Cluster aircraft refined fault-tolerant cooperative control method based on double-event triggering

Abstract

The invention discloses a cluster aircraft refined fault-tolerant cooperative control method based on double event triggering, and the method comprises the steps: firstly, considering the constraint of finite communication resources, constructing an event triggering communication mechanism, and reducing the communication frequency between cluster aircrafts; secondly, designing a distributed observer, and estimating an aircraft reference instruction signal by using discontinuous neighbor state information; and then, a Nussbaum function and a self-adaptive neural network method are adopted to process the actuator fault and the parameter uncertainty. And finally, designing a fractional order sliding mode fault-tolerant control strategy based on an event trigger control mechanism, reducing the updating times of the controller and realizing fine control of the cluster aircraft. The method can be applied to cluster aircraft formation fault-tolerant cooperative control under the condition that communication and computing resources are limited.

Description

Technical Field

[0001] Aiming at the problems of actuator failure and parameter uncertainty encountered by cluster aircraft under limited communication and computing resources, the present invention designs a cluster aircraft refined fault-tolerant collaborative control method based on double event triggering, which belongs to the field of fault-tolerant collaborative control. Background Art

[0002] In recent years, swarm aircraft have played an increasingly important role in many fields. Compared with single aircraft, swarm aircraft have a larger exploration range and can carry more equipment, so swarm aircraft can often perform a variety of complex tasks, such as forest fire monitoring, search and rescue, line inspection, etc. However, as a highly complex system, swarm aircraft itself carries a large number of actuator components, which makes swarm aircraft more susceptible to actuator failures than single aircraft. In addition, when the swarm is large, due to the limited capacity of the onboard computer carried by each aircraft, it is difficult for the aircraft to process a large amount of information at the same time, thus affecting the flight performance of the aircraft. Therefore, how to achieve fault-tolerant collaborative control of swarm aircraft under the constraint of limited computer capabilities is of great significance. Summary of the invention

[0003] Aiming at the problems of actuator failure and parameter uncertainty encountered by cluster aircraft when communication and computing resources are limited, the present invention designs a refined fault-tolerant collaborative control method for cluster aircraft based on dual event triggering to ensure that cluster aircraft can still achieve cluster fault-tolerant collaborative control when communication and computing resources are limited.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions:

[0005] A method for fine-grained fault-tolerant collaborative control of cluster aircraft based on dual event triggering, the control method comprising the following steps:

[0006] Step 1: Establish the aircraft dynamics model.

[0007] Set up a group of formation aircraft consisting of N followers and 1 leader, where the dynamics of the i-th (i=1,2,…,N) follower aircraft is:

[0008]

[0009] Among them, x i ,y i and z i is the three-dimensional coordinate of the i-th aircraft, Represents x i First-order derivative, V i is the speed of the aircraft, χ i represents the heading angle, γi Represents the flight path angle. i , D i , L i and Y i They are respectively the thrust, drag, lift and side force of the aircraft. i is the angle of attack, μ i is the tilt angle, β i is the sideslip angle. m is the mass of the aircraft, g is the coefficient of gravity acceleration;

[0010] Thrust, drag, lift and side force can be expressed as:

[0011]

[0012] Among them, ρ iT is the throttle opening, T max is the maximum thrust, ρ is the air density, s i is the wing area. C iL , C iD and C iY They are lift coefficient, drag coefficient and side force coefficient, and the coefficients are expressed by the following formula:

[0013]

[0014] Among them, C iD0 , C iY0 and C iL0 is a constant, C iDα , C iLα and is the angle of attack α i The correlation coefficient, C iYβ is the side slip angle β i The coefficient of correlation;

[0015] Define u i =[ρ iT ,α i sinμ i ,α i cosμ i ] T Input signal vector and p for the aircraft i =[x i ,y i ,z i ] T is the aircraft position information vector, simplifying (1) to obtain:

[0016]

[0017] Among them, f i and g iTo simplify the obtained matrix, it is expressed as:

[0018]

[0019] Step 2: Establish the aircraft dynamics model under the influence of parameter uncertainty and actuator failure.

