Non-linear multi-agent system output feedback consistency control method

Abstract

The invention discloses a non-linear multi-agent system output feedback consistency control method, and belongs to the technical field of non-linear multi-agent system control. The method comprises the following steps: acquiring a multi-agent system comprising a leader and a plurality of followers; constructing a state observer according to the estimated value of the state variable of the follower; acquiring an auxiliary function and a dynamic surface with a nonlinear filter; on the basis of the state observer, the auxiliary function and the dynamic surface with the nonlinear filter, constructing and updating an actual controller of the multi-agent system by using a backstepping method; wherein the event triggering technology is adopted in the construction process of the actual controller and is used for controlling the updating frequency of the actual controller. According to the invention, the preset precision of the tracking error is set through the auxiliary function; eliminating boundary layer errors in each step of the backstepping method through a dynamic surface with a nonlinear filter; an unmeasurable state is observed through a state observer; the actual controller updating frequency is reduced through the event triggering technology, and resource consumption is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of nonlinear multi-agent system control, and in particular relates to a nonlinear multi-agent system output feedback consistency control method. Background Art

[0002] In real life, many practical control problems require multi-agent systems to meet control requirements through teamwork, such as drone collaborative operation, multi-unmanned vehicle formation and navigation, underwater autonomous machine collaborative exploration, etc. Compared with a single agent, actual projects have higher requirements for the flexibility and robustness of multi-agents.

[0003] However, it is impossible for every state variable in an actual multi-agent system to be measurable. In the prior art, the size of the tracking error range of the multi-agent system can only be adjusted through parameters. This is undoubtedly a waste of time and relies heavily on personal experience. In addition, in order to solve the "differential explosion" problem caused by the backstepping method in the process of designing the multi-agent system controller, the traditional solution is to use dynamic surface technology. However, the traditional dynamic surface technology cannot eliminate the boundary layer error in each step of the backstepping method during use, and when the boundary layer error accumulates to a certain extent, it will directly affect the stability of the system. At the same time, the backstepping method cannot control the update frequency of the controller in the process of designing the multi-agent system controller, resulting in a waste of resources. Summary of the invention

[0004] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a method for output feedback consistency control of a nonlinear multi-agent system, thereby ensuring that the tracking error of the multi-agent system converges to a preset accuracy range, eliminating the boundary layer error in each step of the backstepping method, and reducing the actual controller update frequency.

[0005] The present invention provides the following technical solutions:

[0006] In a first aspect, a method for output feedback consistency control of a nonlinear multi-agent system is provided, comprising: obtaining a multi-agent system including a leader and a plurality of followers; obtaining an auxiliary function pre-constructed according to the tracking error of the followers in the multi-agent system and a dynamic surface with a nonlinear filter pre-constructed according to the boundary error of the followers in the multi-agent system; based on the state observer, the auxiliary function and the dynamic surface with the nonlinear filter, using a backstepping method to construct and update an actual controller of the multi-agent system; wherein, in the process of constructing the actual controller, an event triggering technology is used to control the update frequency of the actual controller.

[0007] As an optional technical solution of the present invention, the dynamic equation of the ξth follower in the multi-agent system is expressed as:

[0008]

[0009] Where ξ represents the serial number of the follower in the multi-agent system, ξ=1,...,N, N represents the total number of followers, Indicates the follower's order, σ represents the total order of followers, Indicates the ξth follower The state variable vector of order, Indicates the ξth follower The state variables of order, express The derivative of ξ represents the input signal of the ξth follower, y ξ represents the output trajectory of the ξ-th follower, represents an unknown smooth and continuous function, represents an unknown smooth inner function, represents all output signals of the ξth follower,

[0010] As an optional technical solution of the present invention, the state observer is used to observe the state variables that cannot be measured in the multi-agent system;

[0011] The state observer is expressed as:

[0012]

[0013] in, and denotes the estimated value of the state variable of the ξth follower, express The derivative of represents a positive constant;

[0014] Constructing the observation vector error

[0015]

[0016] in, represents the observation vector error of the ξth follower of the σth order;

[0017] Observation vector error It is then expressed as:

[0018]

[0019] in, represents the Hurwitz matrix, which satisfies:

[0020]

[0021] For any positive definite matrix J ξ , we can get the matrix K ξ >0, satisfies:

[0022]

[0023] Where I represents the identity matrix.

