Hypersonic flight vehicle cooperative control method based on adaptive dynamic programming

Abstract

The invention discloses a hypersonic flight vehicle cooperative control method based on adaptive dynamic programming, and the method comprises the steps: firstly building a six-degree-of-freedom normalization model for a hypersonic flight vehicle, determining the cooperative tracking control problem of a hypersonic flight vehicle cluster, and employing an adaptive dynamic programming algorithm to achieve the cooperative tracking control of a hypersonic flight vehicle cluster; an optimal tracking control form under limited control input is obtained, a single-evaluation neural network on-line controller is constructed on the basis, an optimal tracking control law is solved on line, the obtained optimal tracking control law is input and applied to a hypersonic aircraft cluster, and cooperative tracking control is achieved. According to the method, for a hypersonic aircraft system described by a six-degree-of-freedom model, cooperative tracking control is achieved on a hypersonic aircraft cluster under the condition that flight constraints are considered, online control is achieved through an adaptive dynamic programming algorithm, and the method is suitable for the field of cluster cooperative control of hypersonic aircrafts.

Description

Technical Field

[0001] The present invention belongs to the technical field of cooperative control of hypersonic aircraft, and in particular relates to a cooperative control method of a hypersonic aircraft based on adaptive dynamic programming. Background Art

[0002] Hypersonic vehicles are of great significance to the scientific field due to their extremely high speed and flexible maneuverability. Not only are they suitable for cruising within the atmosphere, but they can also perform re-entry missions through the atmosphere. They effectively combine the advantages of aircraft and spacecraft. But at the same time, the model of hypersonic vehicle motion exhibits faster time differences, stronger coupling, and greater uncertainty than existing aircraft, which brings unprecedented difficulties and challenges to control system design. Therefore, the existing design theories and methods of existing aircraft control systems cannot be directly transplanted to hypersonic vehicles. It is necessary to study new collaborative control theories and methods without losing the versatility of hypersonic vehicles.

[0003] Adaptive dynamic programming is an emerging optimal control strategy that can effectively solve the dimensionality curse problem brought by the existing optimal control algorithm and can perform online adaptive control of the target under more serious model uncertainty, environmental distortion, etc. Adaptive dynamic programming is of great significance in solving the speed or attitude control problem of hypersonic aircraft, but the problem of cooperative optimal tracking control in the scenario of multi-aircraft cooperative flight has not received enough attention. Therefore, how to apply the online control algorithm based on adaptive dynamic programming to the cooperative tracking control of hypersonic aircraft is an urgent problem to be solved. Summary of the invention

[0004] To solve the above technical problems, the present invention provides a hypersonic aircraft collaborative control method based on adaptive dynamic programming, which calculates the optimal collaborative control input of the aircraft using an adaptive dynamic programming algorithm with a single-evaluation neural network architecture, and is suitable for collaborative tracking control based on adaptive dynamic programming in the field of collaborative control of hypersonic aircraft.

[0005] The technical solution adopted by the present invention is: a hypersonic aircraft cooperative control method based on adaptive dynamic programming, the specific steps are as follows:

[0006] S1. Establish a 6-DOF normalized model for hypersonic vehicles and clarify the collaborative tracking control problem of hypersonic vehicle clusters;

[0007] S2, based on step S1, using an adaptive dynamic programming algorithm to obtain an optimal tracking control form under limited control input;

[0008] S3, based on step S2, construct a single evaluation neural network online controller, and solve the optimal tracking control law online;

[0009] S4. Apply the optimal tracking control law input obtained in step S3 to the hypersonic aircraft cluster to achieve collaborative tracking control.

[0010] Furthermore, the step S1 is specifically as follows:

[0011] S11. Establish a 6-DOF normalized model for the hypersonic vehicle;

[0012] The 6-DOF particle dynamics equation of an unpowered lifting hypersonic vehicle is as follows:

[0013]

[0014] Where r is the radial distance from the center of the earth to the hypersonic vehicle, t is the time, θ and φ are longitude and latitude respectively, V is the earth's relative velocity, ψ is the velocity heading angle relative to the local north direction, γ is the track angle, m and σ are the mass and roll angle of the hypersonic vehicle respectively, D and L are the aerodynamic drag and lift respectively. The angular velocity of the earth is denoted by ω e , the local gravitational acceleration is denoted by g.

