Aircraft formation control method based on fast adaptive non-singular terminal sliding mode

Abstract

The application discloses a kind of aircraft formation control methods based on fast adaptive non-singular terminal sliding mode, step 1, considering the uncertainty and disturbance factor in flight environment, the nonlinear dynamics model of fixed-wing aircraft system is established;Step 2, the information topology between aircrafts is analyzed using graph theory knowledge, a distributed control architecture is designed, so that each aircraft establishes a generalized formation tracking error based on its own state and the information of adjacent aircrafts;Step 3, using non-singular terminal sliding mode control theory, a controller is designed to improve the accuracy and robustness of formation control and reduce chattering phenomenon;Step 4, combined with fast adaptive control technology, real-time adjustment of control parameters to adapt to external disturbance and system state changes.By using non-singular terminal sliding mode control theory, the accuracy and robustness of formation control are improved, and the chattering phenomenon of controller output is reduced;Combined with fast adaptive control technology, real-time adjustment of control parameters improves system stability and robustness.

Description

Technical Field

[0001] This invention belongs to the field of fixed-wing aircraft formation control technology, specifically designing a fixed-wing aircraft formation control method based on distributed fast adaptive non-singular terminal sliding mode. Background Technology

[0002] With the development of aircraft technology, fixed-wing aircraft are being used more and more widely in both military and civilian fields. Due to their high mobility and ease of deployment, fixed-wing aircraft swarms can quickly respond to search and rescue missions, improve the accuracy of damage assessment and the effectiveness of decision-making, and reduce casualties and property losses, making them an important component of new rescue equipment.

[0003] However, in the flight environment, operating conditions are highly variable, and there are many types of disturbances and uncertainties, including constant disturbances such as gravity and slowly changing atmospheric disturbances, as well as dynamic disturbances, namely aerodynamic drag related to the system state, which varies with the speed and attitude of the aircraft. These factors may affect the stability of the aircraft under different flight conditions.

[0004] Existing formation control methods mostly employ centralized control, which provides a general approach to controlling uncertainties and disturbances. This approach has limitations when dealing with formation control in complex environments, particularly in its ability to handle disturbances and uncertainties. Therefore, researching a novel distributed formation control method is of significant practical importance. Summary of the Invention

[0005] The purpose of this invention is to provide a fixed-wing aircraft formation control method based on distributed fast adaptive non-singular terminal sliding mode. Considering uncertainties and disturbances in the flight environment, a nonlinear dynamic model of the fixed-wing aircraft system is established. Graph theory is used to analyze the information topology between aircraft, and a distributed control architecture is designed, enabling each aircraft to establish a generalized formation tracking error based on its own state and information from neighboring aircraft. Non-singular terminal sliding mode control theory is utilized to design a controller to improve the accuracy and robustness of formation control and reduce chattering. Combined with fast adaptive control technology, control parameters are adjusted in real time to adapt to external disturbances and system state changes, effectively handling uncertainties and disturbances in multi-aircraft formation flight and improving system stability and robustness.

[0006] This invention discloses a fixed-wing aircraft formation control method based on distributed fast adaptive non-singular terminal sliding mode, the specific steps of which are as follows:

[0007] The steps include the following:

[0008] Step 1: Considering the uncertainties and disturbances in the flight environment, establish a nonlinear dynamic model of the fixed-wing aircraft system;

[0009] Step 2: Graph theory is used to analyze the information topology between aircraft and design a distributed control architecture so that each aircraft establishes a generalized formation tracking error based on its own state and information from neighboring aircraft.

[0010] Step 3: Using the non-singular terminal sliding mode control theory, design a controller to improve the accuracy and robustness of formation control and reduce chattering.

[0011] Step 4: Combine fast adaptive control technology to adjust control parameters in real time to adapt to external disturbances and changes in system state.

