Abstract
To improve the trajectory-tracking guidance performance for reusable launch vehicle under various uncertainties and distortions, an event-triggered (ET) guidance method based on neural adaptive dynamic programming (ADP) is proposed. Firstly, the reference trajectory and corresponding steady-state control are generated optimally offline based on Gauss pseudo-spectral method. Secondly, the approximate optimal feedback controller based on single-critic ADP is designed. The great adaptation capacity inheriting from reinforcement learning technique ensures the tracking errors to converge to zero, and yet no offline dataset or pre-training is required. Event-triggered mechanism is introduced to reduce online training computation and save data transmission resource. Event-triggered condition is designed and the asymptotic stability of the event-triggered guidance system is proved. Comprehensive simulations are conducted and results validate the effectiveness of the feedback controller based on ADP and the significantly improved efficiency of ET mechanism. Besides, the improved performance of the proposed guidance method over traditional method of linear quadratic regulator has also been verified through simulations.
Similar content being viewed by others
References
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
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
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
Sushnigdha G, Joshi A (2018) Re-entry trajectory optimization using pigeon inspired optimization based control profiles. Adv Sp Res 62:3170–3186. https://doi.org/10.1016/j.asr.2018.08.009
Stevens BL (2016) Aircraft control and simulation: dynamics, Control Design and Autonomous Systems. John Wiley & Sons, Hoboken, NJ, USA
Zhang H, Wang H, Li N et al (2020) Time-optimal memetic whale optimization algorithm for hypersonic vehicle reentry trajectory optimization with no-fly zones. Neural Comput Appl 32:2735–2749. https://doi.org/10.1007/s00521-018-3764-y
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
Qiao H, Sun P, Li X (2019) General reentry trajectory planning method based on improved maneuver coefficient. IEEE Access 7:5447–5456. https://doi.org/10.1109/ACCESS.2018.2889926
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
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
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
Bu X, Lei H (2018) A fuzzy wavelet neural network-based approach to hypersonic flight vehicle direct nonaffine hybrid control. Nonlinear Dyn 94:1657–1668. https://doi.org/10.1007/s11071-018-4447-z
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
Wang X, Li Y, Zhang J (2021) A novel IGC scheme for RLV with the capabilities of online aerodynamic coefficient estimation and trajectory generation. Mathematics 9:1–19. https://doi.org/10.3390/math9020172
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 Sp Res 67:557–570. https://doi.org/10.1016/j.asr.2020.10.006
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
Halbe O, Raja RG, Padhi R (2014) Robust reentry guidance of a reusable launch vehicle using model predictive static programming. J Guid Control Dyn 37:134–148. https://doi.org/10.2514/1.61615
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
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
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
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
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
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
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
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
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
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
Yang X, Liu D, Wei Q, Wang D (2016) Guaranteed cost neural tracking control for a class of uncertain nonlinear systems using adaptive dynamic programming. Neurocomputing 198:80–90. https://doi.org/10.1016/j.neucom.2015.08.119
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 Networks Learn Syst 29:1239–1251. https://doi.org/10.1109/TNNLS.2017.2660070
Tymoshchuk P (2019) A neural circuit model of adaptive robust tracking control for continuous-time nonlinear systems. In: Artificial Neural Networks and Machine Learning – ICANN 2019. pp 819–835
