Exploiting Higher-order Derivatives in Computational Optimal Control

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 firstorder 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.