[0012] Preferably, in step 1, a nonlinear swarm system consisting of N aircraft is considered, and the motion model of each aircraft is as follows:

[0013]

[0014] Where, p i =[x i y i , z i ] T V represents the position of the virtual aircraft in the ground frame, θ represents the velocity, and ψ represents the trajectory angle. vi Indicates the angle of deflection.

[0015]

[0016] Among them, T i It is engine thrust, D i It is resistance, m i Where L is the mass of the aircraft, g is the acceleration due to gravity, and L is the acceleration due to gravity. i It is lift, φ i It's the tilt angle. The thrust T... i Inclination angle φ i and lift L i As a control variable, thrust T i Controlled by throttle, tilt angle φ i Lift L is controlled by the rudder and ailerons. i Controlled by the elevator. External disturbances are considered as d. iv d iθ , This represents the external disturbance received by the system. Calculating drag requires consideration of frontal area, flight speed, angle of attack, and aerodynamic characteristics. To simplify analysis and control design, drag is treated as a nonlinear disturbance.

[0017] Furthermore, by defining indirect variables Equation (2) can be transformed into

[0018]

[0019] Let v i =[V i θ i , ψ vi ] T p i =[x i y i , z i ] T Let be the velocity vector and position vector of the i-th aircraft, respectively. Taking the time derivative of equation (1), we get:

[0020]

[0021] in,

[0022]

[0023] Inserting equation (4) into equation (5), we obtain the following derivation:

[0024]

[0025] u i =[n iT n iL cos(φ i ),n iL sin(φ i )] T

[0026]

[0027] And matrix M i It is reversible. During actual flight, the model parameters of a fixed-wing aircraft may be affected by aerodynamic disturbances. iD The influence of parameter matrix N i It can be broken down into nominal parts With uncertainty

[0028]

[0029] The aircraft dynamics model can be further transformed into the following form:

[0030]

[0031] in, This indicates a multi-source composite disturbance, including external disturbances and internal parameter uncertainties.

[0032] Preferably, in step 2, a directed graph is used to describe the topological connectivity of the multi-aircraft communication network. This graph is represented as follows: The node set Represents a group of N fixed-wing aircraft, edge set This represents information transmission between all neighboring aircraft. If (i, j) ∈ ε, it means that information from the j-th aircraft is available to the i-th aircraft. The neighborhood set of the i-th aircraft can be represented as... The adjacency matrix of a graph is represented as A = [α] ij ]∈R N×N If (i, j) ∈ ε, then a ij =1; otherwise, a ij =0. In-degree matrix D in =diag{d1, ...,d N},in Then we can obtain the Laplace matrix L = D. in -A.

[0033] Furthermore, based on the Laplace matrix L defined above, a normalized directed Laplace matrix can be defined. as follows:

[0034]

[0035] in,

[0036]

[0037] Furthermore, in this patent, we will focus on the formation control of fixed-wing aircraft based on a distributed navigator-follower framework. The kinematic model of the aircraft platforms is given by equation (8), requiring them to reach a given formation configuration within a finite time and maintain coordinated motion with the navigator. Based on a consensus mechanism, the formation error variable can be defined as:

[0038] e ij :=p i -p j -E ij , i, j = 1, ..., N Equation (11)

[0039] Where, p i and p j E represents the positions of the i-th and j-th spacecraft at time t, respectively; ij e represents the expected relative distance between the j-th and i-th spacecraft at time t; ij ∈R 3×1 ,t≤0 indicates the position information error between the i-th and j-th aircraft. It is worth noting that e ij The definition of i, j = L, 1, ..., N does not consider the communication topology. Furthermore, a generalized error state is proposed for the i-th and j-th agents:

[0040]

[0041] Preferably, in step 3, a controller is designed using non-singular terminal sliding mode control theory to improve the accuracy and robustness of formation control and reduce chattering. Next, a novel sliding mode control method is adopted in the overall design process to ensure that the multi-vehicle system achieves formation within a finite time. Considering the sliding mode variables, they are defined as follows:

