A large-scale cluster control method and system for high-speed aircraft in a hostile environment
By using a deep neural network-based control policy network in high-speed aircraft clusters, the challenge of high-speed aircraft cluster control in the environment is solved, and the effects of formation maintenance, threat avoidance and target strikes are achieved.
Patent Information
- Application Number
- CN202310478528.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-04-28
- Publication Date
- 2025-05-23
- Estimated Expiration
- 2043-04-28
AI Technical Summary
In the confrontational environment, high-speed aircraft clusters have challenges in formation control and threat avoidance, and traditional methods are difficult to design adaptive control algorithms that adapt to complex environments.
A deep neural network-based aircraft cluster control policy network is adopted to generate distributed cluster control strategies by acquiring and preprocessing cluster information and environmental information to realize cluster control of high-speed aircraft.
It realizes cluster control of high-speed aircraft clusters in a dynamic confrontation environment, can maintain formation, avoid threat areas and achieve strikes on targets, and has strong generalization capabilities and robustness.
Smart Images
Figure CN116610141B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of aircraft cluster control, and in particular to a large-scale cluster control method and system for high-speed aircraft in a hostile environment. Background Art
[0002] There have been many studies on the control of aircraft swarms. Aircraft swarm control is usually modeled as a multi-objective optimization problem and then solved using an optimization algorithm. For example, reference [1] describes the swarm control of aircraft as a multi-objective optimization problem, introduces the hierarchical learning behavior of pigeon swarms to improve the multi-objective pigeon swarm-inspired optimization algorithm, and realizes distributed swarm control. In addition, reference [2] proposes a multi-objective social learning pigeon swarm-inspired optimization method, which solves the obstacle avoidance problem of aircraft formation based on artificial potential fields. However, this control mode is prone to fall into local optimality when the number of individuals in the swarm is large. Due to the constraints of the computing power of the airborne platform and the difficulty in obtaining an accurate environmental model, it is difficult for the optimization algorithm to find the optimal result within a limited time, which further limits the practical application scenarios of the optimization algorithm. With the advancement of machine learning, learning-based methods are gradually being used to solve the problem of aircraft swarm control. For example, reference [3] uses deep reinforcement learning to learn the swarm control strategy of aircraft to achieve swarming and navigation tasks in complex environments.
[0003] Although there are a lot of achievements on the swarm control of conventional aircraft such as quadrotors and small fixed-wing aircraft, there are still some special problems to be solved for the swarm control of high-speed aircraft. First, high-speed aircraft swarms are often used to perform complex tasks in highly confrontational and highly dynamic environments. Traditional methods often require accurate environment and aircraft models to design control rules, and these models are difficult to implement in real-world environments. Therefore, it is difficult for traditional methods with fixed rules to design adaptive control algorithms that can adapt to complex environments. This makes it necessary to develop a method for high-speed aircraft swarms to enable them to learn to perform tasks in confrontational dynamic environments. In addition, there are threat areas in confrontational environments, and the cluster needs to be able to avoid the threat areas. However, high speed leads to a larger maneuvering radius, which is also a challenge for high-speed aircraft swarms. Summary of the invention
[0004] To this end, the present invention proposes a large-scale cluster control method and system for high-speed aircraft in a confrontation environment, so as to solve the formation control and threat avoidance problems involved in large-scale clusters of high-speed aircraft in a confrontation environment.
[0005] According to one aspect of the present invention, a method for controlling a large-scale cluster of high-speed aircraft in a hostile environment is provided, the method comprising the following steps:
[0006] Step 1: For each individual in the high-speed aircraft cluster, obtain the collected cluster information and environmental information;
[0007] Step 2: preprocessing the cluster information and environment information;
[0008] Step 3: Input the preprocessed cluster information and environmental information of the high-speed aircraft cluster into the pre-trained aircraft cluster control strategy network based on deep neural network to obtain control instructions.
[0009] Furthermore, the cluster information includes relative formation information and relative speed information, the relative formation information is the formation deviation between the aircraft and its multiple nearest individuals, and the relative speed information is the deviation between the aircraft speed and the average speed of the cluster; the environmental information includes threat area information and target information, the threat area information is the relative position vector between the aircraft and the nearest threat area, and the target information is the relative position vector between the aircraft and the target.
