A preset-precision distributed synchronization tracking control method considering input nonlinearity

Abstract

A preset precision distributed synchronization tracking control method considering input nonlinearity is provided, which comprises the following steps: a mathematical model of an unknown input nonlinear multi-agent system is established; a non-affine unknown input nonlinear model is converted into a non-affine model, and a mathematical model of the multi-agent system available for control design is established; a neural network is used to process system modeling uncertainty, a boundary estimation technique is used to process system gain function unknown problem to design a control law; based on a minimum learning parameter technique, an adaptive robust term is designed to estimate a neural network weight vector, and a final control law is obtained. The method can be used for high-precision control of a multi-agent system with unknown prior knowledge of input nonlinearity, and can guarantee the asymptotic convergence stability and control performance of the system.

Description

Technical Field

[0001] This invention relates to flight control technology, and more specifically to a preset accuracy distributed synchronous tracking control method for a multi-agent system that considers the nonlinearity of control input. Background Technology

[0002] In recent years, the synchronization control problem of multi-agent systems has attracted much attention due to its wide application in fields such as spacecraft formation flight, UAV cooperative flight, automated highway system scheduling, and air traffic control. Developing distributed control strategies based on local information of multi-agent systems is of great significance for enhancing the robustness and fault tolerance of these systems.

[0003] In the real world, most multi-agent systems (e.g., multi-UAV systems, intelligent robot systems, etc.) face input nonlinearity problems such as limitations, dead zones, and backlash. Input nonlinearity has a significant adverse impact on the stability and control performance of multi-agent systems, and ignoring input nonlinearity in control design may lead to catastrophic consequences. However, existing multi-agent control design methods that consider input nonlinearity (B. Wang, W. Chen, J. Wang, B. Zhang and P. Shi, Semiglobal Tracking Cooperative Control for Multiagent Systems With Input Saturation: A Multiple Saturation Levels Framework, IEEE Transactions on Automatic Control, Vol. 66, no. 3, pp. 1215-1222, 2021.) only address control design for a specific type of input nonlinearity and cannot cope with problems where the input nonlinearity information is completely unknown or multiple input nonlinearities coexist, lacking universality.

[0004] Furthermore, to address the uncertainty problem in modeling multi-agent systems, existing literature often employs neural networks (NNs) or fuzzy logic systems (FLSs) for approximation estimation (S. Zheng, P. Shi, S. Wang and Y. Shi, Adaptive Neural Control for a Class of Nonlinear Multiagent Systems, IEEE Transactions on Neural Networks and Learning Systems, vol. 32, no. 2, pp. 763-776, 2021.). However, the introduction of NNs and FLSs makes it impossible to achieve asymptotic stability of the closed-loop system in the control design, reducing control convergence performance and preventing the achievement of preset precision control. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention proposes a preset-precision distributed synchronous tracking control method that considers input nonlinearity, specifically including the following steps:

[0006] Step 1: For the following multi-agent system consisting of N agents, considering nonlinear input:

[0007]

[0008] Where t represents time, k = 1, 2, ..., N, i = 1, 2, ..., n, N and n represent the number of agents and the model order of each agent, respectively, and χ k，i Let i be the state variable of the k-th agent. χ is a vector consisting of the first to the ith state variables of the k-th agent. k，i Represents χ k，i The derivative of , where "·" denotes the derivative. Let be the unknown smooth function of the i-th order subsystem of the k-th agent. For ease of representation, let be... Abbreviated as f k，i u k Let v be the desired control input for the k-th agent. k Let y be the actual control input of the k-th agent. k For the system output of the k-th agent, d k，i Let be the unknown external disturbance of the i-th order subsystem of the k-th agent, and satisfy . in Let Φ be an unknown positive constant. k (u k () represents a nonlinear function with completely unknown input information;

[0009] Step 2: Considering the physical limitations of the actual input to the multi-intelligent system, there exists an unknown normal number A. k1 A k2 A k3 A k4 and the unknown constant B k1 B k2 B k3 B k4 The following inequalities must be satisfied:

[0010]

[0011] In addition, there are unknown functions. and Make:

[0012]

[0013] For the sake of convenience, the table will be... Abbreviated as

[0014] Define the transformation function α k and β k as follows:

[0015]

[0016] It is easy to see that the above function satisfies

[0017]

[0018] Among them, three boundary constants α km α kM and β kM The definitions are respectively