[0042]

[0043] Where, α i and β i It is the control gain matrix, and α i =diag(α) i1 α i2 α i3 ), β i =diag(β) i1 ,β i2 ,β i3 ), and satisfy α in >0,β in >0, when n = 1, 2, 3, and 1 < γ < 2. Sliding mode variable S i It will reach zero for any initial value ∈ i (0) and Generalized formation tracking error ∈ i In a finite time t z It converges to zero, satisfying the following inequality:

[0044]

[0045] Where, η i =α i |∈ i |+β i |∈ i Based on this, an equivalent control law is designed, and its formula is as follows:

[0046]

[0047] After completing the design of the non-singular terminal sliding mode controller, in order to further improve the system's adaptability and stability, the next step will be to combine fast adaptive control technology to adjust the control parameters in real time, ensuring that the system can respond quickly and effectively to external disturbances in dynamic environments, thereby enhancing the overall performance of formation control.

[0048] Preferably, step 4 employs fast adaptive control technology to further optimize the formation control of the aircraft cluster. This technology adapts to external environmental disturbances and changes in the internal state of the system by adjusting control parameters in real time, thereby enhancing the stability and robustness of the entire formation system.

[0049]

[0050] sig(S i )=[sig(s 1i )sig(s 2i )sig(s 3i )] T

[0051] sgn(S i )=[sgn(s 1i )sgn(s 2i )sgn(s 3i )] T

[0052] n = 1, 2, 3, i = 1, N

[0053] Among them, control parameters and For positive numbers, 0 < μ < 1, adaptive gain and The update is based on the current and historical values ​​of the sliding mode variable, and is adjusted through a specific adaptive law so that the control law can adapt to changes in system parameters and unknown external disturbances.

[0054]

[0055] Specifically, the control law consists of two parts: one is the model-based equivalent control law. Another is the arrival law control law used to ensure fast convergence. The design of the arrival law control law takes into account the sliding mode variable S. i It also includes multiple positive control parameters and adaptive gains, which are dynamically updated according to the adaptive law.

[0056]

[0057] Ultimately, the control law u proposed in this patent i By merging equivalent control laws and arrival law control law This resulted in a comprehensive control strategy. This strategy not only improved the accuracy of aircraft formation control but also significantly reduced the chattering phenomenon commonly found in control systems, making formation flight more stable and reliable.

[0058] Furthermore, in step four, considering the aggregated disturbances and uncertainties in the system, as well as the adaptive reach control law, we can define the adaptive estimation error, which includes... and And construct the corresponding Lyapunov function.

[0059]

[0060] Based on the previous derivation, the positive definiteness of the Lyapunov function is guaranteed. The derivative of the Lyapunov function expresses the change in the system state, and by calculating its rate of change, an expression for the change in system energy is derived.

[0061]

[0062] Further derivation yields

[0063]

[0064] To facilitate subsequent derivations, the system state is redefined as the relevant state variables, making the stability analysis more intuitive. By analyzing the derivative of the Lyapunov function, its relationship with the sliding mode variable and the adaptive gain can be discovered, thereby further deriving the conditions for system stability.

[0065]

[0066] Finally, by defining some symbols to make the expression more concise, the relationship between the rate of change of the Lyapunov function and the system state is derived. Based on the defined parameters and symbols, it can be proven that under the proposed control law, the Lyapunov function will converge to zero from any initial conditions and satisfy the finite-time stability criterion.

[0067]

[0068] Therefore, the final conclusion is that under the proposed formation control law, the system will be able to reach a stable state in a finite amount of time, and the proof process is now complete.

[0069] Compared with the prior art, the present invention has at least one of the following advantages:

[0070] (1) This invention creatively proposes an aircraft formation control method based on fast adaptive non-singular terminal sliding mode. By adopting non-singular terminal sliding mode control theory, the accuracy and robustness of formation control are improved, and the chattering phenomenon of controller output is reduced.

