Numerical solution of optimization problems in vibrational mechanics using the characteristics method |
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Authors: | YeA Kolpakova NN Subbotina |
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Institution: | 1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;2. Department of Flight Dynamics and Control, Moscow Aviation Institute, Moscow 125993, Russia |
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Abstract: | 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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