A preset performance formation encirclement control method for hypersonic vehicle clusters

Abstract

The present invention belongs to the field of aerospace vehicle control, and relates to a preset performance formation encirclement control method for a hypersonic aircraft cluster. The present invention first establishes a dynamic model for the control of a hypersonic aircraft cluster, and then designs a neural network observer design to estimate unmeasurable flight state variables. Then, the longitudinal and forward control systems are designed respectively, and the auxiliary controllers of each system are designed at the same time, taking into account the key performance indicators that are crucial in the actual hypersonic aircraft cluster environment, including steady-state accuracy and convergence time. With the support of a new elastic preset performance function, the proposed method shows excellent performance under the control of a hypersonic aircraft cluster. At the same time, the auxiliary system is used to deal with input saturation and sensitivity fragility problems. Combined with the designed new neural observer, it is possible to simultaneously process the unmeasurable state and external interference effects.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace vehicle control and relates to a preset performance formation encirclement control method for a hypersonic vehicle cluster. Background Art

[0002] Air-breathing hypersonic vehicles are considered promising tools for long-range strikes and rapid penetration due to their rapid response and flexible maneuverability. In recent years, the coordinated control of hypersonic vehicle clusters has received extensive attention and attention at home and abroad, and has shown great application potential in the aerospace field, such as drone swarm attacks, multi-missile coordinated penetration, and multi-satellite coordinated detection.

[0003] Formation control refers to designing a suitable controller so that the states or outputs of all agents in the cluster form and maintain a specific relative position relationship in the corresponding space. In encirclement control, the agents in the cluster are divided into two categories: leaders and followers. By designing a distributed controller, the states or outputs of all followers can enter the convex hull formed by the states or outputs of multiple leaders. In traditional encirclement control research, it is usually assumed that there is no interaction and coordination between multiple pilot aircraft. However, in actual application scenarios, pilot aircraft often need to cooperate to maintain a specific time-varying formation, and can track reference tracks or specific targets to move in order to better meet mission requirements. For example, when a high-low multi-missile system coordinates an attack, it is required that the high-configuration missiles form the desired relative position relationship through coordination, and at the same time, the low-configuration missiles need to be able to accurately fall into the attack area under the guidance of the high-configuration missiles. In this scenario, a more complex formation encirclement tracking control problem arises. The cluster system has different collaborative control objectives within the layer and collaborative coupling between layers. On the one hand, the leader is required to form a specific formation and track the reference trajectory or target motion, and on the other hand, the followers are required to be able to enter the formation formed by the leader. The formation containment control of hypersonic aircraft systems has made great progress, which can ensure that all follower hypersonic aircraft are located in a convex hull spanned by the leader in various military and civilian missions. However, due to the strong uncertainty, coupling and nonlinearity of hypersonic aircraft, the design of formation containment control faces major challenges.

[0004] In order to achieve the required performance indicators, such as steady-state accuracy and transient response, many effective hypersonic vehicle control methods have attracted widespread attention from researchers. The hypersonic vehicle cluster formation encirclement task usually needs to achieve the required performance requirements, such as user-specified control performance indicators such as steady-state error and transition process time. However, there are currently few related studies that can achieve the above requirements. Current research results include methods based on obstacle Lyapunov functions, methods based on preset performance functions, and intelligent methods. Input saturation is an extremely difficult problem to deal with in hypersonic vehicle formation control, which constitutes the main challenge of multi-agent systems in formation containment control. Although the above work has made great progress in the design of preset performance controllers, the designed preset performance functions still have the problem of sensitivity and fragility. In other words, when the actuator is saturated, the tracking error increases rapidly and may exceed the specified limit. However, it is still a major challenge to integrate measures to solve actuator saturation into the design of multi-hypersonic vehicle formation control. Considering the complex formation and super maneuverability of multiple hypersonic vehicles, these problems must be carefully solved in various flight missions, which requires the development of new flight control designs that are different from existing methods.

[0005] In the "Collaborative Obstacle Avoidance Decision-making Method in the Terminal Guidance Phase of Hypersonic Aircraft" (see "Journal of Ordnance", September 2024, Vol. 45, No. 9, pp. 3147-3160), Hu Yanyang, He Fan, and Bai Chengchao established a kinematic model of a hypersonic aircraft cluster, taking coordinated strike and formation maintenance as typical goals, and overload, communication, and obstacles as constraints. They designed the observation space and action space, and designed the reward function by considering the relative position and speed relationship between aircraft, aircraft and targets, and aircraft and obstacles. By continuously adjusting the reward function weights and training the aircraft, the formation control of the aircraft cluster is achieved. However, the external interference in the actual flight process is not simulated, and there are limitations in practical application.

