Abstract
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.
Highlights
An optimal control solver making use of the direct Hermite-Simpson collocation formulation of optimal control problems was developed
The formulae obtained can be extended to solving ordinary two-point boundary value problems with HermiteSimpson collocation
These first derivatives are estimated using sparse finite-differencing, alternatively they can be obtained with automatic differentiation or symbolic differentiation
Summary
An optimal control solver making use of the direct Hermite-Simpson collocation formulation of optimal control problems was developed. Formulae for determining the analytical first derivative information of the defect constraints of the direct Hermite-Simpson collocation formulation of optimal control problems have been formulated. The formulae obtained can be extended to solving ordinary two-point boundary value problems with HermiteSimpson collocation These first derivatives are estimated using sparse finite-differencing, alternatively they can be obtained with automatic differentiation or symbolic differentiation. Optimal control is a field of study with various application in fields such as aerospace, robotics and chemical engineering It is concerned with the determination of trajectories which optimise some cost function of a given dynamic system. This paper first outlines the general transcription process of an optimal control problem to an Nonlinear Programming (NLP) problem using Hermite-Simpson collocation with linear mean control splines. Following which the first derivatives will be applied with example problems, using Matlab’s Sequential Quadratic Programming (SQP) algorithm
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