• International Journal of Control, Automation, and Systems
• /
• 제3권3호
• /
• pp.419-429
• /
• 2005

This paper considers eigenstructure assignment in high-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related with a type of so-called high-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically very simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effect of the proposed approaches.

• 대한수학회보
• /
• 제54권4호
• /
• pp.1141-1158
• /
• 2017

In this paper, we study the value distribution of the derivative of a Dirichlet L-function $L^{\prime}(s,{\chi})$ at the a-points ${\rho}_{a,{\chi}}={\beta}_{a,{\chi}}+i{\gamma}_{a,{\chi}}$ of $L^{\prime}(s,{\chi})$. We give an asymptotic formula for the sum $${\sum_{{\rho}_{a,{\chi}};0<{\gamma}_{a,{\chi}}{\leq}T}\;L^{\prime}({\rho}_{a,{\chi}},{\chi})X^{{\rho}_{a,{\chi}}}\;as\;T{\rightarrow}{\infty}$$, where X is a fixed positive number and ${\chi}$ is a primitive character mod q. This work continues the investigations of Fujii [4-6], $Garunk{\check{s}}tis$ & Steuding [8] and the authors [12].

• Journal of applied mathematics & informatics
• /
• 제30권1_2호
• /
• pp.305-320
• /
• 2012

In this paper, we study a class of integral boundary value problems for fractional differential equations. By using some fixed point theorems, the results of existence of at least three positive solutions for the boundary value problems are obtained.

• 충청수학회지
• /
• 제35권1호
• /
• pp.53-67
• /
• 2022

Nonlinear system of initial value problems involving R-L fractional derivative is studied. Monotone iterative technique coupled with lower and upper solutions is developed for the problem. It is successfully applied to study qualitative properties of solutions of nonlinear system of initial value problem when the function on the right hand side is nondecreasing.

• 대한기계학회논문집A
• /
• 제39권7호
• /
• pp.673-679
• /
• 2015

본 연구는 비지배 분류 유전알고리즘(NSGA-II)을 이용하여 흐트러진 쿼드콥터의 자세를 빠르게 회복 할 수 있는 최적화된 PID(Proportional-Integral-Derivative) 이득 값을 얻고자 하였다. PID 제어에 앞서 로터가 4 개로 이루어진 쿼드콥터의 간격을 전산유체해석을 통해 정의하였으며, 정의된 쿼드콥터 모델을 통하여 PID 제어 알고리즘을 생성하였다. 반응표면 모델을 생성하기 위해 실험계획법의 하나인 D-최적계획법 이용하여 실험점을 배치 시킨 후 반응표면모델을 생성하였다. Roll 과 Altitude 의 두 값을 동시에 만족할 수 있는 PID 의 이득 값을 NSGA-II 를 통해 쿼드콥터의 최단 시간의 자세제어를 할 수 있는 최적의 이득 값을 얻을 수 있었다.

• Journal of applied mathematics & informatics
• /
• 제34권3_4호
• /
• pp.193-206
• /
• 2016

In this paper, we study boundary value problems for fractional integrodifferential equations involving Caputo derivative in Banach spaces. A generalized singular type Gronwall inequality is given to obtain an important priori bounds. Some sufficient conditions for the existence solutions are established by virtue of fractional calculus and fixed point method under some mild conditions.

• 대한수학회보
• /
• 제50권4호
• /
• pp.1157-1171
• /
• 2013

In this paper, by using the $q$-difference analogue of lemma on the logarithmic derivative lemma to re-establish some estimates of Nevanlinna characteristics of $f(qz)$, we deal with the value distribution and uniqueness of certain types of $q$-difference polynomials.

• Journal of applied mathematics & informatics
• /
• 제30권1_2호
• /
• pp.147-160
• /
• 2012

In this paper, we establish some sufficient conditions for the existence of positive solutions for a class of multi-point boundary value problem for fractional functional differential equations involving the Caputo fractional derivative. Our results are based on two fixed point theorems. Two examples are also provided to illustrate our main results.

• Journal of applied mathematics & informatics
• /
• 제30권5_6호
• /
• pp.773-785
• /
• 2012

In this paper, we establish sufficient conditions for the existence and uniqueness of solutions to a general class of three-point boundary value problems for a coupled system of nonlinear fractional differential equations. The differential operator is taken in the Caputo fractional derivatives. By using Green's function, we transform the derivative systems into equivalent integral systems. The existence is based on Schauder fixed point theorem and contraction mapping principle. Finally, some examples are given to show the applicability of our results.

• Journal of applied mathematics & informatics
• /
• 제35권3_4호
• /
• pp.277-302
• /
• 2017

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of reaction-diffusion type of third order Ordinary Differential Equations (ODEs). The SPBVP is reduced into a weakly coupled system of one first order and one second order ODEs, one without the parameter and the other with the parameter ${\varepsilon}$ multiplying the highest derivative subject to suitable initial and boundary conditions, respectively. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. The weakly coupled system is decoupled by replacing one of the unknowns by its zero-order asymptotic expansion. Finally the present numerical method is applied to the decoupled system. In order to get a numerical solution for the derivative of the solution, the domain is divided into three regions namely two inner regions and one outer region. The Shooting method is applied to two inner regions whereas for the outer region, standard finite difference (FD) scheme is applied. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing. The main advantage of this method is that due to decoupling the system, the computation time is very much reduced.