[0006] In "Cooperative Formation Control Method for Underactuated Hypersonic Gliding Vehicle Clusters" (see "Air and Space Defense" Vol. 7, No. 1, February 2024, pp. 56-62), Yan Honglei, Lu Yuan, Guo Jie and others designed a distributed cluster formation control strategy based on the collaborative guidance architecture and multi-agent consistency theory. The coordination variables are generated by the absolute and relative positions of each aircraft in the formation, and the basic formation control instructions are generated by the dynamic inversion method; the formation is adjusted by designing lateral maneuver control instructions, and the lateral maneuver control of the formation cluster is realized by using a two-stage predictive correction control algorithm. However, this work only considers the formation error as a constraint, and does not consider other disturbances much, which cannot well solve the strong uncertainty disturbance of the hypersonic flight formation.

[0007] In "A large-scale cluster control method and system for high-speed aircraft in a hostile environment" (CN116610141 A), Bai Chengchao, Guo Jifeng, Zheng Hongxing, etc. obtain the collected cluster information and environmental information for each individual in the high-speed aircraft cluster; pre-process the cluster information and environmental information; input the pre-processed 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. However, this method does not take into account the internal and external disturbances involved in the real flight process, cannot be applied to real flight scenarios, and has certain limitations.

[0008] Huang Shan, Lv Yongxi, Zhu Qi, etc., in "Method for collaborative encirclement of unknown targets by clustered UAVs in GPS-denied environments" (CN118502478A), used the ranging information between the UAV and the target and the fixed-time sliding mode estimator to design an encirclement control algorithm to drive a single UAV to encircle a target with unknown speed and position; used the UAV's own heading information and ranging information to design a distributed speed control algorithm and combined it with the encirclement control algorithm to achieve collaborative encirclement of unknown targets by clustered UAVs. However, the method does not take into account the relevant situation of actuator saturation, which has certain limitations. Summary of the invention

[0009] The present invention proposes a preset performance formation encirclement control method for hypersonic aircraft clusters to solve the input saturation and external disturbance effects. Within the framework of multi-hypersonic aircraft formation flight, flexible preset performance functions and auxiliary systems are introduced for hypersonic aircraft clusters to obtain enhanced preset performance and avoid sensitivity and fragility problems. By integrating the extended state observer with the neural network, a neural network observer is designed to flexibly estimate the uncertain hypersonic aircraft state, unpredictable external disturbance effects, including model uncertainty and external disturbances.

[0010] The technical solution of the present invention is as follows:

[0011] A preset performance formation encirclement control method for a hypersonic aircraft cluster comprises the following steps:

[0012] Step (1) Establish a dynamic model for the control of hypersonic vehicle clusters

[0013] Consider a virtual pilot aircraft and A hypersonic cluster system consisting of followers, The dynamic model of a hypersonic vehicle can be expressed as:

[0014] (1)

[0015] Among them, the superscript " " indicates the first-order derivative, and the superscript " ” represents the second-order derivative; represents the vertical position of the ith follower, represents the track angle of the ith follower, represents the angle of attack of the ith follower, represents the pitch angular velocity of the ith follower, represents the pitch angle of the ith follower, represents the speed of the ith follower, represents the forward displacement of the ith follower, represents the quality of the ith follower, represents the gravitational acceleration of the ith follower, represents the moment of inertia of the ith follower, represents the damping coefficient of the ith follower, represents the elastic modal frequency of the ith follower, represents the elastic mode of the ith follower, or i = [ or i , 1 , or ˙ i , 1 , or i , 2 , or ˙ i , 2 ] represents the first two elastic modes of the aircraft, where represents the i-th follower. They are lift, drag, thrust, pitching moment and generalized force, which are calculated by the following expressions:

[0016] { L i = q ¯ i S i C i L ( α i , d i e , or i ) D i = q ¯ i S i C i D ( α i , d i e , or i ) T i = q ¯ i S i [ C i T F ( α i ) F i + C i T ( α i ) + C i T or i or i ] M i = z i T T i + q ¯ i S i c ¯ i C i M ( α i , d i e , or i ) N i j = q ¯ i S i [ N i j α i j 2 α i 2 + N i j α i α i + N i j d i e d i e + N i j 0 + N i j or i or i ] , j = 1 , 2 (2)

[0017] in, represent the dynamic pressure, characteristic area, thrust-torque coupling coefficient and reference characteristic length respectively, represents the fuel equivalence ratio of the ith follower, represents the elevator deflection angle of the i-th follower. is the lift coefficient of the ith follower, is the resistance coefficient of the ith follower, is the thrust coefficient of the ith follower, is the thrust-fuel equivalence ratio coupling coefficient of the ith follower, is the thrust-elastic coupling coefficient of the ith follower, is the torque coefficient of the ith follower, is the generalized force-squared angle of attack coupling coefficient of the j-th mode of the ith follower, is the generalized force-attack angle coupling coefficient of the j-th mode of the ith follower, is the generalized force-elevator coupling coefficient of the j-th mode of the ith follower, is the generalized force coefficient of the jth mode of the ith follower, is the generalized force-elastic coupling coefficient of the j-th mode of the ith follower.

