Multi-aircraft finite time fault-tolerant cooperative control method based on deviation boundary constraint

Abstract

The invention discloses a multi-aircraft finite time fault-tolerant cooperative control method based on deviation boundary constraint, and relates to the field of aircraft fault-tolerant control. According to the method, an actuator fault of an aircraft is considered, a backstepping fault-tolerant control scheme with an autonomous adjustment capability based on preset performance is designed, an adaptive adjustment signal is introduced to increase the robustness of a preset performance boundary to a sudden fault, and a reference signal of an angular rate is obtained by adopting a dynamic surface technology; and an adaptive finite time radial basis function neural network disturbance observer is constructed to process unknown nonlinear terms of coupling actuator faults. The method can solve the problem of finite time guaranteed performance cooperative control under the condition that multiple aircrafts encounter actuator faults, is high in anti-interference and self-adaptability, has high stability and high robustness, can ensure that tracking errors of the multiple aircrafts converge to one domain in finite time under the condition that the actuator faults occur, and can improve the tracking precision of the multiple aircrafts. The method has excellent cluster fault-tolerant cooperative control performance.

Description

Technical Field

[0001] The present application relates to the field of aircraft fault-tolerant control, and in particular to a method for finite-time guaranteed-cost fault-tolerant collaborative control of multiple aircraft based on deviation boundary constraints. Background Art

[0002] In recent years, aircraft have attracted more and more attention for their high flight speed and strong maneuverability. A single aircraft is flexible and maneuverable, with strong concealment and adaptability, but the amount of tasks it can perform is limited. Therefore, aircraft clusters also have great research and development and application potential. However, aircraft fly at extremely high speeds. During the execution of a mission, if a single aircraft encounters a minor actuator failure, it may cause the individual aircraft or the cluster to lose control, resulting in mission failure. This places extremely high demands on the safety and control performance of the multi-aircraft system, requiring the system to quickly identify and regulate sudden failures in a very short time to ensure the smooth completion of the mission. Therefore, it is of great significance to develop a limited-time guaranteed performance collaborative control system for multiple aircraft.

[0003] During the execution of missions by aircraft systems, actuators are prone to failure and maneuverability is reduced. Relevant scholars have improved the control performance of the system by adopting a control strategy that combines a disturbance observer with a controller. In addition, in order to ensure the rapid response of the aircraft to faults, some studies have adopted a finite-time control strategy so that the control system exhibits good characteristics in convergence speed and convergence accuracy, and has anti-interference performance. As for the preset performance control method, it has excellent transient and steady-state performance, and can be better applied to the preset time fault-tolerant tracking control problem of multi-aircraft systems. Therefore, in response to the requirements of cluster aircraft for fast and accurate control response, this application combines the advantages of the aforementioned control strategy and proposes a finite-time guaranteed performance collaborative control method for multiple aircraft under the scenario of actuator failure. The control scheme has high reliability. Summary of the invention

[0004] In response to the above problems and technical requirements, the applicant proposes a multi-aircraft finite-time fault-tolerant collaborative control method based on deviation boundary constraints. The technical solution of this application is as follows:

[0005] A multi-aircraft finite-time fault-tolerant cooperative control method based on deviation boundary constraints comprises the following steps:

[0006] S1, establishing a dynamic model of the i-th aircraft in the aircraft cluster considering actuator failure, wherein the dynamic model of the i-th aircraft includes an unknown nonlinear fault term to be estimated; obtaining a control guidance model of the i-th aircraft according to the dynamic model of the i-th aircraft, wherein the control guidance model reflects the change of the attitude vector of the i-th aircraft at any time;

[0007] Its actual value x i1 With the received command control signal u i0 And change, the integer parameter i∈[1,N], N is the total number of aircraft included in the aircraft cluster;

[0008] S2, design a finite-time radial basis function neural network disturbance observer, and introduce an adaptive adjustment signal into the preset performance function to control the performance threshold boundary of the aircraft in the event of a sudden failure, so as to enhance its robustness;

[0009] S3, constructing a distributed synchronous tracking error between multiple aircrafts according to the attitude deviation of the aircraft, constructing a preset performance function according to the distributed synchronous tracking error between the aircrafts, wherein the preset performance function includes an adaptive adjustment signal; constructing a conversion deviation using the preset performance function, and designing a virtual control signal based on the backstepping method Use dynamic surface technology DSC to obtain the signal x required by the attitude loop i2d and its differential signal Design support system and Ensure that the filtering error generated in the dynamic surface technology converges within a finite time;

[0010] S4, using an adaptive finite-time neural network observer to estimate the unknown nonlinear fault term to obtain an estimated value of the fault term; combining the dynamic model, the conversion deviation, and the adaptive finite-time neural network observer to construct a fault-tolerant controller based on the backstepping method.

