Convergence analysis of orthogonal collocation methods for unconstrained optimal control
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| Publicado en: | ProQuest Dissertations and Theses (2013) |
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ProQuest Dissertations & Theses
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| Acceso en línea: | Citation/Abstract Full Text - PDF |
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| Resumen: | Gauss collocation method, the Radau collocation method and the hp-collocation method applied to unconstrained optimal control problems. Under assumptions of coercivity and smoothness, all three collocation methods have local minimizers and corresponding Lagrange multipliers that converge in the sup-norm to a local minimizer and costate of the continuous- time optimal control problem. Both the Gauss and Radau collocation methods have error estimate of the form [special characters omitted] where l is the number of continuous derivatives in the solution and N is the degree of the polynomials in the Gauss or Radau collocation scheme. The error estimate for the hp-collocation method has the form of [special characters omitted] where h is the length of each subinterval, N is the degree of polynomial in each interval and l is the number of continuous derivatives in the solution. The convergence analysis for the three collocation methods is based on the application of an abstract implicit function theorem in nonlinear spaces and the Lipschitz stability of quadratic programming problems. The analysis requires an estimate of Lebesgue constants associated with three sets of points: (1) the Radau quadrature points, (2) the Radau quadrature points augmented by the point +1, (3) the Gauss quadrature points augmented by the point -1. The estimation for points set (2) is O(logN), and for points sets (1) and (3) are O ( N½) where N is the number of Gauss or Radau quadrature points. These results are extension of Szegõ’s analysis of the Lebesgue constants for interpolation schemes based on the roots of Jacobi polynomials. |
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| ISBN: | 9781339149356 |
| Fuente: | ProQuest Dissertations & Theses Global |