[0015] The 6-DOF particle dynamics equation is normalized and the normalized variable expression is defined as follows:

[0016]

[0017] Among them, R e represents the radius of the earth, and g0 represents the acceleration due to gravity.

[0018] By bringing the normalized variables into the dynamic equation, we can obtain the normalized dynamic equation of the hypersonic vehicle, which is expressed as follows:

[0019]

[0020] S12. Clarify the problem of cooperative tracking control of hypersonic vehicle clusters;

[0021] It is assumed that the hypersonic aircraft cluster has a leader and N followers, wherein the leader is denoted as aircraft No. 0, and the followers are denoted as aircraft No. 1, ..., N respectively.

[0022] The communication network between the hypersonic aircraft clusters is then modeled as a directed graph From a vertex set An edge set and a weighted adjacency matrix If and only if the i-th follower hypersonic vehicle can receive the information of the follower hypersonic vehicle j, a ij >0; otherwise, a ij =0; for a ii =0; node v i The neighbor set of And Figure The edge between the leader hypersonic vehicle and the follower hypersonic vehicle is represented by the matrix It means that when the ith follower hypersonic vehicle has a direct communication link with the leader hypersonic vehicle 0, b i =1, otherwise b i =0.

[0023] Then the normalized leader hypersonic vehicle cooperative control model with distortion taken into account is expressed as follows with respect to time t:

[0024]

[0025] Among them, X0(t) = [r0, θ0, φ0, V0, γ0, ψ0] represents the system state of the leader hypersonic aircraft, u0(t) = [α0, σ0] represents the control input to the leader hypersonic aircraft, α0 represents the angle of attack of the leader hypersonic aircraft, σ0 represents the roll angle of the leader hypersonic aircraft, d0(t) represents the disturbance of the leader hypersonic aircraft, represents the derivative of the system state of the leader hypersonic vehicle. And the input-output mapping of the dynamic equation in equation (3) is denoted as f.

[0026] At the same time, the normalized cooperative control model of the follower hypersonic aircraft in the hypersonic aircraft cluster is set, and the expression is as follows:

[0027]

[0028] Among them, X i (t) = [r i ,θ i ,φ i ,V i ,γ i ,ψ i ] represents the system state of the i-th follower hypersonic vehicle, u i (t) = [α i ,σ i ] represents the control input to the i-th follower hypersonic vehicle, α i represents the angle of attack of the i-th follower hypersonic vehicle, σ irepresents the roll angle of the i-th follower hypersonic vehicle, d i (t) represents the disturbance to the ith follower aircraft, represents the derivative of the system state of the i-th follower hypersonic vehicle.

[0029] Define the normalized distributed cooperative control error e of the i-th follower hypersonic vehicle: i (t), the expression is as follows:

[0030]

[0031] Then the derivative of the normalized distributed cooperative control error of the i-th follower hypersonic vehicle is obtained: The expression is as follows:

[0032]

[0033] Among them, e ij 、e i0 represents the error of the ith follower hypersonic vehicle to its neighbor and the leader respectively, and the cooperative tracking control law of the ith follower hypersonic vehicle is and Unified as u ei , represents the gradient of the error of the i-th follower hypersonic vehicle to its neighbors and the leader, respectively, denotes the gradient of the control input of the i-th follower hypersonic vehicle to its neighbors and the leader, respectively.

[0034] Finally, if satisfied It is considered that the hypersonic aircraft cluster achieves collaborative tracking control.

[0035] Furthermore, the step S2 is specifically as follows:

[0036] The goal of the hypersonic vehicle cluster cooperative control is to control the follower hypersonic vehicle to track the desired trajectory of the leader vehicle from the initial state at the minimum cost, that is, the goal is to determine the tracking control law u ei , so that the cost L(e i (t)) is minimized, and the expression is as follows:

[0037]

[0038] Among them, τ represents the integral variable with respect to time, J(e i (τ),u ei (e i (τ))) represents the utility function consisting of the state-related term Q and the feedback control-related term R. Q is defined as Q(e i)=e i T QUR i , and Q0 is a positive definite diagonal matrix representing the weight of each state element, and T represents the transpose operation.

[0039] Set the saturation constraint of the optimal tracking control law and define R so that the feedback remains within the limit. The expression is as follows:

[0040]

[0041] Where v represents the control input u ei The integral variable, R0 is a positive definite matrix, λ1 and λ2 represent α i and σ i Amplitude limitation.