[0011] Furthermore, a dynamic model considering the actuator failure model of any i-th aircraft in the aircraft cluster is established, including:

[0012] Assume a flight formation consisting of N aircraft, where the mathematical model of the i-th aircraft is expressed as:

[0013]

[0014] Where i = 1, 2, ..., N, m i and g i represent the mass and gravitational acceleration of the ith aircraft respectively; the speed, heading angle and flight path angle of the ith aircraft are represented by V i , χ i and γ i The angle of attack, sideslip angle and bank angle of the i-th aircraft are represented by α i , β i and μ i The thrust, drag, lift and lateral force of the i-th aircraft are represented by T i , D i , Li and Y i express;

[0015] The dynamic model of any aircraft in the aircraft cluster is expressed as:

[0016]

[0017] Among them, the angular velocity of the i-th aircraft is expressed as p i ,q i and r i express:

[0018]

[0019] Among them, the rolling, pitching and yaw moments of the i-th aircraft are represented by L i 、M i and N i The aerodynamic moment L is i 、M i 、N i , aerodynamic moment L i , D i and the aerodynamic moment Y i are given by the following formula:

[0020]

[0021] Among them, q i =0.5ρ i V i 2 represents the dynamic pressure, and the wing area, wingspan and mean aerodynamic chord of the i-th aircraft are represented by s i 、b i and c i Indicates that the valve settings for the maximum thrust and instantaneous thrust of the i-th aircraft are T imax and δ Ti , the deflections of the aileron, elevator, and rudder of the i-th aircraft are represented by δ ia ,δ ie and δ ir Indicates the aerodynamic parameters and inertia term c of the i-th aircraft ij , j=1,2,...,9.

[0022] Furthermore, constructing a control and guidance model for the i-th aircraft includes:

[0023] Convert the aircraft model into a control-oriented model and define x i1 =[μ i , α i , β i ] T , xi2 =[p i ,q i , r i ] T and u i =[δ ia , δ ie , δ ir ] T , the posture model is expressed as:

[0024]

[0025] Among them, g i1 and g i2 is the gain matrix; f1=[f 11 , f 12 , f 13 ] T , f2=[f 21 , f 22 , f 23 ] T , f1 is the parameter matrix related to posture, speed and force, f2 is the parameter matrix related to moment of inertia and product of inertia, Δf i1 is an unknown item;

[0026]

[0027] Set actuator fault u i =ρ i u i0 +b if , substitute the actuator fault model into the control-oriented model, consider the rudder actuator fault, and get the model after the fault fusion:

[0028]

[0029] Among them, ρ i =diag{ρ i1 , ρ i2 , ρ i3} is the efficiency reduction failure matrix, b if =[b if1 , b if2 , b if3 ] T is bias fault, Δ i =g i2 (ρ i u i0 +b if )-g i2 u i0 It is an unknown item caused by a malfunction.

[0030] Furthermore, the adaptive finite-time neural network observer is designed as follows:

[0031]

[0032] Among them, η i1 , η i2 and λ ix is a positive design parameter, is the unknown nonlinear term Δ i An estimated value of

[0033] Using neural networks to approximate the unknown nonlinear term Δ i , unknown nonlinear term △ i Described as:

[0034]

[0035] In the formula, is the estimated value of the unknown nonlinear term △i, Optimal network weights;

[0036]

[0037] is a Gaussian function vector, where the elements of the Gaussian function vector have the following representation:

[0038]

[0039] In the formula, z is the input of the RBF neural network, c j and b j are the center vector and width vector of the Gaussian function respectively; then Expressed as

[0040]

[0041] In the formula, for The estimated value of , the adaptive law is designed as:

[0042]

[0043] Furthermore, based on the distributed synchronous tracking error, a preset performance function is constructed to convert the distributed synchronous tracking error into a new deviation constraint form:

[0044] Define the expected attitude angle x of the i-th aircraft relative to itself i1d =[μ id , α id , β id ] T The tracking error is:

[0045]

[0046] The distributed synchronization tracking error is defined as:

[0047]

[0048] Among them, E i1 =[E i11 , E i12 , E i13 ] T ,λ i1 and λ i2 is a positive number;

[0049] The distributed synchronous tracking error is written as:

[0050]

[0051] Where i = 1, ..., N, E i1 =[E i11 , E i12 , E i13 ] T , and is the Laplacian matrix The elements defined in A=[a ij ]∈R N×N is the weighted adjacency matrix of the information flow topology between aircraft;

[0052]

[0053] In the above formula According to the principle of preset performance, the tracking error E i1 The following constraints are met:

[0054]

[0055] Among them, τ = 1, 2, 3 are the values ​​of the exponential term; K i1τ , For adaptive preset performance boundaries, K i1τ = E i1τ -Ξ i1τ The performance function E i1τ , and adaptive adjustment signal Ξ i1τ composition;

[0056] For the tracking error e i1 For each element in , the preset performance function is constructed as:

[0057]

[0058] in, λ i ∈[0,1), ε 0i ∈[0,1), and, T ai ∈R + , ε pi ∈R + and r i ∈R + , are the parameters to be designed.

