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Optimal 3-dimension trajectory-tracking guidance for reusable launch vehicle based on back-stepping adaptive dynamic programming

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Abstract

An optimal 3-dimension trajectory-tracking guidance method for Reusable Launch Vehicle (RLV) is proposed based on back-stepping Adaptive Dynamic Programming (ADP). The reference trajectory is generated based on the Gaussian pseudo-spectral method with sufficient saturation constraints on inputs. The reentry dynamics are normalized and modeled as position and velocity subsystems, based on which back-stepping approach is applied to derive the velocity virtual command which effectively reduces the position errors. A single-critic ADP structure is designed to achieve the optimal feedback control with an innovative weight iteration algorithm which reduces training computation, accelerates weights convergence and improves guidance accuracy. The proposed RLV guidance method is validated through the Monte Carlo simulations with initial errors, aerodynamic uncertainty and external disturbances. Comparable results with conventional guidance method based on Linear Quadratic Regulator (LQR) and weight iteration algorithm based on gradient decent demonstrate the advantages of the proposed guidance method.

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Data availability

The datasets generated during the current study are not publicly available due to the fund requirements but are available from the corresponding author on reasonable request.

References

  1. Bae S, Shin HS, Savvaris A et al (2020) Multi-objective suborbit/orbit trajectory optimisation for spaceplanes. Acta Astronaut 170:431–442. https://doi.org/10.1016/j.actaastro.2020.01.003

    Article  Google Scholar 

  2. Aprovitola A, Iuspa L, Pezzella G, Viviani A (2021) Phase-A design of a reusable re-entry vehicle. Acta Astronaut 187:141–155. https://doi.org/10.1016/j.actaastro.2021.06.034

    Article  Google Scholar 

  3. Jiang CW, Zhou GF, Yang B et al (2018) Novel guidance model and its application for optimal re-entry guidance. Aeronaut J 122:1811–1825. https://doi.org/10.1017/aer.2018.94

    Article  Google Scholar 

  4. Sushnigdha G, Joshi A (2018) Re-entry trajectory optimization using pigeon inspired optimization based control profiles. Adv Space Res 62:3170–3186. https://doi.org/10.1016/j.asr.2018.08.009

    Article  Google Scholar 

  5. Mao Y, Zhang D, Wang L (2017) Reentry trajectory optimization for hypersonic vehicle based on improved Gauss pseudospectral method. Soft Comput 21:4583–4592. https://doi.org/10.1007/s00500-016-2201-3

    Article  Google Scholar 

  6. Nejat A, Mirzabeygi P, Shariat-Panahi M, Mirzakhalili E (2012) Using improved particle swarm optimization algorithm. ASME Int Mech Eng Congr Expo Proc 7:577–585. https://doi.org/10.1115/IMECE2012-88833

    Article  Google Scholar 

  7. Chai R, Tsourdos A, Savvaris A et al (2020) Real-time reentry trajectory planning of hypersonic vehicles: a two-step strategy incorporating fuzzy multiobjective transcription and deep neural network. IEEE Trans Ind Electron 67:6904–6915. https://doi.org/10.1109/TIE.2019.2939934

    Article  Google Scholar 

  8. Hsu CF, Lin CM, Yeh RG (2013) Supervisory adaptive dynamic RBF-based neural-fuzzy control system design for unknown nonlinear systems. Appl Soft Comput J 13:1620–1626. https://doi.org/10.1016/j.asoc.2012.12.028

    Article  Google Scholar 

  9. Sushnigdha G, Joshi A (2018) Evolutionary method based integrated guidance strategy for reentry vehicles. Eng Appl Artif Intell 69:168–177. https://doi.org/10.1016/j.engappai.2017.11.010

    Article  Google Scholar 

  10. Wang X, Li Y, Zhang J (2021) A novel IGC scheme for RHV with the capabilities of online aerodynamic coefficient estimation and trajectory generation. Mathematics 9:1–19. https://doi.org/10.3390/math9020172

    Article  Google Scholar 

  11. Zhang W, Chen W, Yu W (2018) Entry guidance for high-L/D hypersonic vehicle based on drag-vs-energy profile. ISA Trans 83:176–188. https://doi.org/10.1016/j.isatra.2018.08.012

    Article  Google Scholar 

  12. Omar SR, Bevilacqua R (2019) Hardware and GNC solutions for controlled spacecraft re-entry using aerodynamic drag. Acta Astronaut 159:49–64. https://doi.org/10.1016/j.actaastro.2019.03.051

    Article  Google Scholar 

  13. Li Z, Yang T, Feng Z (2019) Re-entry guidance method based on decoupling control variables and waypoint. Aeronaut J 123:523–535. https://doi.org/10.1017/aer.2019.4

    Article  Google Scholar 

  14. Pan L, Peng S, Xie Y et al (2020) 3D guidance for hypersonic reentry gliders based on analytical prediction. Acta Astronaut 167:42–51. https://doi.org/10.1016/j.actaastro.2019.07.039

