Intelligent control method for spacecraft with time-optimal low-thrust transfer
By combining the neighbor point iteration method and deep neural networks, small thrust samples are quickly generated and fully connected neural networks are trained, solving the problems of high cost and high resource consumption in existing technologies, and realizing efficient solution and online control of time-optimal small thrust transfer.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NAT UNIV OF DEFENSE TECH
- Filing Date
- 2023-03-22
- Publication Date
- 2026-06-05
AI Technical Summary
Existing technologies consume a lot of computational resources and time when generating training sample sets, and the success rate of indirect methods is low, resulting in high training costs and low efficiency of neural networks, making it difficult to quickly solve time-optimal small thrust transfer problems.
A small thrust sample set is generated by the neighbor point iteration method. A deep neural network is used to fit the mapping relationship between state variables, co-state variables and optimal transition time. By combining Newton's iteration method and the indirect method, an efficient sample set is quickly generated, and a fully connected neural network is trained to solve the problem.
It enables rapid generation and efficient solution of optimal control for low-thrust transfer, reduces sample generation costs, and improves solution efficiency and success rate, making it suitable for on-orbit online control of spacecraft.
Smart Images
Figure CN116520873B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of spacecraft control technology, and in particular to a spacecraft intelligent control method for time-optimal low-thrust transfer. Background Technology
[0002] Low-thrust propulsion technology, due to its relatively low engine specific impulse, can significantly save propulsion fuel consumption and is often used in deep space exploration. However, because the thrust is very small, the acceleration process takes a long time, which increases the difficulty of designing low-thrust transfer trajectories. Therefore, transfer time is a key performance indicator that needs to be optimized during low-thrust trajectory changes, giving rise to the time-optimal low-thrust transfer problem. Currently, the theoretical approach to achieving and solving the time-optimal transfer trajectory for low-thrust propulsion is optimal control. Based on whether the index function is directly optimized, optimal control methods are divided into direct methods, indirect methods, and hybrid methods. Direct methods utilize pseudospectral methods to replace nonlinear problems with higher-order interpolation. Indirect methods, based on the Pontryagin minimum principle and variational methods, derive the first-order necessary condition for optimal control from the Hamiltonian function, transforming the low-thrust trajectory optimization problem into a two-point boundary value problem involving state variables and co-state variables. Hybrid methods combine direct and indirect methods. Among these, the direct method has higher solution efficiency but lower accuracy. The greatest advantage of the indirect method is that it yields high-precision solutions, good continuity of control variables, and satisfies the first-order optimality condition. However, during the solution process, the costate variables lack clear physical meaning, initial values are difficult to predict, and it is highly sensitive to boundary and constraint conditions, making the solution of the two-point boundary value problem quite difficult. Currently, in addition to the classic shooting method, a common approach to address the difficulties of solving the two-point boundary value problem using the indirect method is to treat the initial values of the costate variables as parameters to be optimized and use parameter optimization methods such as nonlinear programming and intelligent algorithms. However, this approach still suffers from significant computational burden and a low success rate.
[0003] With the continuous development of machine learning technology, some research has proposed using machine learning methods to solve the two-point boundary value problem, specifically the time-optimal low-thrust transfer problem. Specifically, since deep neural networks can approximate strongly nonlinear models with high accuracy, they can be used to fit the nonlinear model of the two-point boundary value problem, learning the mapping relationship from state variables to costate variables. This allows for the rapid solution of the time-optimal low-thrust transfer problem using the trained neural network model. However, training the neural network requires a large number of training samples, and the generation of existing training samples still relies on indirect methods. This results in high computational costs due to the large amount of computational resources and time required to generate the training sample set. Furthermore, since each training sample is solved individually using indirect methods, the success rate remains low. Summary of the Invention
[0004] To address some or all of the technical problems existing in the prior art, this invention provides a spacecraft intelligent control method for time-optimal low-thrust transfer.