[0059] Further, in combination with the auxiliary system, an adaptive adjustment signal is generated;

[0060] The following auxiliary systems are used to generate adaptive control signals:

[0061]

[0062] Among them, M a ∈R + is the safety margin, k Ξ ∈R + and L Λ ∈R + is an adjustable parameter;

[0063] Define the following conversion function to convert the constrained error to the unconstrained equality error:

[0064]

[0065] The derivative is:

[0066]

[0067] Among them, i1 =[Ψ i1 ,Ψ i2 ,Ψ i3 ] T ,h i1 =diag{h i1 ,h i2 ,h i3}, J i1 =[J i1 , J i2 , J i3 ] T ,τ=1,2,3.

[0068] Furthermore, a backstepping fault-tolerant controller is designed based on the aircraft kinematic model:

[0069] In the kinematic model controller design, the intermediate control signal is expressed as:

[0070]

[0071] Among them, K i∈ ∈R 3×3 is the real diagonal matrix to be designed;

[0072] Using dynamic surface control DSC technology to obtain the signal x of the subsequent attitude loop i2d and its difference X i2d , the expression of DSC is:

[0073]

[0074] in, τ i1 ∈R 3×3 is a diagonal matrix of time constants to be chosen, defining the filter error as Its time derivative is derived as:

[0075]

[0076] Design the following auxiliary power systems:

[0077]

[0078] Where K i1 ∈R 3×3 is the real diagonal matrix to be designed, τ i2 is a positive parameter; defines the compensation synchronization tracking error ∈ i1 =Ψ i1 -η i1 and the angular rate tracking error e i2 =x i2 -x i2d , and along e i2 Taking the derivative, we get:

[0079]

[0080] By differentiating the above formula with respect to time, we get:

[0081]

[0082] The control signal ui0 is designed as:

[0083]

[0084] Design The auxiliary power system is designed to:

[0085]

[0086] Where K i2 ∈R 3×3 is the real diagonal matrix to be designed; λi∈ and τ i3 is a positive parameter, and the compensated angular rate tracking error is defined as:

[0087] ∈ i2 =e i2 -η i2 ;

[0088] right 62 The derivative is:

[0089]

[0090] The beneficial technical effects of this application are:

[0091] The present application discloses a method for finite-time guaranteed performance fault-tolerant cooperative control of multiple aircraft based on deviation boundary constraints. Aiming at the cooperative control problem of multiple aircraft under actuator failure, an adaptive fault-tolerant cooperative control scheme based on a flexible preset performance function boundary is proposed. First, the model of the aircraft is converted into a control-oriented model, and the actuator failure is considered, and it is further converted into two parts: an attitude loop and an angular rate loop. A finite-time radial basis function neural network disturbance observer is designed to estimate the nonlinear term of the fault information. Then, an adaptive adjustment signal is introduced into the prescribed performance function to handle the performance boundary range of the aircraft under sudden failure conditions to enhance its robustness. In addition, in the design of the backstepping control law, a filter is used to process the virtual command signal, thereby suppressing the differential explosion phenomenon and ensuring the reliability of the control signal. The control signal of the subsequent angular rate loop is obtained by using the DSC technology, and the auxiliary system is designed considering the error of the DSC. The simulation results show that the designed multi-aircraft cooperative control method can effectively ensure the finite-time performance stability of the aircraft group system. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 is a communication topology diagram of an aircraft cluster in an example of the present application;

[0093] Figure 2 is a control schematic diagram of any i-th aircraft in an example of the present application;

[0094] Figure 3 This is a simulation result diagram of the attitude tracking effect of four aircraft in an example of the present application under the condition of actuator failure;

[0095] Figure 4 This is a control input diagram simulation result diagram of four aircraft in an example of the present application. DETAILED DESCRIPTION

[0096] The specific implementation of the present application is further described below in conjunction with the accompanying drawings.

