Three-dimensional trajectory optimization for multi-stage launch vehicle mission using a full-space quasi-Lagrange–Newton method


  • Hsuan-Hao Wang
  • Yi-Su Lo
  • Feng-Tai Hwang
  • Feng-Nan Hwang National Central University, Taiwan



Trajectory optimization, KKT condition, Lagrange-Newton algortihm


Many aerospace industrial applications require robust and efficient numerical solutions of large sparse nonlinear constrained parameter optimization problems arising from optimal trajectory problems. A three-dimensional multistage launcher problem is taken as a numerical example for studying the performance and applicability of the full-space Lagrange–Newton–Krylov method. The typical optimal trajectory, control history and other important physical qualities are presented, and the efficiency of the algorithm is also investigated. References
  • J. T. Betts. Practical methods for optimal control and estimation using nonlinear programming. Advances in Design and Control. SIAM, 2nd edition, 2010. doi:10.1137/1.9780898718577.
  • R. T. Marler and J. S. Arora. Survey of multi-objective optimization methods for engineering. Struct. Multidiscip. Opt., 26(6):369–395, 2004. doi:10.1007/s00158-003-0368-6.
  • W. Roh and Y. Kim. Trajectory optimization for a multi-stage launch vehicle using time finite element and direct collocation methods. Eng. Opt., 34:15–32, 2002. doi:10.1080/03052150210912.
  • G. D. Silveira and V. Carrara. A six degrees-of-freedom flight dynamics simulation tool of launch vehicles. J. Aero. Tech. Manag., 7:231–239, 2015. doi:10.5028/jatm.v7i2.433.
  • H.-H. Wang, Y.-S. Lo, F.-T. Hwang, and F.-N. Hwang. A full-space quasi-Lagrange–Newton–Krylov algorithm for trajectory optimization problems. Electron. T. Numer. Anal., 49:103–125, 2018. doi:10.1553/etna_vol49s103.
  • H. Yang, F.-N. Hwang, and X.-C. Cai. Nonlinear preconditioning techniques for full-space Lagrange-Newton solution of PDE-constrained optimization problems. SIAM J. Sci. Comput., 38:A2756–A2778, 2016. doi:10.1137/15M104075X.





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