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  • 1
    ISSN: 1432-0606
    Keywords: Existence and uniqueness ; Semiconductor equations ; LBIC ; 35J65 ; 35D05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper by using anL ∞ estimate for elliptic equations, we study the well-posedness of the stationary semiconductor equations arising from modeling a nondestructive testing technique LBIC. It is shown that when the extra source term is small, the system has a unique weak solution, and the solution is continuously dependent on this source term. The validity of an approximate model derived for the study of the inverse problem is established. The existence result is then extended to the case of constant mobilities without the assumption on the size of the source term.
    Type of Medium: Electronic Resource
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  • 2
    Publication Date: 2019-07-12
    Description: The spline scheme of Banks and Kappel (1979) is used as an aproximation method for calculating optimal feedback gains for control systems governed by functional differential equations. It is shown that the adjoints of the spline-based approximation scheme for delay equations do not converge strongly.
    Keywords: CYBERNETICS
    Type: SIAM Journal on Control and Optimization (ISSN 0363-0129); 26; 1442-145
    Format: text
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  • 3
    Publication Date: 2019-07-12
    Description: The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
    Keywords: NUMERICAL ANALYSIS
    Type: SIAM Journal on Control and Optimization (ISSN 0363-0129); 25; 1379-140
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  • 4
    Publication Date: 2019-07-12
    Description: In this paper existence and construction of stabilizing compensators for linear time-invariant systems defined on Hilbert spaces are discussed. An existence result is established using Galkerin-type approximations in which independent basis elements are used instead of the complete set of eigenvectors. A design procedure based on approximate solutions of the optimal regulator and optimal observer via Galerkin-type approximation is given and the Schumacher approach is used to reduce the dimension of compensators. A detailed discussion for parabolic and hereditary differential systems is included.
    Keywords: NUMERICAL ANALYSIS
    Type: SIAM Journal on Control and Optimization (ISSN 0036-1410); 28; 1251-126
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  • 5
    Publication Date: 2019-07-12
    Description: In this paper a new technique for the estimation of parameters in elliptic partial differential equations is developed. It is a hybrid method combining the output-least-squares and the equation error method. The new method is realized by an augmented Lagrangian formulation, and convergence as well as rate of convergence proofs are provided. Technically the critical step is the verification of a coercivity estimate of an appropriately defined Lagrangian functional. To obtain this coercivity estimate a seminorm regularization technique is used.
    Keywords: NUMERICAL ANALYSIS
    Type: SIAM Journal on Control and Optimization (ISSN 0363-0129); 28; 113-136
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  • 6
    Publication Date: 2019-07-13
    Description: The optimal boundary temperature control of the stationary thermally coupled incompressible Navier-Stokes equation is considered. Well-posedness and existence of the optimal control and a necessary optimality condition are obtained. Optimization algorithms based on the augmented Lagrangian method with second order update are discussed. A test example motivated by control of transport process in the high pressure vapor transport (HVPT) reactor is presented to demonstrate the applicability of our theoretical results and proposed algorithm.
    Keywords: CYBERNETICS
    Type: NASA-CR-199714 , NAS 1.26:199714 , NIPS-95-06066 , Workshop on Optimal Control Design and Control; Apr 08, 1994 - Apr 09, 1994; Blacksburg, VA; United States
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  • 7
    Publication Date: 2019-06-28
    Description: It is shown that the adjoints of a spline based approximation scheme for delay equations do not converge strongly.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-CR-178342 , ICASE-87-47 , NAS 1.26:178342 , AD-A192761
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  • 8
    Publication Date: 2019-06-28
    Description: The linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.
    Keywords: CYBERNETICS
    Type: NASA-CR-178302 , ICASE-87-31 , NAS 1.26:178302 , AD-A192764
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  • 9
    Publication Date: 2019-06-28
    Description: In this report we summarize the results of a three year research program on high pressure vapor transport (HPVT) of compound semiconductors. Most of our work focused onto pnictides, in particular ZnGeP2, as a model system. Access to single crystals of well controlled composition of this material is desired for advancing the understanding and control of its point defect chemistry in the contest of remote, real-time sensing of trace impurities, e.g., greenhouse gases, in the atmosphere by ZnGeP2 optical parametric oscillators (OPO's).
    Keywords: SOLID-STATE PHYSICS
    Type: NASA-CR-199721 , NAS 1.26:199721 , NIPS-95-06074
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  • 10
    Publication Date: 2019-06-28
    Description: A set of equations known as Chandrasekhar equations arising in the linear quadratic optimal control problem is considered. In this paper, we consider the linear time-invariant system defined in Hilbert spaces involving unbounded input and output operators. For a general class of such systems, the Chandrasekhar equations are derived and the existence, uniqueness, and regularity of the results of their solutions established.
    Keywords: CYBERNETICS
    Type: NASA-CR-178303 , ICASE-87-32 , NAS 1.26:178303
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