[0097] The present application discloses a multi-aircraft finite-time fault-tolerant collaborative control method based on deviation boundary constraints. The collaborative control method is aimed at a cluster of multiple aircraft and can solve the fault-tolerant collaborative control problem of the cluster of multiple aircraft encountering actuator failures, ensuring that the performance of the cluster of multiple aircraft remains stable within a finite time and ensuring the smooth completion of the mission.

[0098] There is a communication topology between the aircraft in the aircraft cluster. Each aircraft can establish communication connections with all other aircraft, or only with some other aircraft. The communication connection between aircraft can be unidirectional or bidirectional. Figure 1 In a communication topology diagram of an example shown, a first aircraft establishes a unidirectional communication connection with a second aircraft, the second aircraft establishes a unidirectional communication connection with a third aircraft, the third aircraft establishes a unidirectional communication connection with a fourth aircraft, and the fourth aircraft establishes a unidirectional communication connection with the first aircraft.

[0099] Based on the application scenario of the aircraft cluster, the fault-tolerant collaborative control method of the cluster aircraft includes the following steps:

[0100] Step 1: Establish a dynamic model of any i-th aircraft in the aircraft cluster considering actuator failure.

[0101] This application is aimed at designing a finite-time guaranteed performance fault-tolerant collaborative control scheme for a flight formation consisting of N aircraft. The mathematical model of the i-th aircraft can be expressed as:

[0102]

[0103] Where i = 1, 2, ..., N, m i and g i represents mass and gravitational acceleration respectively. Velocity, heading angle and flight path angle are represented by V i , χ i and γ i The angle of attack, sideslip angle and bank angle are represented by α i , β i and μ i Thrust, drag, lift and lateral force are represented by T i , D i , L i and Y i express.

[0104] The dynamic model of any aircraft in the aircraft cluster is expressed as:

[0105]

[0106] Among them, the angular velocity of the i-th aircraft is expressed as p i ,q i and r i express:

[0107]

[0108] Among them, rolling, pitching and yaw moments are represented by L i 、M i and N i Indicates. Except thrust T i In addition, the aerodynamic moment L i 、M i 、N i , aerodynamic moment L i , D i and the aerodynamic moment Y i are given by the following formula:

[0109]

[0110] Among them, q i =0.5ρ i V i 2 represents the dynamic pressure. The wing area, wingspan and mean aerodynamic chord are represented by s i 、b i and c i The valve settings for maximum thrust and instantaneous thrust are T imax and δ Ti The deflections of the aileron, elevator, and rudder are represented by δ ia ,δ ie and δ ir Indicates. Aerodynamic parameters and inertia term c ij (j=1, 2, ..., 9).

[0111] Inertia term ci j , j=1,2,...,9 The formula is as follows:

[0112] G a =I x I z -I xz 2 , c i1 =[(I y -I z )I z -I xz 2 ] / G a , c i2 =I xz (I x -I y +Iz ) / G a , c i3 =I z / G a .

[0113] c i4 =I xz / G a , c i5 =(I z -I x ) / I y , c i6 =I xz / I y , c i7 =1 / I y , c i8 =[I x (I x -I y )],c i9 =I x / G a

[0114] Step 2: Construct a control and guidance model for the i-th aircraft.

[0115] To facilitate the subsequent controller design, the aircraft model is now converted into a control-oriented model. Define x i1 =[μ i , α i , β i ] T , x i2 =[p i ,q i , r i ] T and u i =[δ ia , δ ie , δ ir ] T ; Therefore, the posture model is expressed as:

[0116]

[0117] Among them, g i1 and g i2 is the gain matrix. 11 , f 12 , f 13 ] T , f2=[f 21 , f 22 , f 23 ] T , Δf i1 It is an unknown item.

[0118] This control method takes into account the actuator fault u i =ρ i u i0 +b if , and the actuator fault model is substituted into the control-oriented model. At the same time, considering that the aerodynamic force generated by the rudder is small, Δf i1 can be ignored. Considering the failure of the rudder actuator, the model after the failure is further obtained:

[0119]

[0120] Among them, ρ i =diag{ρ i1 , ρ i2 , ρ i3} is the efficiency reduction failure matrix, b if =[b if1 , b if2 , b if3 ] T is bias fault, Δ i =g i2 (ρ i u i0 +b if )-g i2 u i0 It is an unknown item caused by a malfunction.

[0121] The control method of this application targets the actuator failure scenario encountered by the aircraft, and uses an adjustable preset performance function to constrain the error to ensure that the attitude μ, α, β of the faulty aircraft can track the ideal attitude signal μ output by the upper guidance loop. d , α d , β d .

[0122] Step 3: Design a finite-time radial basis neural network disturbance observer to handle the nonlinear unknowns caused by the fault.

