Analysis and computation of nonlinear boundary control for heat conduction in nonsmooth domains with point observations /
In this dissertation, we study quadratic regulator (QR)
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
1996.
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| Subjects: | |
| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=739364191&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | In this dissertation, we study quadratic regulator (QR) problems in boundary control systems governed by the heat equation with pointwise observations in nonsmooth domains, which are motivated by the control of heat conduction and contemporary 44smart sensors". Both linear and nonlinear boundary conditions are considered. To settle the well- posedness of our QR problems, regularities of the solution of the heat equation in a Lipschitz cylinder are studied via the method of boundary integral equations. By using classical analytic techniques, the mapping properties of heat po tentials and related boundary integral operators between various Banach spaces are studied extensively. Several new and sharp regularity results on heat potentials are presented. These results extend the corresponding results in the literature. H61der continuity of the solution of the heat equation in a Lipschitz cylinder is proved by utilizing the Neumann function of the heat equation. This is the first time such a result has been proved. For the heat equation with nonlinear boundary conditions, a new constructive method is adopted to establish the existence and uniqueness of the solution in the space of H61der continuous functions. The QR problem is studied via a variational inequality approach in a Banach space setting. A first order optimality condition is derived and then a characterization formula of the optimal control is obtained. Since singularities appear in the optimal control, a singularity decomposition formula is also established, from which the nature of the singularities is clearly exhibited. Based upon the optimality condition and the characterization formula, a numerical algorithm, called the conditioned gradient projection method, coupled with a boundary element method, is designed to approximate the optimal control. Results on convergence and its rate of the above algorithm, together with some numerical experiments, are also presented. |
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| Item Description: | Vita. "Major Subject: Mathematics". |
| Physical Description: | ix, 111 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilms Inc. |
| Bibliography: | Includes bibliographical references: pages 107-110. |