[0005] The technical solution of the present invention is as follows:
[0006] A spacecraft intelligent control method for time-optimal low-thrust transfer is provided, the method comprising:
[0007] Set the optimal time-based low-thrust transfer range for spacecraft's departure and arrival orbits;
[0008] Select a departure track and an arrival track from the departure track range and the arrival track range. Set multiple departure position points on the departure track and multiple arrival position points on the arrival track. Based on the multiple departure position points and multiple arrival position points, generate a small thrust sample set using the neighbor point iteration method. The small thrust sample includes state variables and their corresponding costate variables and optimal transition time. The state variables include the number of track elements at the departure position and the arrival position.
[0009] Constructing deep neural networks;
[0010] A deep neural network was trained using a small thrust sample set to fit the mapping relationship between state variables, co-state variables, and optimal transition time;
[0011] A trained deep neural network is used to solve the time-optimal low-thrust transfer problem, and the costate variables and optimal transfer time are obtained for spacecraft control.
[0012] In some possible implementations, the generation of a small thrust sample set based on multiple departure and arrival points using a neighbor point iteration method includes:
[0013] Step 21: Select the first departure position point on the departure orbit as the initial neighbor point, select the first arrival position point on the arrival orbit as the initial arrival position, and use the indirect method to solve the optimal control solution for the spacecraft from the first departure position point to the first arrival position point.
[0014] Step 22: Use the solution of the optimal control of the spacecraft from the previous departure position to the current arrival position as the initial value of the Newton iteration method, and use the Newton iteration method to solve the solution of the optimal control of the spacecraft from the next departure position to the current arrival position.
[0015] Step 23: Repeat step 22 until the optimal control solution for all departure positions to the first arrival position is obtained;
[0016] Step 24: Take the next arrival position as the arrival position, and take the solution of the optimal control of the spacecraft from the first departure position to the previous arrival position as the initial value of Newton's iteration method. Use Newton's iteration method to solve the optimal control solution of the spacecraft from the first departure position to the current arrival position.
[0017] Step 25: Repeat step 22 until the optimal control solution for all spacecraft that have been transferred from their starting positions to their current arrival positions is obtained;
[0018] Step 26: Repeat steps 24 and 25 until the optimal control solution for the spacecraft, which transfers all departure positions on the departure orbit to all arrival positions on the arrival orbit, is obtained.
[0019] Step 27: Take the solution of optimal control for each spacecraft and the orbital elements of its paired start and end points as a small thrust sample to obtain a set of small thrust samples including multiple small thrust samples. The solution of optimal control for spacecraft includes: co-state variables and optimal transition time.
[0020] In some possible implementations, steps 22 and 24 are performed in parallel.
[0021] In some possible implementations, multiple departure and arrival orbits are selected within the set range of spacecraft departure and arrival orbits, and multiple small thrust samples are generated for each selected departure and arrival orbit.
[0022] In some possible implementations, if the success rate of generating the small thrust sample set is less than a preset success rate threshold, the spacecraft's departure and arrival orbit ranges for time-optimal small thrust transfer are reset, and the small thrust sample set is regenerated based on the reset spacecraft departure and arrival orbit ranges until the success rate of generating the small thrust sample set is above the preset success rate threshold.
[0023] In some possible implementations, the deep neural network is a fully connected neural network.
[0024] In some possible implementations, training the deep neural network using a set of small thrust samples includes:
[0025] The small thrust sample set is divided into a training sample set, a validation sample set, and a test sample set according to a preset division ratio.
[0026] The deep neural network is trained using a set of training samples.
[0027] In some possible implementations, training the deep neural network using a set of training samples includes:
[0028] The deep neural network is trained by using the state variables in the training samples as inputs and the co-state variables and optimal transition time in the training samples as outputs.
[0029] In some possible implementations, training the deep neural network by using the state variables in the training samples as inputs and the costate variables and optimal transition times in the training samples as outputs includes:
[0030] Step 41: Input the state variables from multiple training samples into the deep neural network in sequence to obtain the predicted costate variables and the predicted optimal transition time output by the deep neural network.