[0019]

[0020] In (6), min represents the minimum value and max represents the maximum value;

[0021] Based on the above analysis, v k The expression is

[0022] v k =Φ k (u k )=α k u k +β k (7)

[0023] Based on the above analysis, the multi-agent system model (1) can be represented in the following form that can be used for control design:

[0024]

[0025] Step 3: Introduce the order reduction function Υ k，i :

[0026]

[0027] and switching function κ k，i

[0028]

[0029] Where, ε k，i The design parameters of the i-th subsystem of the k-th intelligent agent set by the user, e k，i The independent variables of the order reduction function and the switching function are the tracking error of the i-th subsystem of the k-th agent;

[0030] It is easy to know the function Υ k，i For e k，i It is smooth, first-order differentiable, and has the following properties:

[0031]

[0032]

[0033] In the formula, [κ k，i ] n Indicates κ k，i The nth power;

[0034] Step 4: Define the synchronization tracking error of the multi-agent system

[0035]

[0036] Among them, y kd For the desired output trajectory, ζ k，i-1 For the virtual control law to be designed for the (i-1)th subsystem of the k-th agent, b kj This represents the communication status between the k-th agent and the j-th agent, b. kj =1 indicates that communication is possible, b kj =0 indicates no communication, a k For positive design parameters; a k (y k -y kd ) in a k The relationship between y and parentheses is multiplication; j The system output representing the j-th agent, according to this definition, is y. kd How to understand this? kd The expected output trajectory represents the system output of the i-th agent, y. k It is the system output of the k-th agent;

[0037] Differentiating the above equation, we get:

[0038]

[0039] Among them, c k The definition of

[0040] Step 5: Define the following generalized disturbance term Δ k，1 Δ k，i Δ k，n :

[0041]

[0042] Introduce a neural network to approximate the above generalized perturbation term:

[0043]

[0044] in Let ψ be the expected weight vector. k，i Given radial basis functions, ι k，i The approximation error is unknown, and there are unknown positive constants. satisfy

[0045] Define the weight function ω k，i Kernel function ψ k，i The subscript k and i represent the i-th subsystem of the k-th agent:

[0046]

[0047] Where τ k，i For the constants used in the definition;

[0048] Step 6: Design the first-level virtual control law ζ k，1 and adaptive law

[0049]

[0050]

[0051] Design the virtual control law at the i-th level ζ k，i and adaptive parameters

[0052]

[0053]

[0054] In the formula, λ k，i σ k，i User-defined constants For ωk，i The estimated value, for The derivative;

[0055] Design the nth i Layer actual control law u k Intermediate control law u′ k Virtual control law ζ k，n and adaptive parameters and

[0056]

[0057] u′ k =-Υ k，n |ζ k，n | (23)

[0058]

[0059]

[0060]

[0061] In the formula, represent The derivative of Represents the adaptive parameter, ρ k，n The user defines the design parameters for the nth subsystem of the kth agent.

[0062] In one embodiment of the present invention, in a multi-UAV system consisting of N UAVs, the specific process of the present invention is as follows:

[0063] Step 1: The following attitude synchronization tracking control model for a multi-UAV system consisting of N UAVs is given:

[0064] R(Ω k )Ω k =ω k (27)

[0065] J k ω k =-S(ω) k )J k ω k +M ak +Ckδ k +J k d ωk (28)

[0066] In the formula, k = 1, 2, ..., N, Ω k =[φ k θ k , ψk ] T Let φ be the Euler attitude angle of the UAV. k θ k , ψ k These are the roll angle, pitch angle, and yaw angle of the k-th UAV, respectively, R(Ω) k ) is the transformation matrix, ω k =[ pk , qk r k ] T p is the angular velocity of the drone. k q k r k These are the roll rate, pitch rate, and yaw rate of the k-th UAV, respectively, J k Let S(ω) be the inertia matrix. k ) is ω k Regarding the antisymmetric matrix, M ak For the aerodynamic torque related to flight conditions, C k For the control effectiveness matrix, δ k =[δ ak δ ek δ rk ] T δ is the actual control surface deflection angle. ak δ ek δ rk These are the aileron deflection angle, elevator deflection angle, and rudder deflection angle of the k-th UAV, respectively, d ωk External disturbance;

[0067] Assume the control surfaces of the UAV are subject to the following nonlinear input:

[0068]

