• Korean Journal of Mathematics
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• 제17권4호
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• pp.419-428
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• 2009

We show the existence of at least one nontrivial solution of the homogeneous mixed type nonlinear elliptic problem. Here mixed type nonlinearity means that the nonlinear part contain the jumping nonlinearity and the critical growth nonlinearity. We first investigate the sub-level sets of the corresponding functional in the Soboles space and the linking inequalities of the functional on the sub-level sets. We next investigate that the functional I satisfies the mountain pass geometry in the critical point theory. We obtain the result by the mountain pass method, the critical point theory and variational method.

• International Journal of Aeronautical and Space Sciences
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• 제17권4호
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• pp.593-603
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• 2016

This paper presents the development of linear quadratic regulation and output tracking algorithms using output feedback when both the measurement and performance output equations contain direct feedthrough terms. Although all physical systems can be modeled without direct feedthrough, there are still many situations where system models with direct feedthrough are important. For this situation, we modify previous work on the same topic for systems without direct feedthrough. It is shown that for the regulation problem, the optimal output feedback gain for a direct feedthrough case can be directly obtained, via a transformation, from the approach used for systems without direct feedthrough. However, for the tracking problem, a new set of coupled matrix equations for determining the optimal output feedback gain is derived from the necessary conditions for minimizing the cost function. The effectiveness of the developed algorithms is demonstrated using numerical examples.

• 한국항공우주학회지
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• 제45권11호
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• pp.967-974
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• 2017

반작용휠은 저속구간에서 마찰로 인해서 비선형 토크 응답을 보인다. 따라서 이 구간에서는 위성의 정밀한 자세제어를 달성하기 어렵다. 기존 연구들은 마찰력 보상이나 디더명령을 인가하는 방법을 사용하여 본 문제를 해결하려 하였다. 하지만 마찰력 모델링의 어려움이나 휠속도의 빈번한 영점 교차 때문에, 이러한 방법을 실제 위성 자세제어에 적용하기에는 어려움이 있다. 이를 해결하기 위해서, 자세오차에 따라서 자세제어기의 이득값을 조절하는 방법을 제안한다.

• International Journal of Aeronautical and Space Sciences
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• 제7권2호
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• pp.14-25
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• 2006

This paper is focused on designing an implementable control law to perform spacecraft various missions using momentum exchange devices such as reaction wheels(RWs) and control moment gyros(CMGs). A compact equation of motion of a spacecraft installed with various momentum exchange devices is derived in this paper. A hybrid control law is proposed for precision attitude control of agile spacecraft. The control law proposed in this paper allocates control torque to the CMGs and the RWs adequately to satisfy the precision attitude control and large angle maneuver simultaneously. The saturation problem of reaction wheels and the singularity problem of control moment gyros are considered. The problems are successfully resolved by using the proposed hybrid closed loop control law. Finally, the proposed hybrid control law is demonstrated by numerical simulations.

• 한국항공우주학회지
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• 제35권7호
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• pp.586-591
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• 2007

예조건화 오일러 방정식의 수렴특성에 미치는 계산 오차의 영향을 해석하였다. 다양한 마하수의 원형 턱이 있는 이차원 관내 유동을 계산하였다. 마하수가 감소함에 따라 차분오차는 증가하는데, 에너지 방정식의 계산 오차는 다른 방정식의 계산 오차보다 빠르게 증가하는 것으로 나타났다. 그리고 예조건 행렬의 역행렬을 곱하여 변형된 지배방정식 형태를 이용하면 계산 오차 문제를 완화할 수 있음을 보였다

• International Journal of Aeronautical and Space Sciences
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• 제18권4호
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• pp.767-779
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• 2017

Automated mission planning for unmanned aerial vehicles (UAVs) is difficult because of the propagation of several sources of error into the solution, as for any large scale autonomous system. To ensure reliable system performance, we quantify all sources of error and their propagation through a mission planner for operation of UAVs in an obstacle rich environment we developed in prior work. In this sequel to that work, we show that the mission planner developed before can be made robust to errors arising from the mapping, sensing, actuation, and environmental disturbances through creating systematic buffers around obstacles using the calculations of uncertainty propagation. This robustness makes the mission planner truly autonomous and scalable to many UAVs without human intervention. We illustrate with simulation results for trajectory generation of multiple UAVs in a surveillance problem in an urban environment while optimizing for either maximal flight time or minimal fuel consumption. Our solution methods are suitable for any well-mapped region, and the final collision free paths are obtained through offline sub-optimal solution of an mTSP (multiple traveling salesman problem).

