Analytical first derivatives of the direct Hermite-Simpson collocation formulation of optimal control problems

In order to assess the capabilities of South Africa as a launch site for commercial satellites, an optimal control solver was developed. The developed solver makes use of direct Hermite-Simpson collocation methods, and can be applied to a general optimal control problem. Analytical first derivative information was obtained for direct Hermite-Simpson collocation methods. Typically, a numerical estimate of the derivative information is used. This paper will present the solver algorithm, and the formulation and derivation of the analytical first derivative information for this approach. A sample problem is provided as validation of the solver.