• The Transactions of the Korean Institute of Electrical Engineers D
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• v.52 no.9
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• pp.511-519
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• 2003

In this paper, we considered the design of gain scheduled controllers for linear systems with saturating actuators. Our basic idea is to design a control that uses higher control gain when the states are smaller, and lower gain when it is higher. By doing this, we can avoid the saturation and we can improve the performance. First, we derive a control and a reachable set expressed as LMI form, which minimizes not only the L$_2$ gain from the disturbance to the measured output but also the control is never saturated within this reachable set. Next, the reachable set is divided as nested subsets, and at each nested subset, the control gain is designed to minimize the L$_2$ gain and it is never saturated. Finally, the control gain is scheduled according to the status of states, i.e., the subset in which the states are located. A numerical example is presented to show that our gain scheduled control significantly improves the performance.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.37-52
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• 2000

This paper is concerned with the impulsive Cauchy problem (equation omitted) where u is a possibly discontinuous vector-valued function and f, $g_{i}$ : $IR^{n}$ -> $IR^{n}$ are suitably smooth functions. We show that the input-output map is Lipschitz continuous and investigate compactness of reachable sets.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.213-230
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• 2002

We deal with the approximate controllability for semilinear systems with time delay in a Hilbert space. First, we show the existence and uniqueness of solutions of the given systems with the mere general Lipschitz continuity of nonlinear operator f from $R\;\times\;V$ to H. Thereafter, it is shown that the equivalence between the reachable set of the semilinear system and that of its corresponding linear system. Finally, we make a practical application of the conditions to the system with only discrete delay.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.361-376
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• 2000

Our purpose is to seek that the reachable set of the semilinear system $\frac{d}{dt}x(t){\;}={\;}Ax(t){\;}+{\;}f(t,x(t)){\;}+{\;}Bu(t)$ is equivalent to that of its corresponding to linear system (the case where f=0).Under the assumption that the system of generalized eigenspaces of A is complete, we will show that the reachable set corresponding to the linear system is independent of t in case A generates $C_0-semigroup$. An illustrative example for retarded system with time delay is given in the last section.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.18 no.1
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• pp.19-29
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• 2020

This paper gives two graph-based algorithms for radioactive decay computation. The first algorithm identifies the connected components of the graph induced from the given radioactive decay dynamics to reduce the size of the problem. The solutions are derived over the precalculated connected components, respectively and independently. The second algorithm utilizes acyclic structure of radioactive decay dynamics. The algorithm evaluates the reachable vertices of the induced system graph from the initially activated vertices and finds the minimal set of starting vertices populating the entire reachable vertices. Then, the decay calculations are performed over the reachable vertices from the identified minimal starting vertices, respectively, with the partitioned initial value over the reachable vertices. Formal arguments are given to show that the proposed graph inspired divide and conquer calculation methods perform the intended radioactive decay calculation. Empirical efforts comparing the proposed radioactive decay calculation algorithms are presented.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.469-481
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• 2020

In this paper, we consider a control system for semilinear differential equations in Hilbert spaces with Lipschitz continuous nonlinear term. Our method is to find the equivalence of approximate controllability for the given semilinear system and the linear system excluded the nonlinear term, which is based on results on regularity for the mild solution and estimates of the fundamental solution.

• Journal of KIISE:Computer Systems and Theory
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• v.29 no.1
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• pp.10-15
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• 2002

This paper proposes the Pipelined Broadcast that broadcasts a message of size m in O(m+n-1) time in an n-dimensional hypercube. It is based on the replication tree, which is derived from the reachable sets. It greatly improves the performance compared to Ho-Kao s algorithm with the time of O(m[n/log(n+1)]). The communication in the broadcast uses all-port wormhole router with message replication capability. This paper includes the algorithm together with performance comparisons to previous schemes in practical implementation.

• International Journal of Control, Automation, and Systems
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• v.5 no.2
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• pp.138-146
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• 2007

The analysis and design method for achieving robust stabilization of Decentralized Dynamic Surface Control (DDSC) is presented for a class of interconnected nonlinear systems. While a centralized design approach of DSC was developed in [1], the decentralized approach to deal with large-scale interconnected systems is proposed under the assumption that interconnected functions among subsystems are unknown but bounded. To provide a closed-loop form with provable stability properties, augmented error dynamics for N nonlinear subsystems with DDSC are derived. Then, the reachable set for errors of the closed-loop systems will be approximated numerically in the form of an ellipsoid in the framework of convex optimization. Finally, a numerical algorithm to calculate the $L_2$ gain of the augmented error dynamics is presented.

• Proceedings of the KIEE Conference
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• 2002.07d
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• pp.2040-2042
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• 2002

In this paper, we consider the design of gam scheduled controllers for linear systems with input saturation. We obtain a reachable set and a control gain, which guarantees that the controls are never saturated inside this reachable set and that the $L_2$ gain is minimized, from matrix inequalities. This proposed gain scheduled control gives better performance than that of static control case, and we present the simulation results to show the usefulness of the proposed control.

• Proceedings of the KIEE Conference
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• 2003.11b
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• pp.335-338
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• 2003

In this paper, we considered the design of gain scheduled controllers for linear systems with input constraints. The gain scheduled control is a method that uses larger control gain when the states are smaller, and smaller gain when it is larger. By doing this, we can use a full actuator capacity. Also we allow the over-saturation in control to improve the performance. First, we derive a control and a reachable set expressed as LMI form, while minimizing the $L_2$ gain from the disturbance to the measured output. Next, the reachable set is divided as nested subsets, and the control gains are obtained by minimizing the $L_2$ gain at each nested subset. Finally, the control gains are scheduled according to the status of states, i.e., the nested-subset in which the states are located. Performance of the proposed technique is illustrated through simulations of a six-story building subject to earthquake ground motion.