[0010] Furthermore, the specific process of step 2 includes:
[0011] The preprocessing method of relative formation information is:
[0012]
[0013] In the formula, R fmt Represents the formation distance scaling factor; i=1,2,...,n represents the formation deviation between the aircraft and its n nearest individuals;
[0014] The preprocessing method of relative speed information is:
[0015]
[0016] Where V fmt Indicates the formation speed scaling factor; It represents the deviation of the aircraft speed from the average speed of the cluster;
[0017] The preprocessing method of threat zone information is as follows:
[0018]
[0019] In the formula, represents the relative position vector between the aircraft and the nearest threat area; f(·) is a piecewise function in the form of:
[0020]
[0021] Where, d 0 is the set safety distance threshold;
[0022] The preprocessing method of target information is:
[0023]
[0024] In the formula, R tgt represents the target distance scaling factor, V represents the speed of the aircraft, and V tgt represents the target speed scaling factor, n V is the unit vector representing the direction of gravity, Represents the relative position vector between the aircraft and the target.
[0025] Furthermore, the output of the aircraft cluster control strategy network in step 3 includes the mean of the control instructions of the aircraft y-axis and z-axis and variance in and are the mean and variance of the y-axis overload command in the body axis coordinate system, and are the mean and variance of the z-axis overload command in the body axis coordinate system, i.e., the output a of the action y and a z The probability density distribution function of is:
[0026]
[0027]
[0028] According to the above probability density distribution function, the action instruction a=[a y ,a z ], then the overload instruction of the high-speed aircraft is:
[0029]
[0030] Where n ky and n kz They represent the maximum overload values of the y-axis and z-axis in the body axis coordinate system of the aircraft respectively; the overload command for the three axes of the aircraft is obtained as n=[0,n y ,n z ].
[0031] According to another aspect of the present invention, a large-scale cluster control system of high-speed aircraft for a hostile environment is provided, the system comprising:
[0032] An information collection module configured to obtain collected cluster information and environmental information for each individual in the high-speed aircraft cluster;
[0033] A preprocessing module configured to preprocess the cluster information and environment information;
[0034] The control module is configured to input the preprocessed cluster information and environmental information of the high-speed aircraft cluster into a pre-trained aircraft cluster control strategy network based on a deep neural network to obtain control instructions.
[0035] Furthermore, the cluster information in the information collection module includes relative formation information and relative speed information, the relative formation information is the formation deviation between the aircraft and its multiple nearest individuals, and the relative speed information is the deviation between the aircraft speed and the average speed of the cluster; the environmental information includes threat area information and target information, the threat area information is the relative position vector between the aircraft and the nearest threat area, and the target information is the relative position vector between the aircraft and the target.
[0036] Furthermore, the specific process of preprocessing in the preprocessing module includes:
[0037] The preprocessing method of relative formation information is:
[0038]
[0039] In the formula, R fmt Indicates the formation distance scaling factor; i=1,2,...,n represents the formation deviation between the aircraft and its n nearest individuals;
[0040] The preprocessing method of relative speed information is:
[0041]
[0042] Where V fmt Indicates the formation speed scaling factor; It represents the deviation of the aircraft speed from the average speed of the cluster;
[0043] The preprocessing method of threat zone information is as follows:
[0044]
[0045] In the formula, represents the relative position vector between the aircraft and the nearest threat area; f(·) is a piecewise function in the form of:
[0046]
[0047] Where, d 0 is the set safety distance threshold;
[0048] The preprocessing method of target information is:
[0049]
[0050] In the formula, R tgtrepresents the target distance scaling factor, V represents the speed of the aircraft, and V tgt represents the target speed scaling factor, n V is the unit vector representing the direction of gravity, Represents the relative position vector between the aircraft and the target.
[0051] Furthermore, the output of the aircraft cluster control strategy network in step 3 of the control module includes the mean of the control instructions of the aircraft y-axis and z-axis and variance in and are the mean and variance of the y-axis overload command in the body axis coordinate system, and are the mean and variance of the z-axis overload command in the body axis coordinate system, i.e., the output a of the action y and a z The probability density distribution function of is:
[0052]
[0053]
[0054] According to the above probability density distribution function, the action instruction a=[a y ,a z ], then the overload instruction of the high-speed aircraft is:
[0055]
[0056] Where n ky and n kz They represent the maximum overload values of the y-axis and z-axis in the body axis coordinate system of the aircraft respectively; the overload command for the three axes of the aircraft is obtained as n=[0,n y ,n z ].