[0071] (2) This invention combines fast adaptive control technology to adjust control parameters in real time to adapt to external disturbances and changes in system state, effectively handle uncertainties and disturbances in multi-aircraft formation flight, and improve the stability and robustness of the system.

[0072] (3) This invention uses graph theory to analyze the information topology between aircraft and designs a distributed control architecture, enabling each aircraft to establish a generalized formation tracking error based on its own state and the information of neighboring aircraft, reducing the dependence on the control center and improving the system scalability. Attached Figure Description

[0073] Figure 1 This is a schematic diagram of the fixed-wing aircraft formation control method of the present invention;

[0074] Figure 2 This is a schematic diagram of the program framework for the fixed-wing aircraft formation control strategy of the present invention.

[0075] Figure 3 This is a schematic diagram of the motion model of the fixed-wing aircraft of the present invention;

[0076] Figure 4 This is a schematic diagram of the fixed-wing aircraft formation communication topology of the present invention;

[0077] Figure 5 This is a schematic diagram of the formation positioning design for the fixed-wing aircraft of the present invention;

[0078] Figure 6 This is a schematic diagram illustrating the formation error performance of the fixed-wing aircraft of the present invention;

[0079] Figure 7 This is a schematic diagram of the three-axis control input for the fixed-wing aircraft formation according to the present invention;

[0080] Figure 8 This is a schematic diagram of the three-dimensional formation flight trajectory of the fixed-wing aircraft of the present invention. Detailed Implementation

[0081] In one embodiment of the present invention, a fixed-wing aircraft formation control method based on distributed fast non-singular terminal sliding mode is provided. The following is in conjunction with the appendix... Figure 1-8 The specific embodiments of the present invention will be described in detail below. The aircraft formation control method first utilizes... Figure 1 The flowchart shown illustrates task planning, and then... Figure 2 A framework for establishing an aircraft cluster control strategy and feedback information system will be implemented. Figure 3 With the support of the motion model, combined with Figure 4 Communication topology representation and Figure 5 The time-varying formation positioning design, through Figure 6 Collection and analysis of formation error information and Figure 7 The three-axis control inputs shown ensure precise control of each aircraft and ultimately achieve... Figure 8 The three-dimensional formation flight trajectory is shown.

[0082] Figure 1The flowchart of the control method of this invention is illustrated. The flowchart begins with startup and includes steps such as establishing the aircraft's motion model, communication topology, and designing control strategies, until the formation control task is completed. Figure 2 The program framework of the control strategy of this invention is illustrated. The program begins by initializing the state of the aircraft cluster, including information such as position, velocity, and attitude. Subsequently, the program enters the main loop, acquiring sensor data from each aircraft in real time and calculating the control inputs according to the distributed control law. The control inputs include thrust, roll angle, and lift, which are used to adjust the motion state of the aircraft to maintain the desired formation.

[0083] This invention includes the following steps:

[0084] Step 1: Considering the uncertainties and disturbances in the flight environment, establish a nonlinear dynamic model of the fixed-wing aircraft system.

[0085] Figure 3 The motion model of the fixed-wing aircraft in this invention is described. This model takes into account the dynamic characteristics of the aircraft, and by establishing a nonlinear dynamic model, this invention can accurately grasp the flight state of each aircraft.

[0086] Step 2: Use graph theory to analyze the information topology between aircraft, design a distributed control architecture, and enable each aircraft to establish a generalized formation tracking error based on its own state and information from neighboring aircraft.

[0087] Figure 4 The communication topology of a fixed-wing aircraft formation network is shown. This topology illustrates the information exchange methods between UAVs and is crucial for the implementation of distributed control strategies.

[0088] Figure 5 It describes the predetermined positions and relative relationships of each aircraft in the formation. These formation designs are the basis for achieving specific formation missions.