[0020] First, consider the parameter uncertainty. The dynamics of the aircraft with parameter uncertainty is expressed as:

[0021]

[0022] Among them, L id , D id and Y id are the unknown lift, drag and side force caused by parameter uncertainty. The remaining parameters are consistent with the aircraft model parameters in step 1;

[0023] The unknown lift, drag and side force and uncertain parameters can be expressed as:

[0024]

[0025] Among them, C iDd , C iYd and C iLd is the unknown aerodynamic parameter, C iD0d , C iDαd , C iY0d , C iYβd , C iL0d and C iLαd is the unknown coefficient;

[0026] By considering the uncertainty of parameters, the vehicle dynamics equation (4) in step 1 is changed to:

[0027]

[0028] Among them, f i and g i Same as the definition in step 1, f id and g id is the unknown matrix caused by parameter uncertainty, which can be expressed as:

[0029]

[0030] Among them, M i It has been given in (5);

[0031] Considering the actuator failure faced by the aircraft, the fault model is expressed as:

[0032] u i =ρi u i0 +f ib (10)

[0033] Among them, ρ i =diag{ρ i1 ,ρ i2 ,ρ i3}, ρ ij ∈(0,1] is the efficiency loss factor, j = 1, 2, 3, f ib =[f ib1 ,f ib2 ,f ib3 ] T represents deviation fault, u i0 is the aircraft control input signal;

[0034] Combined with (8), the aircraft dynamics model considering parameter uncertainty and actuator failure can be expressed as:

[0035]

[0036] Among them, d i =f id +g i f ib +g id (ρ i u i0 +f ib ) is a lumped unknown term formed by the coupling of deviation fault and parameter uncertainty.

[0037] Step three, design an event-triggered communication mechanism and establish a distributed observer to estimate the aircraft reference command signal using the neighbor discontinuous state information.

[0038] Establish an event-triggered communication mechanism to save communication resources. With this communication mechanism, the i-th aircraft can only obtain the status information of neighboring aircraft when an event is triggered. Define the position trigger error of the i-th aircraft as The speed trigger error is in, and is the position and velocity information estimated by the distributed observer, and At the triggering moment The estimated position and velocity information, k i =0, 1, .... The first triggering time is set to The event-triggered communication mechanism is expressed as:

[0039]

[0040] in, Indicates the trigger time The next triggering moment of , inf{*} represents the infimum of a function, χ1, x2, ξ1, ξ2 and ξ3 are positive constants designed, Ω i is a time-varying parameter, and its derivative is:

[0041]

[0042] Among them, Ω i (0) is the initial value of the event parameter, and δ1 is a positive design parameter;

[0043] Due to the event-triggered communication mechanism, the state information of neighboring aircraft received by the aircraft is discontinuous. This discontinuous state information cannot be directly used to design the control law of the aircraft. Therefore, a distributed observer is designed to obtain continuous state information. The designed distributed observer is:

[0044]

[0045] in, and is the position and velocity information estimated by the distributed observer, ψ i1 and ψ i2 The defined estimator coordinates position and velocity deviation, expressed as:

[0046]

[0047] Among them, a ij represents the communication weight between the i-th and j-th aircraft, b i represents the communication weight between the i-th aircraft and the leader aircraft, and is the jth aircraft at the trigger time Estimated position and velocity information, and Represents the leader aircraft at the triggering moment Position and velocity information. ij represents the distance between the i-th aircraft and the j-th aircraft, d i0 Represents the distance between the ith aircraft and the leader aircraft.

[0048] Step 4: Establish an event-triggered control mechanism and a fractional-order sliding surface, use the Nussbaum function and adaptive neural network method to process actuator failures and parameter uncertainties, and design event-triggered fault-tolerant control input signals.

