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Adaptive critic design for enhanced control of waverider vehicles with nonaffine nonlinearities

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Abstract

In this paper, a hybrid fuzzy-neural framework for the solution of waverider vehicles (WVs) flight enhanced control issue is addressed based on adaptive critic design. Hybrid enhanced controllers consisting of an action network and a critic network are developed. The action network, as the basic controller directly stemming from nonaffine nonlinearities of WVs, approximately yields enhanced control protocols. Further, the tracking performance is evaluated and strengthened to a higher degree of accuracy by the critic network. The boundedness of closed-loop system signals is ensured via Lyapunov synthesis. Numerical simulation results infer that highly precise tracking of reference commands is achieved in the presence of parametric perturbations.

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Data availibility

The experimental data used to support the findings of this study are available from the corresponding author upon request.

Abbreviations

m :

Vehicle mass

\({{\bar{\rho }}}\) :

Density of air

\({\bar{q}}\) :

Dynamic pressure

S :

Reference area

h :

Altitude

V :

Velocity

\(\gamma \) :

Flight-path angle

\(\theta \) :

Pitch angle

\(\alpha \) :

Angle of attack (\(\alpha =\theta -\gamma \))

Q :

Pitch rate

T :

Thrust

D :

Drag

L :

Lift

M :

Pitching moment

\({I_{{\text {yy}}}}\) :

Moment of inertia

\({\bar{c}}\) :

Aerodynamic chord

\({z_T}\) :

Thrust moment arm

\(\Phi \) :

Fuel equivalence ratio

\({\delta _e}\) :

Elevator angular deflection

\({N_i}\) :

ith generalized force

\(N_i^{{\alpha _j}}\) :

jth order contribution of \(\alpha \) to \({N_i}\)

\(N_i^0\) :

Constant term in \({N_i}\)

\(N_2^{{\delta _{\text {e}}}}\) :

Contribution of \({\delta _e}\) to \({N_2}\)

\({\beta _i}\left( {h,{\bar{q}}} \right) \) :

ith trust fit parameter

\({\eta _i}\) :

ith generalized elastic coordinate

\({\zeta _i}\) :

Damping ratio for elastic mode \({\eta _i}\)

\({\omega _i}\) :

Natural frequency for elastic mode \({\eta _i}\)

\(C_D^{{\alpha ^i}}\) :

ith order coefficient of \(\alpha \) in D

\(C_D^{\delta _{\text {e}}^i}\) :

ith order coefficient of \({\delta _e}\) in D

\(C_D^0\) :

Constant coefficient in D

\(C_L^{{\alpha ^i}}\) :

ith order coefficient of \(\alpha \) in L

\(C_L^{{\delta _{\text {e}}}}\) :

Coefficient of \({\delta _e}\) contribution in L

\(C_L^0\) :

Constant coefficient in L

\(C_{M,\alpha }^{{\alpha ^i}}\) :

ith order coefficient of \(\alpha \) in M

\(C_{M,\alpha }^0\) :

Constant coefficient in M

\(C_T^{{\alpha ^i}}\) :

ith order coefficient of \(\alpha \) in T

\(C_T^0\) :

Constant coefficient in T

\({h_0}\) :

Nominal altitude for air density approximation

\({{{\bar{\rho }}} _0}\) :

Air density at the altitude \({h_0}\)

\({{\tilde{\psi }} _i}\) :

Constrained beam coupling constant for \({\eta _i}\)

\({c_{\text {e}}}\) :

Coefficient of \({\delta _{\text {e}}}\) in M

\(1/{h_{\text {s}}}\) :

Air density decay rate

\({\Re _{ > 0}}\) :

The set of all real-positive numbers

\(\Re \) :

The set of all real numbers

\(: = \) :

Define as

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Funding

This work was supported by Young Talent Support Project for Science and Technology (Grant No. 18-JCJQ-QT- 007).

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Authors and Affiliations

  1. School of Automation Science and Engineering, Xi’an Jiaotong University, No 28 Xianning Xilu, Xi’an, 710049, Shaanxi, China

    Xiangwei Bu

  2. Air and Missile Defense College, Air Force Engineering University, No 1 Changle Donglu, Xi’an, 710051, Shaanxi, China

    Xiangwei Bu

  3. School of Mechanical Engineering, Xijing University, No 1 Xijing Road, Xi’an, 710123, Shaanxi, China

    Haiying Ma

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  1. Xiangwei Bu
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Correspondence to Xiangwei Bu.

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Bu, X., Ma, H. Adaptive critic design for enhanced control of waverider vehicles with nonaffine nonlinearities. Nonlinear Dyn 112, 1123–1139 (2024). https://doi.org/10.1007/s11071-023-09085-3

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  • DOI: https://doi.org/10.1007/s11071-023-09085-3

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