Midcourse guidance method based on deep neural network

Abstract

The application discloses a midcourse guidance method based on a deep neural network, obtains a guidance instruction through a neural network, and controls flight of a spacecraft under the guidance instruction, and a training set of the neural network is generated by setting an optimal control problem. The midcourse guidance method based on the deep neural network improves guidance accuracy, is robust, and reduces complexity of a guidance model.

Description

Technical Field

[0001] This invention relates to a guidance method, particularly a mid-course guidance method based on deep neural networks, belonging to the field of aircraft control technology. Background Technology

[0002] Guidance and control are the core of an aircraft. The quality of guidance and control directly affects the accuracy of the aircraft and can even determine the success or failure of a mission.

[0003] Currently, the widely used guidance and control methods are relatively mature analytical and numerical iterative methods. These traditional guidance methods can ensure good control effects and high accuracy within a foreseeable range. However, as aerospace missions become increasingly complex and space environment noise interference increases, system dynamics models become highly nonlinear, and many uncertain parameters increase significantly. Traditional methods are finding it difficult to establish accurate and usable models for some missions.

[0004] Furthermore, in complex tasks, even if a relatively accurate model is established, the computational load that a more accurate model inevitably brings is enormous. The computing power of airborne computers is often insufficient to support the real-time calculation of the model, making the model difficult to apply in practice.

[0005] For the reasons mentioned above, it is necessary to propose a guidance method that can solve one of the aforementioned problems. Summary of the Invention

[0006] To overcome the above problems, the inventors conducted in-depth research and designed a mid-course guidance method based on deep neural networks. The guidance commands are obtained through the neural network, and the aircraft flies under the control of the guidance commands.

[0007] Furthermore, the training set for the neural network is generated by setting an optimal control problem.

[0008] The optimal control problem refers to the optimal control parameters corresponding to a certain state of the aircraft.

[0009] The states include the target distance r, the vehicle speed V, and the trajectory inclination angle. The projectile's line-of-sight angle λ, and the initial launch angle. And the initial horizontal distance s0, the optimal control parameter is the lateral acceleration a. c .

[0010] Preferably, the state and the corresponding optimal control parameter form a state-optimal control pair, wherein the state serves as the input to the neural network, and the corresponding optimal control parameter serves as the output of the neural network.

[0011] Preferably, the optimal control problem is represented by an aircraft dynamics model and an aircraft optimization objective.

[0012] The aircraft dynamics model is represented as follows:

[0013]

[0014] Where x is the horizontal coordinate of the aircraft, y is the vertical coordinate of the aircraft, and V is the velocity of the aircraft. Let L be the trajectory inclination angle, L be the lift, m be the vehicle mass, T be the vehicle thrust, α be the angle of attack, g be the gravitational acceleration, and D be the aerodynamic drag. sp For propellant specific impulse, aerodynamic drag D and lift L can be expressed as:

[0015] D = (C D0 +C Dα 2 α 2 )qS

[0016] L=C Lα qSα

[0017] in It is dynamic pressure, S is the characteristic area of ​​the aircraft, ρ,C D0 C Dα C Lα It is the Mach number parameter;

[0018] The optimization objective for the aircraft is expressed as:

[0019]

[0020] Among them, a c Let J be the lateral acceleration of the aircraft, J be the index function, and t be the lateral acceleration. f For the total flight time, -V(t) f ) represents t f The negative velocity of the aircraft at that moment.

[0021] Preferably, the hp-FRPM method is used to solve the optimal control problem, and multiple state-optimal control pairs are obtained.

[0022] Preferably, the neural network is a deep feedforward neural network with three hidden layers, each containing 12 neurons, and each neuron in the hidden layer is fully connected to the neurons in the previous layer.

[0023] Preferably, the training of the neural network using the training set is performed through the following steps:

[0024] Step 1: Normalize and group the training set;

[0025] Step 2: Input training samples and obtain loss values;

[0026] Step 3: Backpropagate the loss value to update the neural network parameters;

[0027] Step 4: Repeat steps 2 and 3 to complete the first generation training of the training samples. Use validation samples and test samples to test the trained neural network. If the loss value reaches the preset value, stop training; otherwise, repeat step 4 to perform the first generation training again.

