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On-line Ascent Phase Trajectory Optimal Guidance Algorithm based on Pseudo-spectral Method and Sensitivity Updates

Published online by Cambridge University Press:  10 June 2015

Da Zhang ,
Lei Liu  and
Yongji Wang
Da Zhang
Affiliation:
(Key Laboratory of Ministry of Education for Image Processing and Intelligent Control, School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China)
Lei Liu*
Affiliation:
(Key Laboratory of Ministry of Education for Image Processing and Intelligent Control, School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China)
Yongji Wang
Affiliation:
(Key Laboratory of Ministry of Education for Image Processing and Intelligent Control, School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China)
*
(E-mail: lei.liu.chn@gmail.com)
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Abstract

The objective of this paper is to investigate an online method to generate an optimal ascent trajectory for air-breathing hypersonic vehicles. A direct method called the Pseudo-spectral method shows promise for real-time optimal guidance. A significant barrier to this optimisation-based control strategy is computational delay, especially when the solution time of the non-linear programming problem exceeds the sampling time. Therefore, an online guidance algorithm for an air-breathing hypersonic vehicles with process constraints and terminal states constraints is proposed based on the Pseudo-spectral method and sensitivity analysis in this paper, which can reduce online computational costs and improve performance significantly. The proposed ascent optimal guidance method can successively generate online open-loop suboptimal controls without the design procedure of an inner-loop feedback controller. Considering model parameters' uncertainties and external disturbance, a sampling theorem is proposed that indicates the effect of the Lipschitz constant of the dynamics on sampling frequency. The simulation results indicate that the proposed method offers improved performance and has promising ability to generate an optimal ascent trajectory for air-breathing hypersonic vehicles.

Keywords

Online optimal guidancePseudo-spectral methodSensitivity analysisAir-breathing hypersonic vehicles

Information

Type
Research Article
Information
The Journal of Navigation , Volume 68 , Issue 6 , November 2015 , pp. 1056 - 1074
Copyright
Copyright © The Royal Institute of Navigation 2015 