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
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
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
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
Wei Q, Liao Z, Shi G (2021) Generalized actor-critic learning optimal control in smart home energy management. IEEE Trans Ind Informatics 17:6614–6623. https://doi.org/10.1109/TII.2020.3042631
Yang Y, Xu C, Yue D et al (2020) Event-triggered ADP control of a class of non-affine continuous-time nonlinear systems using output information. Neurocomputing 378:304–314. https://doi.org/10.1016/j.neucom.2019.08.097
Xu Y, Li T, Bai W et al (2021) Online event-triggered optimal control for multi-agent systems using simplified ADP and experience replay technique. Nonlinear Dyn. https://doi.org/10.1007/s11071-021-06816-2
Mu C, Liao K, Wang K (2021) Event-triggered design for discrete-time nonlinear systems with control constraints. Nonlinear Dyn 103:2645–2657. https://doi.org/10.1007/s11071-021-06218-4
Yang X, He H (2021) decentralized event-triggered control for a class of nonlinear-interconnected systems using reinforcement learning. IEEE Trans Cybern 51:635–648. https://doi.org/10.1109/TCYB.2019.2946122
Cui L, Zhang Y, Wang X, Xie X (2021) Event-triggered distributed self-learning robust tracking control for uncertain nonlinear interconnected systems. Appl Math Comput. https://doi.org/10.1016/j.amc.2020.125871
Chen X, Chen X, Bai W, Guo Z (2021) Event-triggered optimal control for macro-micro composite stage system via single-network ADP method. IEEE Trans Ind Electron 68:4190–4198. https://doi.org/10.1109/TIE.2020.2984462
Zhang G, Zhu Q (2021) Event-triggered optimal control for nonlinear stochastic systems via adaptive dynamic programming. Nonlinear Dyn 105:387–401. https://doi.org/10.1007/s11071-021-06624-8
Zhang P, Yuan Y, Guo L (2021) Fault-tolerant optimal control for discrete-time nonlinear system subjected to input saturation: a dynamic event-triggered approach. IEEE Trans Cybern 51:2956–2968. https://doi.org/10.1109/TCYB.2019.2923011
Xue S, Luo B, Liu D (2021) Event-triggered adaptive dynamic programming for unmatched uncertain nonlinear continuous-time systems. IEEE Trans Neural Netw Learn Syst 32:2939–2951. https://doi.org/10.1109/TNNLS.2020.3009015
Zhang G, Zhu Q (2021) Event-triggered optimized control for nonlinear delayed stochastic systems. IEEE Trans Circuits Syst I Regul Pap 68:3808–3821. https://doi.org/10.1109/TCSI.2021.3095092
Zhang XM, Han QL, Zhang BL (2017) An overview and deep investigation on sampled-data-based event-triggered control and filtering for networked systems. IEEE Trans Ind Inform 13:4–16. https://doi.org/10.1109/TII.2016.2607150
Xu ML, Chen KJ, Liu LH, Tang GJ (2012) Quasi-equilibrium glide adaptive guidance for hypersonic vehicles. Sci China Technol Sci 55:856–866. https://doi.org/10.1007/s11431-011-4727-z
Liu F, Hager WW, Rao AV (2015) Adaptive mesh refinement method for optimal control using nonsmoothness detection and mesh size reduction. J Franklin Inst 352:4081–4106. https://doi.org/10.1016/j.jfranklin.2015.05.028
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
Liu Y, Kao Y, Karimi HR, Gao Z (2016) Input-to-state stability for discrete-time nonlinear switched singular systems. Inf Sci (Ny). https://doi.org/10.1016/j.ins.2016.04.013
Eqtami A, Dimarogonas D V., Kyriakopoulos KJ (2010) Event-triggered control for discrete-time systems. Proc 2010 Am Control Conf ACC 2010 4719–4724. https://doi.org/10.1109/acc.2010.5531089
Agamawi YM, Rao AV (2020) CGPOPS: a C++ software for solving multiple-phase optimal control problems using adaptive gaussian quadrature collocation and sparse nonlinear programming. ACM Trans Math Softw. https://doi.org/10.1145/3390463
Acknowledgements
The research is funded by the Aeronautical Science Fund (2019ZC051009).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there is no conflict of interests regarding the publication of this article.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wang, X., Quan, Z., Li, Y. et al. Event-triggered trajectory-tracking guidance for reusable launch vehicle based on neural adaptive dynamic programming. Neural Comput & Applic 34, 18725–18740 (2022). https://doi.org/10.1007/s00521-022-07468-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-022-07468-y