    Article  Google Scholar 

  15. Sarkar R, Mukherjee J, Patil D, Kar IN (2021) Re-entry trajectory tracking of reusable launch vehicle using artificial delay based robust guidance law. Adv Space Res 67:557–570. https://doi.org/10.1016/j.asr.2020.10.006

    Article  Google Scholar 

  16. Bu X, Qi Q, Jiang B (2021) A simplified finite-time fuzzy neural controller with prescribed performance applied to waverider aircraft. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2021.3089031

    Article  Google Scholar 

  17. Bu X, Jiang B, Lei H (2022) Non-fragile quantitative prescribed performance control of waverider vehicles with actuator saturation. IEEE Trans Aerosp Electron Syst. https://doi.org/10.1109/taes.2022.3153429

    Article  Google Scholar 

  18. Bu X, Qi Q (2022) Fuzzy optimal tracking control of hypersonic flight vehicles via single-network adaptive critic design. IEEE Trans Fuzzy Syst 30:270–278. https://doi.org/10.1109/TFUZZ.2020.3036706

    Article  Google Scholar 

  19. Wang R, Tang S, Zhang D (2019) Short-range reentry guidance with impact angle and impact velocity constraints for hypersonic gliding reentry vehicle. IEEE Access 7:47435–47450. https://doi.org/10.1109/ACCESS.2019.2909589

    Article  Google Scholar 

  20. Li G, Chao T, Wang S, Yang M (2020) Integrated guidance and control for the fixed-trim vehicle against the maneuvering target. Int J Control Autom Syst 18:1518–1529. https://doi.org/10.1007/s12555-018-0824-0

    Article  Google Scholar 

  21. Shao X, Wang H, Zhang H (2015) Enhanced trajectory linearization control based advanced guidance and control for hypersonic reentry vehicle with multiple disturbances. Aerosp Sci Technol 46:523–536. https://doi.org/10.1016/j.ast.2015.09.003

    Article  Google Scholar 

  22. Bu X, Wu X, Huang J, Wei D (2016) Robust estimation-free prescribed performance back-stepping control of air-breathing hypersonic vehicles without affine models. Int J Control 89:2185–2200. https://doi.org/10.1080/00207179.2016.1151080

    Article  MathSciNet  MATH  Google Scholar 

  23. Schierman JD, Ward DG, Hull JR et al (2004) Integrated adaptive guidance and control for re-entry vehicles with flight-test results. J Guid Control Dyn 27:975–988. https://doi.org/10.2514/1.10344

    Article  Google Scholar 

  24. Wang Y, Lei H, Ye J, Bu X (2018) Backstepping sliding mode control for radar seeker servo system considering guidance and control system. Sens Switz. https://doi.org/10.3390/s18092927

    Article  Google Scholar 

  25. Schlanbusch SM, Zhou J, Schlanbusch R (2022) Adaptive attitude control of a rigid body with input and output quantization. IEEE Trans Ind Electron 69:8296–8305. https://doi.org/10.1109/TIE.2021.3105999

    Article  Google Scholar 

  26. Chen ZY, Meng Y, Chen T (2022) NN model-based evolved control by DGM model for practical nonlinear systems. Expert Syst Appl 193:115873. https://doi.org/10.1016/j.eswa.2021.115873

    Article  Google Scholar 

  27. Zhang S, Zhao B, Liu D, Zhang Y (2021) Observer-based event-triggered control for zero-sum games of input constrained multi-player nonlinear systems. Neural Netw 144:101–112. https://doi.org/10.1016/j.neunet.2021.08.012

    Article  Google Scholar 

  28. Liu Y, Xing Z, Chen Z, Xu J (2021) Data-based robust optimal control of discrete-time systems with uncertainties via adaptive dynamic programming. Optim Control Appl Methods. https://doi.org/10.1002/oca.2775

    Article  Google Scholar 

  29. Hu C, Zou Y, Li S (2021) Adaptive dynamic programming-based decentralized event-triggered control of large-scale nonlinear systems. Asian J Control. https://doi.org/10.1002/asjc.2662

    Article  Google Scholar 

  30. De Keyser A, Vansompel H, Crevecoeur G (2021) Real-time energy-efficient actuation of induction motor drives using approximate dynamic programming. IEEE Trans Ind Electron 68:11837–11846. https://doi.org/10.1109/TIE.2020.3044791

    Article  Google Scholar 

  31. Zhang K, Zhang H, Liang X, Wang Z (2019) Neurodynamic programming and tracking control scheme of constrained-input systems via a novel event-triggered PI algorithm. Appl Soft Comput J 83:105629. https://doi.org/10.1016/j.asoc.2019.105629

    Article  Google Scholar 

  32. Mu C, Sun C, Wang D, Song A (2017) Adaptive tracking control for a class of continuous-time uncertain nonlinear systems using the approximate solution of HJB equation. Neurocomputing 260:432–442. https://doi.org/10.1016/j.neucom.2017.04.043