[0018] The model is decomposed as follows: Considering the complex flight environment and flight mission, the hypersonic aircraft cluster system consisting of N followers and 1 virtual navigator inevitably has the problem of actuator saturation. and is the constrained fuel equivalence ratio and elevator deflection angle, which can be expressed as:

[0019] (3)

[0020] in u = [ F i , d i e ] To control the amount, Represents input The upper limit of Represents input The lower limit of .

[0021] For the flight state in the cruise phase, the longitudinal dynamics model can be simplified into the following dynamic system:

[0022] (4)

[0023] in, They are expressed as follows:

[0024] (5)

[0025] in, is the lift-elevator coupling coefficient of the ith follower, is the torque-attack angle quadratic coupling coefficient of the ith follower, is the torque-attack angle coupling coefficient of the ith follower, is the lift-angle-of-attack coupling coefficient of the ith follower, is the torque-elevator coupling coefficient of the ith follower, is the torque coefficient of the i-th follower. The interference terms representing the longitudinal position, track angle, pitch angle, and pitch angular velocity can be specifically expressed as

[0026] (6)

[0027] in, They represent the uncertainties of the longitudinal position, track angle, pitch angle, and pitch angular velocity in the model, respectively, and it can be assumed that these uncertainties are bounded. represents the lift-elastic coupling coefficient of the ith follower, represents the thrust-angle-of-attack coupling coefficient of the ith follower, represents the torque-elastic coupling coefficient of the ith follower. Nonlinear function Due to parameter uncertainty, it is unknown. Therefore, the forward dynamics model can be expressed as:

[0028] (7)

[0029] in, represents the disturbance of the forward displacement, represents the velocity disturbance, represents the constrained fuel equivalence ratio, Respectively expressed as:

[0030] (8)

[0031] in, represents the thrust coefficient of the ith follower, represents the thrust-fuel equivalence ratio coupling coefficient of the ith follower. Among them represents the model uncertainty of the velocity, Expressed as the thrust-elastic coupling coefficient of the ith follower, Expressed as the resistance-elastic coupling coefficient of the i-th follower.

[0032] Step (2) Neural network observer design

[0033] The designed neural network observer is used to estimate the uncertain flight state variables. The observers for longitudinal and forward dynamics are designed as:

[0034] (9)

[0035] In observer design, Represents the positive gain parameter to be designed. They represent the observer's response to the state For and ,definition:

[0036] (10)

[0037] Formula (10) uses and To express and Assume that the aggregate perturbation can be approximated by a single-layer neural network with n neurons as ,in Definition represents a scalar, represents the n-dimensional determinant, Represents a matrix with n rows and n columns. , express The approximate weight matrix of and Represents the basis function vector and approximation error, satisfying as well as . and is an unknown positive constant.

[0038] Next, we design an adaptive law for updating the neural network.

[0039] (11)

[0040] in, and represents the observation error of the longitudinal position and the forward position, represents the parameter matrix to be designed, Represents the positive parameter to be designed.

[0041] Step (3) Design of longitudinal control scheme

[0042] Design the distributed longitudinal tracking controller as follows:

[0043] (12)

[0044] in, Indicates Followers, For the The longitudinal position reference of the aircraft, Indicates Followers, Indicates The relative error of the longitudinal position of each aircraft is: Indicates The relative attitude error of the aircraft is the state observation value. For distributed virtual controllers , the transition reference command is obtained through the first-order command filter , defined as:

[0045] (13)

[0046] in, is the positive parameter to be designed, express The initial value of express In the present invention, the distributed tracking error should satisfy the following performance.

[0047] (14)

[0048] in, They represent the lower and upper bounds of the longitudinal tracking performance, respectively, and have the following relationship:

[0049] (15)

[0050] and

[0051] (16)

[0052] in, is the positive parameter to be designed, represents the initial value of the relative error of the longitudinal position, The output of the auxiliary system shown in formula (17) is:

[0053] (17)

[0054] in, is the positive parameter to be designed, Two variables representing the upper and lower limits of the auxiliary system and control input, respectively, Indicates the pneumatic rudder. represents the upper limit of the amplitude of the aerodynamic rudder, Indicates the lower limit of the amplitude of the aerodynamic rudder.