[0057] The beneficial technical effects of the present invention are:
[0058] The present invention can realize cluster control of a high-speed aircraft cluster in a confrontation environment, obtain cluster information and environmental information of individual aircraft in the cluster respectively, pre-process the information and input it into a pre-trained deep neural network to obtain cluster control instructions, and convert the cluster control instructions into overload instructions for individuals in the cluster, so as to realize cluster control of high-speed aircraft in a dynamic confrontation environment.
[0059] Compared with traditional methods, the present invention has the following advantages: 1) The observation information includes cluster information and environmental information, and the preprocessing of the information enables the individual to accurately perceive the information of cluster configuration maintenance, threat zone distribution and target orientation; 2) The distributed cluster control strategy neural network obtained based on deep reinforcement learning makes the high-speed aircraft cluster control have strong generalization ability, which can achieve the target strike while maintaining the cluster configuration and avoiding the threat zone.
[0060] The cluster control strategy proposed in the present invention adopts a distributed architecture, which can adapt to changes in the number of aircraft clusters and changes in environmental conditions, and can be expanded to large-scale high-speed aircraft cluster application scenarios as needed. BRIEF DESCRIPTION OF THE DRAWINGS
[0061] The present invention can be better understood by referring to the description given below in conjunction with the accompanying drawings, which together with the following detailed description are included in this specification and form a part of this specification, and are used to further illustrate the preferred embodiments of the present invention and explain the principles and advantages of the present invention.
[0062] Figure 1 It is a flow chart of a large-scale cluster control method of high-speed aircraft in a hostile environment according to an embodiment of the present invention.
[0063] Figure 2 This is static target example 1 in the embodiment of the present invention.
[0064] Figure 3 This is static target example 2 in the embodiment of the present invention.
[0065] Figure 4 This is Example 1 of a low-speed dynamic target in an embodiment of the present invention.
[0066] Figure 5 This is Example 2 of a low-speed dynamic target in an embodiment of the present invention.
[0067] Figure 6 This is Example 1 of a high-speed dynamic target in an embodiment of the present invention.
[0068] Figure 7 This is Example 2 of a high-speed dynamic target in an embodiment of the present invention. DETAILED DESCRIPTION
[0069] In order to enable those skilled in the art to better understand the scheme of the present invention, exemplary implementations or embodiments of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described implementations or embodiments are only implementations or embodiments of a part of the present invention, not all of them. Based on the implementations or embodiments of the present invention, all other implementations or embodiments obtained by ordinary technicians in the field without creative work should fall within the scope of protection of the present invention.
[0070] Aiming at the requirements of threat zone avoidance, target strike and cluster configuration maintenance faced by high-speed aircraft cluster control in a confrontation environment, the present invention proposes a large-scale cluster control method and system for high-speed aircraft in a confrontation environment. The detected cluster and environmental information are preprocessed, the preprocessed information is input into a pre-trained deep neural network, and finally the output of the neural network is converted into an overload instruction for individuals in the cluster, so as to realize cluster control of high-speed aircraft.
[0071] A large-scale cluster control method for high-speed aircraft in a hostile environment according to an embodiment of the present invention is as follows: Figure 1 As shown, the following steps are included:
[0072] Step 1: For each individual in the high-speed aircraft cluster, obtain the collected cluster information and environmental information.
[0073] According to an embodiment of the present invention, the cluster information includes relative formation information and relative speed information. The relative formation information is the formation deviation between the aircraft and its nearest n individuals. i=1,2,...,n, relative speed information is the deviation between the aircraft speed and the average speed of the cluster Environmental information includes threat zone information and target information. Threat zone information is the relative position vector between the aircraft and the nearest threat zone. The target information is the relative position vector between the aircraft and the target
[0074] Step 2: Preprocess the cluster information and environmental information corresponding to each individual in the high-speed aircraft cluster.
[0075] According to an embodiment of the present invention, the preprocessing method of the relative formation information is as follows:
[0076]
[0077] In the formula, R fmt is the formation distance scaling factor.
[0078] The preprocessing method of relative speed information is as follows:
[0079]
[0080] Where V fmt is the formation speed scaling factor.