[0031] Step 42: Calculate the preset loss function based on the co-state variables and optimal transition times in multiple training samples and the predicted co-state variables and predicted optimal transition times output by the deep neural network corresponding to multiple training samples.
[0032] Step 43: Determine whether the preset training stop condition has been met. If yes, use the current deep neural network as the deep neural network that has completed training. If no, update the network parameters of the deep neural network using the preset loss function and return to step 41.
[0033] In some possible implementations, the method further includes:
[0034] The prediction accuracy of the trained deep neural network is tested using a set of test samples.
[0035] If the prediction accuracy of the deep neural network is less than the first preset accuracy value but greater than the second preset accuracy value, the deep neural network is improved, and the deep neural network is retrained using the small thrust sample set based on the improved deep neural network.
[0036] If the prediction accuracy of the deep neural network is below the second preset accuracy value, a new set of small thrust samples with a larger number of small thrust samples will be generated, and the deep neural network will be retrained using the small thrust sample set.
[0037] The main advantages of the technical solution of this invention are as follows:
[0038] The spacecraft intelligent control method for time-optimal low-thrust transfer of the present invention can realize the rapid generation of samples for optimal control of low-thrust transfer, improve the sample generation efficiency, reduce the sample generation cost, realize the rapid solution of time-optimal low-thrust transfer problem, with high solution efficiency and high solution success rate, and can be applied to the on-orbit online control of spacecraft. Attached Figure Description
[0039] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and constitute a part of this invention, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:
[0040] Figure 1 This is a flowchart of a spacecraft intelligent control method for time-optimal low-thrust transfer according to an embodiment of the present invention;
[0041] Figure 2 This is a schematic diagram illustrating the relative positional relationship of neighboring points according to an embodiment of the present invention;
[0042] Figure 3 This is a schematic diagram illustrating the parallel computation process of the neighbor point iteration method according to an embodiment of the present invention.
[0043] Figure 4 This is a schematic diagram of the structure of a deep neural network according to an embodiment of the present invention. Detailed Implementation
[0044] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.
[0045] The technical solutions provided by the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
[0046] See Figure 1 An embodiment of the present invention provides a spacecraft intelligent control method for time-optimal low-thrust transfer, the method comprising the following steps 1-5:
[0047] Step 1: Set the spacecraft's departure orbit range and arrival orbit range for time-optimal low-thrust transfer.
[0048] In one embodiment of the present invention, the range of the spacecraft's departure orbit and arrival orbit for time-optimal low-thrust transfer is set according to the departure orbit and arrival orbit that may be involved in the actual on-orbit control of the spacecraft, so as to ensure the reliability of solving the time-optimal low-thrust transfer problem using the deep neural network that has been trained subsequently.
[0049] Step 2: Select the departure track and the arrival track from the departure track range and the arrival track range. Set multiple departure position points on the departure track and multiple arrival position points on the arrival track. Based on the multiple departure position points and multiple arrival position points, generate a small thrust sample set using the neighbor point iteration method. The small thrust sample includes state variables and their corresponding costate variables and optimal transition time. The state variables include the number of track elements at the departure position and the arrival position.
[0050] Specifically, in one embodiment of the present invention, a small thrust sample set is generated based on multiple starting point locations and multiple arriving point locations using a neighbor point iteration method, including the following steps:
[0051] Step 21: Select the first departure position point on the departure orbit as the initial neighbor point, select the first arrival position point on the arrival orbit as the initial arrival position, and use the indirect method to solve the optimal control solution for the spacecraft from the first departure position point to the first arrival position point.
[0052] Step 22: Use the solution of the optimal control of the spacecraft from the previous departure position to the current arrival position as the initial value of the Newton iteration method, and use the Newton iteration method to solve the solution of the optimal control of the spacecraft from the next departure position to the current arrival position.