[0024] As an optional technical solution of the present invention, the auxiliary function is used to set the preset accuracy of the tracking error, which includes the auxiliary function and Respectively expressed as:

[0025]

[0026]

[0027] Where ν represents the preset accuracy, z represents the tracking error, and sgn(·) represents the step function.

[0028] As an optional technical solution of the present invention, the dynamic surface with nonlinear filter is used to eliminate the boundary error of each order in the multi-agent system. The dynamic surface with nonlinear filter is expressed as:

[0029]

[0030] in, Indicates the ξth follower The boundary error of order, Indicates the ξth follower Virtual controller of the first order, Indicates the ξth follower The filter virtual controller of order express The initial value of represents a constant, express The derivative of express The initial value of represents a constant, and Represents an adaptive variable.

[0031] As an optional technical solution of the present invention, the method of constructing and updating the actual controller of the multi-agent system by using the backstepping method includes:

[0032] Define error variables and use radial basis neural network to transform unknown functions in error variables into known functions;

[0033] A Lyapunov function is constructed based on the state observer, and a virtual controller of each order is constructed using a backstepping method.

[0034] As an optional technical solution of the present invention, the step of defining an error variable and converting an unknown function in the error variable into a known function using a radial basis neural network includes:

[0035] The error variable is expressed as:

[0036]

[0037] Among them, y dg represents the expected trajectory, y g represents the output trajectory of the g-th follower, Indicates the ξth follower Order error variable, s ξg Indicates the communication relationship between followers, s ξ0 A scalar representing the communication weight between the leader and the follower;

[0038] Based on the above formula, the radial basis neural network function is used Estimate the unknown terms in the error variable, where

[0039] As an optional technical solution of the present invention, the constructing of the Lyapunov function based on the state observer includes:

[0040] Construct Lyapunov function V ξ,0 , expressed as:

[0041]

[0042] Lyapunov function V ξ,0 Derivative satisfy:

[0043]

[0044] Among them, λ min (J ξ ) represents the positive definite matrix J ξ The smallest eigenvalue of ξ represents the state variable of the ξth follower;

[0045] Using radial basis function Approximation k ξ (x ξ ), approximation error Φ ξ,n0 (H ξ,0 )satisfy in

[0046] get:

[0047]

[0048] in, represents a compact set; represents the weights of the radial basis neural network, i=1,...,r, r represents the total number of nodes of the radial basis neural network weights, ι ξ,0i =[ι ξ,0i1 ,…,ι ξ,0iφ ] T represents the center of the receiving field, e>0 represents the width of the Gaussian function, n=1,…,φ;

[0049] Based on the above formula, we get:

[0050]

[0051] in, Φ ξ,0 (H ξ,0 )=[Φ ξ,10 (H ξ,0 ),…,Φ ξ,φ0 (H ξ,0 )] T ,

[0052] Based on the above formula, we get but ||Γ ξ,0 || 2 ≤γ ξ,1 / r established;

[0053] get:

[0054]

[0055] As an optional technical solution of the present invention, the method of constructing a virtual controller of each order by using the backstepping method includes:

[0056] The first-order Lyapunov function V1 is expressed as:

[0057]

[0058] Among them, β ξ,1 , ξ,1 and θ ξ represent positive real numbers, and Represent the variable γ ξ,1 ,φξ,1 and The error of

[0059] First-order virtual controller α ξ,1 It is expressed as:

[0061]

[0062] Among them, X(χ ξ,1 ) indicates that the first-order variable of the ξth follower is χ ξ,1 Nussbaum-type function of ;

[0063]

[0064] Adaptive Law and Respectively expressed as:

[0065]

[0066]

[0067]

[0068]