[0081] The preprocessing method of aircraft threat zone information is as follows:
[0082]
[0083] Where f(·) is a piecewise function in the form of:
[0084]
[0085] Where, d 0 is the set safety distance threshold.
[0086] The preprocessing method of aircraft target information is as follows:
[0087]
[0088] In the formula, R tgt is the target distance scaling factor, V is the aircraft speed, and V tgt is the target velocity scaling factor, n V is the unit vector in the direction of gravity.
[0089] Step 3: Input the preprocessed cluster information and environmental information of the high-speed aircraft cluster into the pre-trained aircraft cluster control strategy network based on deep neural network to obtain control instructions.
[0090] According to an embodiment of the present invention, based on the design of step two, a reinforcement learning simulation interactive environment is written based on Pytorch using Python programming language, and then deep reinforcement learning is used to complete the pre-training of the deep neural network. The pre-training process is a prior art, and then the output of the neural network is converted into an overload instruction for the aircraft in the cluster.
[0091] According to the mean of the neural network output and variance in and are the mean and variance of the y-axis overload command in the body axis coordinate system, and are the mean and variance of the z-axis overload command in the body axis coordinate system, i.e., the output a of the action y and a z The probability density distribution function of is:
[0092]
[0093] According to the above probability density distribution function, the action instruction a=[ay ,a z ], finally, the overload command of the high-speed aircraft is calculated by the following formula:
[0094]
[0095] Where n ky and n kz They represent the maximum overload of the y-axis and z-axis in the aircraft body axis coordinate system, n x 、n y and n z They represent the three-axis overload of the aircraft respectively. Assuming that the high-speed aircraft has no acceleration capability in the x-axis direction, that is, n x =0. The final three-axis overload command of the aircraft is n=[0,n y ,n z ].
[0096] Experiments are further used to verify the technical effects of the present invention.
[0097] Numerical simulation is used to verify the correctness and rationality of the present invention. First, a high-speed aircraft cluster simulation environment is constructed using the Python programming language, in which the high-speed aircraft model adopts a simplified overload model that ignores the rotation and flattening of the earth. The cluster is initially located at an altitude of 20km, with a horizontal position at the origin in the scene and an initial speed of 1km / s. Several hemispherical threat areas are randomly distributed in the scene. In each simulation, the threat area is rotated at a random angle with an axis perpendicular to the origin pointing to the center of the earth to achieve randomization of the distribution of the threat area. The simulation test software runs in Windows 10+Python3.8, and the hardware environment is Intel9300H CPU+16.0GB RAM. Set the formation distance scaling factor R fmt =5km, formation speed scaling factor V fmt =400m / s, target speed scaling factor V tgt =1000m / s, Threat zone safety distance threshold d 0 =40km, the maximum overload values of the y and z axes are n ky =8 and n kz =8.
[0098] The present invention has carried out simulation experiments to verify the method of the present invention in the scenarios of static targets, low-speed dynamic targets (400m / s) and high-speed dynamic targets (700m / s). The cluster control method of the present invention is randomly run 100 times in each scenario, and the success rate in the above three scenarios is 100%. From the above results, it can be seen that the method of the present invention can realize the cluster control of high-speed aircraft clusters in dynamic and complex environments, and achieve the attack on the target while maintaining the formation and avoiding the threat area, and has a very high success rate, which shows that the method of the present invention has good generalization ability and robustness.
[0099] Examples of high-speed aircraft swarm control tests in static target scenarios include Figure 2 and Figure 3 An example of a high-speed aircraft cluster control test in a low-speed dynamic target scenario is shown in Figure 4 and Figure 5 As shown in the figure, an example of high-speed aircraft cluster control test in a high-speed dynamic target scenario is shown in Figure 6 and Figure 7 As shown in the example diagram, when the target is stationary, moving at a low speed, and moving at a high speed, according to the control method of the present invention, the cluster can maintain the formation and move toward the target point, avoiding the threat area along the way, and finally hit the target.
[0100] The method according to the present invention can realize the control of a high-speed aircraft cluster in a dynamic environment, and provides a feasible technical approach for a high-speed aircraft cluster in a dynamic environment.