[0069] Where δ k δ is the actual control surface deflection angle. ck The deflection angle is the command angle. For unknown input nonlinear functions, it is a function composed of one or more input nonlinear types such as saturation, dead zone, hysteresis, etc., and considers the number of non-differentiable cases in non-affine form;

[0070] Step 2: Convert the multi-drone model into a model that can be used for control as follows:

[0071] Ω k =R -1 (Ω k )ω k (30)

[0072]

[0073] In the formula, α k β k These are functions represented by equation (7);

[0074] Step 3: Introduce the order reduction function Υ k，m (e k，m (m=φ) k θ k , ψ k , pk , qk , rk ):

[0075]

[0076] and switching function κ k，m (e k，m )

[0077]

[0078] Where ε k，m Design parameters set by the user;

[0079] Step 4: Define the synchronization tracking error of the multi-agent system

[0080]

[0081] e ω，k =ω k -ω dk (35) Among them, b kj This represents the communication status between the k-th drone and the j-th drone, b. kj =1 indicates that communication is possible, b kj =0 indicates no communication, a Ωk For positive design parameters; c Ωk The definition of ω dk For virtual control laws;

[0082] Step 5: Define the following generalized disturbance term Δ k :

[0083]

[0084] Where, Δ pk Δ qk Δ rk They are Δ k Components in the roll, pitch, and yaw directions;

[0085] Introducing a neural network to approximate the above generalized perturbation term Δ k The components Δ in the roll, pitch, and yaw directions lk (Δ when l = p, q, r)lk They represent Δ pk Δ qk Δ rk ):

[0086]

[0087] in, ι lk These are the weight vector, radial basis function, and approximation residual of the l-th state of the k-th UAV, respectively, where l = p, q, r;

[0088] For ease of explanation later, the weight function η is defined. kω Kernel function Θ k Intermediate kernel function Θ kl :

[0089]

[0090] in, For ι lk The upper bound of τ lk A user-defined constant, Υ k，m For a reduced-order function, η lk Let Θ be a parameter to be estimated. k Let Θ be a function vector. lk (l=p,q,r) is Θ pk Θ qk Θ rk Simplified representation;

[0091] Step 6: Design the desired angular rate ω dk Actual control law δ ck Intermediate control law δ′ ck Virtual control law δ 0k and adaptive parameters as follows:

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098] Where R is the transformation matrix, z k1 z k2 , ck3 ,ck4 ε wk π wk1 π wk2 All parameters are user-designed, I3 is the identity matrix, and ω dk The desired angular velocity ω dk The derivative of For adaptive parameters The derivative of For adaptive parameters The derivative of .

[0099] Compared with the prior art, the advantages of the present invention are as follows:

[0100] (1) For multi-intelligent systems with multiple input nonlinear functions and completely unknown information, step 1 establishes a general input nonlinear model, but this is difficult to implement for control design. Step 2 uses an approximate transformation method to transform the non-affine form of the input nonlinear function v. k =Φ(u k (t) is converted to pseudo-affine form v k =Φ k (u k (t))=α k (u k )u k +β k (u k In step 6, the boundary estimation method is used to process the unknown gain function, so as to realize the control design for cases where the input nonlinearity type is unknown and there may be multiple input nonlinearity types.

[0101] (2) The present invention introduces a reduced-order smooth switching function in the control design, which can ensure the continuity and differentiability of the control law, and at the same time achieve preset precision control. Attached Figure Description

[0102] Figure 1 The control design flowchart is shown;

[0103] Figure 2 This diagram illustrates the input nonlinearity.

[0104] Figure 3 The system output convergence process is shown under the simultaneous influence of saturation and dead zone.

[0105] Figure 4 The convergence process of the system state variables is shown under the simultaneous influence of saturation and dead zone.

[0106] Figure 5 The convergence process of the adaptive law is shown under the simultaneous influence of saturation and dead zone.

[0107] Figure 6 The system output convergence process is shown under the simultaneous influence of saturation and backlash.

[0108] Figure 7 The convergence process of the system state variables is shown under the simultaneous influence of saturation and backlash.

[0109] Figure 8 The convergence process of the adaptive law is shown under the simultaneous influence of saturation and backlash. Detailed Implementation

[0110] The present invention will now be described in detail with reference to the accompanying drawings.

[0111] The flowchart of the method of the present invention is as follows Figure 1 As shown, the specific steps include the following.

