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Adaptive tracking control for air-breathing hypersonic vehicles with state constraints

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Abstract

We investigate the adaptive tracking problem for the longitudinal dynamics of state-constrained airbreathing hypersonic vehicles, where not only the velocity and the altitude, but also the angle of attack (AOA) is required to be tracked. A novel indirect AOA tracking strategy is proposed by viewing the pitch angle as a new output and devising an appropriate pitch angle reference trajectory. Then based on the redefined outputs (i.e., the velocity, the altitude, and the pitch angle), a modified backstepping design is proposed where the barrier Lyapunov function is used to solve the state-constrained control problem and the control gain of this class of systems is unknown. Stability analysis is given to show that the tracking objective is achieved, all the closed-loop signals are bounded, and all the states always satisfy the given constraints. Finally, numerical simulations verify the effectiveness of the proposed approach.

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References

  • Bemporad, A., 1998. Reference governor for constrained nonlinear systems. IEEE Trans. Autom. Contr., 43(3):415–419. http://dx.doi.org/10.1109/9.661611

    Article  MathSciNet  MATH  Google Scholar 

  • Bolender, M.A., Doman, D.B., 2007. Nonlinear longitudinal dynamical model of an air-breathing hypersonic vehicle. J. Spacecraft Rockets, 44(2):374–387. http://dx.doi.org/10.2514/1.23370

    Article  Google Scholar 

  • Bu, X.W., Wu, X.Y., Ma, Z., et al., 2016. Novel auxiliary error compensation design for the adaptive neural control of a constrained flexible air-breathing hypersonic vehicle. Neurocomputing, 171:313–324. http://dx.doi.org/10.1016/j.neucom.2015.06.058

    Article  Google Scholar 

  • Burger, M., Guay, M., 2010. Robust constraint satisfaction for continuous-time nonlinear systems in strict feedback form. IEEE Trans. Autom. Contr., 55(11):2597–2601. http://dx.doi.org/10.1109/TAC.2010.2061090

    Article  MathSciNet  Google Scholar 

  • Cox, C., Lewis, C., Pap, R., et al., 1995. Prediction of unstart phenomena in hypersonic aircraft. Proc. Int. Aerospace Planes and Hypersonics Technologies, Int. Space Planes and Hypersonic Systems and Technologies Conf. http://dx.doi.org/10.2514/6.1995-6018

  • Fidan, B., Mirmirani, M., Ioannou, P., 2003. Flight dynamics and control of air-breathing hypersonic vehicles: review and new directions. Proc. 12th AIAA Int. Space Planes and Hypersonic Systems and Technologies Conf. http://dx.doi.org/10.2514/6.2003-7081

    Google Scholar 

  • Fiorentini, L., 2010. Nonlinear Adaptive Controller Design for Air-Breathing Hypersonic Vehicles. PhD Thesis, Ohio State University, USA.

    Google Scholar 

  • Fiorentini, L., Serrani, A., 2012. Adaptive restricted trajectory tracking for a non-minimum phase hypersonic vehicle model. Automatica, 48(7):1248–1261. http://dx.doi.org/10.1016/j.automatica.2012.04.006

    Article  MathSciNet  MATH  Google Scholar 

  • Fiorentini, L., Serrani, A., Bolender, M.A., et al., 2009. Nonlinear robust adaptive control of flexible air-breathing hypersonic vehicles. J. Guid. Contr. Dyn., 32(2):402–417. http://dx.doi.org/10.2514/1.39210

    Article  Google Scholar 

  • Gibson, T.E., Crespo, L.G., Annaswamy, A.M., 2009. Adaptive control of hypersonic vehicles in the presence of modeling uncertainties. Proc. American Control Conf., p.3178–3183. http://dx.doi.org/10.1109/ACC.2009.5160746

    Google Scholar 

  • Gilbert, E., Kolmanovsky, I., 2002. Nonlinear tracking control in the presence of state and control constraints: a generalized reference governor. Automatica, 38(12):2063–2073. http://dx.doi.org/10.1016/s0005-1098(02)00135-8

    Article  MathSciNet  MATH  Google Scholar 

  • Gregory, I., Mcminn, J., Shaughnessy, J., et al., 1992. Hypersonic vehicle control law development using H8 and µ-synthesis. Proc. 4th Symp. on Multidisciplinary Analysis and Optimization Conf. http://dx.doi.org/10.2514/6.1992-5010

    Google Scholar 

  • Hu, X., Karimi, H.R., Wu, L., et al., 2014a. Model predictive control-based non-linear fault tolerant control for airbreathing hypersonic vehicles. IET Contr. Theory Appl., 8(13):1147–1153. http://dx.doi.org/10.1049/iet-cta.2013.0986