[0089] Step 3: Using non-singular terminal sliding mode control theory, design a controller to improve the accuracy and robustness of formation control and reduce chattering.

[0090] Step 4: Combine fast adaptive control technology to adjust control parameters in real time to adapt to external disturbances and changes in system state, thereby improving the stability and robustness of the system.

[0091] Figure 6 This invention describes the behavior of formation error during formation flight missions. By designing appropriate control and adaptive laws, this invention can effectively reduce formation error and ensure the accuracy and stability of formation flight.

[0092] Figure 7The invention demonstrates the three-axis control inputs of the aircraft. These control inputs include roll, pitch, and yaw controls along the aircraft's coordinate system, which are used to adjust the aircraft's attitude and trajectory to meet the requirements of formation flying.

[0093] Figure 8 This figure illustrates the three-dimensional trajectories of multiple fixed-wing aircraft performing formation flight missions. Through a distributed control strategy, the aircraft are able to fly collaboratively along predetermined trajectories, maintaining a stable formation structure. This illustration demonstrates the invention's ability to maintain formation in complex space environments.

[0094] Through the above-described embodiments, the present invention not only improves the accuracy and robustness of fixed-wing aircraft formation control, but also enhances the stability and adaptability of the entire system through a distributed control strategy.

[0095] The following specific embodiments describe in detail the initial conditions and preset trajectory of the simulation, the formation topology and formation position design in the multi-fixed-wing aircraft system, to verify the effectiveness of the proposed control method.

[0096] We consider a formation of five fixed-wing aircraft (N=5) with a lead drone, UAV0, whose predetermined trajectory is defined as p0 = [x0, y0, z0]. T The specific system of equations is as follows:

[0097]

[0098] At the start of the simulation, the initial positions of the four follower drones were set as: p1(0) = [-5, 10, 15] T p2(0) = [15, 20, 20] T p3(0) = [20, 15, -10] T p4(0) = [-15, 25, -15] T All drones have the same initial velocity magnitude, initial velocity vector, and attitude angle [v]. i (0), θ i (0), ψ vi (0)] T =[10, 0, 0] T , i = 0, ..., 4.

[0099] The multi-UAV system involved in this invention consists of a leader (represented by subscript 0) and four followers (represented by subscripts 1, 2, 3, and 4, respectively). Figure 4As shown, the communication topology is the foundation for implementing distributed control strategies, detailing the information exchange methods between drones. In this topology, each drone can communicate with its neighbors, ensuring real-time information sharing and rapid command transmission.

[0100] The adjacency matrix A describes the communication connections between drones, where the matrix element aij indicates whether drone i can directly receive information from drone j.

[0101]

[0102] The Laplace matrix L is used to analyze the stability and consistency of the entire formation. It is obtained by calculating the difference between the adjacency matrix and the degree matrix, specifically...

[0103]

[0104] Furthermore, to further improve the adaptability and flexibility of the control strategy, we also designed a normalized Laplace matrix. This matrix is ​​normalized by dividing each element of the Laplacian matrix by the maximum degree in the network, thus making the control policy more robust to changes in network size.

[0105]

[0106] Furthermore, in this embodiment, the leader's position is set at the center of the entire formation, while the followers are arranged around the leader according to a predetermined formation design. The desired relative position between each follower drone and its leader is also specifically defined as the desired formation position E. ij It represents the follower p j With leader p i The relative distance between them is determined by a predefined distance d. i0 The formation direction angle Φ is used to determine the position of each follower drone in three-dimensional space, thus forming a stable and controllable formation structure. The specific formula is as follows:

[0107]

[0108] The relative position in the local coordinate system is X. 10 =-d 10 sin(Φ), Y 10 =d 10 cos(Φ), X 20 =-d 20 sin(Φ), Y 20 =-d 20 cos(Φ), X 30 =-d30 sin(Φ), Y 30 =d 30 cos(Φ), X 40 =-d 40 sin(Φ), Y 40 =-d 40 cos(Φ), and the rotation matrix

[0109] Through this formation topology and positioning design, this invention not only improves the accuracy and robustness of fixed-wing aircraft formation control, but also enhances the stability and adaptability of the entire system through a distributed control strategy. These designs provide a solid foundation for achieving complex formation missions.