[0069] Among them, l ξ,1 、h ξ,1 , β ξ,1 and ω ξ,1 All represent positive numbers, and Respectively represent χ ξ,1 , γ ξ,1 and φ ξ,1 The estimated value of represents the neural network radial basis function, x *,1 =[x 1,1 ,…,x N,1 ] T , Then there exists a positive constant c ξ , so that the variable It is expressed as:

[0070]

[0071] No. Lyapunov function of order It is expressed as:

[0072]

[0073] in, and represent positive real numbers, and Respectively represent variables and The error of

[0074] No. Virtual Controller It is expressed as:

[0075]

[0076] in, Indicates the ξth follower The variables in the order are Nussbaum-type function of ;

[0077]

[0078] Adaptive Law Respectively expressed as:

[0079]

[0080]

[0081]

[0082] in, and All represent positive numbers, and Respectively and The estimated value of represents the radial basis neural network function,

[0083]

[0084] The Lyapunov function V of order σ σ It is expressed as:

[0085]

[0086] Among them, β ξ,σ and λ ξ,σ represent positive real numbers, and Represent the variable γ ξ,σ and φ ξ,σ The error of

[0087] The virtual controller α of the σth order ξ,σ It is expressed as:

[0088]

[0089] Among them, X(χ ξ,σ ) indicates that the variable in the σth order of the ξth follower is χ ξ,σ Nussbaum-type function of ;

[0090]

[0091] Adaptive Law and Respectively expressed as:

[0092]

[0093]

[0094]

[0095] Among them, l ξ,σ 、h ξ,σ , β ξ,σ and ω ξ,σ All represent positive numbers, and Respectively represent χ ξ,σ , γ ξ,σ and φ ξ,σ The estimated value of represents the radial basis neural network function,

[0096]

[0097] As an optional technical solution of the present invention, the event triggering technology is used in the construction process of the actual controller, including:

[0098] The event triggering technique is expressed as:

[0099] u ξ (t) = B ξ (t k ),t∈[t k ,t k+1 ];

[0100]

[0101] Among them, e ξ (t) = B ξ (t)-u ξ (t) represents an event trigger error, t k Indicates the update time of the actual controller, υ ξ ∈(0,1),k ξ >0,λ ξ >k ξ / (1-υ ξ );

[0102] When t∈(t k ,t k+1 ),u ξ =B ξ (t k ),like t1=0 holds, then the control signal is u ξ t k+1 ;

[0103] There is a parameter π ξ,1 (t) and π ξ,2 (t), satisfying And π ξ,1 (t) and π ξ,2 The absolute value of (t) does not exceed 1, and we get:

[0104]

[0105] B(t) satisfies:

[0106]

[0107] Here, tanh represents the hyperbolic tangent function.

[0108] Compared with the prior art, the present invention has the following beneficial effects:

[0109] A nonlinear multi-agent system output feedback consistency control method provided by the present invention realizes setting a preset accuracy of tracking error by introducing an auxiliary function, thereby ensuring that the tracking error of the multi-agent system converges to within the preset accuracy range; by introducing a dynamic surface with a nonlinear filter, the boundary layer error in each step of the backstepping method is eliminated, the stability of the multi-agent system is improved, and the control performance and asymptotic stability of the multi-agent system are ensured; the observation of unmeasurable state variables in the multi-agent system is realized through a state observer; and the update frequency of the actual controller is reduced through event triggering technology to reduce resource consumption. BRIEF DESCRIPTION OF THE DRAWINGS

[0110] Figure 1 is a flow chart of a method for output feedback consistency control of a nonlinear multi-agent system in an embodiment of the present invention;

[0111] Figure 2 is a communication topology diagram of a multi-agent system in an embodiment of the present invention;

[0112] Figure 3 is a schematic diagram of a follower output trajectory in an embodiment of the present invention;

[0113] Figure 4is a schematic diagram of a follower tracking error in an embodiment of the present invention;

[0114] Figure 5 is a schematic diagram of a follower input signal in an embodiment of the present invention;

[0115] Figure 6 4 is a diagram of triggering times of follower input signals in an embodiment of the present invention. DETAILED DESCRIPTION

[0116] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0117] Example 1

[0118] This embodiment provides a nonlinear multi-agent system output feedback consistency control method, such as Figure 1 As shown, the specific steps include:

[0119] Step 1: Obtain a multi-agent system consisting of a leader and several followers.

