Exploiting Higher-order Derivatives in Computational Optimal Control
Ross, I. Michael
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To facilitate generation of real-time solutions to nonlinear optimal control problems, we present a new way of approximating higher-order derivatives that arise in control systems. A Legendre pseudospectral method is presented to efficiently and accurately discretize optimal control problems governed by higher-order dynamical constraints. For mechanical systems, a reduction in the number of unknown variables is immediately realized as a consequence of Newton's second law of motion which is of second order. The reduction in the size of the problem facilitates rapid solutions from nonlinear programming solvers. A rocket launch problem illustrates the differences in using standard state space first order forms and second-order forms. The numerical results show that the second-order form generates faster results with increasing relative computational speed for increasing grid points.
Proceedings of the 10th Mediterranean Conference on Control and Automation -- MED 2002 , Lisbon, Portugal, July7 9-12, 2002
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