[0055] The auxiliary variables of the longitudinal position subsystem are defined as follows:

[0056] (18)

[0057] in, represents the redefined longitudinal position tracking error of the ith follower, represents the redefinition track angle tracking error of the ith follower, represents the redefined pitch angle tracking error of the ith follower, represents the redefined pitch angular velocity tracking error of the ith follower. Described as:

[0058] (19)

[0059] in, They represent the positive parameters to be designed, Represent the coefficients of track angle, pitch angle and pitch rate respectively. Virtual control quantity , , and the actual controller Designed for:

[0060] (20)

[0061] in, are the parameters to be designed, .

[0062] Step (4) Forward control scheme design

[0063] The distributed forward tracking controller is designed as follows:

[0064] (twenty one)

[0065] in, represents the forward position reference of the ith aircraft, Indicates The relative error of the forward position of each aircraft is: Indicates The relative error of the longitudinal position of the aircraft. is the state observation value. Distributed Virtual Controller Obtained through a first-order command filter, defined as:

[0066] (twenty two)

[0067] in, is a parameter to be designed. In the design of the present invention, the distributed tracking error should meet the following performance requirements

[0068] (twenty three)

[0069] in, They represent the lower and upper bounds of the forward tracking performance, respectively, and are defined as:

[0070] (twenty four)

[0071] in is the design parameter, Represents the output of the forward control auxiliary system:

[0072] (25)

[0073] in, are the parameters to be designed. Respectively represent two variables in the auxiliary system related to the upper and lower limits of the control input, Indicates the fuel equivalence ratio, Indicates the upper limit of the fuel equivalence ratio. Indicates the lower limit of the fuel equivalence ratio. The auxiliary variables of the forward subsystem are defined as follows

[0074] (26)

[0075] Among them, auxiliary system It is expressed as follows:

[0076] (27)

[0077] in, It is a parameter to be designed.

[0078] Forward Virtual Controller and the actual controller Designed for:

[0079] (28)

[0080] in, , is the positive parameter to be designed, .

[0081] Beneficial effects of the present invention:

[0082] The technical advantages of the present invention are:

[0083] 1) The proposed method takes into account a wider range of key performance indicators that are critical in the actual hypersonic vehicle cluster environment, including steady-state accuracy, convergence time, and overshoot. From this perspective, supported by the new elastic preset performance function, the proposed method shows excellent performance in the control of hypersonic vehicle clusters.

[0084] 2) Unlike existing hypersonic vehicle approaches based on preset performance functions, which may suffer from inherent fragility issues, the present invention introduces an auxiliary system to manage input saturation and performance constraints simultaneously. In particular, a novel neural network observer is enhanced to simultaneously handle external disturbances.

[0085] The key points of the present invention are:

[0086] 1. By establishing a distributed neural network observer, the uncertain flight state and external interference are estimated, providing an important basis for the predetermined formation containment control.

[0087] 2. Different from traditional hypersonic cluster control, this method not only considers unpredictable states and external disturbances, but also deals with actuator saturation to achieve flexible and predetermined performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1It is a flow chart for implementing a preset performance formation encirclement control method for a cluster of hypersonic aircraft;

[0089] Figure 2 It is the flight trajectory diagram of the aircraft;

[0090] Figure 3 This is the simulation result diagram of the longitudinal channel;

[0091] Figure 4 is the longitudinal channel error result diagram;

[0092] Figure 5 This is the forward channel simulation result diagram;

[0093] Figure 6 This is the forward channel error result diagram. DETAILED DESCRIPTION

[0094] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0095] like Figure 1 As shown, a preset performance formation encirclement control method for a hypersonic aircraft cluster of the present invention comprises the following implementation steps:

[0096] Step 1: Establish a dynamic model for hypersonic vehicle cluster control.

[0097] Step 2: Design a neural network observer to estimate uncertain flight conditions and external interference.

[0098] Step 3: Design a longitudinal control scheme.

[0099] Step 4: Design the forward control scheme.

