Gaussian Distribution–Based Control Vector Parameterization Method for Constrained Hypersonic Vehicle Reentry Trajectory Optimization
Publication: Journal of Aerospace Engineering
Volume 36, Issue 6
Abstract
This study proposes a Gaussian-discretization control vector parametrization (CVP) algorithm to improve the reentry trajectory optimization accuracy of a hypersonic vehicle (HV) with a complex path and terminal state constraints. First, the reentry trajectory optimization problem (TOP) of the HV is established by analyzing the equations of motion and constraints. Second, a Gaussian distribution strategy is derived to obtain a suitable control parametrization time grid for improving control quality. By combining the handling strategies for path and terminal constraints, an efficient, non-uniform control parametrization trajectory optimization method is established, and the HV trajectory optimization algorithm framework is provided in detail. Lastly, the proposed algorithms are implemented on a widely studied common aero vehicle model. Numerical simulation tests are conducted on terminal-time-free and terminal-time-fixed TOPs to optimize the reentry downrange. Test results show that the proposed method has a stable solving ability with high satisfaction of terminal constraints. Simulation results reveal that the proposed method efficiently increases the downrange compared with other CVP methods under the tested scenario, thus showing the effectiveness of the proposed distribution strategy.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (61803060), and the Natural Science Foundation Project of Chongqing (2022NSCQ-MSX2519).
References
Betts, J. T. 2010. Practical methods for optimal control and estimation using nonlinear programming. Philadelphia: Society for Industrial and Applied Mathematics.
Binder, T., A. Cruse, C. A. Cruz Villar, and W. Marquardt. 2000. “Dynamic optimization using a wavelet based adaptive control vector parameterization strategy.” Comput. Chem. Eng. 24 (2): 1201–1207. https://doi.org/10.1016/S0098-1354(00)00357-4.
Chai, R., A. Savvaris, A. Tsourdos, S. Chai, and Y. Xia. 2019. “A review of optimization techniques in spacecraft flight trajectory design.” Prog. Aerosp. Sci. 109 (Aug): 100543. https://doi.org/10.1016/j.paerosci.2019.05.003.
Ding, Y., X. Yue, G. Chen, and J. Si. 2022. “Review of control and guidance technology on hypersonic vehicle.” Chin. J. Aeronaut. 35 (7): 1–18. https://doi.org/10.1016/j.cja.2021.10.037.
Engelbrecht, A. P. 2007. Computational intelligence. An introduction. New York: Wiley.
Goldberg, D. E. 1989. Genetic algorithms in search, optimization and machine learning. Boston: Addison Wesley.
Hu, Y., X. Liu, and A. Xue. 2013. “A penalty method for solving inequality path constrained optimal control problems.” Acta Autom. Sin. 39 (12): 1996–2001. https://doi.org/10.3724/SP.J.1004.2013.01996.
Jiang, C., Q. Lin, C. Yu, K. L. Teo, and G. R. Duan. 2012. “An exact penalty method for free terminal time optimal control problem with continuous inequality constraints.” J. Optim. Theory Appl. 154 (1): 30–53. https://doi.org/10.1007/s10957-012-0006-9.
Jorris, T. R. 2007. “Common aero vehicle autonomous reentry trajectory optimization satisfying waypoint and no-fly zone constraints.” Theses and dissertations, Dept. of the Air, Air Force Institute of Technology. https://scholar.afit.edu/etd/2904.
Lee, H. W. J., K. L. Teo, V. Rehbock, and L. S. Jennings. 1999. “Control parametrization enhancing technique for optimal discrete-valued control problems.” Automatica 35 (8): 1401–1407. https://doi.org/10.1016/S0005-1098(99)00050-3.
Liu, P., Y. Hu, J. Liao, L. Fan, X. Li, and X. Liu. 2019a. “Optimization operation of electric locomotive based on two-stage adaptive Gauss re-collocation pseudospectral approach.” Acta Autom. Sin. 45 (12): 2344–2354. https://doi.org/10.16383/j.aas.c190211.
Liu, P., G. Li, X. Liu, L. Xiao, Y. Wang, C. Yang, and W. Gui. 2018a. “A novel non-uniform control vector parameterization approach with time grid refinement for flight level tracking optimal control problems.” ISA Trans. 73 (Feb): 66–78. https://doi.org/10.1016/j.isatra.2017.12.008.