[0123] The design of the adaptive finite-time neural network observer in this application is as follows:

[0124]

[0125] Among them, η i1 , η i2 and λ ix is a positive design parameter, xi2=x i2 -x i2 ,△ i It will be defined later. In order to estimate the unknown term caused by the fault, a radial basis function NN is constructed and a neural network is used to approximate the unknown nonlinear term Δ i , the unknown nonlinear term Δi It can be described as:

[0126]

[0127] In the formula, is the unknown nonlinear term Δ i The estimated value of W * is the optimal network weight.

[0128]

[0129] is the Gaussian function vector, that is:

[0130]

[0131] In the formula, z is the input of the RBF neural network, c j and b j are the center vector and width vector of the Gaussian function respectively. It can be expressed as

[0132]

[0133] In the formula, is the estimated value of W*. The adaptive law is designed as:

[0134]

[0135] The following proves the finite time convergence property of the observer. Consider the following Lyapunov function:

[0136]

[0137] For any value x i , positive design parameter λ i , i=1,...,n, there is the following functional relationship:

[0138]

[0139] where sign(·) is the sign function, and

[0140] Derivative the above equation and substitute it into the designed adaptive law:

[0141]

[0142] Among them, the ideal network weight W * The default is a constant, W *T W * is a constant greater than 0. ix >0,ι i=0.5(λ i1 +1) and satisfies κ i1 =min{2η i1 , 2η i3 Γ i1},

[0143] According to the lemma, it can be proved that the designed finite-time neural network observer can converge within a finite time. Its convergence domain and convergence time are:

[0144]

[0145] Its time domain can be obtained by the following formula:

[0146]

[0147] Step 4: Based on the tracking error, a preset performance function is constructed, and an adaptive adjustment signal is generated in combination with the auxiliary system.

[0148] Define the expected attitude angle x of the i-th aircraft relative to itself i1d =[μ id , α id , β id ] T The tracking error is:

[0149]

[0150] At this time, the distributed synchronous tracking error can be defined as:

[0151]

[0152] where i=1, 2,...,N,E i1 =[E i11 , E i12 , E i13 ] T ,λ i1 and λ i2 is a positive number. Further, the distributed synchronous tracking error can be transformed into:

[0153]

[0154] Where i = 1, ..., N, E i1 =[e i11 , e i12 , e i13 ] T , and is the Laplacian matrix The elements defined in A=[aij ]∈R N×N is the weighted adjacency matrix of the information flow topology between aircraft.

[0155]

[0156] In the above formula According to the principle of preset performance, the tracking error E i1 The following constraints should be met:

[0157]

[0158] Among them, i=1,...,N, τ=1, 2, 3; K i1τ , For adaptive preset performance boundaries, K i1τ = E i1τ -Ξ i1τ The performance function E i1τ , and adaptive adjustment signal Ξ i1τ composition.

[0159] For the tracking error e i1 For each element in , the performance function is constructed as:

[0160]

[0161] in, l i ∈[0,1), ε 0i ∈[0,1), and, T ai ∈R + , ε pi ∈R + and r i ∈R + , are the parameters to be designed.

[0162] The following auxiliary systems are used to generate adaptive control signals:

[0163]

[0164]

[0165] Among them, when Λ i1τ =0; and when M a ∈R + is the safety margin, k Ξ ∈R + and L Λ ∈R + is an adjustable parameter, Λ i1τ(t)∈R + The error fluctuation caused by the sudden interference can be detected. i1τ (t) A feedback mechanism between burst interference and performance envelope is established.

[0166] In order to facilitate the design of the subsequent control law, the following conversion function is defined to convert the constrained error into the unconstrained equation error:

[0167]

[0168] The derivative is:

[0169]

[0170] Among them, i1 =[Ψ i1 ,Ψ i2 ,Ψ i3 ] T ,h i1 =diag{h i1 ,h i2 ,h i3}, J i1 =[J i1 , J i2 , J i3 ] T , and τ = 1, 2, 3. If the error after conversion is bounded Ψ iτ , then the specified synchronous tracking performance is obtained. Further using the new error Ψ iτ A finite-time tracking scheme is designed.

[0171] Step 5: Design a controller based on the aircraft kinematic model.

[0172] In the kinematic model controller design, the intermediate control signal can be expressed as:

[0173]

[0174] Among them, K i∈ ∈R 3×3 is the real diagonal matrix to be designed. We will define ∈ i1 .