[0100] The specific steps are as follows:

[0101] Step 1: Establish a dynamic model for hypersonic vehicle cluster control

[0102] Consider a system consisting of a virtual pilot aircraft and A hypersonic cluster system consisting of followers, The dynamic model of a hypersonic vehicle can be expressed as:

[0103] (29)

[0104] in, represents the vertical position of the ith follower, represents the track angle of the ith follower, represents the attack angle of the ith follower, represents the pitch angular velocity of the ith follower, represents the pitch angle of the ith follower, represents the speed of the ith follower, represents the forward displacement of the ith follower, represents the quality of the ith follower, represents the gravitational acceleration of the ith follower, represents the moment of inertia of the ith follower, represents the damping coefficient of the ith follower, represents the elastic modal frequency of the ith follower, represents the elastic mode of the ith follower, or i = [ or i , 1 , or ˙ i , 1 , or i , 2 , or ˙ i , 2 ] represents the first two elastic modes of the aircraft, where represents the i-th follower. They are lift, drag, thrust, pitching moment and generalized force, which are calculated by the following expressions:

[0105] { L i = q ¯ i S i C i L ( α i , d i e , or i ) D i = q ¯ i S i C i D ( α i , d i e , or i ) T i = q ¯ i S i [ C i T F ( α i ) F i + C i T ( α i ) + C i T or i or i ] M i = z i T T i + q ¯ i S i c ¯ i C i M ( α i , d i e , or i ) N i j = q ¯ i S i [ N i j α i j 2 α i 2 + N i j α i α i + N i j d i e d i e + N i j 0 + N i j or i or i ] , j = 1 , 2 (30)

[0106] in, represent the dynamic pressure, characteristic area, thrust-torque coupling coefficient and reference characteristic length respectively, represents the fuel equivalence ratio of the ith follower, represents the elevator deflection angle of the i-th follower.

[0107] is the lift coefficient of the ith follower, is the resistance coefficient of the ith follower, is the thrust coefficient of the ith follower, is the thrust-fuel equivalence ratio coupling coefficient of the ith follower, is the thrust-elastic coupling coefficient of the ith follower, is the torque coefficient of the ith follower, is the generalized force-squared angle of attack coupling coefficient of the j-th mode of the ith follower, is the generalized force-attack angle coupling coefficient of the j-th mode of the ith follower, is the generalized force-elevator coupling coefficient of the j-th mode of the ith follower, is the generalized force coefficient of the jth mode of the ith follower, is the generalized force-elastic coupling coefficient of the j-th mode of the ith follower.

[0108] The model is decomposed as follows: Considering the complex flight environment and flight mission, the hypersonic aircraft cluster system consisting of N followers and 1 virtual navigator inevitably has the problem of actuator saturation. and is the constrained fuel equivalence ratio and elevator deflection angle, which can be expressed as:

[0109] (31)

[0110] in u = [ F i , d i e ] To control the amount, Represents input The upper limit of Represents input The lower limit of .

[0111] For the flight state in the cruise phase, the longitudinal dynamics model can be simplified into the following dynamic system:

[0112] (32)

[0113] in, They are expressed as follows:

[0114] (33)

[0115] in, is the lift-elevator coupling coefficient of the ith follower, is the torque-attack angle quadratic coupling coefficient of the ith follower, is the torque-attack angle coupling coefficient of the ith follower, is the lift-angle-of-attack coupling coefficient of the ith follower, is the torque-elevator coupling coefficient of the ith follower, is the torque coefficient of the i-th follower. The interference terms representing the longitudinal position, track angle, pitch angle, and pitch angular velocity can be specifically expressed as

[0116] (34)

[0117] in, They represent the uncertainties of the longitudinal position, track angle, pitch angle, and pitch angular velocity in the model, respectively, and it can be assumed that these uncertainties are bounded. represents the lift-elastic coupling coefficient of the ith follower, represents the thrust-angle-of-attack coupling coefficient of the ith follower, represents the torque-elastic coupling coefficient of the ith follower. Nonlinear function Due to parameter uncertainty, it is unknown. Therefore, the forward dynamics model can be expressed as:

[0118] (35)

[0119] in, represents the disturbance of the forward displacement, represents the velocity disturbance, represents the constrained fuel equivalence ratio, Respectively expressed as:

[0120] (36)

[0121] in, represents the thrust coefficient of the ith follower, represents the thrust-fuel equivalence ratio coupling coefficient of the ith follower. Among them represents the model uncertainty of the velocity, Expressed as the thrust-elastic coupling coefficient of the ith follower, Expressed as the resistance-elastic coupling coefficient of the i-th follower.

[0122] Step 2: Neural Network Observer Design

[0123] At this stage, the following neural network observers are used to estimate the uncertain flight state variables. The observers for longitudinal and forward dynamics are designed as:

[0124] (37)

[0125] In the above design, for Each variable has and Represents the positive gain parameter to be designed. They represent the observer's response to the state For and ,definition:

[0126] (38)

[0127] Formula (38) uses and To express and Assume that the aggregate perturbation can be approximated by a single-layer neural network with n neurons as ,in Definition represents a scalar, represents the n-dimensional determinant, Represents a matrix with n rows and n columns. , express The approximate weight matrix of and Represents the basis function vector and approximation error, satisfying as well as . and is an unknown positive constant.