Liu, P., G. Li, J. Yang, and X. Liu. 2019b. “Fast optimal control numerical approach for the swing control of container load.” Control Theory Appl. 36 (8): 1275–1282. https://doi.org/10.7641/CTA.2018.80352.
Liu, P., X. Li, X. Liu, and Y. Hu. 2017. “An improved smoothing technique-based control vector parameterization method for optimal control problems with inequality path constraints.” Optim. Control. Appl. Methods 38 (4): 586–600. https://doi.org/10.1002/oca.2273.
Liu, P., X. Liu, P. Wang, G. Li, L. Xiao, J. Yan, and Z. Ren. 2018b. “Control variable parameterisation with penalty approach for hypersonic vehicle reentry optimization.” Int. J. Control 92 (9): 2015–2024. https://doi.org/10.1080/00207179.2018.1426882.
Liu, X., Y. Hu, J. Feng, and K. Liu. 2014. “A novel penalty approach for nonlinear dynamic optimization problems with inequality path constraints.” IEEE Trans. Autom. Control 59 (10): 2863–2867. https://doi.org/10.1109/TAC.2014.2317293.
NOAA (National Oceanic and Atmospheric Administration). 1976. US Standard atmosphere. Washington, DC: NOAA.
Pontani, M., and B. A. Conway. 2010. “Particle swarm optimization applied to space trajectories.” J. Guid. Control Dyn. 33 (5): 1429–1441. https://doi.org/10.2514/1.48475.
Su, Z., H. Wang, and P. Yao. 2016. “A hybrid backtracking search optimization algorithm for nonlinear optimal control problems with complex dynamic constraints.” Neurocomputing 186 (Aug): 182–194. https://doi.org/10.1016/j.neucom.2015.12.067.
Sun, Y., and M. Zhang. 2011. “Optimal reentry range trajectory of hypersonic vehicle by gauss pseudospectral method.” In Proc., 2nd Int. Conf. on Intelligent Control and Information Processing, 545–549. New York: IEEE. https://doi.org/10.1109/ICICIP.2011.6008304.
Vinh, N. X. 1981. “Optimal trajectories in atmospheric flight.” In Proc., XXXII Int. Astronautical Federation Congress. Amsterdam, Netherlands: Elsevier.
Yong, E., L. Chen, and G. J. Tang. 2008. “Trajectory optimization of hypersonic gliding reentry vehicle based on the physical programming.” Acta Aeronaut. Astronaut. Sin. 29 (5): 1091–1097. https://doi.org/10.3321/j.issn:1000-6893.2008.05.001.
Yu, C. J., K. L. Teo, L. S. Zhang, and Y. Q. Bai. 2010. “A new exact penalty function method for continuous inequality constrained optimization problems.” J. Ind. Manage. Optim. 6 (4): 895–910. https://doi.org/10.3934/jimo.2010.6.895.
Zhang, M., Y. Sun, and G. Duan. 2010. “Reentry trajectory optimization of hypersonic vehicle with enhancing parametrization method.” In Proc., 3rd Int. Symp. on Systems and Control in Aeronautics and Astronautics2010, 40–45. New York: IEEE. https://doi.org/10.1109/ISSCAA.2010.5633024.
Zhao, H. 1997. Spacecraft reentry dynamics and guidance. Changsha, China: Press of National Univ. of Defence Technology.
Zhao, Z. T., W. Huang, L. Yan, and Y. G. Yang. 2020. “An overview of research on wide-speed range waverider configuration.” Prog. Aerosp. Sci. 113 (Feb): 100606. https://doi.org/10.1016/j.paerosci.2020.100606.
Zhou, H., X. Wang, and N. Cui. 2020. “Glide guidance for reusable launch vehicles using analytical dynamics.” Aerosp. Sci. Technol. 98 (Mar): 105678. https://doi.org/10.1016/j.ast.2019.105678.
Information & Authors
Information
Published In
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Jun 13, 2022
Accepted: Jun 20, 2023
Published online: Aug 18, 2023
Published in print: Nov 1, 2023
Discussion open until: Jan 18, 2024
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.