[0120] 11. Specifically, the dynamic equation of the ξth follower in the multi-agent system is expressed as:

[0121]

[0122] Where ξ represents the serial number of the follower in the multi-agent system, ξ=1,…,N, N represents the total number of followers, Indicates the follower's order, σ represents the total order of followers, Indicates the ξth follower The state variable vector of order, Indicates the ξth follower The state variables of order, express The derivative of ξ represents the input signal of the ξth follower, y ξ represents the output trajectory of the ξ-th follower, represents an unknown smooth and continuous function, represents an unknown smooth inner function, represents all output signals of the ξth follower,

[0123] Furthermore, there exists a non-negative smooth function and an unknown constant greater than 0 satisfy:

[0124] Step 2: Construct a state observer based on the estimated values ​​of the state variables of the follower in the multi-agent system.

[0125] Specifically, the state observer is used to observe state variables that cannot be measured in the multi-agent system.

[0126] The state observer is expressed as:

[0127]

[0128] in, and denotes the estimated value of the state variable of the ξth follower, express The derivative of Represents a positive constant.

[0129] Constructing the observation vector error

[0130]

[0131] in, represents the observation vector error of the ξ-th follower of the σ-th order.

[0132] Observation vector error It is then expressed as:

[0133]

[0134] in, represents the Hurwitz matrix, which satisfies:

[0135]

[0136] For any positive definite matrix J ξ , we can get the matrix K ξ >0, satisfies:

[0137]

[0138] Where I represents the identity matrix.

[0139] Step three: Obtain an auxiliary function pre-constructed according to the tracking error of the follower in the multi-agent system and a dynamic surface with a nonlinear filter pre-constructed according to the boundary error of the follower in the multi-agent system.

[0140] 3.1. The auxiliary function is used to set the preset accuracy of the tracking error, which includes the auxiliary function and Respectively expressed as:

[0141]

[0142]

[0143] Where ν represents the preset accuracy, z represents the tracking error, and sgn(·) represents the step function.

[0144] Furthermore, the auxiliary function and There are two A continuously differentiable function of order , with the following properties: (1)

[0146]

[0147] in,

[0148] (2) If and only if |z|≤ν, therefore,

[0149] 3.2. The dynamic surface with nonlinear filter is used to eliminate the boundary error of each order in the multi-agent system. The dynamic surface with nonlinear filter is expressed as:

[0150]

[0151] in, Indicates the ξth follower The boundary error of order, Indicates the ξth follower Virtual controller of the first order, Indicates the ξth follower The filter virtual controller of order express The initial value of represents a constant, express The derivative of express The initial value of represents a constant, and Represents an adaptive variable.

[0152] Step 4: Based on the state observer, auxiliary function and dynamic surface with nonlinear filter, the actual controller of the multi-agent system is constructed and updated by backstepping method. Specifically, it includes:

[0153] 4.1. Define the error variable and use the radial basis neural network to transform the unknown function in the error variable into a known function.

[0154] Specifically, the error variable is expressed as:

[0155]

[0156] Among them, y dg represents the expected trajectory, y g represents the output trajectory of the g-th follower, Indicates the ξth follower Order error variable, s ξg Indicates the communication relationship between followers, s ξ0 A scalar representing the communication weight between the leader and followers.

[0157] Based on the above formula, the radial basis neural network function is used Estimate the unknown terms in the error variable, where

[0158] 4.2. Based on the state observer, a Lyapunov function is constructed, and a virtual controller of each order is constructed using the inverse method. Including:

[0159] 4.2.1. Constructing the Lyapunov function V ξ,0 , expressed as:

[0160]

[0161] Lyapunov function V ξ,0 Derivative satisfy:

[0162]

[0163] Among them, λ min (J ξ ) represents the positive definite matrix J ξ The smallest eigenvalue of ξ Represents the state variable of the ξth follower.