[0042] Then the Hamiltonian function is obtained through the HJB equation, and the expression is as follows:

[0043]

[0044] in, represents the augmented form of the gradient of the error of the ith follower hypersonic vehicle, represents the augmented form of the gradient of the control input of the ith follower hypersonic vehicle, Indicates L(e i ) with respect to ei. Then the optimal cost function L(e i ) * The expression is as follows:

[0045]

[0046] Where Ψ(Ω) represents u ei According to Bellman's optimality principle V(e i ) * is the solution of the HJB equation, expressed as follows:

[0047]

[0048] in, Represents the optimal tracking control law, by solving The partial differential equation of is obtained, and the expression is as follows:

[0049]

[0050] in, Indicates L(e i ) * For e i The partial derivative of .

[0051] Furthermore, the step S3 is specifically as follows:

[0052] First, a single neural network is used to i (e i ), the number of neurons in the hidden layer is represented by l, the weight matrix between the input layer and the hidden layer is represented by Y, and the weight matrix between the hidden layer and the output layer is represented by W. The single evaluation network is selected as a three-layer feedforward neural network, and the output expression of the three-layer neural network is as follows:

[0053]

[0054] Among them, Ξ represents the activation function, and b represents the activation function threshold.

[0055] Then, according to the high-order Weierstrass approximation theorem, the optimal cost function L obtained by fitting the single-evaluation neural network is ci (e i ) * Its gradient is represented by an infinite-dimensional linearly independent basis function set, and an evaluation neural network with a finite-dimensional activation function is used to construct L ci (e i ) * , the expression is as follows:

[0056]

[0057] in, represents the weight vector of the neural network. And L ci (e i ) * About e i The first-order partial derivative and second-order partial derivative expressions are as follows:

[0058]

[0059] Then L ci (e i ) * , The construction error expressions are as follows:

[0060]

[0061] Based on the derivation of equations (13)-(17), u ei The approximate value expression of is as follows:

[0062]

[0063] And L i (e i ) *Error e i is continuous, then a linearized neural network can be obtained as the evaluation network of adaptive dynamic programming, that is, the observation form of equations (15) and (16) is obtained, and the expression is as follows:

[0064]

[0065] in, represents the optimal weight of the single-evaluation neural network of the i-th follower hypersonic vehicle, Right now Approximation of ∈ c represents the approximate error that converges to zero after appropriate training under continuous excitation conditions. The expression of the approximate cost function in practice is as follows:

[0066]

[0067] Then the gradient descent method is used to update the weights of the single evaluation network. First, the error function of the single evaluation network is defined, and the expression is as follows:

[0068]

[0069] Then the goal of weight update is to minimize the loss function, which is expressed as follows:

[0070]

[0071] Finally, using the principle of gradient descent, the online update rule expression of the network weight parameters is designed as follows:

[0072]

[0073] Among them, K W represents a positive learning rate.

[0074] Beneficial effects of the present invention: The method of the present invention first establishes a 6-DOF normalized model for a hypersonic aircraft, and clarifies the problem of collaborative tracking control of a cluster of hypersonic aircraft. An adaptive dynamic programming algorithm is used to obtain the optimal tracking control form under limited control input. On this basis, a single-evaluation neural network online controller is constructed to solve the optimal tracking control law online. The optimal tracking control law input is applied to a cluster of hypersonic aircraft to achieve collaborative tracking control. The method of the present invention is aimed at a hypersonic aircraft system described by a 6-DOF model, and considers the collaborative tracking control of a cluster of hypersonic aircraft under the condition of flight constraints, and uses an adaptive dynamic programming algorithm to achieve online control. It is suitable for the field of cluster collaborative control of hypersonic aircraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1The present invention is a flowchart of a hypersonic aircraft collaborative control method based on adaptive dynamic programming.

[0076] Figure 2 Schematic diagram of the communication topology of a multi-robot system hypersonic aircraft in an embodiment of the present invention.

[0077] Figure 3 This is a rendering of the cooperative tracking behavior presented after the method of the present invention is deployed on the hypersonic aircraft in an embodiment of the present invention. DETAILED DESCRIPTION

[0078] The method of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0079] like Figure 1 As shown, a flow chart of a hypersonic aircraft cooperative control method based on adaptive dynamic programming of the present invention is shown, and the specific steps are as follows:

[0080] S1. Establish a 6-DOF normalized model for hypersonic vehicles and clarify the collaborative tracking control problem of hypersonic vehicle clusters;

[0081] S2, based on step S1, using an adaptive dynamic programming algorithm to obtain an optimal tracking control form under limited control input;

[0082] S3, based on step S2, construct a single evaluation neural network online controller, and solve the optimal tracking control law online;

[0083] S4. Apply the optimal tracking control law input obtained in step S3 to the hypersonic aircraft cluster to achieve collaborative tracking control.