[0175] This application uses dynamic surface control (DSC) technology to obtain the signal x of the subsequent attitude loop i2d and its difference X i2d , the expression of DSC is:

[0176]

[0177] in, τ i1 ∈R3×3 is a diagonal matrix of time constants to be chosen. The filter error is defined as Its time derivative can be derived as:

[0178]

[0179] Design the following auxiliary power systems:

[0180]

[0181] Where K i1 ∈R 3×3 is the real diagonal matrix to be designed. τ i2 is a positive parameter. Define the compensation synchronization tracking error ∈ i1 =Ψ i1 -η i1 and the angular rate tracking error e i2 =x i2 -x i2d , and along e i2 Taking the derivative, we get:

[0182]

[0183] By substituting (21) into (27) and taking the time derivative of (27), we can obtain:

[0184]

[0185] Then, by integrating (27) and (31), we can obtain:

[0186]

[0187] In order to stabilize i2 , the control signal ui0 is designed as:

[0188]

[0189] At the same time, the auxiliary power system is designed to:

[0190]

[0191] Where K i2 ∈R 3×3 is the real diagonal matrix to be designed. i∈ and τ i3 is a positive parameter. The compensated angular rate tracking error is defined as:

[0192] ∈ i2 =e i2 -η i2 ;

[0193] Take ∈ i2 The time derivative of the trajectory (6) can be obtained:

[0194]

[0195] Step 6: Stability analysis of the control method.

[0196] In order to prove the stability of the finite-time guaranteed cost cooperative control method for multiple aircraft under the actuator failure scenario of this application, it is necessary to prove the stability of the motion state and fault approximation term of the aircraft system in finite time. The following Lyapunov function candidates are selected:

[0197]

[0198] By substituting (34) and (38), we get L i The time derivative of is:

[0199]

[0200] By using Young's inequality, we get the inequality:

[0201]

[0202] From the proof of the finite-time neural network observer, we can see that Converges to Δ in finite time i ,therefore, is bounded. At this point we can get:

[0203]

[0204] At this point, we can get

[0205]

[0206] in,

[0207] At the same time, the auxiliary system needs to be taken into consideration. The Lyapunov function for selecting the auxiliary system is:

[0208]

[0209] L ia The derivative with respect to time is:

[0210]

[0211] Using Young's inequality, we can get the following inequality:

[0212]

[0213] in, When Z i Pick X i Take separately or When Z i Pick X i Pick and

[0214] At this point, we can get the following inequality:

[0215]

[0216] Among them, the values ​​of and,

[0217] That is:

[0218]

[0219] Where l3 = min{l3}, l4 = min{l4}, i = 1, 2, ..., N, and σ2 = ∑σ i2 ,

[0220] It can be concluded that the motion trajectory of the system is stable for a finite time, and its boundary is:

[0221]

[0222] Where, 0<a1<1. The setting time T3 value range is:

[0223]

[0224] The results show that the designed backstepping adaptive fault-tolerant cooperative control scheme based on prescribed performance can converge within a finite time.

[0225] In order to better understand the implementation of the present invention, the present invention uses MATLAB software to simulate the tracking control of aircraft clusters to verify its reliability. The aircraft cluster containing 4 aircraft is controlled by the fault-tolerant collaborative control method of the present invention. The communication network is as follows: Figure 1 shown.

[0226] In order to verify the effectiveness of the proposed control scheme, four networked aircraft were simulated. The performance parameters are λ i =0.8, ε 0i =0.2,ε pi =0.2, Tai =10, r i =2,L Λ =0.01, M a =0.2,λ i∈ =0.5, k Ξ =1. The virtual control law parameters are K i1 =diag{2,5,2},K i∈ =diag{1,1,1},λ i1 =1.2,λ i2 =1,τ i1 =0.05, τ i2 =0.2. The weighted adjacency matrix A = [0, 1, 0, 1; 1, 0, 1, 1; 0, 1, 0, 1; 1, 1, 1, 0;]. In addition, the relevant parameters in the control design are configured as K i2 =diag{20,50,10},τ i3 =0.2. The parameters in the observer are selected as η i1 =1.1,η i2 =1.8,λ ix =0.9. The parameters in the adaptive law are selected as Γ i1 =1.2,η i3 =1.5. Under the proposed decentralized finite-time fault-tolerant synchronous tracking control scheme, the four aircrafts effectively tracked the attitude angles after the actuator failures at t=15s, t=20s and t=30s.

[0227] Figure 3 The attitude tracking effect of the aircraft under actuator failure is shown. It can be seen that the synchronous tracking error converges to the predefined residual set within the preset time before the failure occurs. When the aircraft encounters a failure, the attitude synchronous tracking error increases, and due to the adaptive adjustment signal introduced in the control scheme design, adaptive adjustment to the actuator failure can be achieved, so that the synchronous tracking error is always within the performance boundary. The tracking error is effectively controlled through control signal adjustment.