[0028] Preferably, in step one, the normalization is expressed as:

[0029]

[0030] Where z represents the state in the training set. Or any element in the optimal control parameters, z min z represents the minimum value of this type of element. max z represents the maximum value of this type of element. norm This represents the result after normalization.

[0031] Preferably, in step two, the loss function is the mean squared error loss function.

[0032] Preferably, in step three, the update can be expressed as:

[0033] x k+1 =x k -(J F T J F +μI) -1 J F T e

[0034] Where, x k Indicates the parameter before the update, x k+1 Indicates the updated parameter, J F Let be the Jacobian matrix, μ be the trust region radius, which can be adaptively adjusted with an initial value of 0.001, I be the identity matrix, and e be the error vector.

[0035] Preferably, when the loss value of the neural network training decreases, the value of μ is reduced; when the loss value of the neural network training increases, the value of μ is increased.

[0036] The beneficial effects of this invention include:

[0037] (1) The use of neural network to output guidance commands improves guidance accuracy while reducing the complexity of the guidance model and has strong robustness.

[0038] (2) It has wide applicability. Different aircraft can use the same method to achieve the optimal guidance command without adjusting the model according to the characteristics of the aircraft.

[0039] (3) Using the hp-FRPM algorithm in the dataset production process greatly shortens the dataset generation time, eliminates the process of guessing initial values, and improves the accuracy of neural network guidance.

[0040] (4) The designed parameter update method can train a more accurate neural network in a shorter time, shorten the deployment time in engineering, and improve the guidance accuracy. Attached Figure Description

[0041] Figure 1 A schematic diagram of a mid-course guidance method based on a deep neural network according to a preferred embodiment of the present invention is shown.

[0042] Figure 2 The diagram shows a schematic diagram of a deep feedforward neural network structure in a mid-course guidance method based on a deep neural network according to a preferred embodiment of the present invention.

[0043] Figure 3 A schematic diagram of the neural network training loss value in a mid-course guidance method based on a deep neural network according to a preferred embodiment of the present invention is shown.

[0044] Figure 4 This diagram illustrates the ballistic trajectory during the mid-course guidance process in Example 1.

[0045] Figure 5 The velocity curve of the aircraft during mid-course guidance in Example 1 is shown. Detailed Implementation

[0046] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Through these descriptions, the features and advantages of the present invention will become clearer and more apparent.

[0047] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

[0048] According to the mid-course guidance method based on deep neural networks provided by the present invention, guidance commands are no longer obtained by traditional analytical or numerical iteration methods. Instead, guidance commands are obtained directly through neural networks. The aircraft flies under the control of the guidance commands until it enters the terminal guidance phase and hits the target.

[0049] The guidance method described in this invention can provide the maximum ballistic velocity under the attack angle constraint for unguided aircraft, thereby reducing the terminal guidance time. In this invention, there are no restrictions on the control method of the aircraft in the terminal guidance phase, and any known terminal guidance control method can be used.

[0050] Traditional neural networks are trained using historical data as the training set.

[0051] The inventors discovered that the neural network directly trained from historical aircraft status and guidance commands did not perform well, resulting in poor guidance accuracy, especially in complex interference environments where it was difficult to output accurate guidance commands. The challenge of this invention lies in how to obtain an effective training set to train the neural network so that it can output accurate guidance commands.

[0052] In this invention, an optimal control problem is set, and a training set for a neural network is generated based on this optimal control problem, such as... Figure 1 As shown.

[0053] In this invention, a training set is generated based on the optimal control problem, which not only solves the problem of non-optimal results in the traditional neural network training set, but also solves the problem of the influence of different interference environments on the output of the neural network under complex systems, enabling the neural network to be applied to the guidance field with extremely high accuracy requirements.

[0054] Specifically, the optimal control problem refers to the optimal control parameters corresponding to a certain state of the aircraft, where the state includes the target-missile distance r, the aircraft velocity V, and the trajectory inclination angle. The projectile's line-of-sight angle λ, and the initial launch angle. The initial horizontal distance s0 can be represented as a column vector. The optimal control parameter is the lateral acceleration a. c The missile-target distance refers to the distance between the aircraft and the target.

[0055] The state and the corresponding optimal control parameters form a state-optimal control pair, wherein the state serves as the input to the neural network and the corresponding optimal control parameters serve as the output of the neural network.