[0084] In this embodiment, the step S1 is specifically as follows:

[0085] S11. Establish a 6-DOF normalized model for the hypersonic vehicle;

[0086] The 6-DOF particle dynamics equation of an unpowered lifting hypersonic vehicle is as follows:

[0087]

[0088] Among them, r represents the radial distance from the center of the earth to the hypersonic vehicle, t represents time; θ and φ represent longitude and latitude respectively; V represents the relative speed of the earth; ψ represents the speed heading angle relative to the local north direction, γ represents the track angle; m and σ represent the mass and roll angle of the hypersonic vehicle respectively; D and L represent aerodynamic drag and lift respectively, which are related to the aerodynamic coefficient, angle of attack and speed. The angular velocity of the earth is denoted by ω e , the local gravitational acceleration is denoted by g.

[0089] In order to make the mathematical model of hypersonic vehicle cooperative control suitable for adaptive dynamic programming, the 6-DOF particle dynamics equation is normalized. The normalized variable expression is defined as follows:

[0090]

[0091] Among them, R e represents the radius of the earth, and g0 represents the acceleration due to gravity.

[0092] By bringing the normalized variables into the dynamic equation, the normalized dynamic equation of the hypersonic vehicle (6-DOF normalized model) can be obtained as follows:

[0093]

[0094] S12. Clarify the problem of cooperative tracking control of hypersonic vehicle clusters;

[0095] It is assumed that the hypersonic aircraft cluster has a leader and N followers, where the leader is recorded as aircraft No. 0, and the followers are recorded as aircraft No. 1, ..., N. The communication topology diagram of the multi-robot system hypersonic aircraft in this embodiment is as follows Figure 2 shown.

[0096] The communication network between the hypersonic aircraft clusters is then modeled as a directed graph From a vertex set An edge set and a weighted adjacency matrix If and only if the i-th follower hypersonic vehicle can receive the information of the follower hypersonic vehicle j, a ij >0; otherwise, a ij =0; for a ii =0; node v i The neighbor set of And Figure The edge between the leader hypersonic vehicle and the follower hypersonic vehicle is represented by the matrix It means that when the ith follower hypersonic vehicle has a direct communication link with the leader hypersonic vehicle 0, b i =1, otherwise b i =0.

[0097] Then the normalized leader hypersonic vehicle cooperative control model with distortion taken into account is expressed as follows with respect to time t:

[0098]

[0099] Among them, X0(t) = [r0, θ0, φ0, V0, γ0, ψ0] represents the system state of the leader hypersonic aircraft, u0(t) = [α0, σ0] represents the control input to the leader hypersonic aircraft, α0 represents the angle of attack of the leader hypersonic aircraft, σ0 represents the roll angle of the leader hypersonic aircraft, d0(t) represents the disturbance of the leader hypersonic aircraft, represents the derivative of the system state of the leader hypersonic vehicle. And for the convenience of representation, the input-output mapping of the dynamic equation in equation (3) is denoted as f.

[0100] At the same time, the normalized cooperative control model of the follower hypersonic aircraft in the hypersonic aircraft cluster is set, and the expression is as follows:

[0101]

[0102] Among them, X i (t) = [r i ,θ i ,φ i ,V i ,γ i ,ψ i ] represents the system state of the i-th follower hypersonic vehicle, u i (t) = [α i ,σ i ] represents the control input to the i-th follower hypersonic vehicle, α i represents the angle of attack of the i-th follower hypersonic vehicle, σ i represents the roll angle of the i-th follower hypersonic vehicle, d i (t) represents the disturbance to the ith follower aircraft, represents the derivative of the system state of the i-th follower hypersonic vehicle.

