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 HermiteSimpson 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.

Digitalization: An Opportunity for Contributing to Sustainability From Knowledge Creation

“…In the operational field, the study of the optimal trajectory has been broadly researched [69][70][71], in most of the cases linked to FCO. The FCO in the air transport sector is an old topic [72], and aside from the obvious business interests, sustainability is making it again a trending topic [73][74][75][76].…”

“…In this direction, the Trajectory Sharing Platform (TSP) is the last initiative under analysis. The idea behind TSP comes from the "Flight and Flow Information for a Collaborative Environment" (FF-ICE, ICAO's project) [83], and it is specifically based on evidence of the importance of optimal trajectory management to improve operations' efficiency [69,84,85].…”

“…The optimal flight path recommended by the FPO is usually not feasible to follow due to ATC restrictions or surrounding traffic. Not allowing the aircraft to adapt its trajectory to the optimal has a direct impact on fuel consumption [69], and it could imply extra fuel consumption of up to 30% on airport arrival procedures [88], or in the case of the continuous cruise phase of an Airbus A320 between 1% and 2% of the trip fuel [89].…”

Analyzing the Departure Runway Capacity Effects of Integrating Optimized Continuous Climb Operations

“…F. Fahroo and I. M. Ross presented at [12] the demonstration of the fact that Chebyshev-Gauss-Lobatto (CGL) method yields more accurate results than those obtained from the traditional collocation method. Recently, in [13], an intensive analysis on different direct collocation methods to solve a classical problem on ATM was presented. Once again, pseudospectral collocation method has proven better results on accuracy and computational time but uncertainties in vertical trajectories during a climb/descent.…”

Different optimization strategies for the optimal control of tumor growth

“…Previous comparative studies between direct and indirect control given in [38], where this paper two different approaches (direct and indirect) for the numerical solution of fractional optimal control problems (FOCPs) based on a spectral method using Chebyshev polynomial are presented. Moreover, in [18] a comparative study between singular arc method (without con-sidering inequality constraints) as indirect method and three different direct methods namely Hermite-Simpson's collocation method, 5 th degree Gauss-Lobatto collocation method, Radau Psuedospectral collocation method using GPOP [34]. In [9] a comparative study between dynamic programming, indirect methods and direct methods is presented.…”