• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.501-501
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• 2000

In this paper, the theoretical development to stabilize a class of uncertain time-delay systems via sliding mode control is presented. The system under consideration is described in state space model containing state delay, uncertain parameters and disturbance. The main idea is to reduce the state of delayed system, by employing the generalize linear transformation, into an equivalent one with no delay inside, which is easier to analyze its behavior and stability. Then, the sliding control approach is employed to find the stabilizing control law. Finally, a numerical simulation is illustrated to show the algorithm for applying the proposed theorems and the efffetiveness of the designed control law in stabilizing the controlled systems.

• Journal of Korea Society of Industrial Information Systems
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• v.7 no.1
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• pp.75-80
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• 2002

We investigate sorry: asymptotic stabilities of the zero solution for the perturbed linear differential system dx/dt=A(t)x+e(t, x)+f(t,x), by using Perron's method and integral inequalities, etc. and we also find some sufficient conditions that ensure some asymptotic stabilities of the zero solution of the system And hence we obtain several results of it.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.67 no.1
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• pp.103-113
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• 2018

In this paper, an improved integral variable structure regulation controller is designed by using a special integral sliding surface and a disturbance observer for the improved regulation control of highly nonlinear rigid robot manipulators with prescribed output performance. The sliding surface having the integral state with a special initial condition is employed in this paper to exactly predetermine the ideal sliding trajectory from a given initial condition to the desired reference without any reaching phase. And a continuous sliding mode input using the disturbance observer is also introduced in order to effectively follow the predetermined sliding trajectory within the prescribed accuracy without large computation burden. The performance of the prescribed tracking accuracy to the predetermined sliding trajectory is clearly investigated in detail through the two theorems, together with the closed loop stability. The design of the proposed regulation controller is separated into the performance design and robustness design in each independent link. The usefulness of the algorithm has been demonstrated through simulation studies on the regulation control of a two-link robot under parameter uncertainties and payload variations.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.1
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• pp.1-21
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• 2015

This paper presents two algorithms based on the Jamshidian equation which is from the Black-Scholes partial differential equation. The first algorithm is for American call options and the second one is for American put options. They compute numerically free boundary and then option price, iteratively, because the free boundary and the option price are coupled implicitly. By the upwind finite-difference scheme, we discretize the Jamshidian equation with respect to asset variable s and set up a linear system whose solution is an approximation to the option value. Using the property that the coefficient matrix of this linear system is an M-matrix, we prove several theorems in order to formulate a bisection method, which generates a sequence of intervals converging to the fixed interval containing the free boundary value with error bound h. These algorithms have the accuracy of O(k + h), where k and h are step sizes of variables t and s, respectively. We prove that they are unconditionally stable. We applied our algorithms for a series of numerical experiments and compared them with other algorithms. Our algorithms are efficient and applicable to options with such constraints as r > d, $r{\leq}d$, long-time or short-time maturity T.

• Journal of IKEEE
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• v.8 no.1 s.14
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• pp.96-107
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• 2004

In this paper, a new integral variable structure regulation controller(IVSRC) is designed by using a special integral sliding surface and a disturbance observer for the improved regulation control of highly nonlinear robot manipulators with prescribed output performance. The sliding surface having the integral state with a special initial condition is employed in this paper to exactly predetermine the ideal sliding trajectory from a given initial condition to origin without any reaching phase. And a continuous sliding mode input using the disturbance observer is also introduced in oder to effectively follow the predetermined sliding trajectory within the prescribed accuracy without large computation burden. The performance of the prescribed tracking accuracy to the predetermined sliding trajectory is clearly investigated in detail through the two theorems together with the closed loop stability. The design of the proposed IVSRC is separated into the performance design and robustness design in each independent link. The usefulness of the algorithm has been demonstrated through simulation studies on the regulation control of a two link manipulator under parameter uncertainties and payload variations, in view of no reaching phase, no overshoot, predetermined response with prescribed accuracy, easy change of output performance, separation of design phase, and so on.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.12 no.4
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• pp.1786-1795
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• 2011

The trajectory control for omni-directional mobile robot is not easy. Especially, the tracking control which system uncertainty problem is included is much more difficult. This paper develops trajectory controller of 3-wheels omni-directional mobile robot using fuzzy multi-layered algorithm. The fuzzy control method is able to solve the problems of classical adaptive controller and conventional fuzzy adaptive controllers. It explains the architecture of a fuzzy adaptive controller using the robust property of a fuzzy controller. The basic idea of new adaptive control scheme is that an adaptive controller can be constructed with parallel combination of robust controllers. This new adaptive controller uses a fuzzy multi-layered architecture which has several independent fuzzy controllers in parallel, each with different robust stability area. Out of several independent fuzzy controllers, the most suited one is selected by a system identifier which observes variations in the controlled system parameter. This paper proposes a design procedure which can be carried out mathematically and systematically from the model of a controlled system; related mathematical theorems and their proofs are also given. Finally, the good performance of the developed mobile robot is confirmed through live tests of path control task.