[0103] Define the normalized distributed cooperative control error e of the i-th follower hypersonic vehicle: i (t), the expression is as follows:

[0104]

[0105] Then the derivative of the normalized distributed cooperative control error of the i-th follower hypersonic vehicle is obtained: The expression is as follows:

[0106]

[0107] Among them, e ij 、e i0represents the error of the ith follower hypersonic vehicle to its neighbor and the leader respectively, and the cooperative tracking control law of the ith follower hypersonic vehicle is and Unified as u ei , represents the gradient of the error of the i-th follower hypersonic vehicle to its neighbors and the leader, respectively, denotes the gradient of the control input of the i-th follower hypersonic vehicle to its neighbors and the leader, respectively.

[0108] Finally, if satisfied It is considered that the hypersonic aircraft cluster achieves collaborative tracking control.

[0109] In this embodiment, step S2 is specifically as follows:

[0110] The goal of the hypersonic vehicle cluster cooperative control is to control the follower hypersonic vehicle to track the desired trajectory of the leader vehicle from the initial state at the minimum cost, that is, the goal is to determine the tracking control law u ei , so that the cost L(e i (t)) is minimized, and the expression is as follows:

[0111]

[0112] Among them, τ represents the integral variable with respect to time, J(e i (τ),u ei (e i (τ))) represents the utility function consisting of the state-related term Q and the feedback control-related term R. Q is defined as Q(e i )=e i T QUR i , and Q0 is a positive definite diagonal matrix representing the weight of each state element, and T represents the transpose operation.

[0113] Set the saturation constraint of the optimal tracking control law and define R so that the feedback remains within the limit. The expression is as follows:

[0114]

[0115] Where v represents the control input u ei The integral variable, R0 is a positive definite matrix, λ1 and λ2 represent α i and σ i Amplitude limitation.

[0116] Then the Hamiltonian function is obtained through the HJB equation, and the expression is as follows:

[0117]

[0118] in, represents the augmented form of the gradient of the error of the ith follower hypersonic vehicle, represents the augmented form of the gradient of the control input of the ith follower hypersonic vehicle, Indicates L(e i ) with respect to ei. Then the optimal cost function L(e i ) * The expression is as follows:

[0119]

[0120] Where Ψ(Ω) represents u ei According to Bellman's optimality principle V(e i ) * is the solution of the HJB equation, expressed as follows:

[0121]

[0122] in, Represents the optimal tracking control law, by solving The partial differential equation of is obtained, and the expression is as follows:

[0123]

[0124] in, Indicates L(e i ) * For e i The partial derivative of .

[0125] In this embodiment, step S3 is specifically as follows:

[0126] First, a single neural network is used to i (e i ), the number of neurons in the hidden layer is represented by l, the weight matrix between the input layer and the hidden layer is represented by Y, and the weight matrix between the hidden layer and the output layer is represented by W. The single evaluation network is selected as a three-layer feedforward neural network, and the output expression of the three-layer neural network is as follows:

[0127]

[0128] Among them, Ξ represents the activation function, and b represents the activation function threshold.

[0129] Then, according to the high-order Weierstrass approximation theorem, the optimal cost function L obtained by fitting the single-evaluation neural network is ci (e i ) *Its gradient is represented by an infinite-dimensional linearly independent basis function set, and an evaluation neural network with a finite-dimensional activation function is used to construct L ci (e i ) * , the expression is as follows:

[0130]

[0131] in, represents the weight vector of the neural network. And L ci (e i ) * About e i The first-order partial derivative and second-order partial derivative expressions are as follows:

[0132]

[0133] Then L ci (e i ) * , The construction error expressions are as follows:

[0134]

[0135] Based on the derivation of equations (13)-(17), u ei The approximate value expression of is as follows:

[0136]

[0137] Due to L i (e i ) * Error e i is continuous, then a linearized neural network can be obtained as the evaluation network of adaptive dynamic programming, that is, the observation form of equations (15) and (16) is obtained, and the expression is as follows:

[0138]

[0139] in, represents the optimal weight of the single-evaluation neural network of the i-th follower hypersonic vehicle, Right now Approximation of ∈ c represents the approximate error that converges to zero after appropriate training under continuous excitation conditions. The expression of the approximate cost function in practice is as follows:

[0140]

[0141] Then the gradient descent method is used to update the weights of the single evaluation network. First, the error function of the single evaluation network is defined, and the expression is as follows:

[0142]

[0143] Then the goal of weight update is to minimize the loss function, which is expressed as follows:

[0144]

[0145] Finally, using the principle of gradient descent, the online update rule expression of the network weight parameters is designed as follows:

[0146]

[0147] Among them, K W represents a positive learning rate.