    Article  Google Scholar 

  • Hu, X., Wu, L., Hu, C., et al., 2014b. Dynamic output feedback control of a flexible air-breathing hypersonic vehicle via T-S fuzzy approach. Int. J. Syst. Sci., 45(8):1740–1756. http://dx.doi.org/10.1080/00207721.2012.749547

    Article  MathSciNet  MATH  Google Scholar 

  • Jin, X., Kwong, R.H.S., 2015. Adaptive fault tolerant control for a class of MIMO nonlinear systems with input and state constraints. Proc. American Control Conf., p.2254–2259. http://dx.doi.org/10.1109/ACC.2015.7171068

    Google Scholar 

  • Krstic, M., Kanellakopoulos, I., Kokotovic, P.V., 1995. Nonlinear and Adaptive Control Design. Wiley.

    MATH  Google Scholar 

  • Li, G.J., Meng, B., 2015. Actuators coupled design based adaptive backstepping control of air-breathing hypersonic vehicle. IFAC-PapersOnLine, 48(28):508–513. http://dx.doi.org/10.1016/j.ifacol.2015.12.179

    Article  Google Scholar 

  • Li, S.H., Sun, H.B., Sun, C.Y., 2012. Composite controller design for an airbreathing hypersonic vehicle. Proc. Instit. Mech. Eng. Part I, 226(5):651–664. http://dx.doi.org/10.1177/0959651811428837

    Google Scholar 

  • Liu, Y.J., Li, D.J., Tong, S.C., 2014. Adaptive output feedback control for a class of nonlinear systems with full-state constraints. Int. J. Contr., 87(2):281–290. http://dx.doi.org/10.1080/00207179.2013.828854

    Article  MathSciNet  MATH  Google Scholar 

  • Mayne, D.Q., Rawlings, J.B., Rao, C.V., et al., 2000. Constrained model predictive control: stability and optimality. Automatica, 36(6):789–814. http://dx.doi.org/10.1016/s0005-1098(99)00214-9

    Article  MathSciNet  MATH  Google Scholar 

  • Mirmirani, M., Kuipers, M., Levin, J., et al., 2009. Flight dynamic characteristics of a scramjet-powered generic hypersonic vehicle. Proc. American Control Conf., p.2525–2532. http://dx.doi.org/10.1109/ACC.2009.5160500

    Google Scholar 

  • Ngo, K.B., Mahony, R., Jiang, Z.P., 2005. Integrator backstepping using barrier functions for systems with multiple state constraints. Proc. 44th IEEE Conf. on Decision and Control, p.8306–8312. http://dx.doi.org/10.1109/CDC.2005.1583507

    Chapter  Google Scholar 

  • Oland, E., Schlanbusch, R., Kristiansen, R., 2013. Underactuated translational control of a rigid spacecraft. Proc. IEEE Aerospace Conf., p.1–7. http://dx.doi.org/10.1109/AERO.2013.6497324

    Google Scholar 

  • Parker, J.T., Serrani, A., Yurkovich, S., et al., 2007. Controloriented modeling of an air-breathing hypersonic vehicle. J. Guid. Contr. Dyn., 30(3):856–869. http://dx.doi.org/10.2514/1.27830

    Article  Google Scholar 

  • Pettersen, K.Y., 2015. Underactuated marine control systems. In: Baillieul, J., Samad, T. (Eds.), Encyclopedia of Systems and Control, p.1499–1503. http://dx.doi.org/10.1007/978-1-4471-5058-9_125

    Chapter  Google Scholar 

  • Qiu, J.B., Feng, G., Gao, H.J., 2013. Static-output-feedback H8 control of continuous-time T-S fuzzy affine systems via piecewise Lyapunov functions. IEEE Trans. Fuzzy Syst., 21(2):245–261. http://dx.doi.org/10.1109/TFUZZ.2012.2210555

    Article  Google Scholar 

  • Qiu, J.B., Wei, Y.L., Karimi, H.R., 2015. New approach to delay-dependent H8 control for continuous-time Markovian jump systems with time-varying delay and deficient transition descriptions. J. Franklin Instit., 352(1):189–215. http://dx.doi.org/10.1016/j.jfranklin.2014.10.022

    Article  MATH  Google Scholar 

  • Qiu, J.B., Ding, S.X., Gao, H.J., et al., 2016. Fuzzymodel-based reliable static output feedback H8 control of nonlinear hyperbolic PDE systems. IEEE Trans. Fuzzy Syst., 24(2):388–400. http://dx.doi.org/10.1109/TFUZZ.2015.2457934

    Article  Google Scholar 

  • Serrani, A., 2013. Nested zero-dynamics redesign for a non-minimum phase longitudinal model of a hypersonic vehicle. Proc. 52nd IEEE Conf. on Decision and Control, p.4833–4838. http://dx.doi.org/10.1109/CDC.2013.6760647

    Chapter  Google Scholar 

  • Shaughnessy, J.D., Pinckney, S.Z., McMinn, J.D., et al., 1990. Hypersonic Vehicle Simulation Model: Winged-Cone Configuration. NASA Technical Memorandum 102610, USA.