• 한국우주과학회:학술대회논문집(한국우주과학회보)
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• 한국우주과학회 1992년도 한국우주과학회보 제1권1호
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• pp.11-11
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• 1992

The most celebrated problem in artificial satellite theory is undoubtedly the critical inclination problem. The KITSAT-1 satellite launched by Arian 42P from Guiana in August 11, 1992 has orbital inclination close to the critical value cos-1(1/rs). In that case, there is a singularity in some perturbation terms and therefore perigee will be fixed because do/dt is equals to zero. But actually the long periodic behaviour in argument of perigee, u is affected by luni-solar gravity andrelativistic effect, etc. Luni-solar gravity induces periodic perturbations in allorbital elements except the semi-major axis, and secular variations in 0, u and M.We have obtained nodal rate and inclination variations in case of the KITSAT-1.In this paper, we will also show the geopotential perturbations in 0, M of the Satellite in CIUding J2, J3, J4, J22 terms.

• 대한수학회지
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• 제54권2호
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• pp.697-711
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• 2017

Let X, Y be real normed vector spaces. We exhibit all the solutions $f:X{\rightarrow}Y$ of the functional equation f(rx + sy) + rsf(x - y) = rf(x) + sf(y) for all $x,y{\in}X$, where r, s are nonzero real numbers satisfying r + s = 1. In particular, if Y is a Banach space, we investigate the Hyers-Ulam stability problem of the equation. We also investigate the Hyers-Ulam stability problem on a restricted domain of the following form ${\Omega}{\cap}\{(x,y){\in}X^2:{\parallel}x{\parallel}+{\parallel}y{\parallel}{\geq}d\}$, where ${\Omega}$ is a rotation of $H{\times}H{\subset}X^2$ and $H^c$ is of the first category. As a consequence, we obtain a measure zero Hyers-Ulam stability of the above equation when $f:\mathbb{R}{\rightarrow}Y$.

• Journal of Astronomy and Space Sciences
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• 제19권2호
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• pp.107-122
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• 2002

Multi-body spacecraft attitude and configuration control formulations based on the use of collaborative control theory are considered. The control formulations are based on two-player, nonzero-sum, differential game theory applied using a Nash strategy. It is desired that the control laws allow different components of the multi-body system to perform different tasks. For example, it may be desired that one body points toward a fixed star while another body in the system slews to track another satellite. Although similar to the linear quadratic regulator formulation, the collaborative control formulation contains a number of additional design parameters because the problem is formulated as two control problems coupled together. The use of the freedom of the partitioning of the total problem into two coupled control problems and the selection of the elements of the cross-coupling matrices are specific problems ad-dressed in this paper. Examples are used to show that significant improvement in performance, as measured by realistic criteria, of collaborative control over conventional linear quadratic regulator control can be achieved by using proposed design guidelines.

• Journal of Astronomy and Space Sciences
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• 제25권3호
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• pp.255-266
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• 2008

The current paper presents application of a new analytic solution in general relative motion to spacecraft formation flying in an elliptic orbit. The calculus of variations is used to analytically find optimal trajectories and controls for the given problem. The inverse of the fundamental matrix associated with the dynamic equations is not required for the solution in the current study. It is verified that the optimal thrust vector is a function of the fundamental matrix of the given state equations. The cost function and the state vector during the reconfiguration can be analytically obtained as well. The results predict the form of optimal solutions in advance without having to solve the problem. Numerical simulation shows the brevity and the accuracy of the general analytic solutions developed in the current paper.