[0128] Next, we design an adaptive law for updating the neural network.

[0129] (39)

[0130] in, and represents the observation error of the longitudinal position and the forward position, represents the parameter matrix to be designed, Represents the positive parameter to be designed.

[0131] Step 3: Design of vertical control scheme

[0132] Next, a distributed longitudinal tracking controller is designed.

[0133] (40)

[0134] in, Indicates Followers, For the The longitudinal position reference of the aircraft, Indicates Followers, Indicates The relative error of the longitudinal position of each aircraft is: Indicates The relative attitude error of the aircraft is the state observation value. For distributed virtual controllers , the transition reference command is obtained through the first-order command filter , defined as:

[0135] (41)

[0136] in, is the positive parameter to be designed, express The initial value of express In this embodiment, .

[0137] In the present invention, the distributed tracking error should satisfy the following performance.

[0138] (42)

[0139] in, represents the time-varying performance bound, with the following relationship:

[0140] (43)

[0141] and

[0142] (44)

[0143] in, is the positive parameter to be designed, represents the initial value of the relative error of the longitudinal position, The output of the auxiliary system shown in formula (45) is:

[0144] (45)

[0145] The auxiliary variables of the longitudinal position subsystem are defined as follows:

[0146] (46)

[0147] in, represents the redefined longitudinal position tracking error of the ith follower, represents the redefinition track angle tracking error of the ith follower, represents the redefined pitch angle tracking error of the ith follower, represents the redefined pitch angular velocity tracking error of the ith follower. Described as:

[0148] (47)

[0149] in, All are selected as 0.5, Represent the coefficients of track angle, pitch angle and pitch rate respectively. Virtual control quantity , , and the actual controller Designed for:

[0150] (48)

[0151] in, .

[0152] Step 4: Forward control scheme design

[0153] Next, we design a distributed forward tracking controller.

[0154] (49)

[0155] in, represents the forward position reference of the ith aircraft, Indicates The relative error of the forward position of each aircraft is: Indicates The relative error of the longitudinal position of the aircraft. is the state observation value. Distributed Virtual Controller Obtained through a first-order command filter, defined as:

[0156] (50)

[0157] in, is a parameter to be designed. In the design of the present invention, the distributed tracking error should meet the following performance requirements

[0158] (51)

[0159] in, They represent the lower and upper bounds of the forward tracking performance, respectively, and are defined as:

[0160] (52)

[0161] in, , Represents the output of the forward control auxiliary system:

[0162] (53)

[0163] in, Select 0.2 for both. Respectively represent two variables in the auxiliary system related to the upper and lower limits of the control input, Indicates the fuel equivalence ratio, Indicates the upper limit of the fuel equivalence ratio. Indicates the lower limit of the fuel equivalence ratio. The auxiliary variables of the forward subsystem are defined as follows

[0164] (54)

[0165] Among them, auxiliary system It is expressed as follows

[0166] (55)

[0167] in, .

[0168] The forward virtual controller and actual controller are designed as follows:

[0169] (56)

[0170] in . .

[0171] Step 5: Simulation Verification

[0172] In order to verify the effectiveness of the proposed neural preset formation pinning control, a simulation was carried out on a hypersonic vehicle swarm system consisting of 1 virtual leader hypersonic vehicle and N = 4 follower hypersonic vehicles.

[0173] In the simulation, the initial values ​​of the longitudinal state, forward state and elastic mode are selected as shown in Table 1. In addition, the uncertain aerodynamic coefficients are described as ,in is the nominal parameter, D i = [ − 0 . 3 ， 0 . 3 ] , is the uncertainty of the parameters. According to the actual engineering characteristics, The control constraint condition of the following hypersonic vehicle is set as F i ∈ [ 0 , 1 ] 、 d i e ∈ [ − 2 0 , 2 0 ] d e g The external disturbances set in the simulation are as follows: The disturbances are set within 2 seconds to 20 seconds: , , set the disturbance between 40 seconds and 60 seconds: , , , .

[0174] Table 1 Initial values ​​of longitudinal state, forward state and elastic mode

[0175]

[0176] The simulation results are as follows Figure 3 ~ 6 shown. Figure 2 The flight trajectory of the hypersonic aircraft cluster is given. It can be clearly seen from the figure that the hypersonic aircraft cluster is in a cruising state throughout the flight. Figure 3 ~ Figure 6The convergence of the longitudinal and forward channels of a hypersonic vehicle cluster to a neighborhood near zero is presented starting from different initial longitudinal positions. In particular, the introduced preset performance function effectively constrains the graph-based error, ensuring that the desired formation shape remains constant under the proposed control strategy even in the presence of controller saturation and external disturbances. As can be seen from the figure, satisfactory tracking performance can be achieved for both longitudinal and forward dynamics.