    Google Scholar 

  • Slotine, J.J.E., Li, W., 1991. Applied Nonlinear Control. Prentice-Hall Englewood Cliffs, New Jersey, USA.

  • Sun, H.B., Li, S.H., Sun, C.Y., 2013. Finite time integral sliding mode control of hypersonic vehicles. Nonl. Dyn., 73(1):229–244. http://dx.doi.org/10.1007/s11071-013-0780-4

    Article  MathSciNet  MATH  Google Scholar 

  • Sun, H.F., Yang, Z.L., Zeng, J.P., 2013. New tracking-control strategy for airbreathing hypersonic vehicles. J. Guid. Contr. Dyn., 36(3):846–859. http://dx.doi.org/10.2514/1.57739

    Article  Google Scholar 

  • Tee, K.P., Ge, S.S., 2011. Control of nonlinear systems with partial state constraints using a barrier Lyapunov function. Int. J. Contr., 84(12):2008–2023. http://dx.doi.org/10.1080/00207179.2011.631192

    Article  MathSciNet  MATH  Google Scholar 

  • Tee, K.P., Ge, S.S., Tay, E.H., 2009. Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica, 45(4):918–927. http://dx.doi.org/10.1016/j.automatica.2008.11.017

    Article  MathSciNet  MATH  Google Scholar 

  • Wang, T., Gao, H., Qiu, J., 2016. A combined adaptive neural network and nonlinear model predictive control for multirate networked industrial process control. IEEE Trans. Neur. Netw. Learn. Syst., 27(2):416–425. http://dx.doi.org/10.1109/TNNLS.2015.2411671

    Article  MathSciNet  Google Scholar 

  • Wolff, J., Weber, C., Buss, M., 2007. Continuous control mode transitions for invariance control of constrained nonlinear systems. Proc. 46th IEEE Conf. on Decision and Control, p.542–547. http://dx.doi.org/10.1109/CDC.2007.4434916

    Google Scholar 

  • Wu, H.N., Liu, Z.Y., Guo, L., 2014. Robust L8-gain fuzzy disturbance observer-based control design with adaptive bounding for a hypersonic vehicle. IEEE Trans. Fuzzy Syst., 22(6):1401–1412. http://dx.doi.org/10.1109/TFUZZ.2013.2292976

    Article  Google Scholar 

  • Xu, B., Gao, D.X., Wang, S.X., 2011. Adaptive neural control based on HGO for hypersonic flight vehicles. Sci. China Inform. Sci., 54(3):511–520. http://dx.doi.org/10.1007/s11432-011-4189-8

    Article  MathSciNet  MATH  Google Scholar 

  • Xu, B., Sun, F., Liu, H., et al., 2012. Adaptive Kriging controller design for hypersonic flight vehicle via backstepping. IET Contr. Theory Appl., 6(4):487–497. http://dx.doi.org/10.1049/iet-cta.2011.0026

    Article  Google Scholar 

  • Xu, H.J., Mirmirani, M.D., Ioannou, P.A., 2004. Adaptive sliding mode control design for a hypersonic flight vehicle. J. Guid. Contr. Dyn., 27(5):829–838. http://dx.doi.org/10.2514/1.12596

    Article  Google Scholar 

  • Yang, J., Li, S.H., Sun, C.Y., et al., 2013. Nonlineardisturbance-observer-based robust flight control for airbreathing hypersonic vehicles. IEEE Trans. Aerosp. Electron. Syst., 49(2):1263–1275. http://dx.doi.org/10.1109/taes.2013.6494412

    Article  Google Scholar 

  • Zong, Q., Wang, J., Tao, Y., 2013. Adaptive high-order dynamic sliding mode control for a flexible air-breathing hypersonic vehicle. Int. J. Robust Nonl. Contr., 23(15):1718–1736. http://dx.doi.org/10.1002/rnc.3040

    MathSciNet  MATH  Google Scholar 

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Correspondence to Gong-jun Li.

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Project supported by the National Natural Science Foundation of China (Nos. 61333008 and 61273153)

ORCID: Gong-jun LI, http://orcid.org/0000-0001-8503-2973

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Li, Gj. Adaptive tracking control for air-breathing hypersonic vehicles with state constraints. Frontiers Inf Technol Electronic Eng 18, 599–614 (2017). https://doi.org/10.1631/FITEE.1500464

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  • DOI: https://doi.org/10.1631/FITEE.1500464

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