[0056] Furthermore, the optimal control problem can be represented by an aircraft dynamics model and an aircraft optimization objective, wherein the aircraft dynamics model is expressed as:

[0057]

[0058] Where x is the horizontal coordinate of the aircraft, y is the vertical coordinate of the aircraft, and V is the velocity of the aircraft. Let L be the trajectory inclination angle, L be the lift, m be the vehicle mass, T be the vehicle thrust, α be the angle of attack, g be the gravitational acceleration, and D be the aerodynamic drag. sp For propellant specific impulse.

[0059] Furthermore, the aerodynamic drag D and lift L can be expressed as:

[0060] D = (CD0 +C Dα 2 α 2 )qS

[0061] L=C Lα qSα

[0062] in It is dynamic pressure, S is the characteristic area of ​​the aircraft, ρ,C D0 C Dα C Lα It is the Mach number parameter, which can be obtained by looking up a table.

[0063] The optimization objective for the aircraft is expressed as:

[0064]

[0065] Among them, a c Let J be the lateral acceleration of the aircraft, J be the index function, and t be the lateral acceleration. f For the total flight time, -V(t) f ) represents t f The negative velocity of the aircraft at a given moment, i.e., the optimization objective, represents the lateral acceleration corresponding to the minimum negative velocity of the aircraft at the end of the total flight.

[0066] According to the present invention, multiple state-optimal control pairs are obtained by solving the optimal control problem, and the multiple state-optimal control pairs form a training set.

[0067] Since the optimal control problem is a highly nonlinear problem with no analytical solution and requires a large number of state-optimal control pairs to form a training set, how to quickly obtain a solution with good convergence is one of the problems that this invention aims to solve.

[0068] The inventors proposed a method for solving optimal control problems using the hp-FRPM method. The hp-FRPM method (hp-adaptive version of the Radau pseudospectral method, also known as the hp adaptive Flipped Radau pseudospectral method) is a nonlinear programming method used to solve optimal control problems established under different initial conditions.

[0069] The hp-FRPM method can adaptively increase or decrease discrete points according to the magnitude of changes in state and control variables. It has more discrete points in locations with larger variable changes and fewer discrete points in locations with less drastic changes. This makes the optimal data distribution more reasonable and more conducive to the full training of the neural network.

[0070] Furthermore, this method is not sensitive to initial value guessing and has a fast convergence speed. Other methods require several minutes to solve for an optimal control pair, while this method can solve for an optimal control pair in only 0.8 to 1.5 seconds under the same hardware conditions.

[0071] In a preferred embodiment, the training set includes at least 3 million state-optimal control pairs, such as 5 million, to ensure the accuracy of the trained neural network.

[0072] The neural network is preferably a deep feedforward neural network, and the structure of the deep feedforward neural network is as follows: Figure 2 As shown.

[0073] Preferably, in this invention, the neural network has three hidden layers, each with 12 neurons, and each neuron in the hidden layer is fully connected to the neurons in the previous layer.

[0074] Through extensive experimentation, the inventors determined the parameters for the number of hidden layers and neurons. Compared to other parameters, the neural network outputs with these parameters achieves higher accuracy and requires less computing power, making it suitable for airborne computers.

[0075] Preferably, in the neural network, the relationship between the next layer and the previous layer can be represented as follows:

[0076] L i+1 =σ(W i L i +b i )

[0077] The subscripts indicate different layers, W i Let b be the weight matrix of the i-th layer. i Let L be the bias matrix of the i-th layer. i L represents the output of the i-th layer. i+1 Let σ represent the output of the (i+1)th layer, and let σ represent the nonlinear activation function.

[0078] Preferably, the activation function is the tanh function, expressed as follows: This function performs better on fitting problems.

[0079] When training a neural network using a training set, preferably, the following steps are performed:

[0080] Step 1: Normalize and group the training set;

[0081] Preferably, the normalization is expressed as:

[0082]

[0083] Where z represents the state in the training set. Or any element in the optimal control parameters, z min z represents the minimum value of this type of element. max z represents the maximum value of this type of element. norm This represents the result after normalization. Through the above normalization, the training speed and stability of the neural network are greatly increased.

[0084] Similar to the traditional neural network training set grouping method, the grouping involves dividing the training set into training samples, validation samples, and test samples. Preferably, 70% of the training set data is used as training samples, 15% as validation samples, and 15% as test samples.