[0049] Establish an event-triggered control mechanism to save computing resources. Design the following control signal update mechanism:

[0050]

[0051] Among them, u i0 (t) is the aircraft control input signal, is the event triggering time, m i =0, 1, .... v i is the designed virtual control signal;

[0052] Design the following event trigger mechanism and update the control law when the event is triggered:

[0053]

[0054] in, Event trigger time The next triggering moment, z i (t) = v i )t)-u i0 (t) represents the controller trigger error, 0<α i1 <1 and β i1 >0 is the designed parameter;

[0055] Design fractional-order sliding surfaces to fine-tune the control performance of swarm aircraft. The fractional sliding surface is as follows:

[0056]

[0057] Among them, c i1 、c i2 and c i3 is a positive parameter of the design. and for e i The fractional derivative of i1 <1 and 0 <a i2 <1 is a fractional-order operator;

[0058] Define a time-varying vector r i =[γ i1 ,γ i2 ,γ i3 ] T , the Nussbaum function form used is γ i The derivative expression of is:

[0059]

[0060] Among them, λ i =diag{λ i1 ,λ i2 ,λi3} is the designed matrix, λ i1 , i2 and λ i3 is a designed normal number. is the estimated value of the weight matrix, φ i (p i ,v i ) is the basis function, is the estimated value of the estimated bias;

[0061] Define X i =[p i ,v i ] T Indicates the aircraft status information, φ i (p i ,v i )=φ i (X i ) is a basis function containing n nodes, denoted as φ i (X i )=[φ i1 (X i ),φ i2 (X i ),…,φ ij (X i ),…φ in (X i )] T , where φ ij (X i ) is defined in Gaussian form:

[0062]

[0063] Among them, exp[a] represents the exponential to the power of a, υ i is the center value, N c For width, it needs to be adjusted carefully;

[0064] and The derivative of is expressed as:

[0065]

[0066] Among them, k i2 and k i3 is the positive parameter of the design;

[0067] Define a virtual time-varying vector ε i =[ε i1 ,ε i2 ,ε i3 ] T , which can be expressed as:

[0068]

[0069] in, Yes i diagonal matrix;

[0070] The designed virtual control signal is:

[0071]

[0072] Among them, diag(ε i ) = diag{ε i1 ,ε i2 ,ε i3} is ε i The diagonal matrix of is a constant term, Λ i1 and Λ i2 is the designed time-varying vector, expressed as:

[0073]

[0074] Among them, tanh(*) is the hyperbolic tangent function, g i1 , g i2 and g i3 is the matrix g in step 1 i The column vector of i =[g i1 ,g i2 ,g i3 ], is a positive parameter.

[0075] Afterwards, the real control input signal u can be obtained through the event-triggered control mechanism. i0 .

[0076] The present invention has the following beneficial effects:

[0077] (1) The present invention takes into account the fault-tolerant control problem of cluster aircraft encountering actuator failures and parameter uncertainties, and the designed fault-tolerant collaborative control method ensures the safe collaborative flight of the cluster aircraft system.

[0078] (2) The present invention adopts a dual event trigger mechanism, namely, event-triggered communication and event-triggered control mechanism, which not only reduces the communication frequency between aircraft, but also reduces the update frequency of the controller, and can effectively reduce the consumption of communication and computing resources.

[0079] (3) The present invention adopts a fractional-order control method, which adds adjustable parameters at the operator level and can achieve fine-grained adjustment of the aircraft control performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 It is the topological structure diagram of the cluster aircraft;

[0081] Figure 2 This is a control architecture diagram for the aircraft;

[0082] Figure 3 It is the flight position diagram of the cluster aircraft;

[0083] Figure 4 is the flight speed diagram of the cluster aircraft;

[0084] Figure 5 is the tracking error diagram of the follower aircraft to the command signal;

[0085] Figure 6 It is a graph of the number of event-triggered communications and time-triggered communications of the aircraft;

[0086] Figure 7 It is the frequency diagram of event-triggered control and time-triggered control of the aircraft;

[0087] Figure 8 This is the control input signal diagram for aircraft #1;

[0088] Fig. 9 This is the control input signal diagram for aircraft #2;

[0089] Fig.10 Tracking error diagram for vehicle #1 using different fractional-order operators. DETAILED DESCRIPTION

[0090] The control method of the present invention is further explained in conjunction with the attached diagrams.