[0053] Step 23: Repeat step 22 until the optimal control solution for all departure positions to the first arrival position is obtained;
[0054] Step 24: Take the next arrival position as the arrival position, and take the solution of the optimal control of the spacecraft from the first departure position to the previous arrival position as the initial value of Newton's iteration method. Use Newton's iteration method to solve the optimal control solution of the spacecraft from the first departure position to the current arrival position.
[0055] Step 25: Repeat step 22 until the optimal control solution for all spacecraft that have been transferred from their starting positions to their current arrival positions is obtained;
[0056] Step 26: Repeat steps 24 and 25 until the optimal control solution for the spacecraft, which transfers all departure positions on the departure orbit to all arrival positions on the arrival orbit, is obtained.
[0057] Step 27: Take the solution of optimal control for each spacecraft and the orbital elements of its paired start and end points as a small thrust sample to obtain a set of small thrust samples including multiple small thrust samples. The solution of optimal control for spacecraft includes: co-state variables and optimal transition time.
[0058] In the process of generating small thrust samples using the neighbor point iteration method, if the solution for the optimal control from a certain departure position to a certain arrival position fails, the solution for the small thrust samples corresponding to the current departure track and arrival track will be terminated directly.
[0059] refer to Figure 2 For the optimal trajectory transfer problem, points that are close to each other on the same trajectory can be considered as neighboring points, such as... Figure 2 In this invention, departure position-1 and departure position-2 can be considered as two neighboring points, and arrival position-1 and arrival position-2 can also be considered as two neighboring points. In one embodiment of the invention, the solution of the optimal control of the spacecraft corresponding to the previous departure position is used as the initial value for Newton's iteration method. Newton's iteration method is then used to solve for the optimal control of the spacecraft corresponding to its neighboring points, i.e., the optimal control solution for the spacecraft corresponding to the next departure position. Similarly, the solution of the optimal control of the spacecraft corresponding to the previous arrival position is used as the initial value for Newton's iteration method, and Newton's iteration method is used to solve for the optimal control solution for the spacecraft corresponding to its neighboring points. This enables rapid solution for the optimal control of small thrust transfer, quickly generates a large number of small thrust samples, and has a high success rate.
[0060] Since the specific processes of solving the optimal control solution for the spacecraft from the departure position to the arrival position using the indirect method and the Newton-Raphson iteration method are already public knowledge in this field, they will not be elaborated here.
[0061] refer to Figure 2 In order to further improve the success rate of solving the problem and ensure the accuracy of the solution obtained by using Newton's iteration method, in one embodiment of the present invention, the difference θ between the mean apogee angles of two adjacent position points on the track is less than a preset angle threshold ε.
[0062] The angle threshold ε is determined based on the actual sample set size required, and can be set to 5° to 30°. The smaller ε is, the more position points are on each starting and ending track, and the more small thrust samples are generated accordingly.
[0063] refer to Figure 3 In one embodiment of the present invention, in the specific steps of generating a small thrust sample set using the neighbor point iteration method described above, the numerical calculations of steps 22 and 24 are independent of each other. Therefore, steps 22 and 24 can be performed in parallel. Specifically, after calculating the optimal control solution corresponding to a position point, the optimal control solutions corresponding to multiple neighbor points can be calculated simultaneously through parallel computing, further improving the generation efficiency of small thrust samples.
[0064] Furthermore, in one embodiment of the present invention, multiple departure and arrival orbits are selected within the set spacecraft departure orbit range and arrival orbit range, and multiple small thrust samples are generated for each selected departure and arrival orbit.
[0065] Specifically, for the selected departure and arrival tracks, multiple small thrust samples are generated using the aforementioned neighbor point iteration method, and all generated small thrust samples are combined into a small thrust sample set.
[0066] By selecting multiple departure and arrival trajectories and generating multiple small thrust samples for each selected departure and arrival trajectories, a larger number of small thrust samples can be obtained to ensure the accuracy of the deep neural network trained subsequently.