[0101] Another embodiment of the present invention provides a large-scale cluster control system for high-speed aircraft in a hostile environment, the system comprising:
[0102] An information collection module configured to obtain the collected cluster information and environmental information for each individual in the high-speed aircraft cluster;
[0103] A preprocessing module configured to preprocess the cluster information and environment information;
[0104] The control module is configured to input the preprocessed cluster information and environmental information of the high-speed aircraft cluster into a pre-trained aircraft cluster control strategy network based on a deep neural network to obtain control instructions.
[0105] In this embodiment, preferably, the cluster information in the information acquisition module includes relative formation information and relative speed information, the relative formation information is the formation deviation between the aircraft and its multiple nearest individuals, and the relative speed information is the deviation between the aircraft speed and the average speed of the cluster; the environmental information includes threat zone information and target information, the threat zone information is the relative position vector between the aircraft and the nearest threat zone, and the target information is the relative position vector between the aircraft and the target.
[0106] In this embodiment, preferably, the specific process of preprocessing in the preprocessing module includes:
[0107] The preprocessing method of relative formation information is:
[0108]
[0109] In the formula, R fmt Represents the formation distance scaling factor; i=1,2,...,n represents the formation deviation between the aircraft and its n nearest individuals;
[0110] The preprocessing method of relative speed information is:
[0111]
[0112] Where V fmt Indicates the formation speed scaling factor; It represents the deviation of the aircraft speed from the average speed of the cluster;
[0113] The preprocessing method of threat zone information is as follows:
[0114]
[0115] In the formula, represents the relative position vector between the aircraft and the nearest threat area; f(·) is a piecewise function in the form of:
[0116]
[0117] Where, d 0 is the set safety distance threshold;
[0118] The preprocessing method of target information is:
[0119]
[0120] In the formula, R tgt represents the target distance scaling factor, V represents the aircraft speed, V tgt represents the target speed scaling factor, n V is the unit vector representing the direction of gravity, Represents the relative position vector between the aircraft and the target.
[0121] In this embodiment, preferably, the output of the aircraft cluster control strategy network in the control module includes the mean of the control instructions of the aircraft y-axis and z-axis and variance in and are the mean and variance of the y-axis overload command in the body axis coordinate system, and are the mean and variance of the z-axis overload command in the body axis coordinate system, i.e., the output a of the action y and a z The probability density distribution function of is:
[0122]
[0123]
[0124] According to the above probability density distribution function, the action instruction a=[a y ,a z ], then the overload instruction of the high-speed aircraft is:
[0125]
[0126] Where n ky and n kz They represent the maximum overload values of the y-axis and z-axis in the body axis coordinate system of the aircraft respectively; the overload command for the three axes of the aircraft is obtained as n=[0,n y ,n z ].
[0127] The functions of a large-scale cluster control system of high-speed aircraft for a hostile environment according to an embodiment of the present invention can be described by the aforementioned large-scale cluster control method of high-speed aircraft for a hostile environment. Therefore, for the parts not described in detail in the system embodiment, please refer to the above method embodiment and will not be repeated here.
[0128] Although the present invention has been described according to a limited number of embodiments, it will be apparent to those skilled in the art, with the benefit of the above description, that other embodiments are contemplated within the scope of the invention thus described. The disclosure of the present invention is intended to be illustrative rather than restrictive of the scope of the invention, which is defined by the appended claims.
[0129] The documents cited in the present invention are as follows:
[0130] [1]Qiu H, Duan HA multi-objective pigeon-inspired optimization approach to UAV distributed flocking among obstacles[J]. Information Sciences, 2020, 509:515-529.
[0131] [2]Ruan W,Duan H.Multi-UAV obstacle avoidance control via multi-objective social learning pigeon-inspired optimization[J].Frontiers ofInformation Technology&Electronic Engineering,2020,21:740-748.
[0132] [3]Wang C,Wang J,Zhang X.A deep reinforcement learning approach toflocking and navigation of uavs in large-scale complex environments[C] / / 2018IEEE Global Conference on Signal and Information Processing(GlobalSIP).IEEE,2018:1228-1232.