[0091] The present application provides a method for refined fault-tolerant collaborative control of cluster aircraft based on dual event triggering. First, an aircraft dynamics model is constructed, and the influence of parameter uncertainty and actuator failure on the model is considered. The model is further changed to obtain a model under the influence of parameter uncertainty and actuator failure. Secondly, an event-triggered communication mechanism is constructed to communicate only when a specific event is triggered, and a distributed observer is constructed to estimate the aircraft reference command signal based on the discontinuous state information obtained by the event-triggered communication mechanism. After that, the Nussbaum function and adaptive neural network method are used to process actuator failures and parameter uncertainties. Finally, a fractional-order sliding mode fault-tolerant control strategy based on the event-triggered control mechanism is designed to reduce the consumption of computing resources and realize refined control of cluster aircraft.

[0092] (a) Establish the aircraft dynamics model.

[0093] Set up a group of formation aircraft consisting of N followers and 1 leader, where the dynamics of the i-th (i=1,2,…,N) follower aircraft is:

[0094]

[0095] Among them, x i ,y i and z i is the three-dimensional coordinate of the i-th aircraft, Represents x i First-order derivative, V i is the speed of the aircraft, χ i represents the heading angle, γ i Represents the flight path angle. i , D i , L i and Y i They are respectively the thrust, drag, lift and side force of the aircraft. i is the angle of attack, μ i is the tilt angle, β i is the sideslip angle. m is the mass of the aircraft, g is the coefficient of gravity acceleration;

[0096] Thrust, drag, lift and side force can be expressed as:

[0097]

[0098] Among them, ρ iT is the throttle opening, T max is the maximum thrust, ρ is the air density, s i is the wing area. iL , C iD and C iY They are lift coefficient, drag coefficient and side force coefficient, and the coefficients are expressed by the following formula:

[0099]

[0100] Among them, C iD0 , C iY0 and C iL0 is a constant, C iDα , C iLα and is the angle of attack α i The correlation coefficient, C iYβ is the side slip angle β i The coefficient of correlation;

[0101] Define u i =[ρ iT ,α i sinμ i,α i cosμ i ] T Input signal vector and p for the aircraft i =[x i ,y i ,z i ] T is the aircraft position information vector, simplifying (1) to obtain:

[0102]

[0103] Among them, f i and g i To simplify the obtained matrix, it is expressed as:

[0104]

[0105] (b) Establish the aircraft dynamics model under the influence of parameter uncertainty and actuator failure.

[0106] First, consider the parameter uncertainty. The dynamics of the aircraft with parameter uncertainty is expressed as:

[0107]

[0108] Among them, L id , D id and Y id are the unknown lift, drag and side force caused by parameter uncertainty. The remaining parameters are consistent with the aircraft model parameters in (a);

[0109] The unknown lift, drag and side force and uncertain parameters can be expressed as:

[0110]

[0111] Among them, C iDd , C iYd and C iLd is the unknown aerodynamic parameter, C iD0d , C iDαd , C iY0d , C iYβd , C iL0d and C iLαd is the unknown coefficient.

[0112] By considering the uncertainty of parameters, the vehicle dynamics equation (4) in step 1 is changed to:

[0113]

[0114] Among them, f i and g iSame as the definition in step 1, f id and g id is the unknown matrix caused by parameter uncertainty, which can be expressed as:

[0115]

[0116] Among them, M i It is given in (5).

[0117] Considering the actuator failure faced by the aircraft, the fault model is expressed as:

[0118] u i =ρ i u i0 +f ib (10) Among them, ρ i =diag{ρ i1 ,ρ i2 ,ρ i3}, ρ ij ∈(0,1] is the efficiency loss factor, j = 1, 2, 3, f ib =[f ib1 ,f ib2 ,f ib3 ] T represents deviation fault, u i0 It is the aircraft control input signal.

[0119] Combined with (8), the aircraft dynamics model considering parameter uncertainty and actuator failure can be expressed as:

[0120]

[0121] Among them, d i =f id +g i f ib +g id (ρ i u i0 +f ib ) is a lumped unknown term formed by the coupling of deviation fault and parameter uncertainty.

[0122] (c) Design an event-triggered communication mechanism and establish a distributed observer to estimate the aircraft reference command signal using the neighbor’s discontinuous state information.