[0067] Furthermore, in one embodiment of the present invention, if the success rate of generating the small thrust sample set is less than a preset success rate threshold, the spacecraft departure orbit range and arrival orbit range for time-optimal small thrust transfer are reset, and the small thrust sample set is regenerated based on the reset spacecraft departure orbit range and arrival orbit range until the success rate of generating the small thrust sample set is above the preset success rate threshold, wherein the success rate of generating the small thrust sample set = actual number of small thrust samples generated / theoretical number of small thrust samples generated × 100%.
[0068] In one embodiment of the present invention, the success rate threshold is specifically set according to the actual number of samples required and the accuracy of the deep neural network, for example, it can be 80%, 85% or 90%.
[0069] In one embodiment of the present invention, the aforementioned neighbor point iteration method is applicable to different two-body orbital dynamics models, including two-body dynamics models in rectangular coordinate systems, spherical coordinate systems, cylindrical coordinate systems, and orbital dynamics models based on the improved vernal equinox.
[0070] Step 3: Construct a deep neural network.
[0071] In one embodiment of the present invention, the deep neural network is a fully connected neural network.
[0072] refer to Figure 4 Specifically, a fully connected neural network consists of an input layer, a hidden layer, and an output layer connected in sequence, with the ReLU function used as the non-linear activation function between layers.
[0073] Step 4: Use a small thrust sample set to train a deep neural network to fit the mapping relationship between state variables, co-state variables, and optimal transition time.
[0074] In one embodiment of the present invention, training a deep neural network using a set of small thrust samples includes:
[0075] The small thrust sample set is divided into a training sample set, a validation sample set, and a test sample set according to a preset division ratio. The training sample set is used to train the deep neural network, the validation sample set is used to test the deep neural network during the training process so as to adjust the hyperparameters of the deep neural network based on the test results, and the test sample set is used to test the prediction accuracy of the trained deep neural network.
[0076] The division ratio can be set according to actual needs, for example, it can be 8:1:1.
[0077] Furthermore, in one embodiment of the present invention, training the deep neural network using a training sample set includes:
[0078] The deep neural network is trained by using the state variables in the training samples as inputs and the co-state variables and optimal transition time in the training samples as outputs.
[0079] The input to a deep neural network is a state variable, namely the number of orbital elements at the starting and ending positions, which is 12-dimensional. The output of a deep neural network is a co-state variable and an optimal transition time, which are 7-dimensional, including 6-dimensional co-state variables and 1-dimensional optimal transition time.
[0080] Specifically, in one embodiment of the present invention, the state variables in the training samples are used as the input of the deep neural network, and the costate variables and optimal transition time in the training samples are used as the output of the deep neural network to train the deep neural network, including the following steps 41-43:
[0081] Step 41: Input the state variables from multiple training samples into the deep neural network in sequence to obtain the predicted co-state variables and the predicted optimal transition time output by the deep neural network.
[0082] In one embodiment of the present invention, the state variables in the training samples are input from the input end of the deep neural network, processed sequentially by the parameters of each layer in the deep neural network, and output from the output end of the deep neural network. The information output from the output end is the predicted costate variable and the predicted optimal transition time corresponding to the state variable.
[0083] In one embodiment of the present invention, the deep neural network can be an untrained or incompletely trained network model. Each layer of the network model is set with initialization parameters, and the parameters of each layer can be continuously updated and adjusted during the training process of the network model.
[0084] Step 42: Calculate the preset loss function based on the co-state variables and optimal transition times in multiple training samples and the predicted co-state variables and predicted optimal transition times output by the deep neural network corresponding to multiple training samples.
[0085] Specifically, the loss function used for training the deep neural network is pre-defined, and the pre-defined loss function is calculated based on the co-state variables and optimal transition times in multiple training samples and the predicted co-state variables and predicted optimal transition times output by the deep neural network.
[0086] In one embodiment of the present invention, the loss function is an absolute error loss function or a relative error loss function.
[0087] Step 43: Determine whether the preset training stop condition has been met. If yes, use the current deep neural network as the deep neural network that has completed training. If no, update the parameters of the deep neural network using the preset loss function and return to step 41.
