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

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.

Keywords

Hypersonic vehicle / Constraints / Output redefinition / Barrier Lyapunov function

References

[1] Bemporad, A., 1998. Reference governor for constrained nonlinear systems.IEEE Trans. Autom. Contr., 43(3):415–419.

[2] Bolender, M.A., Doman, D.B., 2007. Nonlinear longitudinal dynamical model of an air-breathing hypersonic vehicle.J. Spacecraft Rockets, 44(2):374–387.

[3] Bu, X.W., Wu, X.Y., Ma, Z. , , 2016. Novel auxiliary error compensation design for the adaptive neural control of a constrained flexible air-breathing hypersonic vehicle.Neurocomputing, 171:313–324.

[4] 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.

[5] Cox, C., Lewis, C., Pap, R., , 1995. Prediction of unstart phenomena in hypersonic aircraft.Proc. Int. Aerospace Planes and Hypersonics Technologies, Int. Space Planes and Hypersonic Systems and Technologies Conf.

[6] 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.

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

[8] Fiorentini, L., Serrani , A., 2012. Adaptive restricted trajectory tracking for a non-minimum phase hypersonic vehicle model.Automatica, 48(7):1248–1261.

[9] Fiorentini, L., Serrani , A., Bolender, M.A. , , 2009. Nonlinear robust adaptive control of flexible air-breathing hypersonic vehicles.J. Guid. Contr. Dyn., 32(2):402–417.

[10] 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.

[11] 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.

[12] Gregory, I., Mcminn, J., Shaughnessy, J. , , 1992. Hypersonic vehicle control law development using H∞ and μ-synthesis.Proc. 4th Symp. on Multidisciplinary Analysis and Optimization Conf.

[13] Hu, X., Karimi, H.R., Wu, L. , , 2014a. Model predictive control-based non-linear fault tolerant control for airbreathing hypersonic vehicles.IET Contr. Theory Appl., 8(13):1147–1153.

[14] Hu, X., Wu, L., Hu, C., , 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.

[15] 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.

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

[17] Li, G.J., Meng, B., 2015. Actuators coupled design based adaptive backstepping control of air-breathing hypersonic vehicle.IFAC-PapersOnLine, 48(28):508–513.

[18] 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.

[19] 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.

[20] Mayne, D.Q., Rawlings , J.B., Rao, C.V. , , 2000. Constrained model predictive control: stability and optimality.Automatica, 36(6):789–814.

[21] Mirmirani, M., Kuipers , M., Levin, J. , , 2009. Flight dynamic characteristics of a scramjet-powered generic hypersonic vehicle.Proc. American Control Conf., p.2525–2532.

[22] 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.

[23] Oland, E., Schlanbusch , R., Kristiansen, R. , 2013. Underactuated translational control of a rigid spacecraft.Proc. IEEE Aerospace Conf., p.1–7.

[24] Parker, J.T., Serrani , A., Yurkovich, S. , , 2007. Controloriented modeling of an air-breathing hypersonic vehicle.J. Guid. Contr. Dyn., 30(3):856–869.

[25] Pettersen, K.Y., 2015. Underactuated marine control systems. In: Baillieul, J., Samad, T. (Eds.), Encyclopedia of Systems and Control, p.1499–1503.

[26] Qiu, J.B., Feng, G., Gao, H.J., 2013. Static-output-feedback H_∞ control of continuous-time T-S fuzzy affine systems via piecewise Lyapunov functions.IEEE Trans. Fuzzy Syst., 21(2):245–261.

[27] Qiu, J.B., Wei, Y.L., Karimi, H.R. , 2015. New approach to delay-dependent H_∞ control for continuous-time Markovian jump systems with time-varying delay and deficient transition descriptions.J. Franklin Instit., 352(1):189–215.

[28] Qiu, J.B., Ding, S.X., Gao, H.J. , , 2016. Fuzzymodel-based reliable static output feedback H∞ control of nonlinear hyperbolic PDE systems.IEEE Trans. Fuzzy Syst., 24(2):388–400.

[29] 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.

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

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

[32] 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.

[33] 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.

[34] 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.

[35] 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.

[36] 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.

[37] 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.

[38] Wu, H.N., Liu, Z.Y., Guo, L. , 2014. Robust L∞-gain fuzzy disturbance observer-based control design with adaptive bounding for a hypersonic vehicle.IEEE Trans. Fuzzy Syst., 22(6):1401–1412.

[39] 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.

[40] Xu, B., Sun,F., Liu, H., , 2012. Adaptive Kriging controller design for hypersonic flight vehicle via backstepping.IET Contr. Theory Appl., 6(4):487–497.

[41] 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.

[42] Yang, J., Li, S.H., Sun, C.Y. , , 2013. Nonlineardisturbance-observer-based robust flight control for airbreathing hypersonic vehicles.IEEE Trans. Aerosp. Electron. Syst., 49(2):1263–1275.

[43] 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.

RIGHTS & PERMISSIONS

Zhejiang University and Springer-Verlag Berlin Heidelberg