• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.479-497
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• 2018

This paper deals with an optimal control on semilinear stochastic functional differential equations with Poisson jumps in a Hilbert space. The existence of an optimal control is derived by the solution of proposed system which satisfies weakly sequentially compactness. Also the stochastic maximum principle for the optimal control is established by using spike variation technique of optimal control with a convex control domain in Hilbert space. Finally, an application of retarded type stochastic Burgers equation is given to illustrate the theory.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.115-126
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• 1998

We study the optimal control problem of system governed by retarded functional differential $$ x'(t) = A_0 x(t) + A_1 x(t - h) + \\ulcorner\ulcorner\ulcorner_{-h}^{0} a(s)A_2 x(t + s)ds + B_0 u(t) $$ in Hilbert space H. After the fundamental facts of retarded system and the description of condition so called a weak backward uniqueness property are established, the technically important maximal principle and the bang-bang principle are given. its corresponding linear system.

• 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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.81-97
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• 1999

This paper deals with the time optimal control problem for the retarded semilinear system by using the construction of fundamental solution in case where the principal operators are unbounded operators.

• Journal of the Korean Mathematical Society
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• v.36 no.2
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• pp.317-332
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• 1999

In this paper we deal with the optimal control problem for the semilinear functional differential equations with unbounded delays. We will also establish the regularity for solutions of the given system. By using the penalty function method we derive the optimal conditions for optimality of an admissible state-control pairs.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2001.05a
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• pp.207-212
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• 2001

In this paper, a method to be able to decide the possible maximum gain of P, PI control for the retarded processes under stable condition is proposed. At first, adjustable parameter set causing stability limit are obtained based on the frequency domain condition which makes the roots of transfer function locate on the $j\omega$ axis. And the cut-in frequency $\omega{_p}$ to bring the parameter set to P control from PI control is derived by an equation with 2 parameters L and $T_m$ given, then $\omega{_p}$ is used to compute the maximum gain with stable condition. For the calculation, the controlled process of first order system with time delay element is introduced and all parameters are presumed to be time invariant.

• East Asian mathematical journal
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• v.19 no.1
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• pp.133-150
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• 2003

This paper will show that the relation (1.1) $$L^1({\Omega}){\subset}C_0(\bar{\Omega}){\subset}H_{p,q}$$ if 1/p'-1/n(1-2/q')<0 where p'=p/(p-1) and q'=q/(q-1) where $H_{p.q}=(W^{1,p}_0,W^{-1,p})_{1/q,q}$. We also intend to investigate the control problems for the retarded systems with $L^1(\Omega)$-valued controller in $H_{p,q}$.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1930-1933
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• 1991

In this paper, the robustness of self turning controller on the continuous time-delay system is investigated. The polynomial identification method using continuous time exponentially weighted least square algorithm is used for estimating the time.-delay system parameters. The pole-zero and pole placement method are adopted for the control algorithm. On considering the control weighting factor and reliability filter the effect of unmodeled dynamics of the plant are examined by the simulation.

• Journal of Advanced Marine Engineering and Technology
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• v.25 no.5
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• pp.1086-1090
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• 2001

In this paper, a method deciding the permissible gains of the P and PT controllers for a retarded process under stable condition is proposed. For analysis, the controlled process is assumed to be first-order system with time delay. At first, the adjustable parameter sets causing stability limit are obtained based on the frequency domain condition which makes the roots of the characteristic equation locate on the imaginary axis. And the cut-in frequency ${\omega}_p$ to bring the parameter set to P control from PI control is derived is derived in terms of L and $T_m$ then ${\omega}_p$ is used to compute the maximum gain with stable condition. The results indicate that the permissible controller gains can be described by a unique if parameters L and $T_m$ are know.