[0088] In one embodiment of the present invention, the training stopping condition is specifically set according to the actual situation, for example, when the number of training iterations reaches a set number of iterations.
[0089] Furthermore, in one embodiment of the present invention, the parameters of the deep neural network can be updated using the following formula:
[0090]
[0091] Where, Θ t+1 Θ represents the parameters of the deep neural network at the (t+1)th iteration. t Let θ represent the parameters of the deep neural network at the t-th iteration, Δ[·] represent the optimizer, η represent the learning rate, L represent the loss function, and Θ represent the parameters of the deep neural network. The optimizer is specific to the actual situation, such as Adam or SGD, and the learning rate is preset to control the speed of parameter updates.
[0092] Furthermore, in one embodiment of the present invention, the method further includes:
[0093] The prediction accuracy of the trained deep neural network is tested using a set of test samples.
[0094] If the prediction accuracy of the deep neural network is less than the first preset accuracy value but greater than the second preset accuracy value, the deep neural network is improved, and the deep neural network is retrained using the small thrust sample set based on the improved deep neural network.
[0095] If the prediction accuracy of the deep neural network is below the second preset accuracy value, a new set of small thrust samples with a larger number of small thrust samples will be generated, and the deep neural network will be retrained using the small thrust sample set.
[0096] The preset accuracy value is set according to the actual situation. For example, the first preset accuracy value is 90%, and the second preset accuracy value is 70%.
[0097] In one embodiment of the present invention, improving the deep neural network includes adjusting at least one of the hyperparameters of the deep neural network, such as the number of network layers, the number of neurons in each layer, the learning rate, and the number of iterations.
[0098] Step 5: Use the trained deep neural network to solve the time-optimal small thrust transfer problem, and obtain the costate variables and the optimal transfer time for spacecraft control.
[0099] Specifically, when solving the time-optimal low-thrust transfer problem, the orbital elements of the spacecraft's departure and arrival positions are determined, and the orbital elements of the spacecraft's departure and arrival positions are input into a trained deep neural network to obtain the costate variables and optimal transfer time output by the deep neural network.
[0100] The spacecraft intelligent control method for time-optimal low-thrust transfer provided in one embodiment of the present invention can realize the rapid generation of samples for optimal control of low-thrust transfer, improve the sample generation efficiency, reduce the sample generation cost, realize the rapid solution of time-optimal low-thrust transfer problem, with high solution efficiency and solution success rate, and can be applied to the on-orbit online control of spacecraft.
[0101] It should be noted that, in this document, relational terms such as “first” and “second” are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus.
[0102] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A spacecraft intelligent control method for time-optimal low-thrust transfer, characterized in that, include: Set the optimal time-based low-thrust transfer range for spacecraft's departure and arrival orbits; Select a departure track and an arrival track from the departure track range and the arrival track range. Set multiple departure position points on the departure track and multiple arrival position points on the arrival track. Based on the multiple departure position points and multiple arrival position points, generate a small thrust sample set using the neighbor point iteration method. The small thrust sample includes state variables and their corresponding costate variables and optimal transition time. The state variables include the number of track elements at the departure position and the arrival position. Constructing deep neural networks; A deep neural network was trained using a small thrust sample set to fit the mapping relationship between state variables, co-state variables, and optimal transition time; A trained deep neural network is used to solve the time-optimal low-thrust transfer problem, and the costate variables and optimal transfer time are obtained for spacecraft control. The method of generating a small thrust sample set based on multiple departure and arrival points using a neighbor point iteration method includes: Step 21: Select the first departure position point on the departure orbit as the initial neighbor point, select the first arrival position point on the arrival orbit as the initial arrival position, and use the indirect method to solve the optimal control solution for the spacecraft from the first departure position point to the first arrival position point. Step 22: Use the solution of the optimal control of the spacecraft from the previous departure position to the current arrival position as the initial value of the Newton iteration method, and use the Newton iteration method to solve the solution of the optimal control of the spacecraft from the next departure position to the current arrival position. Step 23: Repeat step 22 until the optimal control solution for all departure positions to the first arrival position is obtained; Step 24: Take the next arrival position as the arrival position, and take the solution of the optimal control of the spacecraft from the first departure position to the previous arrival position as the initial value of Newton's iteration method. Use Newton's iteration method to solve the optimal control solution of the spacecraft from the first departure position to the current arrival position. Step 25: Repeat step 22 until the optimal control solution for all spacecraft that have been transferred from their starting positions to their current arrival positions is obtained; Step 26: Repeat steps 24 and 25 until the optimal control solution for the spacecraft, which transfers all departure positions on the departure orbit to all arrival positions on the arrival orbit, is obtained. Step 27: Take the solution of optimal control for each spacecraft and the orbital elements of its paired start and end points as a small thrust sample to obtain a set of small thrust samples including multiple small thrust samples. The solution of optimal control for spacecraft includes: co-state variables and optimal transition time.