Claims

1. A preset performance formation encirclement control method for a hypersonic aircraft cluster, characterized in that: The steps include: Step (1) Establish a dynamic model for the control of hypersonic vehicle clusters Considering a hypersonic cluster system consisting of a virtual pilot aircraft and N followers, the dynamic model of the i-th hypersonic aircraft is expressed as: Wherein, the superscript "·" represents the first-order derivative, and the superscript "··" represents the second-order derivative; h i represents the longitudinal position of the ith follower, γ i represents the track angle of the i-th follower, α i represents the attack angle of the ith follower, Q i represents the pitch angular velocity of the ith follower, θ i =γ i +α i represents the pitch angle of the ith follower, V i represents the speed of the ith follower, x i represents the forward displacement of the ith follower, m i represents the quality of the ith follower, g i represents the gravitational acceleration of the ith follower, I iyy represents the moment of inertia of the ith follower, ζ ij represents the damping coefficient of the ith follower, ω ij represents the elastic modal frequency of the ith follower, η ij represents the elastic mode of the ith follower, represents the first two elastic modes of the aircraft, where i = 1, 2, ..., N represents the i-th follower; L i ,D i ,T i ,M i ,N ij They are lift, drag, thrust, pitching moment and generalized force, which are calculated by the following expressions: in, They represent the dynamic pressure, characteristic area, thrust-torque coupling coefficient and reference characteristic length, respectively, i represents the fuel equivalence ratio of the ith follower, δ ie is the elevator deflection angle of the ith follower; C iL (α i ,δ ie ,η i ) is the lift coefficient of the ith follower, C iD (α i ,δ ie ,η i ) is the resistance coefficient of the ith follower, C iT (α i ) is the thrust coefficient of the ith follower, C iTΦ (α i ) is the thrust-fuel equivalence ratio coupling coefficient of the ith follower, is the thrust-elastic coupling coefficient of the ith follower, C iM (α i ,δ ie ,η i ) is the torque coefficient of the ith follower, is the generalized force-squared angle of attack coupling coefficient of the j-th mode of the ith follower, is the generalized force-attack angle coupling coefficient of the j-th mode of the ith follower, is the generalized force-elevator coupling coefficient of the j-th mode of the ith follower, is the generalized force coefficient of the jth mode of the ith follower, is the generalized force-elastic coupling coefficient of the j-th mode of the ith follower; The model is decomposed as follows: S(Φ i ) and S(δ ie ) is the constrained fuel equivalence ratio and elevator deflection angle, expressed as: where u=[Φ i ,δ ie ] is the control quantity, u max represents the upper limit of input u, u min Indicates the lower limit of input u; For the flight state in the cruise phase, the longitudinal dynamics model is simplified to the following dynamic system: Among them, f iγ ,f iQ ,g ih ,g iγ ,g iθ ,g iQ They are expressed as follows: in, is the lift-elevator coupling coefficient of the ith follower, is the torque-attack angle quadratic coupling coefficient of the ith follower, is the torque-attack angle coupling coefficient of the ith follower, is the lift-angle-of-attack coupling coefficient of the ith follower, is the torque-elevator coupling coefficient of the ith follower, is the torque coefficient of the ith follower; d ih ,d iγ ,d iθ ,d iQ The interference terms representing the longitudinal position, track angle, pitch angle, and pitch angular velocity are specifically expressed as Among them, Δ ih ,Δ iγ ,Δ iθ ,Δ iQ They represent the uncertainties of the longitudinal position, track angle, pitch angle, and pitch angle velocity in the model respectively; represents the lift-elastic coupling coefficient of the ith follower, represents the thrust-angle-of-attack coupling coefficient of the ith follower, represents the torque-elastic coupling coefficient of the ith follower; the nonlinear function f iγ ,f iQ Due to parameter uncertainty, it is unknown; thus the forward dynamics model is expressed as: Among them, d ix represents the disturbance of the forward displacement, d iV represents the velocity disturbance, represents the constrained fuel equivalence ratio, g ix ,f iV ,g iV Respectively expressed as: Among them, C iT (α i ) represents the thrust coefficient of the ith follower, C iTΦ (α i ) represents the thrust-fuel equivalence ratio coupling coefficient of the ith follower; disturbance In which Δ iV represents the model uncertainty of the velocity, Expressed as the thrust-elastic coupling coefficient of the ith follower, Expressed as the resistance-elastic coupling coefficient of the ith follower; Step (2) Neural network observer design The designed neural network observer is used to estimate the uncertain flight state variables; the observers for longitudinal and forward dynamics