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Numerical solution of optimization problems in vibrational mechanics using the characteristics method

✍ Scribed by Ye.A. Kolpakova; N.N. Subbotina

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
272 KB
Volume
74
Category
Article
ISSN
0021-8928

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✦ Synopsis

Optimal control problems with a terminal pay-off functional are considered. The dynamics of the control system consists of rapid oscillatory and slow non-linear motions. A numerical method for solving these problems using the characteristics of the Hamilton-Jacobi-Bellman equation is presented. Estimates of the accuracy of the method are obtained. A theorem is proved which enables one to determine the class of functions containing the optimal preset control to be obtained. The results of the numerical solution of a terminal optimization problem for a fast non-linear pendulum are presented.

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A unified framework for the numerical solution of optimal control problems using pseudospectral methods
✍ Divya Garg; Michael Patterson; William W. Hager; Anil V. Rao; David A. Benson; G πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 559 KB

A unified framework is presented for the numerical solution of optimal control problems using collocation at Legendre-Gauss (LG), Legendre-Gauss-Radau (LGR), and Legendre-Gauss-Lobatto (LGL) points. It is shown that the LG and LGR differentiation matrices are rectangular and full rank whereas the LG