[0123] Establish an event-triggered communication mechanism to save communication resources. With this communication mechanism, the i-th aircraft can only obtain the status information of neighboring aircraft when an event is triggered. Define the position trigger error of the i-th aircraft as The speed trigger error is in, and is the position and velocity information estimated by the distributed observer, and At the triggering moment The estimated position and velocity information, k i =0, 1, .... The first triggering time is set to The event-triggered communication mechanism is expressed as:

[0124]

[0125] in, Indicates the trigger time The next triggering moment of , inf{*} represents the infimum of a function, χ1, χ2, ξ1, ξ2 and ξ3 are positive constants designed, Ω i is a time-varying parameter, and its derivative is:

[0126]

[0127] Among them, Ω i (0) is the initial value of the event parameter, and δ1 is a positive design parameter.

[0128] Due to the event-triggered communication mechanism, the state information of neighboring aircraft received by the aircraft is discontinuous. This discontinuous state information cannot be directly used to design the control law of the aircraft. Therefore, a distributed observer is designed to obtain continuous state information. The designed distributed observer is:

[0129]

[0130] in, and is the position and velocity information estimated by the distributed observer, ψ i1 and ψ i2 The defined estimator coordinates position and velocity deviation, expressed as:

[0131]

[0132] Among them, a ij represents the communication weight between the i-th and j-th aircraft, b i represents the communication weight between the i-th aircraft and the leader aircraft, and is the jth aircraft at the trigger time Estimated position and velocity information, and Represents the leader aircraft at the triggering moment Position and velocity information.ij represents the distance between the i-th aircraft and the j-th aircraft, d i0 Represents the distance between the ith aircraft and the leader aircraft.

[0133] (d) An event-triggered control mechanism and fractional-order sliding surface are established. The Nussbaum function and adaptive neural network method are used to deal with actuator failures and parameter uncertainties, and event-triggered fault-tolerant control input signals are designed.

[0134] Establish an event-triggered control mechanism to save computing resources. Design the following control signal update mechanism:

[0135]

[0136] Among them, u i0 (t) is the aircraft control input signal, is the event triggering time, m i =0, 1, .... ν i It is the designed virtual control signal.

[0137] Design the following event trigger mechanism and update the control law when the event is triggered:

[0138]

[0139] in, Event trigger time The next triggering moment, z i (t) = v i (t)-u i0 (t) represents the controller trigger error, 0<α i1 <1 and β i1 >0 is the designed parameter.

[0140] Design fractional-order sliding surfaces to fine-tune the control performance of swarm aircraft. The fractional sliding surface is as follows:

[0141]

[0142] Among them, c i1 、c i2 and c i3 is a positive parameter of the design. and for e i The fractional derivative of i1 <1 and 0 <a i2 <1 is a fractional-order operator.

[0143] Define a time-varying vector γ i =[γi1 ,γ i2 ,γ i3 ] T , the Nussbaum function form used is γ i The derivative expression of is:

[0144]

[0145] Among them, λ i =diag{λ i1 ,λ i2 ,λ i3} is the designed matrix, λ i1 , i2 and λ i3 is a designed normal number. is the estimated value of the weight matrix, φ i (p i ,v i ) is the basis function, is the estimated value of the estimated bias.

[0146] Define X i =[p i ,v i ] T Indicates the aircraft status information, φ i (p i ,v i )=φ i (X i ) is a basis function containing n nodes, denoted as φ i (X i )=[φ i1 (X i ),φ i2 (X i ),…,φ ij (X i ),…φ in (X i )] T , where φ ij (X i ) is defined in Gaussian form:

[0147]

[0148] Among them, exp[a] represents the exponential to the power of a, υ i is the center value, N c For the width, it needs to be adjusted carefully.

[0149] and The derivative of is expressed as:

[0150]

[0151] Among them, k i2 and k i3 is a positive parameter of the design.

