• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.89-106
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• 2022

We are concerned with finding a common solution to an equilibrium problem associated with a bifunction, and a constrained convex minimization problem. We propose an iterative fixed point algorithm and prove that the algorithm generates a sequence strongly convergent to a common solution. The common solution is identified as the unique solution of a certain variational inequality.

• Journal of the military operations research society of Korea
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• v.8 no.2
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• pp.57-68
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• 1982

Bimatrix games are the two-person non-zero-sum non-cooperative games. These games were studied by Mills, Lemke, Howson, Millham, Winkels, and others. This paper is a systematic and synthetic survey relevant to bimatrix games. Among the many aspects of researches on bimatrix games, emphasis in this paper is placed on the relation of the equilibrium set to Nash subsets. Topics discussed are as follows: Properties of equilibrium point; The structure of equilibrium set; Relation of Nash subsets to equilibrium set; Algorithm for finding the equilibrium points; Concepts of solutions on bimatrix games.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.607-614
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• 1998

In this note we shall give a new existence theorem of equilibrium in social systems with coordination under general assump-tions by using the Kakutani fixed point theorem.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.10
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• pp.1006-1013
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• 2011

In this paper, we propose an optimal posture control law for an unmanned bicycle by deriving linear bicycle model from fully nonlinear differential equations. We calculate each equilibrium point of a bicycle under any given turning radius and angular speed of rear wheel. There is only one equilibrium point when a bicycle goes straight, while there are a lot of equilibrium points in case of turning. We present an optimal equilibrium point which makes the leaning input minimum when a bicycle is turning. As human riders give rolling torque by moving center of gravity of a body, many previous studies use a movable mass to move center of gravity like humans do. Instead we propose a propeller as a new leaning input which generates rolling torque. The propeller thrust input makes bicycle model simpler and removes input magnitude constraint unlike a movable mass. The proposed controller can hold optimal equilibrium points using both steering input and leaning input. The simulation results on linear control for circular motion are demonstrated to show the validity of the proposed approach.

• Journal of Advanced Marine Engineering and Technology
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• v.21 no.4
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• pp.393-403
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• 1997

In this paper, we proposed an optimal identification method of identifying the membership func¬tions and the fuzzy rules for the stabilization controller of the nonlinear system by RVEGA( Real Variable Elitist Genetic Algo rithm l. Although fuzzy logic controllers have been successfully applied to industrial plants, most of them have been relied heavily on expert's empirical knowl¬edge. So it is very difficult to determine the linguistic state space partitions and parameters of the membership functions and to extract the control rules. Most of conventional approaches have the drastic defects of trapping to a local minima. However, the proposed RVEGA which is similiar to the processes of natural evolution can optimize simulta¬neously the fuzzy rules and the parameters of membership functions. The validity of the RVEGA - based fuzzy controller was proved through applications to the stabi¬lization problems of an inverted pendulum system with highly nonlinear dynamics. The proposed RVEGA - based fuzzy controller has a swing -. up control mode(swing - up controller) and a stabi¬lization one(stabilization controller), moves a pendulum in an initial stable equilibrium point and a cart in an arbitrary position, to an unstable equilibrium point and a center of the rail. The stabi¬lization controller is composed of a hierarchical fuzzy inference structure; that is, the lower level inference for the virtual equilibrium point and the higher level one for position control of the cart according to the firstly inferred virtual equilibrium point. The experimental apparatus was imple¬mented by a DT -- 2801 board with AID, D/A converters and a PC - 586 microprocessor.

• Proceedings of the KIEE Conference
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• 1996.07b
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• pp.1104-1106
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• 1996

In this paper, a hierarchical fuzzy controller is proposed for the stabilization control of the inverted pendulum system. The design of controller for that system is difficult because of its complicated nonlinear mathematical model with unknown parameters. Conventional fuzzy control strategy based only on dynamics of pendulum made have failed to stabilize. However, proposed control strategies are to swing pendulum from natural stable up equilibrium point to an unstable equilibrium point and are to transport a cart from an arbitrary position toward a center of rail. Thus, the proposed fuzzy stabilization controller have a hierarchical fuzzy inference structure; that is, the lower level is for inference interface for the virtual equilibrium point and the higher level one for the position control of cart according to the firstly inferred virtual equilibrium point.

• Journal of the Korean Institute of Landscape Architecture
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• v.21 no.2
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• pp.120-128
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• 1993

This study suggests one hypothesis: The strength of the catchment forces of urban community parks can be represented as an equilibrium point model, which is derived from a centrality index for. That model was designed by Reilly(1931) and developed by Godlund(1956). An equilibrium point model for the catchments is represented as followed formulae: m=$\frac{CA2}{CA-CB}$ m=$\frac {{{{{L SQRT {{C}_{A}$.$ {C}_{B}} {CA-CB} Here, m is distance from the center of park A to the cetner of park B. r is radius of a circle where the catchment between park A and B is equal pointed traces. CA is index of the centrality of park A from Reilly's Law. CB is an index of the centrality of park B from Reilly's Law. L is an the distance between park A and B. The equilibrium point model is testified in the case of Chong-ju community parks. The testification has been limited to the application to such manifest outdoor recreational facilities as bentches, even though there are statistically and economically problems for a quantitative model to be testified. But the testification could be a rationale for the catchment forces of urban community parks, which was quantitatively represented that the distance between two or there parks should be related with the feasibility of the parks. Therefore, the urban community park should be planned to be located, hiving separately its identity that might be considered with the facility diversification and the locational competitiveness of a park.

• Journal of Korean Society of Transportation
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• v.28 no.6
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• pp.159-166
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• 2010

Trip distribution is to connect travel demand for each OD pair based on travel cost, trip production and attraction derived from trip generation step. In real world the travel cost is a function of travel demand, but existing models could not fully consider such functional relation between travel cost and demand, which leads to an equilibrium in trip distribution model. This paper proves the equilibrium trip distribution by using gravity model. In order to obtain such equilibrium this paper also presents a solution algorithm based on fixed point theorem. The algorithm will be tested with an example and confirmed the equilibrium solution of trip distribution.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.367-377
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• 2014

In this paper, we first introduce a generalized concept of Berge strong equilibrium for a generalized game $\mathcal{G}=(X_i;T_i,f_i)_{i{\in}I}$ of normal form, and using a fixed point theorem for compact acyclic maps in admissible convex sets, we establish the existence theorem of generalized Berge strong equilibrium for the game $\mathcal{G}$ with acyclic values. Also, we have demonstrated by examples that our new approach is useful to produce generalized Berge strong equilibria.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.1
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• pp.19-26
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• 2006

In this paper, using the fixed point theorem for acyclic factorizable multifunctions, we shall prove an existence theorem of general best proximity pairs and equilibrium pairs for free generalized games.