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Riccati equation in quadratic optimal control problem of damped second order system
하준홍,Shin-ichi Nakagiri 대한수학회 2013 대한수학회지 Vol.50 No.1
This paper studies the properties of solutions of the Riccati equation arising from the quadratic optimal control problem of the general damped second order system. Using the semigroup theory, we establish the weak differential characterization of the Riccati equation for a general class of the second order distributed systems with arbitrary damping terms.
SOLUTIONS OF QUASILINEAR WAVE EQUATION WITH STRONG AND NONLINEAR VISCOSITY
황진수,Shin-ichi Nakagiri,Hiroki Tanabe 대한수학회 2011 대한수학회지 Vol.48 No.4
We study a class of quasilinear wave equations with strong and nonlinear viscosity. By using the perturbation method for semilinear parabolic equations, we have established the fundamental results on existence, uniqueness and continuous dependence on data of weak solutions.
Identification of constant parameters in perturbed sine-Gordon equations
하준홍,Shin-ichi Nakagiri 대한수학회 2006 대한수학회지 Vol.43 No.5
We study the identification problems of constant parametersappearing in the perturbed sine-Gordon equation with the Neumannboundary condition. The existence of optimal parameters is proved,and necessary conditions are established for several types ofobservations by utilizing quadratic optimal control theory due toLions [ref{Lions:op}].
Junhong Ha,Shin-ichi Nakagiri 대한수학회 2004 대한수학회지 Vol.41 No.3
Identification problems for the system governed by abstract nonlinear damped second order evolution equations are studied. Since unknown parameters are included in the diffusion operator, we can not simply identify them by using the usual optimal control theories. In this paper we present how to solve our identi- fication problems via the method of transposition.
RICCATI EQUATION IN QUADRATIC OPTIMAL CONTROL PROBLEM OF DAMPED SECOND ORDER SYSTEM
Ha, Junhong,Nakagiri, Shin-Ichi Korean Mathematical Society 2013 대한수학회지 Vol.50 No.1
This paper studies the properties of solutions of the Riccati equation arising from the quadratic optimal control problem of the general damped second order system. Using the semigroup theory, we establish the weak differential characterization of the Riccati equation for a general class of the second order distributed systems with arbitrary damping terms.
Identification problems of damped sine-Gordon equations with constant parameters
Junhong Ha,Shin-ichi Nakagiri 대한수학회 2002 대한수학회지 Vol.39 No.4
We study the problems of identification for the damped sine-Gordonequations with constant parameters. That is, we establish theexistence and necessary conditions for the optimal constantparameters based on the fundamental optimal control theory and thetransposition method studied in Lions and Magenes [ref{Lions-Magenes}].
SOLUTIONS OF QUASILINEAR WAVE EQUATION WITH STRONG AND NONLINEAR VISCOSITY
Hwang, Jin-Soo,Nakagiri, Shin-Ichi,Tanabe, Hiroki Korean Mathematical Society 2011 대한수학회지 Vol.48 No.4
We study a class of quasilinear wave equations with strong and nonlinear viscosity. By using the perturbation method for semilinear parabolic equations, we have established the fundamental results on existence, uniqueness and continuous dependence on data of weak solutions.
IDENTIFICATION OF CONSTANT PARAMETERS IN PERTURBED SINE-GORDON EQUATIONS
Ha, Jun-Hong,Nakagiri, Shin-Ichi Korean Mathematical Society 2006 대한수학회지 Vol.43 No.5
We study the identification problems of constant parameters appearing in the perturbed sine-Gordon equation with the Neumann boundary condition. The existence of optimal parameters is proved, and necessary conditions are established for several types of observations by utilizing quadratic optimal control theory due to Lions [13].