[0152] Define a virtual time-varying vector ε i =[ε i1 ,ε i2 ,ε i3 ] T , which can be expressed as:

[0153]

[0154] in, Yes i diagonal matrix;

[0155] The designed virtual control signal is:

[0156]

[0157] Among them, diag(ε i ) = diag{ε i1 ,ε i2 ,ε i3} is ε i The diagonal matrix of is a constant term, Λ i1 and Λ i2 is the designed time-varying vector, expressed as:

[0158]

[0159] Among them, tanh(*) is the hyperbolic tangent function, g i1 , g i2 and g i3 is the matrix g in step 1 i The column vector of i =[g i1 ,g i2 ,g i3 ], is a positive parameter.

[0160] Afterwards, the real control input signal u can be obtained through the event-triggered control mechanism. i0 .

[0161] (e) Use the designed fault-tolerant control law to track the reference command signal.

[0162] In order to verify the effectiveness of the present invention, the following experiments and analyses were performed:

[0163] Consider a fleet of four follower aircraft and one leader aircraft. The topology of the fleet is as follows: Figure 1 As shown. The topological weights are designed as: b1 = 1, b2 = 1, a 12 =0.7, a 13 =0.4, a 14 =0.4, a 23 =0.4, a 24 =0.4, a 34 =0.2. The control parameters are designed as follows: χ1=1, χ2=0.5, ξ1=0.01, ξ2=0.01, ξ3=0.01, δ1=0.1, α 11 =α 21 =α 31 =α 41 =0.05, β 11 =β 21 =β 31 =β 41 =0.02, c ij =0.1,i=1,2,3,4,j=1,2,3,a 11 =a 21 =a 31 =a 41 =0.35, a 12 =a 22 =a 32 =a 42 =0.65,λ 11 =λ 21 =λ 31 =5,λ 41 =10,λ 12 =λ 22 =λ 32 =20,λ 42 =10,λ 13 =λ 23 =λ 33 =λ4 43 =10, k 12 =k 22 =k 32 =k 42 =10, k 13 =k 23 =k 33 =k 43 =1, The parameter uncertainty is set to 20% of the normal parameter, i.e., C iDd =0.2C iD , C iYd =0.2C iY , C iLd =0.2C iL, i = 1, 2, 3, 4. Add actuator failure to aircraft #1 at t = 60s: ρ 11 =0.7,ρ 12 =1,ρ 13 =1,f 1b1 =0.2, f 1b2 =0,f 1b3 = 0. The flight path of the leader aircraft is: x0 = 0 + 30t, y0 = 0 - 2sin (0.1t), z0 = 1200 - 2sin (0.1t), and the preset distance between aircraft is: d 10 =[0,0,50] T , d 12 =[0,0,100] T , d 13 =[0,50,50] T , d 14 =[0,-50,50] T , d 20 =[0,0,-50] T , d 23 =[0,50,-50] T , d 24 =[0,-50,-50] T , d 34 =[0,-100,0] T . Figure 2 The structure of the designed fault-tolerant control method is presented.

[0164] The simulation results show that the dual-event triggered refined fault-tolerant collaborative control method designed in the present invention can effectively realize cluster collaboration and enable the aircraft to track the reference command signal. Figure 3 The position curve of the cluster aircraft is shown. It can be seen from the figure that each aircraft can fly in formation well, and the curve change trend is consistent with the position curve change trend of the leader aircraft, proving that the follower aircraft can follow the leader aircraft. Figure 4 This is the speed change curve of the cluster aircraft. It can be seen that the speed of the aircraft has a large oscillation in the initial stage, but as the controller takes effect, the amplitude decreases rapidly and finally tends to be consistent with the speed of the leader aircraft. Figure 5 The figure shows the tracking error of the follower vehicle to the reference command signal estimated by the distributed observer. It can be seen that the designed controller can track the reference signal well. Even when an actuator failure occurs, the controller can still work well to ensure that the tracking error does not exceed a certain range and finally converges the tracking error. Figure 6The figure shows the comparison between the number of event-triggered communications and the number of time-triggered communications. It can be seen that the use of event-triggered communication mechanism can effectively reduce the number of communications and save communication resources. Figure 7 and Figure 6 Similarly, the number of times the event-triggered control signal and the time-triggered control signal are updated is shown. It can be clearly seen that the use of the event-triggered control mechanism can significantly reduce the number of controller updates and save computing resources. Figure 8 and Fig. 9 The control input signals of aircraft #1 and aircraft #2 are shown respectively, from which we can see the role of event-triggered control. The signal will only change when the control input is updated, otherwise the control input remains unchanged. Compared with aircraft #2 without actuator failure, the control input u 01 There is a rapid increasing trend after adding the actuator failure to weaken the impact of the actuator failure, which proves that the designed fault-tolerant control method can effectively cope with sudden actuator failures. Fig.10 The tracking errors of aircraft #1 obtained using different fractional-order operators are shown. It can be seen that by adjusting the fractional-order operator, fine-tuning of the control performance can be achieved.