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References

REFERENCES

Benson, D. (2005). A Gauss pseudospectral transcription for optimal control. Doctoral dissertation, Massachusetts Institute of Technology.Google Scholar
Betts, J.T. (1998). Survey of numerical methods for trajectory optimization. Journal of Guidance, Control, and Dynamics, 21(2), 193–207.CrossRefGoogle Scholar
Bollino, K.P., Ross, I.M., and Doman, D.D. (2006). Optimal nonlinear feedback guidance for re-entry vehicles. In AIAA Guidance, Navigation and Control Conference.CrossRefGoogle Scholar
Clarke, F. (2004). Lyapunov functions and feedback in nonlinear control. In Optimal Control, Stabilization and Non-smooth Analysis, 267–282, Springer Berlin Heidelberg.CrossRefGoogle Scholar
Conway, B.A. (2012). A survey of methods available for the numerical optimization of continuous dynamic systems. Journal of Optimization Theory and Applications, 152(2), 271–306.CrossRefGoogle Scholar
Dukeman, G., and Calise, A.J. (2003). Enhancements to an atmospheric ascent guidance algorithm. AIAA paper, 5638.CrossRefGoogle Scholar
Dukeman, G.A. (2002). Atmospheric ascent guidance for rocket-powered launch vehicles. AIAA paper, 4559, 5–8.CrossRefGoogle Scholar
Fiacco, A.V. (1976). Sensitivity analysis for nonlinear programming using penalty methods. Mathematical programming, 10(1), 287–311.CrossRefGoogle Scholar
García, I.M. (2005). Nonlinear trajectory optimization with path constraints applied to spacecraft reconfiguration maneuvers (Doctoral dissertation, Massachusetts Institute of Technology).Google Scholar
Grüne, L., and Pannek, J. (2011). Nonlinear model predictive control, 43–66, Springer London.CrossRefGoogle Scholar
Henry, J.R., and McLellan, C.H. (1971). Air-Breathing Launch Vehicle for Earth-Orbit Shuttle-New Technology and Development Approach. Journal of Aircraft, 8(5), 381–387.CrossRefGoogle Scholar
Huang, G., Lu, Y., and Nan, Y. (2012). A survey of numerical algorithms for trajectory optimization of flight vehicles. Science China Technological Sciences, 55(9), 2538–2560.CrossRefGoogle Scholar
Huntington, G.T. (2007). Advancement and analysis of a Gauss pseudospectral transcription for optimal control problems. Doctoral dissertation, University of Florida.Google Scholar
Jiang, C., Teo, K.L., and Duan, G.R. (2012). A suboptimal feedback control for nonlinear time-varying systems with continuous inequality constraints. Automatica, 48(4), 660–665.CrossRefGoogle Scholar
Li, S., Jiang, X., and Liu, Y. (2014). High-precision Mars entry integrated navigation under large uncertainties. The Journal of Navigation, 67(02), 327–342.CrossRefGoogle Scholar
Murillo, O.J., and Lu, P. (2010). Fast ascent trajectory optimization for hypersonic air-breathing vehicles. In Proceedings of the AIAA Guidance, Navigation, and Control Conference, 5–8.CrossRefGoogle Scholar
Patterson, M.A., and Rao, A.V. (2014). GPOPS-II: A MATLAB software for solving multiple-phase optimal control problems using HP-adaptive Gaussian quadrature collocation methods and sparse non-linear programming. ACM Transactions on Mathematical Software (TOMS), 41(1), 1.CrossRefGoogle Scholar
Pirnay, H., López-Negrete, R., and Biegler, L.T. (2012). Optimal sensitivity based on IPOPT. Mathematical Programming Computation, 4(4), 307–331.CrossRefGoogle Scholar
Prasanna, H.M., Ghose, D., Bhat, M.S., Bhattacharyya, C., and Umakant, J. (2005). Interpolation-aware trajectory optimization for a hypersonic vehicle using nonlinear programming. AIAA Paper, 6063.CrossRefGoogle Scholar
Rao, A.V., Benson, D.A., Darby, C., Patterson, M.A., Francolin, C., Sanders, I., and Huntington, G. T. (2010). Algorithm 902: GPOPS, a MATLAB software for solving multiple-phase optimal control problems using the Gauss Pseudospectral method. ACM Transactions on Mathematical Software (TOMS), 37(2), 22.CrossRefGoogle Scholar
Ross, I.M., Gong, Q., Fahroo, F., and Kang, W. (2006). Practical stabilization through real-time optimal control. In American Control Conference, IEEE.CrossRefGoogle Scholar
Ross, I.M., Sekhavat, P., Fleming, A., and Gong, Q. (2008). Optimal feedback control: foundations, examples, and experimental results for a new approach. Journal of Guidance, Control, and Dynamics, 31(2), 307–321.CrossRefGoogle Scholar
Saraf, A., Leavitt, J.A., Chen, D.T., and Mease, K.D. (2004). Design and evaluation of an acceleration guidance algorithm for entry. Journal of Spacecraft and Rockets, 41(6), 986–996.CrossRefGoogle Scholar
Vinh, N. (1981). Optimal trajectories in atmospheric flight (Vol. 1). Elsevier.Google Scholar
Yamamoto, T., and Kawaguchi, J.I. (2007). A new real-time guidance strategy for aerodynamic ascent flight. Acta Astronautica, 61(11), 965–977.CrossRefGoogle Scholar
Yang, X., and Biegler, L.T. (2013). Advanced-multi-step nonlinear model predictive control. Journal of Process Control, 23(8), 1116–1128.CrossRefGoogle Scholar
Zavala, V.M., and Biegler, L.T. (2009). The advanced-step NMPC controller: Optimality, stability and robustness. Automatica, 45(1), 86–93.CrossRefGoogle Scholar
Zhang, D., Lu, X., Liu, L., and Wang, Y. (2012). An online ascent phase trajectory reconstruction algorithm using Gauss pseudospectral method. In Modelling, Identification & Control (ICMIC), 2012 Proceedings of International Conference on, 1184–1189, IEEE.Google Scholar