• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.3
• /
• pp.501-516
• /
• 2013

The well-known Vlasov-Poisson equation describes plasma physics as nonlinear first-order partial differential equations. Because of the nonlinear condition from the self consistency of the Vlasov-Poisson equation, many problems occur: the existence, the numerical solution, the convergence of the numerical solution, and so on. To solve the problems, a viscosity term (a second-order partial differential equation) is added. In a viscosity term, the Vlasov-Poisson equation changes into a parabolic equation like the Fokker-Planck equation. Therefore, the Schauder fixed point theorem and the classical results on parabolic equations can be used for analyzing the Vlasov-Poisson equation. The sequence and the convergence results are obtained from linearizing the Vlasove-Poisson equation by using a fixed point theorem and Gronwall's inequality. In numerical experiments, an implicit first-order scheme is used. The numerical results are tested using the changed viscosity terms.

• Journal of applied mathematics & informatics
• /
• v.29 no.1_2
• /
• pp.211-225
• /
• 2011

In this paper, a class of bi-directional associative memory (BAM) fuzzy cellular neural networks with distributed delays and impulses is formulated and investigated. By employing an integro-differential inequality with impulsive initial conditions and the topological degree theory, some sufficient conditions ensuring the existence and global exponential stability of equilibrium point for impulsive BAM fuzzy cellular neural networks with distributed delays are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on the delay kernel functions and system parameters. It is believed that these results are significant and useful for the design and applications of BAM fuzzy cellular neural networks. An example is given to show the effectiveness of the results obtained here.

• Journal of Power Electronics
• /
• v.13 no.4
• /
• pp.712-718
• /
• 2013

This paper proposes a control method for reducing the total harmonic distortion (THD) of the grid current of three-phase grid-connected inverter systems when the grid voltage is distorted. The THD of the grid current caused by grid voltage harmonics is derived by considering the phase delay and magnitude attenuation due to the hardware low-pass filter (LPF). The Cauchy-Schwarz inequality theory is used in order to search more easily for the minimum point of the THD. Both the gain and angle of the compensation voltage at the minimum point of the THD of the grid current are derived with the variation of cut-off frequencies of the hardware LPF. Simulation and experimental results show the validity of the proposed control methods.

• Journal of the Korean Statistical Society
• /
• v.25 no.2
• /
• pp.243-253
• /
• 1996

Let X and Y be random vectors in R$^{n}$ . A random vector X is 'more associated' than Y if and only if P(X $\in$ A ∩ B) - P(X $\in$ A)P(X $\in$ B) $\geq$ P(Y $\in$ A ∩ B)-P(Y $\in$ A)P(Y $\in$ B) for all open upper sets A and B. By requiring the above inequality to hold for some open upper sets A and B various notions of positive dependence orderings which are weaker than 'more associated' ordering are obtained. First a general theory is given and then the results are specialized to some concepts of a particular interest. Various properties and interrelationships are derived.

• Journal of Institute of Control, Robotics and Systems
• /
• v.16 no.1
• /
• pp.1-4
• /
• 2010

Based on the sliding mode control theory, a decentralized controller design method is developed for a large scale system with a poly topic model. In terms of LMIs, we derive sufficient conditions for the existence of the decentralized controller guaranteeing a stable sliding motion. We also give an LMI-based control design algorithm. Finally, the proposed method is applied to decentralized stabilization of double-inverted pendulums. Simulation results show that our method gives not only the robust stability but perfect rejection of norm-bounded uncertainties.

• Journal of Institute of Control, Robotics and Systems
• /
• v.20 no.10
• /
• pp.995-1001
• /
• 2014

In the aftermath of the financial crisis of 2008, while numerous members of the general public lost their homes and jobs, many of the largest banks held responsible for the crisis have been successfully rescued by bailouts. In this paper, through the analysis of income inequality, unemployment, tax cuts, and bailouts, we show that the interests of the general public are different from the interests of politicians and bankers. While the small elite group of politicians and bankers could set the deregulation policies with inordinate power based on full information, most people were ignorant and unconcerned about the policies, and hence did not oppose them. Specifically, we model the credit change in the financial markets of the United States by a finite state machine, and design three local supervisors representing three groups with different interests. It is then shown that the deregulation policies were adopted according to the difference of the supervisors' powers.

• The Transactions of the Korean Institute of Electrical Engineers D
• /
• v.49 no.4
• /
• pp.183-190
• /
• 2000

It is well-known that the poles of a system are closely related with the dynamics of the systems, and the pole assignment problem, which locates the poles in the desired regions, in one of the major problem in control theory. Also, it is always possible to assign poles to specific points for exactly known linear systems. But, it is impossible for the uncertain linear systems because of the uncertainties that originate from modeling error, system variations, sensing error and disturbances, so we must consider some regions instead of points. In this paper, we consider both the analysis and the design of robust pole assignment problem of linear system with time-varying uncertainty. The considered uncertainties are the unstructured uncertainty and the structured uncertainty, and the considered region is the circular region. Based on Lyapunov stability theorem and linear matrix inequality(LMI), we first present the analysis result for robust pole assignment, and then we present the design result for robust pole assignment. Finally, we give some numerical examples to show the applicability and usefulness of our presented results.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.4 no.3
• /
• pp.300-305
• /
• 2004

This paper concerns controller design for the Takagi-Sugeno (TS) fuzzy systems. The design method proposed in this paper is derived in the framework of the optimal control theory utilizing the piecewise quadratic optimal value functions. The major part of the proposed design procedure consists of solving linear matrix inequalities (LMIs). Since LMIs can be solved efficiently within a given tolerance by the recently developed interior point methods, the design procedure of this paper is useful in practice. A design example is given to illustrate the applicability of the proposed method.

• Honam Mathematical Journal
• /
• v.31 no.1
• /
• pp.75-85
• /
• 2009

We show the existence of the nontrivial periodic solution for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition by critical point theory and linking arguments. We investigate the geometry of the sublevel sets of the corresponding functional of the system, the topology of the sublevel sets and linking construction between two sublevel sets. Since the functional is strongly indefinite, we use the linking theorem for the strongly indefinite functional and the notion of the suitable version of the Palais-Smale condition.

• Journal of Electrical Engineering and Technology
• /
• v.13 no.1
• /
• pp.418-429
• /
• 2018

This paper studies the decentralized position/force control problem for constrained reconfigurable manipulator without torque sensing. A novel joint torque estimation scheme that exploits the existing structural elasticity of the manipulator joint with harmonic drive model is applied for each joint module. Based on the estimated joint torque and dynamic output feedback technique, a decentralized position/force control strategy is presented. In order to solve the problem of controller parameter perturbation, the non-fragile robust technique is introduced into the dynamic output feedback controller. Subsequently, the stability of the closed-loop system is proved using the Lyapunov theory and linear matrix inequality (LMI) technique. Finally, two 2-DOF constrained reconfigurable manipulators with different configurations are applied to verify the effectiveness of the proposed control scheme in numerical simulation.