[0112] Step 1: For the following multi-agent system consisting of N agents, considering nonlinear input:

[0113]

[0114] Where t represents time, k = 1, 2, ..., N, i = 1, 2, ..., n, N and n represent the number of agents and the model order of each agent, respectively, and χ k，i Let i be the state variable of the k-th agent. χ is a vector consisting of the first to the ith state variables of the k-th agent. k，i Represents χ k，i The derivative of , where "·" denotes the derivative. Let be the unknown smooth function of the i-th order subsystem of the k-th agent. For ease of representation, let be... Abbreviated as f k，i u k Let v be the desired control input for the k-th agent. k Let y be the actual control input of the k-th agent. k For the system output of the k-th agent, d k，i Let be the unknown external disturbance of the i-th order subsystem of the k-th agent, and satisfy . in Let Φ be an unknown positive constant. k (u k ) represents a completely unknown input nonlinear function, Φ k (u k ) can be Figure 2 One or more waveforms.

[0115] Step 2: Considering the physical limitations of the actual input to the multi-intelligent system, there exists an unknown normal number A. k1 A k2 A k3 A k4 and the unknown constant B k1 Bk2 B k3 B k4 The following inequalities must be satisfied:

[0116]

[0117] In addition, there are unknown functions. and Make:

[0118]

[0119] For ease of expression, Abbreviated as

[0120] Define the transformation function α k and β k as follows:

[0121]

[0122] It is easy to see that the above function satisfies

[0123]

[0124] Among them, three boundary constants α km α kM and β kM The definitions are respectively

[0125]

[0126] In (6), min represents the minimum value and max represents the maximum value.

[0127] Based on the above analysis, v can be... k The expression is

[0128] v k =Φ k (u k )=α k u k +β k (7)

[0129] Based on the above analysis, the multi-agent system model (1) can be represented in the following form, which can be used for control design:

[0130]

[0131] Step 3: Introduce the order reduction function Υ k，i :

[0132]

[0133] and switching function κk，i

[0134]

[0135] Where, ε k，i The design parameters of the i-th subsystem of the k-th intelligent agent set by the user, e k，i The independent variables of the order reduction function and the switching function are the tracking error of the i-th subsystem of the k-th agent.

[0136] It is easy to know the function Υ k，i For e k，i It is smooth, first-order differentiable, and has the following properties:

[0137]

[0138]

[0139] In the formula, [κ k，i ] n Indicates κ k，i The nth power.

[0140] Step 4: Define the synchronization tracking error of the multi-agent system

[0141]

[0142] Among them, y kd For the desired output trajectory, ζ k，i-1 For the virtual control law to be designed for the (i-1)th subsystem of the k-th agent, b kj This represents the communication status between the k-th agent and the j-th agent, b. kj =1 indicates that communication is possible, b kj =0 indicates no communication, a k These are positive design parameters. k (y k -y kd ) in a k The relationship between y and parentheses is multiplication. j The system output represents the j-th agent.

[0143] Differentiating the above equation, we get:

[0144]

[0145] Among them, c k The definition of

[0146] Step 5: Define the following generalized disturbance term Δ k，1 Δ k，i Δ k，n :

[0147]

[0148] Introduce a neural network to approximate the above generalized perturbation term:

[0149]

[0150] in Let ψ be the expected weight vector. k，i Given radial basis functions, ι k，i The approximation error is unknown, and there are unknown positive constants. satisfy

[0151] Define the weight function ω k，i Kernel function ψ k，i (subscript) k，i (Representing the i-th subsystem of the k-th agent):

[0152]

[0153] Where τ k，i These are constants used for definition.

[0154] Step 6: Design the first-level virtual control law and adaptive law

[0155]

[0156]

[0157] Design the virtual control law at the i-th level ζ k，i and adaptive parameters

[0158]

[0159]

[0160] In the formula, λ k，i σ k，i User-defined constants For ω k，i The estimated value, for The derivative of σ. k，i (|e k，i |-ε k，i ) in σ k，i The relationship between the parentheses and the expression indicates multiplication.

[0161] Design the nth i Layer actual control law u k Intermediate control law u′ kVirtual control law ζ k，n and adaptive parameters and

[0162]

[0163] u′ k =-Υ k，n |ζ k，n | (23)

[0164]

[0165]

[0166]

[0167] In the formula, represent The derivative of Represents the adaptive parameter, ρ k，n The user defines the design parameters for the nth subsystem of the kth agent. Specific Implementation

[0169] According to the specific implementation steps of the technical solution of the present invention, the following embodiment is given.