are designed as: In observer design, k ij＊ (*=h,θ,γ,Q,δ,x,V,Φ) represents the positive gain parameters to be designed; They represent the observer's response to the state variable h i ,h j ,θ i ,γ i ,Q i ,x i ,V i For ξ=h,γ,θ,Q and ψ=x,V, define: Formula (10) and To express i =h i ,γ i ,θ i ,Q i and ψ i =x i ,V i The observation error is assuming that the lumped perturbation is approximated by a single-layer neural network with n neurons: Where s = h, γ, θ, Q, x, V; definition represents a scalar, represents the n-dimensional determinant, Represents a matrix of n rows and n columns; express The approximate weight matrix of and Represents the basis function vector and approximation error, satisfying as well as and ν is >0 is an unknown normal number; The following is an adaptive law designed for neural network update; in, and represents the observation error of the longitudinal position and the forward position, represents the parameter matrix to be designed, represents the positive parameter to be designed; Step (3) Design of longitudinal control scheme Design the distributed longitudinal tracking controller as follows: Where i=1,2,…,N represents the i-th follower, h ir is the longitudinal position reference of the i-th aircraft, j = 1, 2, ..., N represents the j-th follower, e ih represents the relative error of the longitudinal position of the ith aircraft, e iθ Represents the relative attitude error of the i-th aircraft is the state observation value; for the distributed virtual controller Get the transition reference command through the first-order command filter Defined as: in, is the positive parameter to be designed, express The initial value of express The initial value of; In the present invention, the distributed tracking error should satisfy the following performance; in, They represent the lower and upper bounds of the longitudinal tracking performance, respectively, and have the following relationship: and in, υ h , ih (i=1,2,3,4) is the positive parameter to be designed, e h (0) represents the initial value of the longitudinal position relative error, ψ h (t) represents the output of the auxiliary system shown in formula (17): Among them, m 1h 、m 2h is the positive parameter to be designed, σ 1h (t),σ 2h (t) represent the two variables in the auxiliary system and the upper and lower limits of the control input, respectively, δ ie Indicates the pneumatic rudder. represents the upper limit of the amplitude of the aerodynamic rudder, Indicates the lower limit of the amplitude of the aerodynamic rudder; The auxiliary variables of the longitudinal position subsystem are defined as follows: Among them, z ih represents the redefined longitudinal position tracking error of the ith follower, z iγ represents the redefinition track angle tracking error of the ith follower, z iθ represents the redefined pitch angle tracking error of the ith follower, z iQ represents the redefined pitch angular velocity tracking error of the ith follower; the auxiliary system β iγ , β iθ , β iQ Described as: Among them, μ iγ ,μ iθ ,μ iQ They represent the positive parameters to be designed, g iγ ,g iθ ,g iQ Respectively represent the coefficients of track angle, pitch angle and pitch angular velocity; virtual control amount γ id ,θ id , Q id and the actual controller δ ie Designed for: Among them, k ih >0, k iγ >0, k iθ >0, k iQ >0 is the parameter to be designed, Step (4) Forward control scheme design The distributed forward tracking controller is designed as follows: Where i = 1, 2, ..., N, x ir represents the forward position reference of the i-th aircraft, e ix represents the relative error of the forward position of the i-th aircraft, e iV represents the relative error of the longitudinal position of the i-th aircraft; is the state observation value; Distributed virtual controller V id Obtained through a first-order command filter, defined as: Among them, τ iV is a parameter to be designed; in the design of the present invention, the distributed tracking error should meet the following performance requirements in, They represent the lower and upper bounds of the forward tracking performance, respectively, and are defined as: in υ x , ix (i=1,2,3,4) are the parameters to be designed, ψ x (t) represents the output of the forward control auxiliary system: Among them, m 1x 、m 2x is the parameter to be designed; σ 1x (t),σ 2x (t) represent two variables in the auxiliary system related to the upper and lower limits of the control input, respectively, Φ i Indicates the fuel equivalence ratio, Indicates the upper limit of the fuel equivalence ratio. Indicates the lower limit of the fuel equivalence ratio; the auxiliary variables of the forward subsystem are defined as follows Among them, the auxiliary system β iV It is expressed as follows: Among them, μ iV is the parameter to be designed; The forward virtual controller and actual controller are designed as follows: Among them, k ix >0, k iV >0 is a positive parameter to be designed,

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