[0165] In summary, when actuator failures and parameter uncertainties occur in a cluster aircraft system with limited communication and computing resources, the refined fault-tolerant collaborative control method based on dual event triggering designed in the present invention can save communication and computing resources while achieving safe collaboration of cluster aircraft.

Claims

1. A method for fine-grained fault-tolerant collaborative control of cluster aircraft based on dual event triggering, characterized in that: The method comprises the following steps: Step 1: Establish the aircraft dynamics model; Step 2: Establish the aircraft dynamics model under the influence of parameter uncertainty and actuator failure; Step 3: Design an event-triggered communication mechanism and establish a distributed observer to estimate the aircraft reference command signal using the neighbor discontinuous state information; Step 4: Establish an event-triggered control mechanism and fractional-order sliding mode, use Nussbaum function and adaptive neural network method to deal with actuator failures and parameter uncertainties, and design event-triggered fault-tolerant control input signals.

2. The method according to claim 1, characterized in that: The aircraft dynamics model established in step 1 is as follows: Suppose a group of N followers and 1 leader flying in formation, where the dynamics of the i-th follower aircraft, i = 1, 2, ..., N, is: Among them, x i ,y i and z i is the three-dimensional coordinate of the i-th aircraft, Represents x i First-order derivative, V i is the speed of the aircraft, χ i represents the heading angle, γ i represents the flight path angle; T i , D i , L i and Y i They are respectively the thrust, drag, lift and side force of the aircraft; α i is the angle of attack, μ i is the tilt angle, β i is the sideslip angle; m is the mass of the aircraft, g is the coefficient of gravity acceleration; The thrust, drag, lift and side force are expressed as: Among them, ρ iT is the throttle opening, T max is the maximum thrust, ρ is the air density, C is the wing area; iL , C iD and C iY They are lift coefficient, drag coefficient and side force coefficient, and the coefficients are expressed by the following formula: Among them, C iD0 , C iY0 and C iL0 is a constant, C iDα , C iLα and is the angle of attack α i The correlation coefficient, C iYβ is the side slip angle β i The coefficient of correlation; Define u i =[ρ iT ,α i sinμ i ,α i cosμ i ] T Input signal vector and p for the aircraft i =[x i ,y i ,z i ] T is the aircraft position information vector, and formula (1) is simplified to: Among them, f i and g i To simplify the obtained matrix, it is expressed as:

3. The method according to claim 1, characterized in that: The aircraft dynamics model under the influence of parameter uncertainty and actuator failure established in step 2 is as follows: The dynamics of the aircraft with parameter uncertainty is assumed to be: Among them, L id , D id and Y id are the unknown lift, drag and side force caused by parameter uncertainty, respectively; The unknown lift, drag and side force and uncertain parameters are expressed as: Among them, C iDd , C iYd and C iLd is the unknown aerodynamic parameter, C iD0d , C iDαd , C iY0d , C iYβd , C iL0d and C iLαd is the unknown coefficient; Change the aircraft dynamics equation (4) in step 1 to: Among them, f i and g i Same as the definition in step 1, f id and g id is the unknown matrix caused by parameter uncertainty, expressed as: Among them, M i It has been given in (5); Considering the actuator failure faced by the aircraft, the fault model is expressed as: in i =ρ i in i0 +f ib (10) Among them, ρ i =diag{ρ i1 ,ρ i2 ,ρ i3 }, ρ ij ∈(0,1] is the efficiency loss factor, j = 1, 2, 3, f ib =[f ib1 ,f ib2 ,f ib3 ] T represents deviation fault, u i0 is the aircraft control input signal; Combined with (8), the aircraft dynamics model considering parameter uncertainty and actuator failure is expressed as: Among them, d i =f id +g i f ib +g id (ρ i u i0 +f ib ) is a lumped unknown term formed by the coupling of deviation fault and parameter uncertainty.