[0170] Step 1: The following attitude synchronization tracking control model for a multi-UAV system consisting of N UAVs is given:

[0171] R(Ω k )Ω k =ω k (27)

[0172] J k ω k =-S(ω) k )J k ω k +M ak +Ckδ k +J k d ωk (28)

[0173] In the formula, k = 1, 2, ..., N, Ω k =[φ k θ k , ψ k ] T Let φ be the Euler attitude angle of the UAV. k θ k , ψ k These are the roll angle, pitch angle, and yaw angle of the k-th UAV, respectively, R(Ω) k ) is the transformation matrix, ωk =[p k q k r k ] T p is the angular velocity of the drone. k q k r k These are the roll rate, pitch rate, and yaw rate of the k-th UAV, respectively, J k Let S(ω) be the inertia matrix. k ) is ω k Regarding the antisymmetric matrix, M ak For the aerodynamic torque related to flight conditions, C k For the control effectiveness matrix, δ k =[δ ak δ ek δ rk ] T δ is the actual control surface deflection angle. ak δ ek δ rk These are the aileron deflection angle, elevator deflection angle, and rudder deflection angle of the k-th UAV, respectively, d ωk This is an external disturbance.

[0174] Assume the control surfaces of the UAV are subject to the following nonlinear input:

[0175]

[0176] Where δ k δ is the actual control surface deflection angle. ck The deflection angle is the command angle. For unknown input nonlinear functions, it is a function composed of one or more input nonlinear types such as saturation, dead zone, hysteresis, etc., and considers the number of nondifferentiable cases in nonaffine form.

[0177] Step 2: Following the steps of this invention, convert the multi-UAV model into a controllable model as follows:

[0178] Ω k =R -1 (Ω k )ω k (30)

[0179]

[0180] In the formula, α k β k These are functions represented by equation (7).

[0181] Step 3: Introduce the order reduction function Υ k，m (e k，m (m=φ)k θ k , ψ k p k q k r k ):

[0182]

[0183] and switching function κ k，m (e k，m )

[0184]

[0185] Where ε k，m Design parameters set by the user.

[0186] Step 4: Define the synchronization tracking error of the multi-agent system

[0187]

[0188] e ω，k =ω k -ω dk (35)

[0189] Among them, b kj This represents the communication status between the k-th drone and the j-th drone, b. kj =1 indicates that communication is possible, b kj =0 means communication is not possible, This is a positive design parameter. Ωk The definition of ω dk This is a virtual control law.

[0190] Step 5: Define the following generalized disturbance term Δ k :

[0191]

[0192] Where, Δ pk Δ qk Δ rk They are Δ k The components in the roll, pitch, and yaw directions.

[0193] Introducing a neural network to approximate the above generalized perturbation term Δ k The components Δ in the roll, pitch, and yaw directions lk (Δ when l = p, q, r) lk They represent Δ pk Δ qk Δ rk ):

[0194]

[0195] in, ι lk These are the weight vector, radial basis function, and approximation residual of the l-th (l = p, q, r) state of the k-th UAV, respectively.

[0196] For ease of explanation later, the weight function η is defined. kω Kernel function Θ k Intermediate kernel function Θ kl :

[0197]

[0198] in, For ι lk The upper bound of τ lk A user-defined constant, Υ k，m Let η be the order reduction function defined above. lk Let Θ be a parameter to be estimated. k Let Θ be a function vector. lk (l=p,q,r) is Θ pk Θ qk Θ rk A simplified representation of .

[0199] Step 6: Design the desired angular rate ω dk Actual control law δ ck Intermediate control law δ′ ck Virtual control law δ 0k and adaptive parameters as follows:

[0200]

[0201]

[0202]

[0203]

[0204]

[0205]

[0206] Where R is the transformation matrix, z k1 z k2 c k3 c k4 ε wk π wk1 π wk2 All parameters are user-designed, I3 is the identity matrix, and ωdk The desired angular velocity ω dk The derivative of For adaptive parameters The derivative of For adaptive parameters The derivative of .

[0207] Simulations were performed to verify the effects of saturation and dead zone on the control input of the multi-agent system, and simultaneously on saturation and backlash.