[0085] Step 2: Input training samples and obtain loss values;

[0086] The state values ​​from the training sample data are input into the neural network, and the output value of the neural network is compared with the optimal control parameters in the training sample. The loss value is obtained according to the loss function.

[0087] Preferably, the loss function is the mean squared error loss function.

[0088] Step 3: Backpropagate the loss value to update the neural network parameters;

[0089] The backpropagation algorithm is used to propagate the loss value into the neural network, updating the weights and bias parameters in the neural network.

[0090] Preferably, the update can be expressed as:

[0091] x k+1 =x k -(J F T J F +μI) -1 J F T e

[0092] Where, x k Indicates the parameter before the update, x k+1 Indicates the updated parameter, J F Let be the Jacobian matrix, μ be the trust region radius, which can be adaptively adjusted with an initial value of 0.001, I be the identity matrix, and e be the error vector.

[0093] The above-mentioned update method is a nonlinear least squares algorithm. This update method has the advantages of both Newton's method and gradient descent method, and can adjust the update strategy itself. In this invention, it has a faster convergence speed than methods such as Adam and SGD, and can train a more accurate neural network in a shorter time. This not only shortens the deployment time in engineering, but also improves the guidance accuracy of the aircraft.

[0094] More preferably, when the loss value of the neural network training decreases, the value of μ is reduced to μ', such as setting μ' = 0.1μ, which can speed up the convergence speed; conversely, if the loss value of the neural network training increases, the value of μ is increased to μ', such as setting μ' = 10μ.

[0095] In this invention, adaptive adjustment of μ can achieve the fastest convergence speed, which is especially suitable for the Levenberg-Marquardt method when training smaller neural networks.

[0096] Step 4: Repeat steps 2 and 3 to complete the first generation training of the training samples. Use validation samples and test samples to test the trained neural network. If the loss value reaches the preset value, stop training; otherwise, repeat step 4 to perform the first generation training again.

[0097] Step four is the same as the training process of a conventional neural network, and will not be described in detail in this invention.

[0098] Furthermore, the inventors discovered that, due to the use of the Levenberg-Marquardt method and adaptive adjustment, the training process converges extremely quickly, such as... Figure 3 As shown, in practical use, only about 200 generations of training are needed to complete the training of a neural network.

[0099] According to the present invention, the trained neural network is loaded into the onboard computer of the aircraft. Since the neural network has a simple structure, it can quickly output the optimal guidance command. After the aircraft is launched, the onboard computer acquires a set of state vectors s of the aircraft at regular intervals and inputs them into the neural network. The neural network can quickly calculate the optimal guidance command required at this time. The aircraft only needs to follow the command output by the neural network to achieve the maximum terminal velocity under the attack angle constraint.

[0100] Example

[0101] Example 1

[0102] For a certain aircraft, a neural network is used to obtain guidance commands. The training set of the neural network is generated by setting an optimal control problem.

[0103] The optimal control problem can be represented by an aircraft dynamics model and an aircraft optimization objective.

[0104] The aircraft dynamics model is represented as follows:

[0105]

[0106] The aircraft optimization objective is expressed as:

[0107]

[0108] The hp-FRPM method was used to solve the optimal control problem established under different initial conditions. Specifically, 15,000 initial conditions (initial launch angle and target position) were randomly generated, and the solution accuracy of GPOPS-II was set to 1×10⁻⁶. -8 The solution yielded approximately 5 million optimal control pairs.

[0109] The neural network has three hidden layers, each with 12 neurons. Each neuron in a hidden layer is fully connected to the neurons in the layer above it. The relationship between the layers in this neural network can be represented as follows:

[0110] L i+1 =σ(W i L i +b i )

[0111] The activation function between layers is the tanh function.

[0112] When training a neural network, the Levenberg-Marquardt method is used to update the network parameters. The Levenberg-Marquardt method is expressed as follows:

[0113] x k+1 =x k -(J F T J F +μI) -1 J F T e

[0114] The initial value of μ is 0.001. When the loss value of the neural network training decreases, the value of μ is reduced to μ', μ' = 0.1μ; conversely, if the loss of the neural network increases, the value of μ is increased to μ', μ' = 10μ.

