• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.1
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• pp.39-63
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• 2019

In this paper, we study the effect of Cytotoxic T Lymphocyte (CTL) and antibody immune responses on the virus dynamics with both virus-to-cell and cell-to-cell transmissions. The infection rate is given by Holling type-II. We first show that the model is biologically acceptable by showing that the solutions of the model are nonnegative and bounded. We find the equilibria of the model and investigate their global stability analysis. We derive five threshold parameters which fully determine the existence and stability of the five equilibria of the model. The global stability of all equilibria of the model is proven using Lyapunov method and applying LaSalle's invariance principle. To support our theoretical results we have performed some numerical simulations for the model. The results show the CTL and antibody immune response can control the disease progression.

• Journal of information and communication convergence engineering
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• v.17 no.3
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• pp.167-173
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• 2019

This study investigates the problem of leader-following consensus for multi-agent systems with output saturations. This study assumes that the agents are described as a neutrally stable system, and the leader agent generates the bounded trajectory within the saturation level. Then, the objective of the leader-following consensus is to track the trajectory of the leader by exchanging information with neighbors. To solve this problem, we propose an observer-based distributed consensus algorithm. Then, we provide a consensus analysis by applying the Lyapunov stability theorem and LaSalle's invariance principle. The result shows that the agents achieve the leader-following consensus in a global sense. Moreover, we can achieve the consensus by choosing any positive control gain. Finally, we perform a numerical simulation to demonstrate the validity of the proposed algorithm.

• Journal of Advanced Marine Engineering and Technology
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• v.39 no.2
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• pp.159-165
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• 2015

Motion control schemes are generally classified into three categories (point stabilization, trajectory tracking, and path following). This paper deals with the problem which is associated with the initial deployment of a group of Unmanned Surface Vehicle (USVs) and corresponding point stabilization. To keep the formation of a group of USVs, it is necessary to set the relationship between each vehicle. A forcing functions such as potential fields are designed to keep the formation and a graph Laplacian is used to represent the connectivity between vehicle. In case of fixed topology of the graph representing the communication between the vehicles, the graph Laplacian is assumed constant. However the graph topologies are allowed to change as the vehicles move, and the system dynamics become discontinuous in nature because the graph Laplacian changes as time passes. To check the stability in the stage of deployment, the system is modeled with Kronecker algebra notation. Filippov's calculus of differential equations with discontinuous right hand sides is then used to formally characterize the behavior of USVs. The stability of the system is analyzed with Lyapunov's stability theory and LaSalle's invariance principle, and the validity is shown by checking the variation of state norm.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.14 no.4
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• pp.284-291
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• 2021

In this paper, we study the consensus problem for multi-agent systems with input saturations. The goal of consensus is to achieve a swarming behavior of multi-agent systems by reaching the agreement through information exchange. This paper considers agents modeled by first-order dynamics with input saturations. In order to guarantee the global convergence of the agents, it is assumed that the agents are stable. Moreover, considering the disturbances, we propose the PI based duplex control method to achieve the consensus. The proposed P controller and I controller are composed of different information network. Then, we investigate the conditions of the information networks and the control gains of P, I controllers to achieve the consensus applying the Lyapunov stability theorem and the Lasalle's Invariance Principle. Finally, we conduct the simulations to validate the theoretical results.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.27 no.1
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• pp.109-116
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• 2023

In this paper, we study the containment control problem for second-order multi-agent systems, which consists of multiple leaders and followers. The goal is to drive the followers toward the convex hull spanned by the leaders. Thus, the swarm behavior can be obtained by controlling the entire group by the leaders. This paper considers the leaders move at a constant speed and the followers have input saturations. Moreover, we assume that the followers can exchange information with neighbors, and only relative state information is available. Under these assumptions, we propose the Proportional-Integral based distributed control algorithm to solve the containment control problem with moving leaders. Moreover, based on Lasalle's invariance principle, the conditions for the control gains that guarantee the convergence of the followers to the convex hull spanned by the leaders are investigated, and it was shown that it can be designed only using the system parameter. Finally, the simulations are conducted to validate the theoretical result.