[0208] Figures 1-3 The simulation results are for the effects of saturation and dead zone.

[0209] Figures 4-6 The simulation results are for the effects of saturation and backlash.

[0210] Depend on Figures 1-6 It is evident that regardless of the type of input nonlinearity affecting the control input, regardless of whether the input nonlinearity information is unknown, and regardless of whether there is only one type of input nonlinearity or multiple types of input nonlinearities, the method of this invention can guarantee the stability of the system and has good control performance. The closed-loop system can achieve asymptotic stability and can achieve preset precision control.

[0211] This invention proposes a novel pre-precision adaptive control method for multi-agent systems affected by unknown input nonlinearity. This method effectively overcomes the technical shortcomings of existing multi-agent system control methods, which can only handle deterministic input nonlinearity and cannot achieve pre-precision control. It can handle control problems where the input nonlinearity information is completely unknown, as well as control problems where multiple input nonlinearities coexist. The method includes: establishing a mathematical model of the multi-agent system with unknown input nonlinearity; transforming the nonlinear model with unknown input into a nonlinear model to establish a mathematical model of the multi-agent system suitable for control design; using neural networks to handle the uncertainty in system modeling; using boundary estimation techniques to handle the unknown system gain function and designing a control law; and designing an adaptive robust term based on minimum learning parameter techniques to estimate the neural network weight vector and obtain the final control law. This method can be used for high-precision control of multi-agent systems with unknown prior knowledge of input nonlinearity, ensuring the asymptotic convergence stability and control performance of the system.

Claims

1. A preset-precision distributed synchronous tracking control method considering input nonlinearity, characterized in that, Specifically, the following steps are included: Step 1: For the following multi-agent system consisting of N agents, considering nonlinear input: Where t represents time, k = 1, 2, ..., N, i = 1, 2, ..., n, N and n represent the number of agents and the model order of each agent, respectively, and χ k，i Let i be the state variable of the k-th agent. It is a vector consisting of the first to the ith state variables of the k-th agent. Represents χ k，i The derivative, where "·" denotes the derivative. Let be the unknown smooth function of the i-th order subsystem of the k-th agent. For ease of representation, let be... Abbreviated as f k,i ,u k Let v be the desired control input for the k-th agent. k Let y be the actual control input of the k-th agent. k For the system output of the k-th agent, d k，i Let be the unknown external disturbance of the i-th order subsystem of the k-th agent, and satisfy . in Let Φ be an unknown positive constant. k (u k () represents a nonlinear function with completely unknown input information; Step 2: Considering the physical limitations of the actual input to the multi-intelligent system, there exists an unknown normal number A. k1 A k2 A k3 A k4 and the unknown constant B k1 B k2 B k3 B k4 The following inequalities must be satisfied: In addition, there are unknown functions. and Make: For ease of expression, Abbreviated as Define the transformation function α k and β k as follows: It is easy to see that the above function satisfies Among them, three boundary constants α km α kM and β kM The definitions are respectively In (6), min represents the minimum value and max represents the maximum value; Based on the above analysis, v k The expression is v k =Φ k (u k )=a k you k +b k (7) Based on the above analysis, the multi-agent system model (1) can be represented in the following form that can be used for control design: Step 3: Introduce the order reduction function Υ k，i : and switching function κ k,i Where, ε k，i The design parameters of the i-th subsystem of the k-th intelligent agent set by the user, e k，i The independent variables of the order reduction function and the switching function are the tracking error of the i-th subsystem of the k-th agent; It is easy to know the function Υ k，i For e k,i It is smooth, first-order differentiable, and has the following properties: In the formula, [κ k，i ] n Indicates κ k，i The nth power; Step 4: Define the synchronization tracking error of the multi-agent system Among them, y kd For the desired output trajectory, ζ k,i-1 For the virtual control law to be designed for the (i-1)th subsystem of the k-th agent, b kj This represents the communication status between the k-th agent and the j-th agent, b. kj =1 indicates that communication is possible, b kj =0 indicates no communication, a k For positive design parameters; a k (y k -y kd ) in a k The relationship between y and parentheses is multiplication; j y represents the system output of the j-th agent. kd The expected output trajectory represents the system output of the i-th agent, y. k It is the system output of the k-th agent; Differentiating the above equation, we get: Among them, c k The definition of Step 5: Define the following generalized disturbance term Δ k，1 Δ k，i Δ k，n : Introduce a neural network to approximate the above generalized perturbation term: in Let ψ be the expected weight vector. k，i Given radial basis functions, ι k，i The approximation error is unknown, and there are unknown positive constants. satisfy Define the weight function ω k，i Kernel function The subscript k, i represents the i-th subsystem of the k-th agent: Where τ k，i For the constants used in the definition; Step 6: Design the first-level virtual control law ζ k，1 and adaptive law Design the virtual control law at the i-th level ζ k，i and adaptive parameters In the formula, λ k，i σ k，i User-defined constants For ω k，i The estimated value, for The derivative; Design the nth i Layer actual control law u k Intermediate control law u′ k Virtual control law ζ k，n and adaptive parameters and In the formula, represent The derivative of Represents the adaptive parameter, ρ k，n The user defines the design parameters for the nth subsystem of the kth agent.