2. The spacecraft intelligent control method for time-optimal low-thrust transfer according to claim 1, characterized in that, Steps 22 and 24 are performed in parallel.
3. The spacecraft intelligent control method for time-optimal low-thrust transfer according to claim 1, characterized in that, Multiple departure and arrival orbits are selected within the set spacecraft departure and arrival orbit ranges, and multiple small thrust samples are generated for each selected departure and arrival orbit.
4. The spacecraft intelligent control method for time-optimal low-thrust transfer according to claim 1, characterized in that, If the success rate of generating the low-thrust sample set is less than the preset success rate threshold, the spacecraft's departure and arrival orbit ranges for time-optimal low-thrust transfer are reset, and the low-thrust sample set is regenerated based on the reset spacecraft departure and arrival orbit ranges until the success rate of generating the low-thrust sample set is above the preset success rate threshold.
5. The spacecraft intelligent control method for time-optimal low-thrust transfer according to claim 1, characterized in that, The deep neural network is a fully connected neural network.
6. The spacecraft intelligent control method for time-optimal low-thrust transfer according to claim 1 or 5, characterized in that, The method of training a deep neural network using a set of small thrust samples includes: The small thrust sample set is divided into a training sample set, a validation sample set, and a test sample set according to a preset division ratio. The deep neural network is trained using a set of training samples.
7. The spacecraft intelligent control method for time-optimal low-thrust transfer according to claim 6, characterized in that, The training of the deep neural network using a training sample set includes: The deep neural network is trained by using the state variables in the training samples as inputs and the co-state variables and optimal transition time in the training samples as outputs.
8. The spacecraft intelligent control method for time-optimal low-thrust transfer according to claim 7, characterized in that, The step of training a deep neural network by using state variables from training samples as input and co-state variables and optimal transition times from training samples as output includes: Step 41: Input the state variables from multiple training samples into the deep neural network in sequence to obtain the predicted costate variables and the predicted optimal transition time output by the deep neural network. Step 42: Calculate the preset loss function based on the co-state variables and optimal transition times in multiple training samples and the predicted co-state variables and predicted optimal transition times output by the deep neural network corresponding to multiple training samples. Step 43: Determine whether the preset training stop condition has been met. If yes, use the current deep neural network as the deep neural network that has completed training. If no, update the network parameters of the deep neural network using the preset loss function and return to step 41.
9. The spacecraft intelligent control method for time-optimal low-thrust transfer according to claim 6, characterized in that, The method further includes: The prediction accuracy of the trained deep neural network is tested using a set of test samples. If the prediction accuracy of the deep neural network is less than the first preset accuracy value but greater than the second preset accuracy value, the deep neural network is improved, and the deep neural network is retrained using the small thrust sample set based on the improved deep neural network. If the prediction accuracy of the deep neural network is below the second preset accuracy value, a new set of small thrust samples with a larger number of small thrust samples will be generated, and the deep neural network will be retrained using the small thrust sample set.