[0228] Figure 4 A plot of the control inputs for the four vehicles is shown. When an actuator failure occurs, the input signals are altered to ensure that the vehicles track the desired attitude.

[0229] The above are only preferred embodiments of the present application, and the present application is not limited to the above embodiments. It is understood that other improvements and changes directly derived or associated by those skilled in the art without departing from the spirit and concept of the present application should be considered to be included in the protection scope of the present application.

Claims

1. A multi-aircraft finite-time fault-tolerant cooperative control method based on deviation boundary constraints, characterized in that: The method comprises the following steps: S1, establishing a dynamic model of the i-th aircraft in the aircraft cluster considering actuator failure, wherein the dynamic model of the i-th aircraft includes an unknown nonlinear fault term to be estimated; obtaining a control guidance model of the i-th aircraft according to the dynamic model of the i-th aircraft, wherein the control guidance model reflects the change of the attitude vector of the i-th aircraft at any time; Its actual value x i1 With the received command control signal u i0 The integer parameter i∈[1, N] is changed, where N is the total number of aircraft included in the aircraft cluster; S2, design a finite-time radial basis function neural network disturbance observer, and introduce an adaptive adjustment signal into the preset performance function to control the performance threshold boundary of the aircraft in the event of a sudden failure, so as to enhance its robustness; S3, constructing a distributed synchronous tracking error between multiple aircrafts according to the attitude deviation of the aircraft, constructing a preset performance function according to the distributed synchronous tracking error between the aircrafts, wherein the preset performance function includes an adaptive adjustment signal; constructing a conversion deviation using the preset performance function, and designing a virtual control signal based on the backstepping method Use dynamic surface technology DSC to obtain the signal x required by the attitude loop i2d and its differential signal Design support system and Ensure that the filtering error generated in the dynamic surface technology converges within a finite time; S4, using an adaptive finite-time neural network observer to estimate the unknown nonlinear fault term to obtain an estimated value of the fault term; combining the dynamic model, the conversion deviation, and the adaptive finite-time neural network observer to construct a fault-tolerant controller based on the backstepping method.

2. The method for multi-aircraft finite-time guaranteed cost fault-tolerant cooperative control based on deviation boundary constraints according to claim 1 is characterized in that: Establish a dynamic model of any i-th aircraft in the aircraft cluster considering the actuator failure model, including: Assume a flight formation consisting of N aircraft, where the mathematical model of the i-th aircraft is expressed as: Where i = 1, 2, ..., N, m i and g i represent the mass and gravitational acceleration of the ith aircraft respectively; the speed, heading angle and flight path angle of the ith aircraft are represented by V i , χ i and γ i The angle of attack, sideslip angle and bank angle of the i-th aircraft are represented by α i , β i and μ i The thrust, drag, lift and lateral force of the i-th aircraft are represented by T i , D i , L i and Y i express; The dynamic model of any aircraft in the aircraft cluster is expressed as: Among them, the angular velocity of the i-th aircraft is expressed as p i ,q i and r i express: Among them, the rolling, pitching and yaw moments of the i-th aircraft are represented by L i 、M i and N i The aerodynamic moment L is i 、M i 、N i , aerodynamic moment L i , D i and the aerodynamic moment Y i are given by the following formula: Among them, q i =0.5ρ i V i 2 represents the dynamic pressure, and the wing area, wingspan and mean aerodynamic chord of the i-th aircraft are represented by s i 、b i and c i Indicates that the valve settings for the maximum thrust and instantaneous thrust of the i-th aircraft are T imax and δ Ti , the deflections of the aileron, elevator, and rudder of the i-th aircraft are represented by δ ia ,δ ie and δ ir Indicates the aerodynamic parameters and inertia term c of the i-th aircraft ij , j=1,2,...,9.

3. The method for multi-aircraft finite-time guaranteed cost-tolerant cooperative control based on deviation boundary constraints according to claim 2 is characterized in that: Constructing a control and guidance model for the i-th aircraft, including: Convert the aircraft model into a control-oriented model and define x i1 =[μ i , α i , β i ] T , x i2 =[p i ,q i ,r i ] T and u i =[δ ia , δ ie , δ ir ] T , the posture model is expressed as: Among them, g i1 and g i2 is the gain matrix; f1=[f 11 , f 12 , f 13 ]T, f2=[f 21 , f 22 , f 23 ] T , f1 is the parameter matrix related to posture, speed and force, f2 is the parameter matrix related to moment of inertia and product of inertia, Δf i1 is an unknown item; Set actuator fault u i =ρ i u i0 +b if , substitute the actuator fault model into the control-oriented model, consider the rudder actuator fault, and get the model after the fault fusion: Among them, ρ i =diag{ρ i1 ,ρ i2 ,ρ i3 } is the efficiency reduction failure matrix, b if =[b if1 ,b if2 ,b if3 ] T is bias fault, Δ i =g i2 (ρ i u i0 +b if )-g i2 u i0 It is an unknown item caused by a malfunction.

