• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1990년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 26-27 Oct. 1990
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• pp.1060-1065
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• 1990

In general it is difficult to determine a Liapunov function for a given asymptotically stable, nonlinear differential equations system. But, in the system with control inputs, it is feasible to make a given positive function, except for a small area, globally satisfy the conditions of the Liapunov function for the system. We call such a positive function a Liapunov-like function, and propose a method of nonlinear optimal regulator using this Liapunov-like function. We also use the periodic Liapuitov-like friction that suits the system whose equilibrium points exist periodically. The relationship between the Liapunov function and cost function which this nonlinear regulator minimizes is considered using inverse optimal method.

• 대한수학회지
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• 제36권4호
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• pp.757-771
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• 1999

We consider a system of functional differential equations x'(t)=F(t, $x_t$) and obtain conditions on a Liapunov functional and a Liapunov function to ensure the instability of the zero solution.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2004년도 ICCAS
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• pp.1623-1628
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• 2004

In the 3-dimensional cyclic Lotka-Volterra equations, we show the solution on the invariant hyperplane. In addition, we show the existence of the invariant hyperplane by the center manifold theorem under the some conditions. With this result, we can lead the hyperplane of the n-dimensional cyclic Lotka-Volterra equaions. In other section, we study the 3- or 4-dimensional Hamiltonian Lotka-Volterra equations which satisfy the Jacobi identity. We analyze the solution of the Hamiltonian Lotka- Volterra equations with the functions called the split Liapunov functions by [4], [5] since they provide the Liapunov functions for each region separated by the invariant hyperplane. In the cyclic Lotka-Volterra equations, the role of the Liapunov functions is the same in the odd and even dimension. However, in the Hamiltonian Lotka-Volterra equations, we can show the difference of the role of the Liapunov function between the odd and the even dimension by the numerical calculation. In this paper, we regard the invariant hyperplane as the important item to analyze the motion of Lotka-Volterra equations and occur the chaotic orbit. Furtheremore, an example of the asymptoticaly stable and stable solution of the 3-dimensional cyclic Lotka-Volterra equations, 3- and 4-dimensional Hamiltonian equations are shown.

• 대한수학회보
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• 제34권3호
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• pp.371-383
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• 1997

In recent years M. Pinto introduced the notion of h-stability. He extended the study of exponential stability to a variety of reasonable systems called h-systems. We investigate h-stability for the nonlinear differential systems using the notions of $t_\infty$-similarity and Liapunov functions.

• 한국통신학회논문지
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• 제9권2호
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• pp.77-84
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• 1984

本論文에서는 二次元인 순회형 디지틀 필터의 安定度判別에 관한 한 方法을 提案하였다. 二次元系에서의 安定度에 관한 Liapunov의 定理를 기초로 하여 二次元傳達函數로부터 그의 狀態空間式을 유도하여 系行列에 Liapunov의 定理를 적용시켰다. 그 결과 종래의 像에 의하여 구한 결과와 일치하였으며 그의 계산양도 줄어들었음을 알 수 있다.

• 대한수학회지
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• 제35권1호
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• pp.135-148
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• 1998

We propose the new controls constructed via the second or direct method of Liapunov to solve the collision avoidance control problems for moving objects and a robot arm in the plane. We also explicate the controlling effect by the simulations.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1992년도 하계학술대회 논문집 A
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• pp.374-376
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• 1992

This paper proposes a stable locomotion control rule for non-holonomic mobile robot. Stability of the rule is proved through the use of a Liapunov function. We have two controller for locomotion control. One is velocity controller, the other is position controller. The proposed controller is position controller whose input to robot are a reference posture and reference velocities. The major objective of this paper is to propose a control rule to find a reasonable velocity command under a assumption which is velocity controller is ideal controller.

• Journal of applied mathematics & informatics
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• 제6권3호
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• pp.835-850
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• 1999

The present paper deals with the problem of nonselective harvesting in a partly infected prey and predator system in which both the susceptible prey and the predator follow the law of logistic growth and some preys avoid predation by hiding. The dynamical behaviour of the system has been studied in both the local and global sense. The optimal policy of exploitation has been derived by using Pontraygin's maximal principle. Numerical analysis and computer simulation of the results have been performed to investigate the golbal properties of the system.

• Smart Structures and Systems
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• 제15권5호
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• pp.1177-1202
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• 2015

The present paper is concerned with the optimal control and/or design of symmetric and antisymmetric composite laminate with two piezoelectric layers bonded to the opposite surfaces of the laminate, and placed symmetrically with respect to the middle plane. For the optimal control problem, Liapunov-Bellman theory is used to minimize the dynamic response of the laminate. The dynamic response of the laminate comprises a weight sum of the control objective (the total vibrational energy) and a penalty functional including the control force. Simultaneously with the active control, thicknesses and the orientation angles of layers are taken as design variables to achieve optimum design. The formulation is based on various plate theories for various boundary conditions. Explicit solutions for the control function and controlled deflections are obtained in forms of double series. Numerical results are given to demonstrate the effectiveness of the proposed control and design mechanism, and to investigate the effects of various laminate parameters on the control and design process.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2001년도 하계종합학술대회 논문집(5)
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• pp.131-134
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• 2001

This paper proposes a stable control rule for nonlinear unicycle-type mobile robot. The control method uses a local error coordinate system, velocity and distance constants $\kappa$$\_$x/, $\kappa$$\_$y/, and he. Stability of control rule is proved Liapunov function. System input to the mobile robot is reference posture ($\chi$$\_$r/, y$\_$r/, $\theta$$\_$r/)/sup/ $\tau$/ and reference e velocity (ν$\_$r/,$\omega$$\_$r/)$\^$$\tau$/. System output of the mobi-le robot is velocity of driving wheels. We introduce limit velocity for preventing high initial speed. From simulation results, we can see the proposed control rule is stable.