[0110] Finally, in the implementation of this invention, the selection of control parameters is crucial for achieving the desired tracking performance and overall system stability. The following are design guidelines and specific values ​​for the control parameters of the proposed Adaptive Fast Non-Singular Terminal Sliding Mode Control (DFANTSM) method. Relevant formulas can be found above; for ease of reading, some key formulas are expressed below.

[0111]

[0112] To ensure system stability when faced with disturbances, control gain The settings of parameters such as μ = 0.8 are intended to balance the system's response speed with the smoothness of the control signal. Sliding surface design parameter a i =diag(2,2,2),β i =diag(1,1,1) and The convergence speed and amplitude of formation error are affected. Adaptive gain. It has a significant impact on the convergence rate of adaptive estimation error, and the value can effectively reduce the adaptation time while avoiding saturation and overshoot of the control input.

[0113] Through the design of the above control parameters, this invention enables efficient formation control in multi-fixed-wing aircraft systems. The rational selection of these parameters ensures the system's stability and robustness in the face of uncertainties and external disturbances, providing a solid foundation for achieving precise formation flight.

Claims

1. A method for aircraft formation control based on fast adaptive non-singular terminal sliding mode, characterized in that, The steps include the following: Step 1: Considering the uncertainties and disturbances in the flight environment, establish a nonlinear dynamic model of the fixed-wing aircraft system; Consider a nonlinear swarm system consisting of N aircraft. The motion model of each aircraft is as follows: Where, p i =[x i ,y i ,z i ] T V represents the position of the virtual aircraft in the ground frame, θ represents the velocity, and ψ represents the trajectory angle. vi Indicates the angle of deflection; Among them, T i It is engine thrust, D i It is resistance, m i Where L is the mass of the aircraft, g is the acceleration due to gravity, and L is the acceleration due to gravity. i It is lift, φ i It is the tilt angle; the thrust T i Inclination angle φ i and lift L i As a control variable; thrust T i Controlled by throttle, tilt angle φ i Lift L is controlled by the rudder and ailerons. i Controlled by elevator; external disturbances are considered as d. iv ,d iθ , This represents the external disturbance received by the system; the calculation of drag requires consideration of frontal area, flight speed, angle of attack and aerodynamic characteristics. In order to simplify the analysis and control design, drag is regarded as a nonlinear disturbance. By defining indirect variables Equation (2) can be transformed into Let v i =[V i ,θ i ,ψ vi ] T ,p i =[x i ,y i ,z i ] T Let be the velocity vector and position vector of the i-th aircraft, respectively. Taking the time derivative of equation (1), we get: in, Inserting equation (4) into equation (5), we obtain the following derivation: you i =[n iT ,n iL cos(φ i ),n iL sin(φ i )] T And matrix M i It is reversible; During actual flight, the model parameters of a fixed-wing aircraft may be affected by aerodynamic disturbances. iD The influence of parameter matrix N i It can be broken down into nominal parts With uncertainty The aircraft dynamics model can be further transformed into the following form: in, This indicates a multi-source composite disturbance, including external disturbances and internal parameter uncertainties; Step 2: Graph theory is used to analyze the information topology between aircraft and design a distributed control architecture. This allows each aircraft to establish a generalized formation tracking error ∈ based on its own state and information from neighboring aircraft. i ; Step 3: Using non-singular terminal sliding mode control theory, a controller is designed to improve the accuracy and robustness of formation control and reduce chattering; a sliding mode control method is adopted to ensure that the multi-vehicle system can form up within a finite time. Consider sliding mode variables, defined as follows: Where, α i and β i It is the control gain matrix, and α i =diag(α) i1 ,α i2 ,α i3 ), β i =diag(β) i1 ,β i2 ,β i3 ), and satisfy α in >0,β in >0, when n=1,2,3, and 1<γ<2; sliding mode variable S i It will reach zero for any initial value ∈ i (0) and Generalized formation tracking error ∈ i In a finite time t z It converges to zero, satisfying the following inequality: Where, η i =α i |∈ i |+β i |∈ i | γ Based on this, an equivalent control law is designed, and its formula is as follows: l ii l ij The coefficients of the Laplacian matrix of the directed graph; p j Let E be the position of the j-th spacecraft at time t; ij Let represent the expected relative distance between the j-th and i-th aircraft at time t; Step 4: Combine fast adaptive control technology to adjust control parameters in real time to adapt to external disturbances and changes in system state.

