A Comparison of Optimal Control Methods for Minimum Fuel Cruise at Constant Altitude and Course with Fixed Arrival Time

Abstract The current lack of efficiency in the use of airspace, enforced by the economic crisis an the increasing competitiveness among air transport companies are drivers for a renewed interest for the application of optimization techniques to find answers to overcame current inefficiencies. The main objective of the present paper is to assess and compare different optimal aircraft trajectories techniques applied to the minimum fuel cruise problem at constant altitude and course with fixed arrival time, International Standard Atmosphere and without wind. Four trajectory optimization methods have been used: Hermite-Simpson, 5th degree Gauss-Lobatto and Radau pseudospectral collocation methods and the singular arc solution. Hermite-Simpson and 5th degree methods have been programmed in Ampl modeling language with an IPOPT solver and Radau pseudospectral method using gpops matlab tool with SNOPT solver. 5th degree Gauss-Lobatto collocation method gives the less fuel consumption solution followed by Radau pseudospectral, Hermite-Simpson and singular arc. In considering the program execution time, Hermite-Simpson collocation method is the fastest method followed by 5th degree and Radau pseudospectral. Also, taking into account the time for developing the program code the Radau pseudospectral is the most user friendly. Moreover, it has been observed that increasing the sample points in the Hermite- Simpson and 5th degree, the solution converge to the minimum fuel consumption solution. On the other hand, gpops does not show much sensitivity to the number of sample points.

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