Optimization of Multiphase Aircraft Trajectories Using Hybrid Optimal Control

An approach to optimize multiphase trajectories of commercial transport aircraft is presented. The approach is based on the theory of hybrid optimal control, and it is applied to the case of minimum-fuel trajectories. The multiphase trajectories are composed of three types of phases, climb, cruise, and descent, in a given sequence. In each phase, the optimal control is scalar and of the bang–singular–bang type, and the optimal path is formed by a singular arc and two minimum/maximum-control arcs joining the singular arc with the initial and final switching points. An indirect numerical method is developed, which takes into account the structure of the solution directly in the algorithm and exploits the singular character of the problem. In the analysis, the effects of horizontal winds are taken into account; general along-track wind and crosswind profiles are considered, dependent both on altitude and along-track position. The optimal trajectories are computed for a model of a Boeing 767-300ER performing ...

[1]  Heinz Erzberger,et al.  FIXED-RANGE OPTIMUM TRAJECTORIES FOR SHORT-HAUL AIRCRAFT , 1976 .

[2]  Arthur E. Bryson,et al.  Energy-state approximation in performance optimization of supersonic aircraft , 1969 .

[3]  Alfonso Valenzuela,et al.  Optimization of Aircraft Cruise Procedures Using Discrete Trajectory Patterns , 2014 .

[4]  J. Sørensen,et al.  Airborne Method to Minimize Fuel with Fixed Time-of-Arrival Constraints , 1981 .

[5]  D. H. Williams,et al.  Flight evaluation of the CTAS descent advisor trajectory prediction , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[6]  Antonio Franco,et al.  Optimization of Unpowered Descents of Commercial Aircraft in Altitude-Dependent Winds , 2012 .

[7]  H. Maurer,et al.  Numerical solution of singular control problems using multiple shooting techniques , 1976 .

[8]  Damián Rivas,et al.  Minimum-Fuel Cruise at Constant Altitude with Fixed Arrival Time , 2010 .

[9]  Manuel Soler,et al.  Collocation Methods to Minimum-Fuel Trajectory Problems with Required Time of Arrival in ATM , 2016, J. Aerosp. Inf. Syst..

[10]  R. L. Schultz,et al.  Aircraft performance optimization. , 1972 .

[11]  Alberto Olivares,et al.  Engineering Notes Hybrid Optimal Control Approach to Commercial Aircraft Trajectory Planning , 2010 .

[12]  Richard B. Vinter,et al.  Optimal multiprocesses , 1989 .

[13]  J. W. Burrows.  Fuel-optimal aircraft trajectories with fixed arrival times , 1981 .

[14]  H. Erzberger,et al.  Constrained optimum trajectories with specified range , 1980 .

[15]  Ignacio E. Grossmann,et al.  Retrospective on optimization , 2004, Comput. Chem. Eng..

[16]  Panagiotis Tsiotras,et al.  Drag-law effects in the goddard problem , 1991, Autom..

[17]  Panos J. Antsaklis,et al.  Optimal control of switched systems based on parameterization of the switching instants , 2004, IEEE Transactions on Automatic Control.

[18]  Peter E. Caines,et al.  On the Hybrid Optimal Control Problem: Theory and Algorithms , 2007, IEEE Transactions on Automatic Control.

[19]  C. Iung,et al.  Linear quadratic optimization for hybrid systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[20]  A. Valenzuela,et al.  Compressibility Effects on Maximum Range Cruise at Constant Altitude , 2009 .

[21]  Antonio Franco,et al.  Analysis of optimal aircraft cruise with fixed arrival time including wind effects , 2014 .

[22]  R. Irons,et al.  Energy state approximation and minimum-fuel fixed-range trajectories , 1971 .

[23]  H. Gardner Moyer,et al.  3 Singular Extremals , 1967 .

[24]  R.B. Vinter,et al.  A Maximum Principle for Hybrid Optimal Control Problems with Pathwise State Constraints , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[25]  V. Borkar,et al.  A unified framework for hybrid control: model and optimal control theory , 1998, IEEE Trans. Autom. Control..

[26]  H. Sussmann,et al.  A maximum principle for hybrid optimal control problems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[27]  J. W. Burrows.  Fuel optimal trajectory computation , 1982 .

[28]  Damián Rivas,et al.  Minimum-Cost Cruise at Constant Altitude of Commercial Aircraft Including Wind Effects , 2011 .

[29]  B.D.O. Anderson,et al.  Singular optimal control problems , 1975, Proceedings of the IEEE.

[30]  Mark D. Ardema,et al.  Flight Path Optimization at Constant Altitude , 2005 .

[31]  Yiyuan Zhao,et al.  Sensitivity of Trajectory Prediction in Air Traffic Management , 1999 .

[32]  J. P. Mcdanell,et al.  Necessary Conditions Joining Optimal Singular and Nonsingular Subarcs , 1971 .

[33]  E. Kreindler,et al.  Minimum-fuel, three-dimensional flight paths for jet transports , 1985 .

[34]  A. Chakravarty,et al.  Four-dimensional fuel-optimal guidance in the presence of winds , 1985 .