Hypersonic technology plays an important role in prompt global strike. Because the flight dynamics of a hypersonic vehicle is nonlinear, uncertain, and highly coupled, the controller design is challenging, especially to design its guidance and control law during the attack of a maneuvering target. In this paper, the sliding mode control (SMC) method is used to develop the guidance law from which the desired flight path angle is derived. With the desired information as control command, the adaptive neural control in discrete time is investigated ingeniously for the longitudinal dynamics of the hypersonic missile. The proposed guidance and control laws are validated by simulation of a hypersonic missile against a maneuvering target. It is demonstrated that the scheme has good robustness and high accuracy to attack a maneuvering target in the presence of external disturbance and missile model uncertainty.

The hypersonic missile can propel the development of the prompt global strike. Controller design is crucial in making it feasible. To control the hypersonic vehicle whose flight dynamics is nonlinear, uncertain, and coupled, many researches were carried out. In [

The SMC is used to control a generic hypersonic vehicle in [

In these literatures, the control outputs are flight velocity and altitude which are driven to track the reference trajectory that increases from zero to constant value after a transient phase. When the hypersonic missile is used to attack targets, the dynamics will change greatly in the endgame phase due to the angle and angle rate changes. More problems exist in the control of the hypersonic missile in attack scenarios, and researchers began to pay more attention to them. The control of the hypersonic missile attacking a ground stationary target with a different vector-output and time-varying commanded output trajectories is using nonlinear control [

In this paper, the guidance and control law of a hypersonic missile attacking a maneuvering target instead of a ground stationary target are discussed. It is a more challenging task owing to the uncertainties of target maneuvers. To solve this problem, the SMC guidance law and the back-stepping control law are designed to guarantee the robustness. The SMC method is one of the robust control design methods which is robust to parameter perturbations and external disturbances [

Back-stepping design [

With the development of hardware, the research on discrete-time control has received a considerable attention [

In this paper, we first design the sliding mode guidance law from which the desired flight path angle is derived. Then, we design the controller with the back-stepping scheme recursively. We take into consideration the nominal nonlinearity for feedback design and the neural network (NN) is used to approximate the system uncertainty. In order to avoid the circular construction of control inputs, the upper bound is taken instead of the nominal value for coefficient design. The idea of the guidance and control design is shown in Figure

This model comprises five state variables

The control input is defined as

The geometry of an idealized interception in which the missile and the target are closing on each other at constant speed is shown in Figure

Interception geometry.

The control schematic diagram.

Equations (

Since

The velocity can be considered as constant during the hypersonic missile attacking the target.

The velocity subsystem (

The altitude tracking error is defined as

Define

With the Euler expansion for the sampling period

(1) Define

The virtual controller

Define

The NN updating law is proposed as

The first difference of

(2) Define

Design virtual control

Define

The NN updating law is given as

(3) According to the definition of

The elevator deflection

Combining (

The NN updating law is given as

By selecting

Now, the following theorem can be obtained.

Consider system (

For the velocity subsystem, the controller in [

The parameters for the guidance law are selected as

The simulation results are shown in Figures

Interception trajectory.

Altitude tracking error.

Flight path angle.

Flight path angle tracking error.

Velocity.

Angle of attack.

Elevator deflection.

Throttle setting.

NN weights response (1).

NN weights response (2).

Taking the target maneuver into consideration, this paper proposes the sliding mode guidance law and adaptive neural controller for the hypersonic missile via the back-stepping method. The flight path angle is designed as the guidance command instead of normal acceleration. The nominal part of the nonlinearity during each step is eliminated and the NN is used to approximate the system uncertainty. Simulation results show the effectiveness of the proposed guidance and control laws. For future work, the energy management control should be considered to derive more effective velocity control.

In this paper, only one-step-ahead model is used for controller design. For future work, we will work on how to develop a new algorithm based on the equivalent prediction model developed in [

The authors declare that they have no competing interests.

This work was supported by the National Natural Science Foundation of China under Grants 61104195, 90816027, and 91216104 and by the NWPU Basic Research Fund under Grant GEKY1003.