# An Intelligent Autonomous Morphing Decision Approach for Hypersonic Boost-Glide Vehicles Based on DNNs

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## Abstract

**:**

## 1. Introduction

- (1)
- Compared with reinforcement learning, the Gaussian pseudo-spectrum method can obtain a continuous sequence of state quantities and control quantities while considering state constraints, giving full play to the full potential in the variable range of sweep angle.
- (2)
- Instead of fitting the sweep angle as a function of flight state quantity, a DNN essentially realizes a mapping function from input to output, which is suitable for solving problems with complex internal mechanisms. It can realize online rapid decision-making of the sweep angle according to flight status.
- (3)
- Compared with an ordinary glide vehicle, hypersonic boost-glide vehicles have additional propulsion systems and control dimensions.

## 2. Hypersonic Morphing Vehicle Dynamics Modeling

## 3. Intelligent Decision-Making Method Based on a DNN

#### 3.1. Gaussian Pseudo-Spectral Principle

#### 3.1.1. Time Domain Transformation

#### 3.1.2. The Optimal Control Problem Is Parameterized to the NLP Problem

- State quantity discretization.

- Performance indicators discretization.

- Discretization of boundary conditions.

#### 3.2. Segmentation Optimization Based on Gaussian Pseudo-Spectrum Method

- (1)
- Based on the optimized reference trajectory for entry conditions, height and velocity disturbances are applied to the hypersonic aircraft every 3 km, resulting in multiple entry conditions.
- (2)
- Based on the multi-group deviation entry conditions, the Gaussian pseudo-spectrum method is employed to optimize the trajectory multiple times. This process generates data pairs, consisting of the state quantity $(H,V)$ and the output quantity $[\lambda ,\alpha ,Kr]$, at each moment. These data pairs are then used to construct a trajectory sample library.
- (3)
- Use the neural network to approximate the complex nonlinear model between the state quantity and the control quantity; that is, $[\lambda ,\alpha ,Kr]=f(H,V)$, where $f$ represents neural network approximation. Steps (1)~(3) are completed offline.
- (4)
- The neural network intelligent morphing decision-maker and the hypersonic vehicle motion model form a closed loop. The neural network decision-maker receives the flight state data, and output the sweep angle and other control quantities.

#### 3.3. DNN Training Based on Trajectory Sample Database

#### 3.3.1. Forward Propagation

#### 3.3.2. Error Backpropagation

## 4. Hypersonic Vehicle Morphing Decision Simulation

#### 4.1. Generation of Datum Trajectory and Interference Trajectory

#### 4.2. Intelligent Morphing Decision and Instruction Morphing Decision Comparison Simulation

^{2}. In contrast, the intelligent morphing showed a significantly lower peak heat flux density of only 3.05 MW/m

^{2}under the same interference. This reduction in peak heat flux amounted to approximately 10.2%, highlighting the robustness of the intelligent decision-making morphing method.

## 5. Conclusions

## 6. Limitations and Potential Future Directions

- (1)
- Integration of control methods: While this paper primarily concentrates on shape decision-making, it is crucial to acknowledge that shape changes can significantly impact the aircraft’s aerodynamic characteristics. Subsequent research should involve the design of advanced control methods, such as LPV control and adaptive control, to improve the tracking effect and enhance the morphing stability of the aircraft.
- (2)
- Conducting physical experiments: The research on hypersonic morphing vehicles in this paper is primarily based on simulation experiments. However, achieving favorable decision-making results in simulations does not guarantee the same effectiveness when implemented in practical engineering. Therefore, it is necessary for future research to construct physical models of hypersonic morphing vehicles and validate the designed decision-making system’s effectiveness on these models.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Intelligent morphing decision-making method of hypersonic morphing vehicle based on a DNN.

Intelligent Morphing Decision-Making Based on a DNN | |
---|---|

Generate trajectory sample | while Descend to terminal altitude if Follow the reference trajectory descend >3 km Add interference Update initial conditions Trajectory optimization end end |

Neural network training | Input: Trajectory sample 1. The linear relation coefficient matrix W and deviation vector b of each hidden layer and output layer are initialized as a random value. 2. For iter from 1 to MAX 2.1 For i = 1 to m (a) Set the input ${a}^{l}$ to DNN to x (b) For i = 2… L, forward propagation computation (c) Calculate the output layer output by the loss function (d) For i = 2… L, backpropagate the error 2.2 For i = 2… L, update the ${W}^{l}$ and ${b}^{l}$ of layer l 2.3 If all of the changes in $W$ and $b$ are less than the threshold for stopping the iteration, the loop goes to step 3 3. The linear relation coefficient matrix W and bias vector b of each hidden layer and output layer are output. |

Intelligent decision process | Input: V and H of the current state of the hypersonic vehicle Process: Intelligent decision-making computing Output: Sweep angle command Attack angle command Throttle command |

Quantity of State | Initial Boundary Constraint | Terminal Boundary Constraint |
---|---|---|

Altitude (km) | 80 | 45 |

Velocity (Ma) | 26.52 | 7 |

X-direction displacement (km) | 0 | 18,000 |

Y-direction displacement (km) | 0 | 8000 |

Structure Name | Parameter Setting |
---|---|

Number of layers and number of neurons | [36,36,12] |

Number of iterations | 1500 |

Learning rate | 0.01 |

Maximum number of failures | 12 |

Target mean square error | 0.0004 |

Attack Angle | Sweep Angle | Throttle Coefficient | |
---|---|---|---|

BP | 0.0262 | 0.0031 | 5.61 × 10^{−6} |

DNN | 0.0085 | 6.28 × 10^{−4} | 3.12 × 10^{−6} |

Lift Is Reduced by 5% | Lift Is Increased by 5% | Drag Reduced by 5% | Drag Increased by 5% | |
---|---|---|---|---|

Program morphing displacement (km) | 18,533 | 20,468 | 20,529 | 18,557 |

Intelligent morphing displacement (km) | 18,733 | 21,708 | 21,686 | 18,914 |

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**MDPI and ACS Style**

Hou, L.; Liu, H.; Yang, T.; An, S.; Wang, R.
An Intelligent Autonomous Morphing Decision Approach for Hypersonic Boost-Glide Vehicles Based on DNNs. *Aerospace* **2023**, *10*, 1008.
https://doi.org/10.3390/aerospace10121008

**AMA Style**

Hou L, Liu H, Yang T, An S, Wang R.
An Intelligent Autonomous Morphing Decision Approach for Hypersonic Boost-Glide Vehicles Based on DNNs. *Aerospace*. 2023; 10(12):1008.
https://doi.org/10.3390/aerospace10121008

**Chicago/Turabian Style**

Hou, Linfei, Honglin Liu, Ting Yang, Shuaibin An, and Rui Wang.
2023. "An Intelligent Autonomous Morphing Decision Approach for Hypersonic Boost-Glide Vehicles Based on DNNs" *Aerospace* 10, no. 12: 1008.
https://doi.org/10.3390/aerospace10121008