2. The aircraft formation control method based on fast adaptive non-singular terminal sliding mode as described in claim 1, characterized in that, Step 2 uses a directed graph to describe the topological connectivity of the multi-aircraft communication network; this graph is represented as... The node set Represents a group of N fixed-wing aircraft, edge set Represents information transmission between all neighboring aircraft; if (i,j)∈ε, it means that the information of the j-th aircraft is available to the i-th aircraft; the neighborhood set of the i-th aircraft is represented as... The adjacency matrix of a graph is represented as A = [a ij ]∈R N×N If (i,j)∈ε, then a ij =1; otherwise a ij =0; In-degree matrix D in =diag{d1,…,d N },in Then we obtain the Laplace matrix L = D. in -A.

3. The aircraft formation control method based on fast adaptive non-singular terminal sliding mode as described in claim 2, characterized in that, Based on the Laplace matrix L defined above, a normalized directed Laplace matrix can be defined. as follows: in, The focus of this study is on formation control of fixed-wing aircraft based on a distributed leader-follower framework. The kinematic model of the aircraft platforms is given by equation (8), requiring them to reach a given formation shape within a finite time and maintain coordinated motion with the leader. Based on a consensus mechanism, the formation error variable is defined as: e ij :=p i -p j -E ij ,i,j=1,…,N Equation (14) Where, p i and p j E represents the positions of the i-th and j-th spacecraft at time t, respectively; ij e represents the expected relative distance between the j-th and i-th spacecraft at time t; ij ∈R 3×1 ,t≤0 indicates the position information error between the i-th and j-th aircraft; it is worth noting that e ij The definition of ,i,j=L,1,…,N does not consider the communication topology; furthermore, a generalized error state is proposed for the i-th and j-th agents:

4. The aircraft formation control method based on fast adaptive non-singular terminal sliding mode as described in claim 3, characterized in that, In step 4, the control parameters are adjusted in real time to adapt to disturbances in the external environment and changes in the internal state of the system, thereby enhancing the stability and robustness of the entire formation system. say(S i )=[say(s 1i (s) 2i (s) 3i )] T sgn(S i )=[sgn(s 1i )sgn(s 2i )sgn(s 3i )] T n = 1, 2, 3, i = 1, ..., N Among them, control parameters and For positive numbers, 0 < μ < 1, adaptive gain and The update is based on the current and historical values ​​of the sliding mode variable, and is adjusted through a specific adaptive law so that the control law can adapt to changes in system parameters and unknown external disturbances.

5. The aircraft formation control method based on fast adaptive non-singular terminal sliding mode as described in claim 4, characterized in that, The control law consists of two parts: one is the model-based equivalent control law. Another is the arrival law control law used to ensure fast convergence. The design of the arrival law control law takes into account the sliding mode variable S. i It also includes multiple positive control parameters and adaptive gains, which are dynamically updated according to the adaptive law; Ultimately, the control law u i By merging equivalent control laws and arrival law control law This led to the formation of a comprehensive control strategy.

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