;{\rho}>0, \atop 1,\;{\rho}<0.}$$ Consequently, the equation (1) has at least one solution due to the Brouwer degree d_𝜌,h ≠ 0.

• Journal of Applied and Pure Mathematics
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• 제4권5_6호
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• pp.269-286
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• 2022

In this article we exhibit univariate and multivariate quantitative approximation by Kantorovich-Choquet type quasi-interpolation neural network operators with respect to supremum norm. This is done with rates using the first univariate and multivariate moduli of continuity. We approximate continuous and bounded functions on ℝ^N , N ∈ ℕ. When they are also uniformly continuous we have pointwise and uniform convergences. Our activation functions are induced by the arctangent, algebraic, Gudermannian and generalized symmetrical sigmoid functions.

• 대한수학회보
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• 제36권1호
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• pp.147-159
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• 1999

Tabanov investigated the global symmetric perturbation of the integrable billiard mapping in the ellipse [3]. He showed the nonintegrability of the Birkhoff billiard in the perturbed domain by proving that the principal separatrices splitting angle is not zero.In this paper, using the exact separatrix map of an one-degree-of freedom Hamiltoniam system with time periodic perturbation, we show the existence the stochastic layer including the uniformly hyperbolic invariant set which implies the nonintegrability near the separatrices of a Birkhoff's billiard in the domain bounded by $C^2$ convex simple curve constructed by the generic global perturbation of the ellipse.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1992년도 하계학술대회 논문집 A
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• pp.371-373
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• 1992

This note proposes a novel robust adaptive control algorithm for systems with unknown disturbances by introducing an additional term in the control input. This additional term is easily implementable by estimating the upper bound of the unknown disturbances. By this term, the output error can be made to be uniformly ultimately bounded in a desired region via Lyapunov second stability theorem when the relative degree of system is one.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1996년도 추계학술대회 논문집 학회본부
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• pp.58-61
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• 1996

For a class of single-input single-output continuous-time nonlinear systems, a multilayer neural network-based controller that feedback-linearizes the system is presented. Control action is used to achieve tracking performance for a state-feedback linearizable but unknown nonlinear system. The multilayer neural network(NN) is used to approximate nonlinear continuous function to any desired degree of accuracy. The weight-update rule of multilayer neural network is derived to satisfy Lyapunov stability. It is shown that all the signals in the closed-loop system are uniformly bounded. Initialization of the network weights is straightforward.

• 전기전자학회논문지
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• 제9권1호
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• pp.72-78
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• 2005

본 논문은 단일입력 단일출력 비선형 계통에 대해서 강인한 출력궤환 제어기를 제시한다. 이전의 출력궤환 비선형 제어기가 모두 동적인 관측기 기반으로 설계된 반면 본 논문에서는 출력의 과거값들만을 이용하여 상태변수를 추정하는 새로운 방식을 제안하고 이를 후방차분 상태추정기라 명했다. 실제 상태변수값과 추정치와의 오차를 보상하기 위해서 제어입력에 강인제어항을 추가하였고 그것의 이득을 자동으로 조정하는 적응 알고리듬을 채택했다. 전체 폐루프 시스템은 출력 추종 오차가 점근적으로 안정하도록 그리고 모든 신호가 유계이도록 제어입력과 적응법칙이 설계된다. 제시된 제어기를 역진자 계통에 적용한 모의실험을 통해서 성능을 검증하였다.