Claims
1. A method for large-scale cluster control of high-speed aircraft in an adversarial environment, characterized in that, it includes the following steps: Step 1: For each individual in the high-speed aircraft cluster, obtain the collected cluster information and environmental information; the cluster information includes relative formation information and relative speed information, the relative formation information is the formation deviation between the aircraft and its nearest multiple individuals, and the relative speed information is the deviation between the aircraft speed and the cluster average speed; the environmental information includes threat area information and target information, the threat area information is the relative position vector between the aircraft and the nearest threat area, and the target information is the relative position vector between the aircraft and the target; Step 2: Preprocess the cluster information and environmental information; including: The preprocessing method for relative formation information is: where R fmt represents the formation distance scaling factor; represents the formation deviation between the aircraft and its n nearest individuals; The preprocessing method for relative speed information is: Where V fmt Indicates the formation speed scaling factor; It represents the deviation of the aircraft speed from the average speed of the cluster; The preprocessing method for threat area information is: In the formula, represents the relative position vector between the aircraft and the nearest threat area; f(·) is a piecewise function in the form of: Where, d 0 is the set safety distance threshold; The preprocessing method for target information is: In the formula, R tgt represents the target distance scaling factor, V represents the aircraft speed, V tgt represents the target speed scaling factor, n V is the unit vector representing the direction of gravity, Represents the relative position vector between the aircraft and the target; Step 3: Input the preprocessed cluster information and environmental information of the high-speed aircraft cluster into a pre-trained aircraft cluster control strategy network based on a deep neural network respectively to obtain control instructions.
2. A method for large-scale cluster control of high-speed aircraft in an adversarial environment according to claim 1, characterized in that, The output of the aircraft cluster control strategy network in step 3 includes the mean of the control instructions of the aircraft y-axis and z-axis and variance in and are the mean and variance of the y-axis overload command in the body axis coordinate system, and are the mean and variance of the z-axis overload command in the body axis coordinate system, i.e., the output a of the action y and a z The probability density distribution function of is: According to the above probability density distribution function, the action instruction a=[a y ,a z ], then the overload instruction of the high-speed aircraft is: Where n ky and n kz They represent the maximum overload values of the y-axis and z-axis in the body axis coordinate system of the aircraft respectively; the overload command for the three axes of the aircraft is obtained as n=[0,n y ,n z ].
3. A large-scale cluster control system for high-speed aircraft in an adversarial environment, characterized in that, it includes: An information collection module configured to obtain the collected cluster information and environmental information for each individual in the high-speed aircraft cluster; The cluster information in the information collection module includes relative formation information and relative speed information, the relative formation information is the formation deviation between the aircraft and its nearest multiple individuals, and the relative speed information is the deviation between the aircraft speed and the cluster average speed; the environmental information includes threat area information and target information, the threat area information is the relative position vector between the aircraft and the nearest threat area, and the target information is the relative position vector between the aircraft and the target; A preprocessing module configured to preprocess the cluster information and environmental information; including: The preprocessing method for relative formation information is: where, R fmt represents the formation distance scaling factor; represents the formation deviation between the aircraft and its n nearest individuals; The preprocessing method for relative speed information is: Where V fmt Indicates the formation speed scaling factor; It represents the deviation of the aircraft speed from the average speed of the cluster; The preprocessing method for threat area information is: In the formula, represents the relative position vector between the aircraft and the nearest threat area; f(·) is a piecewise function in the form of: Where, d 0 is the set safety distance threshold; The preprocessing method for target information is: In the formula, R tgt represents the target distance scaling factor, V represents the speed of the aircraft, and V tgt represents the target speed scaling factor, n V is the unit vector representing the direction of gravity, Represents the relative position vector between the aircraft and the target; A control module configured to input the preprocessed cluster information and environmental information of the high-speed aircraft cluster into a pre-trained aircraft cluster control strategy network based on a deep neural network respectively to obtain control instructions.
4. A large-scale cluster control system for high-speed aircraft in an adversarial environment according to claim 3, characterized in that, The output of the aircraft cluster control strategy network in the control module includes the mean of the control instructions of the aircraft y-axis and z-axis and variance in and are the mean and variance of the y-axis overload command in the body axis coordinate system, and are the mean and variance of the z-axis overload command in the body axis coordinate system, i.e., the output a of the action y and a z The probability density distribution function of is: According to the above probability density distribution function, the action instruction a=[a y ,a z ], then the overload instruction of the high-speed aircraft is: Where n ky and n kz They represent the maximum overload values of the y-axis and z-axis in the body axis coordinate system of the aircraft respectively; the overload command for the three axes of the aircraft is obtained as n=[0,n y ,n z ].