[0148] In this embodiment, step S4 inputs the optimal cooperative tracking control law calculated in step S3 into the hypersonic aircraft cluster, and can realize the cooperative tracking control of the hypersonic aircraft under the condition of considering the flight constraints. The final effect is as follows: Figure 3 shown.

[0149] In summary, the method of the present invention is aimed at a hypersonic aircraft system described by a 6-DOF model, considers the collaborative tracking control of a hypersonic aircraft cluster under the condition of flight constraints, and adopts an adaptive dynamic programming algorithm to achieve online control, which is suitable for the field of cluster collaborative control of hypersonic aircraft.

[0150] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A hypersonic vehicle cooperative control method based on adaptive dynamic programming, the specific steps are as follows: S1. Establish a 6-DOF normalized model for hypersonic vehicles and clarify the collaborative tracking control problem of hypersonic vehicle clusters; S2, based on step S1, using an adaptive dynamic programming algorithm to obtain an optimal tracking control form under limited control input; S3, based on step S2, construct a single evaluation neural network online controller, and solve the optimal tracking control law online; S4. Apply the optimal tracking control law input obtained in step S3 to the hypersonic aircraft cluster to achieve collaborative tracking control.

2. The method for coordinated control of a hypersonic vehicle based on adaptive dynamic programming according to claim 1, characterized in that: The step S1 is specifically as follows: S11. Establish a 6-DOF normalized model for the hypersonic vehicle; The 6-DOF particle dynamics equation of an unpowered lifting hypersonic vehicle is as follows: Where r is the radial distance from the center of the earth to the hypersonic vehicle, t is the time; θ and φ are the longitude and latitude respectively; V is the earth's relative velocity; ψ is the velocity heading angle relative to the local north direction, γ is the track angle; m and σ are the mass and roll angle of the hypersonic vehicle respectively; D and L are the aerodynamic drag and lift respectively; the angular velocity of the earth is recorded as ω e , the local gravitational acceleration is denoted as g; The 6-DOF particle dynamics equation is normalized and the normalized variable expression is defined as follows: Among them, R e represents the radius of the earth, g0 represents the acceleration due to gravity; By bringing the normalized variables into the dynamic equation, we can obtain the normalized dynamic equation of the hypersonic vehicle, which is expressed as follows: S12. Clarify the problem of cooperative tracking control of hypersonic vehicle clusters; Assume that the hypersonic aircraft cluster has a leader and N followers, where the leader is recorded as aircraft No. 0, and the followers are recorded as aircraft No. 1, ..., N respectively; The communication network between the hypersonic aircraft clusters is then modeled as a directed graph From a vertex set An edge set and a weighted adjacency matrix If and only if the i-th follower hypersonic vehicle can receive the information of the follower hypersonic vehicle j, a ij >0; otherwise, a ij =0; for Node v i The neighbor set of And Figure The edge between the leader hypersonic vehicle and the follower hypersonic vehicle is represented by the matrix It means that when the ith follower hypersonic vehicle has a direct communication link with the leader hypersonic vehicle 0, b i =1, otherwise b i =0; Then the normalized leader hypersonic vehicle cooperative control model with distortion taken into account is expressed as follows with respect to time t: Among them, X0(t) = [r0, θ0, φ0, V0, γ0, ψ0] represents the system state of the leader hypersonic aircraft, u0(t) = [α0, σ0] represents the control input to the leader hypersonic aircraft, α0 represents the angle of attack of the leader hypersonic aircraft, σ0 represents the roll angle of the leader hypersonic aircraft, d0(t) represents the disturbance of the leader hypersonic aircraft, represents the derivative of the system state of the leader hypersonic vehicle; and the input-output mapping of the dynamic equation in equation (3) is denoted as f; At the same time, the normalized cooperative control model of the follower hypersonic aircraft in the hypersonic aircraft cluster is set, and the expression is as follows: Among them, X i (t) = [r i ,θ i ,φ i ,V i ,γ i ,ψ i ] represents the system state of the i-th follower hypersonic vehicle, u i (t) = [α i ,σ i ] represents the control input to the i-th follower hypersonic vehicle, α i represents the angle of attack of the i-th follower hypersonic vehicle, σ i represents the roll angle of the i-th follower hypersonic vehicle, d i (t) represents the disturbance to the ith follower aircraft, represents the derivative of the system state of the i-th follower hypersonic vehicle; Define the normalized distributed cooperative control error e of the i-th follower hypersonic vehicle: i (t), the expression is as follows: Then the derivative of the normalized distributed cooperative control error of the i-th follower hypersonic vehicle is obtained: The expression is as follows: Among them, e ij 、e i0 represents the error of the ith follower hypersonic vehicle to its neighbor and the leader respectively, and the cooperative tracking control law of the ith follower hypersonic vehicle is and Unified as u ei , represents the gradient of the error of the i-th follower hypersonic vehicle to its neighbors and the leader, respectively, represents the gradient of the control input of the i-th follower hypersonic vehicle to the neighbor and the leader respectively; Finally, if satisfied It is considered that the hypersonic aircraft cluster achieves collaborative tracking control.