4. The method for multi-aircraft finite-time guaranteed cost-tolerant cooperative control based on deviation boundary constraints according to claim 3 is characterized in that: The adaptive finite-time neural network observer is designed as follows: Among them, η i1 , η i2 and λ ix is a positive design parameter, is the unknown nonlinear term Δ i An estimated value of Using neural networks to approximate the unknown nonlinear term Δ i , the unknown nonlinear term Δ i Described as: In the formula, is the unknown nonlinear term Δ i The estimated value of Optimal network weights; is a Gaussian function vector, where the elements of the Gaussian function vector have the following representation: In the formula, z is the input of the RBF neural network, c j and b j are the center vector and width vector of the Gaussian function respectively; then Expressed as In the formula, for The estimated value of , the adaptive law is designed as:

5. The method for multi-aircraft finite-time guaranteed cost fault-tolerant cooperative control based on deviation boundary constraints according to claim 4 is characterized in that: Based on the distributed synchronous tracking error, a preset performance function is constructed to convert the distributed synchronous tracking error into a new deviation constraint form: Define the expected attitude angle x of the i-th aircraft relative to itself i1d =[μ id ,α id ,β id ] T The tracking error is: The distributed synchronization tracking error is defined as: Among them, E i1 =[E i11 ,E i12 ,E i13 ] T ,λ i1 and λ i2 is a positive number; The distributed synchronous tracking error is written as: Where i = 1, ..., N, E i1 =[E i11 , E i12 , E i13 ] T , and is the Laplacian matrix The elements defined in A=[a ij ]∈R N×N is the weighted adjacency matrix of the information flow topology between aircraft; In the above formula According to the principle of preset performance, the tracking error E i1 The following constraints are met: Among them, τ = 1, 2, 3 are the values ​​of the exponential term; For adaptive preset performance boundaries, Then the performance function E i1τ , and adaptive adjustment signal Ξ i1τ composition; For the tracking error E i1 For each element in , the preset performance function is constructed as: in, l i ∈[0,1), ε 0i ∈[0,1), and, T ai ∈R + , εp i ∈R + and r i ∈R + , are the parameters to be designed.

6. The method for finite-time guaranteed cost coordinated control of multiple aircraft under actuator failure scenarios according to claim 5, characterized in that: Combined with auxiliary systems, adaptive adjustment signals are generated; The following auxiliary systems are used to generate adaptive control signals: Among them, M a ∈R + is the safety margin, k Ξ ∈R + and L Λ ∈R + is an adjustable parameter; Define the following conversion function to convert the constrained error to the unconstrained equality error: The derivative is: Among them, Ps i1 =[Ψ i1 ,P i2 ,P i3 ] T ,h i1 =diag{h i1 ,h i2 ,h i3 },J i1 =[J i1 ,J i2 ,J i3 ] T , τ=1, 2, 3.

7. The method for finite-time guaranteed cost coordinated control of multiple aircraft under actuator failure scenarios according to claim 6, characterized in that: Design a backstepping fault-tolerant controller based on the aircraft kinematic model: In the kinematic model controller design, the intermediate control signal is expressed as: Among them, K i∈ R 3×3 is the real diagonal matrix to be designed; Using dynamic surface control DSC technology to obtain the signal x of the subsequent attitude loop i2d and its difference x i2d , the expression of DSC is: in, τ i1 ∈R 3×3 is a diagonal matrix of time constants to be chosen, defining the filter error as Its time derivative is derived as: Design the following auxiliary power systems: Where K i1 ∈R 3×3 is the real diagonal matrix to be designed, τ i2 is a positive parameter; defines the compensation synchronization tracking error ∈ i1 =Ψ i1 -η i1 and the angular rate tracking error e i2 =x i2 -x i2d , and along e i2 Taking the derivative, we get: By differentiating the above formula with respect to time, we get: The control signal u i0 Designed for: Design The auxiliary power system is designed to: Where K i2 ∈R 3×3 is the real diagonal matrix to be designed; λ i∈ and τ i3 is a positive parameter, and the compensated angular rate tracking error is defined as: ∈ i2 =e i2 -or i2 ; Pair∈ i2 The derivative is:

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