2. The preset precision distributed synchronous tracking control method considering input nonlinearity as described in claim 1, characterized in that, In a multi-UAV system consisting of N UAVs, the specific process is as follows: Step 1: The following attitude synchronization tracking control model for a multi-UAV system consisting of N UAVs is given: In the formula, k = 1, 2, ..., N, Ω k =[φ k θ k , ψ k ] T Let φ be the Euler attitude angle of the UAV. k θ k , ψ k These are the roll angle, pitch angle, and yaw angle of the k-th UAV, respectively, R(Ω) k ) is the transformation matrix, ω k =[p k q k r k ] T p is the angular velocity of the drone. k q k r k These are the roll rate, pitch rate, and yaw rate of the k-th UAV, respectively, J k Let S(ω) be the inertia matrix. k ) is ω k Regarding the antisymmetric matrix, M ak For the aerodynamic torque related to flight conditions, C k For the control effectiveness matrix, δ k =[δ ak δ ek δ rk ] T δ is the actual control surface deflection angle. ak δ ek δ rk These are the aileron deflection angle, elevator deflection angle, and rudder deflection angle of the k-th UAV, respectively, d ωk External disturbance; Assume the control surfaces of the UAV are subjected to the following nonlinear input: Where δ k δ is the actual control surface deflection angle. ck This is the command deflection angle. For unknown input nonlinear functions, it is a function composed of one or more input nonlinear types such as saturation, dead zone, hysteresis, etc., and considers the number of non-differentiable cases in non-affine form; Step 2: Convert the multi-drone model into a model that can be used for control as follows: In the formula, α k β k These are functions represented by equation (7); Step 3: Introduce the order reduction function Υ k，m (e k，m ), m=φ k θ k , ψ k p k q k r k : and switching function κ k，m (e k，m ) Where ε k,m Design parameters set by the user; Step 4: Define the synchronization tracking error of the multi-agent system e ω,k =ω k -oh dk (35) Among them, b kj This represents the communication status between the k-th drone and the j-th drone, b. kj =1 indicates that communication is possible, b kj =0 indicates no communication, a Ωk For positive design parameters; c Ωk The definition of ω dk For virtual control laws; Step 5: Define the following generalized disturbance term Δ k : Where, Δ pk Δ qk Δ rk They are Δ k Components in the roll, pitch, and yaw directions; Introducing a neural network to approximate the above generalized perturbation term Δ k The components Δ in the roll, pitch, and yaw directions lk (Δ when l = p, q, r) lk They represent Δ pk Δ qk Δ rk) : in, ι lk These are the weight vector, radial basis function, and approximation residual of the l-th state of the k-th UAV, respectively, where l = p, q, r; For ease of explanation later, the weight function η is defined. kω Kernel function Intermediate kernel function Θ kl : in, For ι lk The upper bound of τ lk A user-defined constant, Υ k，m For a reduced-order function, η lk For a parameter to be estimated, Let Θ be a function vector. lk (l = p, q, r) is Θ pk Θ qk Θ rk Simplified representation; Step 6: Design the desired angular rate ω dk Actual control law δ ck Intermediate control law δ′ ck Virtual control law δ 0k and adaptive parameters as follows: Where R is the transformation matrix, z k1 z k2 c k3 c k4 ε wk π wk1 π wk2 All parameters are user-designed; I3 is the identity matrix. The desired angular velocity ω dk The derivative of For adaptive parameters The derivative of For adaptive parameters The derivative of .

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