    Article  Google Scholar 

  33. Xu D, Wang Q, Li Y (2020) Optimal guaranteed cost tracking of uncertain nonlinear systems using adaptive dynamic programming with concurrent learning. Int J Control Autom Syst 18:1116–1127. https://doi.org/10.1007/s12555-019-0165-7

    Article  Google Scholar 

  34. Liu L, Wang Z, Zhang H (2018) Neural-network-based robust optimal tracking control for MIMO discrete-time systems with unknown uncertainty using adaptive critic design. IEEE Trans Neural Netw Learn Syst 29:1239–1251. https://doi.org/10.1109/TNNLS.2017.2660070

    Article  Google Scholar 

  35. Wang D, Mu C (2018) Adaptive-critic-based robust trajectory tracking of uncertain dynamics and its application to a spring-mass-damper system. IEEE Trans Ind Electron 65:654–663. https://doi.org/10.1109/TIE.2017.2722424

    Article  Google Scholar 

  36. Zhang K, Zhang H, Jiang H, Wang Y (2018) Near-optimal output tracking controller design for nonlinear systems using an event-driven ADP approach. Neurocomputing 309:168–178. https://doi.org/10.1016/j.neucom.2018.05.010

    Article  Google Scholar 

  37. Zhang W, Yi W (2021) Composite adaptive dynamic programming for missile interception systems with multiple constraints and less sensor requirement. ISA Trans 117:40–53. https://doi.org/10.1016/j.isatra.2021.01.040

    Article  Google Scholar 

  38. Cui L, Wang S, Zhang J et al (2021) Learning-based balance control of wheel-legged robots. IEEE Robot Autom Lett 6:7667–7674. https://doi.org/10.1109/LRA.2021.3100269

    Article  Google Scholar 

  39. Wei Q, Liao Z, Shi G (2021) Generalized actor-critic learning optimal control in smart home energy management. IEEE Trans Ind Inform 17:6614–6623. https://doi.org/10.1109/TII.2020.3042631

    Article  Google Scholar 

  40. Zang L, Lin D, Chen S et al (2019) An on-line guidance algorithm for high L/D hypersonic reentry vehicles. Aerosp Sci Technol 89:150–162. https://doi.org/10.1016/j.ast.2019.03.052

    Article  Google Scholar 

  41. Liu F, Hager WW, Rao AV (2015) Adaptive mesh refinement method for optimal control using nonsmoothness detection and mesh size reduction. J Frankl Inst 352:4081–4106. https://doi.org/10.1016/j.jfranklin.2015.05.028

    Article  MathSciNet  MATH  Google Scholar 

  42. Bu X (2018) Air-breathing hypersonic vehicles funnel control using neural approximation of non-affine dynamics. IEEE/ASME Trans Mechatron 23:2099–2108. https://doi.org/10.1109/TMECH.2018.2869002

    Article  Google Scholar 

  43. Vamvoudakis KG, Lewis FL (2010) Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem. Automatica 46:878–888. https://doi.org/10.1016/j.automatica.2010.02.018

    Article  MathSciNet  MATH  Google Scholar 

  44. Zhang H, Cui L, Zhang X, Luo Y (2011) Data-driven robust approximate optimal tracking control for unknown general nonlinear systems using adaptive dynamic programming method. IEEE Trans Neural Netw 22:2226–2236. https://doi.org/10.1109/TNN.2011.2168538

    Article  Google Scholar 

  45. Yang Y, Fan X, Xu C et al (2021) State consensus cooperative control for a class of nonlinear multi-agent systems with output constraints via ADP approach. Neurocomputing 458:284–296. https://doi.org/10.1016/j.neucom.2021.05.046

    Article  Google Scholar 

  46. Cui L, Xie X, Wang X et al (2019) Event-triggered single-network ADP method for constrained optimal tracking control of continuous-time non-linear systems. Appl Math Comput 352:220–234. https://doi.org/10.1016/j.amc.2019.01.066

    Article  MathSciNet  MATH  Google Scholar 

  47. Sun H, Zhang S (2020) Skip re-entry trajectory detection and guidance for maneuvering vehicles. Sens Switz. https://doi.org/10.3390/s20102976

    Article  Google Scholar 

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Acknowledgements

The research is funded by Aeronautical Science Fund (2019ZC051009).

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  1. School of Instrument Science and Opto-Electronics Engineering, Beihang University, Beijing, 100191, China

    Xueyun Wang, Zhiyuan Quan & Jingjuan Zhang

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Wang, X., Quan, Z. & Zhang, J. Optimal 3-dimension trajectory-tracking guidance for reusable launch vehicle based on back-stepping adaptive dynamic programming. Neural Comput & Applic 35, 5319–5334 (2023). https://doi.org/10.1007/s00521-022-07972-1

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