[0115] The trained neural network was tested using 500 Monte Carlo simulations. Some simulation results are as follows: Figure 4 , 5 As shown, the solid line represents the optimal trajectory, and the dashed line represents the trajectory under neural network control. Figure 4The trajectory of the ballistics during the mid-course guidance process is shown in the figure, and it can be seen from the figure that the two have a very high degree of overlap; Figure 5 The figure shows the aircraft's velocity curve during the mid-course guidance process. As can be seen from the figure, the flight speed of the aircraft under neural network control is very close to the optimal value, indicating that the control commands output by the neural network have extremely high accuracy.

[0116] In the description of this invention, it should be noted that the terms "upper," "lower," "inner," "outer," "front," and "rear," etc., indicate the orientation or positional relationship based on the orientation or positional relationship in the working state of this invention, and are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention. Furthermore, the terms "first," "second," "third," and "fourth" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0117] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0118] The present invention has been described above with reference to preferred embodiments; however, these embodiments are merely exemplary and illustrative. Various substitutions and modifications can be made to the present invention based on these embodiments, all of which fall within the scope of protection of the present invention.

Claims

1. A mid-course guidance method based on a deep neural network, characterized in that, The aircraft receives guidance commands through a neural network and flies under the control of these commands. The training set for the neural network is generated by setting an optimal control problem. The optimal control problem refers to the optimal control parameters corresponding to a certain state of the aircraft. The state includes the distance between the bullet and the target. aircraft speed Ballistic inclination angle Bullet eye view angle Initial launch angle and initial horizontal distance The optimal control parameter is lateral acceleration. , The optimal control problem is represented by an aircraft dynamics model and an aircraft optimization objective. The aircraft dynamics model is represented as follows: in, The horizontal coordinates of the aircraft The vertical coordinates of the aircraft For the speed of the aircraft, For the trajectory inclination angle, For lift, For the mass of the aircraft, For aircraft thrust, For the angle of attack, It is the acceleration due to gravity. For aerodynamic drag, For propellant specific impulse, aerodynamic drag and lift It can be represented as: in, It is dynamic pressure. The characteristic area of ​​the aircraft, It is the Mach number parameter. The air density at the location of the aircraft. Zero-lift drag coefficient, The induced drag coefficient, The lift coefficient; The optimization objective for the aircraft is expressed as: in, The lateral acceleration of the aircraft. For index functions, Total flight time express At the moment, the aircraft's negative velocity, The hp-FRPM method is used to solve the optimal control problem, obtaining multiple state-optimal control pairs. The hp-FRPM method can adaptively increase or decrease discrete points based on the magnitude of changes in state and control variables, having more discrete points in areas with greater variable changes and fewer discrete points in areas with less drastic changes.

2. The mid-course guidance method based on a deep neural network according to claim 1, characterized in that, The state and the corresponding optimal control parameters form a state-optimal control pair, wherein the state serves as the input to the neural network and the corresponding optimal control parameters serve as the output of the neural network.

3. The mid-course guidance method based on a deep neural network according to claim 1, characterized in that, The neural network is a deep feedforward neural network with three hidden layers, each containing 12 neurons. The neurons in each hidden layer are fully connected to the neurons in the previous layer.

4. The mid-course guidance method based on a deep neural network according to claim 1, characterized in that, When training a neural network using a training set, the following steps are performed: Step 1: Normalize and group the training set; Step 2: Input training samples and obtain loss values; Step 3: Backpropagate the loss value to update the neural network parameters; Step 4: Repeat steps 2 and 3 to complete the first generation training of the training samples. Use validation samples and test samples to test the trained neural network. If the loss value reaches the preset value, stop training; otherwise, repeat step 4 to perform the first generation training again.

5. The mid-course guidance method based on a deep neural network according to claim 4, characterized in that, In step one, the normalization is expressed as: in, Represents the state in the training set Or any element in the optimal control parameters, This represents the minimum value of that type of element. This represents the maximum value of that type of element. This represents the result after normalization.

6. The mid-course guidance method based on a deep neural network according to claim 5, characterized in that, In step three, the update can be expressed as: in, This indicates the parameters before the update. Indicates the updated parameters. For Jacobian matrices, This is the trust region radius, which can be adaptively adjusted, with an initial value of 0.

001. Represents the identity matrix. This represents the error vector.

7. The mid-course guidance method based on a deep neural network according to claim 6, characterized in that, When the loss value during neural network training decreases, the shrinkage occurs. Value; as the loss value during neural network training increases, the expansion value.

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