4. The method according to claim 1, characterized in that: The event-triggered communication mechanism and distributed observer established in step 3 are as follows: Design event-triggered communication mechanism: The i-th aircraft can only obtain the status information of neighboring aircraft when the event is triggered; the position trigger error of the i-th aircraft is defined as and the speed trigger error is in, and is the position and velocity information estimated by the distributed observer, and At the triggering moment The estimated position and velocity information, k i =0, 1, ...; the first triggering time is set to The event-triggered communication mechanism is: in, Indicates the trigger time The next triggering moment of , inf{*} represents the infimum of a function, χ1, χ2, ξ1, ξ2 and ξ3 are positive constants designed, Ω i is a time-varying parameter, and its derivative is: Among them, Ω i (0) is the initial value of the event parameter, and δ1 is a positive design parameter; A distributed observer is designed to obtain continuous state information. The distributed observer is: in, and is the position and velocity information estimated by the distributed observer, ψ i1 and ψ i2 The defined estimator coordinates position and velocity deviation, expressed as: Among them, a ij represents the communication weight between the i-th and j-th aircraft, b i represents the communication weight between the i-th aircraft and the leader aircraft, and is the jth aircraft at the trigger time Estimated position and velocity information, and Represents the leader aircraft at the triggering moment Position and velocity information; d ij represents the distance between the i-th aircraft and the j-th aircraft, d i0 Represents the distance between the ith aircraft and the leader aircraft.

5. The method according to claim 1, characterized in that: The step 4 is specifically as follows: Establish event-triggered control mechanisms: Design the following control signal update mechanism: Among them, u i0 (t) is the aircraft control input signal, is the event triggering time, m i =0, 1, ...; v i is the designed virtual control signal; Design the following event trigger mechanism and update the control law when the event is triggered: in, Event trigger time The next triggering moment, z i (t) = v i (t)-u i0 (t) represents the controller trigger error, 0<α i1 <1 and β i1 >0 is the designed parameter; Design the fractional sliding surface and define The fractional sliding surface is as follows: Among them, S i is the designed sliding surface, c i1 、c i2 and c i3 is the positive parameter of the design; and Represents e i The fractional derivative of i1 <1 and 0 <a i2 <1 is a fractional-order operator; Define a time-varying vector r i =[γ i1 ,γ i2 ,γ i3 ] T , the Nussbaum function form used is γ i The derivative expression of is: Among them, λ i =diag{λ i1 ,λ i2 ,λ i3 } is the designed diagonal matrix, λ i1 , i2 and λ i3 is a designed normal number; is the estimated value of the weight matrix, φ i (p i ,v i ) is the basis function, is the estimated value of the estimated bias; Define X i =[p i ,v i ] T Indicates the aircraft status information, φ i (p i ,v i )=φ i (X i ) is a basis function containing n nodes, represented by φ i (X i )=[φ i1 (X i ),φ i2 (X i ),…,φ ij (X i ),…φ in (X i )] T , where φ ij (X i ) is in Gaussian form: Among them, exp[a] represents the exponential a, v i is the center value, N c is the width; and The derivative of is expressed as: Among them, k i2 and k i3 is the positive parameter of the design; Define a virtual time-varying vector ε i =[ε i1 ,ε i2 ,ε i3 ] T , which is expressed as: in, Yes i diagonal matrix; Design the virtual control signal as: Among them, diag(ε i ) = diag{ε i1 ,ε i2 ,ε i3 } is ε i The diagonal matrix of is a constant term, Λ i1 and Λ i2 is the designed time-varying vector, expressed as: Among them, tanh(*) is the hyperbolic tangent function, g i1 , g i2 and g i3 is the matrix g in step 1 i The column vector of i =[g i1 ,g i2 ,g i3 ], is a positive parameter.

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