3. The method for coordinated control of a hypersonic vehicle based on adaptive dynamic programming according to claim 1, characterized in that: The step S2 is specifically as follows: The goal of the hypersonic vehicle cluster cooperative control is to control the follower hypersonic vehicle to track the desired trajectory of the leader vehicle from the initial state at the minimum cost, that is, the goal is to determine the tracking control law u ei , so that the cost L(e i (t)) is minimized, and the expression is as follows: Among them, τ represents the integral variable with respect to time, J(e i (τ),u ei (e i (τ))) represents the utility function consisting of the state-related term Q and the feedback control-related term R; Q is defined as Q(e i )=e i T QUR i , and Q0 is a positive definite diagonal matrix, representing the weight of each state element, and T represents the transpose operation; Set the saturation constraint of the optimal tracking control law and define R so that the feedback remains within the limit. The expression is as follows: Where v represents the control input u ei The integral variable, R0 is a positive definite matrix, λ1 and λ2 represent α i and σ i Amplitude limitation; Then the Hamiltonian function is obtained through the HJB equation, and the expression is as follows: in, represents the augmented form of the gradient of the error of the ith follower hypersonic vehicle, represents the augmented form of the gradient of the control input of the ith follower hypersonic vehicle, Indicates L(e i ) with respect to ei; then the optimal cost function L(e i ) * The expression is as follows: Where Ψ(Ω) represents u ei The admissible control domain; According to Bellman's optimality principle V(e i ) * is the solution of the HJB equation, expressed as follows: in, represents the optimal tracking control law, by solving The partial differential equation is obtained, and the expression is as follows: in, Indicates L(e i ) * For e i The partial derivative of .

4. The method for coordinated control of a hypersonic vehicle based on adaptive dynamic programming according to claim 1, characterized in that: The step S3 is specifically as follows: First, a single neural network is used to i (e i ), the number of neurons in the hidden layer is represented by l, the weight matrix between the input layer and the hidden layer is represented by Y, and the weight matrix between the hidden layer and the output layer is represented by W; the single evaluation network is selected as a three-layer feedforward neural network, and the output expression of the three-layer neural network is as follows: Wherein, Ξ represents the activation function, and b represents the activation function threshold; Then, according to the high-order Weierstrass approximation theorem, the optimal cost function L obtained by fitting the single-evaluation neural network is ci (e i ) * Its gradient is represented by an infinite-dimensional linearly independent basis function set, and an evaluation neural network with a finite-dimensional activation function is used to construct L ci (e i ) * , the expression is as follows: in, represents the weight vector of the neural network; and L ci (e i ) * About e i The first-order partial derivative and second-order partial derivative expressions are as follows: Then L ci (e i ) * , The construction error expressions are as follows: Based on the derivation of equations (13)-(17), u ei The approximate value expression of is as follows: And L i (e i ) * Error e i is continuous, then a linearized neural network can be obtained as the evaluation network of adaptive dynamic programming, that is, the observation form of equations (15) and (16) is obtained, and the expression is as follows: in, represents the optimal weight of the single-evaluation neural network of the i-th follower hypersonic vehicle, Right now Approximation of ∈ c represents the approximate error that converges to zero after appropriate training under continuous excitation conditions; then the expression of the approximate cost function in practice is as follows: Then the gradient descent method is used to update the weights of the single evaluation network. First, the error function of the single evaluation network is defined, and the expression is as follows: Then the goal of weight update is to minimize the loss function, which is expressed as follows: Finally, using the principle of gradient descent, the online update rule expression of the network weight parameters is designed as follows: Among them, K W represents a positive learning rate.

Images