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Neural control of hypersonic flight vehicle model via time-scale decomposition with throttle setting constraint

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Abstract

Considering the use of digital computers and samplers in the control circuitry, this paper describes the controller design in discrete time for the longitudinal dynamics of a generic hypersonic flight vehicle (HFV) with Neural Network (NN). Motivated by time-scale decomposition, the states are decomposed into slow dynamics of velocity, altitude and fast dynamics of attitude angles. By command transformation, the reference command for γ−θ p −q subsystem is derived from h−γ subsystem. Furthermore, to simplify the backstepping design, we propose the controller for γ−θ p −q subsystem from prediction function without virtual controller. For the velocity subsystem, the throttle setting constraint is considered and new NN adaption law is designed by auxiliary error dynamics. The uniformly ultimately boundedness (UUB) of the system is proved by Lyapunov stability method. Simulation results show the effectiveness of the proposed algorithm.

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Acknowledgements

This work was supported by the DSO National Laboratories of Singapore through a Strategic Project Grant (Project No. DSOCL10004), National Science Foundation of China (Grant No. 61134004, 61005085), NWPU Basic Research Funding (Grant No. JC20120236) and Fundamental Research Funds for the Central Universities (2012QNA4024).

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Authors and Affiliations

  1. School of Automation, Northwestern Polytechnical University, Xi’an, China

    Bin Xu & Zhongke Shi

  2. School of Computing and Mathematics, Plymouth University, Plymouth, UK

    Chenguang Yang

  3. Department of Control Engineering, Naval Aeronautical and Astronautical University, Yantai, China

    Shixing Wang

Authors
  1. Bin Xu
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  2. Zhongke Shi
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  3. Chenguang Yang
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  4. Shixing Wang
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Corresponding author

Correspondence to Bin Xu.

Appendices

Appendix A: Hypersonic aircraft model description

The related definitions of the HFV dynamics in [23] are given as: r=h+R E , \(\bar{q}=\frac{1}{2}\rho V^{2}\), \(L = \bar{q}SC_{L}\), \(D =\nobreak \bar{q} SC_{D}\), \(T = \bar{q}SC_{T}\), \(M_{yy} = \bar{q} S\bar{c} [C_{M} (\alpha) + C_{M} (\delta e) + C_{M} (q) ]\), C L =0.6203α, C D =0.6450α 2+0.0043378α+0.003772, C M (α)=−0.035α 2+0.036617α+5.3261×10−6, \(C_{M} (q) = (\bar{c}/2V)\*q( - 6.796\alpha^{2} + 0.3015\alpha - 0.2289)\).

The control-input-related definition is as

where ρ denotes the air density, S is the reference area, \(\bar{c}\) is the reference length and R E is the radius of the Earth. C x , x=L,D,T,M are the force and moment coefficients.

Appendix B: Definition for nonlinear functions f i and g i , i=1,2,3,V

\({f_{1}} = - ( {\mu - {V^{2}}r} )\cos\gamma/({V{r^{2}}})-0.6203\bar{q}S\gamma/(mV)\), \({g_{1}} = 0.6203\bar{q}S/(mV)\), f 2=0, g 2=1, \({f_{3}} = \bar{q}S\bar{c}[ {C_{M}}( \alpha ) + {C_{M}}( q ) - 0.0292\alpha]/{I_{yy}}\), \({g_{3}} = {0.0292\bar{q}S\bar{c}}/I_{yy}\).

If β>1, \({f_{V}} = -(D/m + \mu\sin\gamma/r^{2})+ 0.0224\bar{q}S \cos \alpha/m \), \(g_{V}=0.00336\bar{q} S \cos\alpha/m\). Otherwise f V =−(D/m+μsinγ/r 2), \(g_{V}= 0.02576\bar{q} S\cos\alpha/m\).

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Xu, B., Shi, Z., Yang, C. et al. Neural control of hypersonic flight vehicle model via time-scale decomposition with throttle setting constraint. Nonlinear Dyn 73, 1849–1861 (2013). https://doi.org/10.1007/s11071-013-0908-6

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