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Radial basis function dissertation
RBF, and constraints are satisfied at arbitrary discrete nodes (collocation points) to convert the continuous-time optimal control problem to a nonlinear programming (NLP) problem. Committee Member, imam, Ibrahim. The second proposed method is a hybrid approach combining RBF interpolation with Galerkin error projection for solving optimal control problems. Several examples are provided to verify the feasibility and viability of the RBF method and the RBF-Galerkin approach as means of finding accurate solutions to general optimal control problems. Document Type, doctoral Dissertation, degree Name,. Electronic Theses and Dissertations. Comparisons between these two techniques are made in this work to illustrate how the local method can obtain very similar accuracy to the global method while only using a small subset of available points, and thus using substantially less computer memory. Most traditional numerical methods for approximating the solutions of problems in science, engineering, and mathematics require the data to be arranged in a structured pattern and to be contained in a simply shaped region, such as a rectangle or circle. Committee Chair, inanc, Tamer, committee Co-Chair (if applicable dePuy, Gail.
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As a result, the shape of the domain may be determined by the application and not the numerical method. Finally, radial basis function methods are applied to solve systems of nonlinear partial differential equations (PDEs) that model pattern formation in mathematical biology. Document Type, thesis, first Advisor, scott Sarra, second Advisor. Edu/etd/243, download, downloads, since June 04, 2012. Radial basis function methods can be implemented both globally and locally. Committee Member, mcIntyre, Michael, committee Member, zurada, Jacek. A multiple receding horizon control (mrhc) approach based on the RBF-Galerkin method is developed for individualized dosing of an anemia drug for hemodialysis patients. Abstract, this work presents two direct methods based on the radial basis function (RBF) interpolation and arbitrary discretization for solving continuous-time optimal control problems: RBF Collocation Method and, rBF-Galerkin Method. The resulted NLP is quite sparse and can be efficiently solved by well-developed sparse solvers. Theses, Dissertations and Capstones. In many important applications, this severe restriction on structure cannot be met, and traditional numerical methods cannot be applied.
The proposed solution, called the RBF-Galerkin method, applies a Galerkin projection to the residuals of the optimal control problem that make them orthogonal to every member of the RBF basis functions. RBF methods are applicable with scattered data locations.
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