[0164] Using radial basis function Approximation k ξ (x ξ ), approximation error Φ ξ,n0 (H ξ,0 )satisfy in

[0165] get:

[0166]

[0167] in, represents a compact set; represents the weights of the radial basis neural network, r represents the total number of nodes of the radial basis neural network weights, i ξ,0i =[l ξ,0i1 ,...,l ξ,0iφ ] T represents the center of the receiving field, e>0 represents the width of the Gaussian function, and n=1,...,φ.

[0168] Based on the above formula, we get:

[0169]

[0170] in, Φ ξ,0 (H ξ,0 )=[Φ ξ,10 (H ξ,0 ),...,Φ ξ,φ0 (H ξ,0 )] T ,

[0171] Based on the above formula, we get but ||Γ ξ,0 || 2 ≤γ ξ,1 / r established;

[0172] get:

[0173]

[0174] 4.2.2. Use the backstepping method to construct a virtual controller for each order, including:

[0175] The first-order Lyapunov function V1 is expressed as:

[0176]

[0177] Among them, β ξ,1 , ξ,1 and θ ξ represent positive real numbers, and Represent the variable γ ξ,1 ,φ ξ,1 and of error.

[0178] First-order virtual controller α ξ,1 It is expressed as:

[0180]

[0181] Among them, X(χ ξ,1 ) indicates that the first-order variable of the ξth follower is χ ξ,1 Nussbaum-type function of ;

[0182]

[0183] Adaptive Law and Respectively expressed as:

[0184]

[0185]

[0186]

[0187]

[0188] Among them, l ξ,1 、h ξ,1 , β ξ,1 and ω ξ,1 All represent positive numbers, and Respectively represent χ ξ,1 , γ ξ,1 and φ ξ,1 The estimated value of represents the neural network radial basis function, x *,1 =[x 1,1 ,...,x N,1 ] T , Then there exists a positive constant c ξ , so that the variable It is expressed as:

[0189]

[0190] No. Lyapunov function of order It is expressed as:

[0191]

[0192] in, and represent positive real numbers, and Respectively represent variables and of error.

[0193] No. Virtual Controller It is expressed as:

[0194]

[0195] in, Indicates the ξth follower The variables in the order are Nussbaum-type function of ;

[0196]

[0197] Adaptive Law Respectively expressed as:

[0198]

[0199]

[0200]

[0201] in, and All represent positive numbers, and Respectively and The estimated value of represents the radial basis neural network function,

[0202] The Lyapunov function V of order σ σ It is expressed as:

[0203]

[0204] Among them, β ξ,σ and λ ξ,σ represent positive real numbers, and Represent the variable γ ξ,σ and φ ξ,σ of error.

[0205] The virtual controller α of the σth order ξ,σ It is expressed as:

[0206]

[0207] Among them, X(χ ξ,σ ) indicates that the variable in the σth order of the ξth follower is χ ξ,σ Nussbaum-type function of ;

[0208]

[0209] Adaptive Law and Respectively expressed as:

[0210]

[0211]

[0212]

[0213] Among them, l ξ,σ 、h ξ,σ , β ξ,σ and ω ξ,σ All represent positive numbers, and Respectively represent χ ξ,σ , γ ξ,σ and φ ξ,σ The estimated value of represents the radial basis neural network function,

[0214] Furthermore, the Nussbaum-type function includes: 2 sin(ξ), and cos(ξ)ξ 2 The Nussbaum-type function G(ξ) has the following properties:

[0215]

[0216] Among them, inf means taking the infimum, and sup means taking the supremum.

[0217] At the same time, for the continuous smooth function V(t), t>0 and the function function It has the following properties:

[0218]

[0219] Among them, (ε1,ε2)∈[0,+∞), F represents a constant, V(t), as well as exist The above is bounded.

[0220] 4.3. In the process of constructing the actual controller, event triggering technology is used to control the update frequency of the actual controller.

[0221] The event triggering technique is expressed as:

[0222] u ξ (t) = B ξ (t k ),t∈[t k ,t k+1 ];

[0223]

[0224] Among them, e ξ (t) = B ξ (t)-u ξ (t) represents an event trigger error, t k Indicates the update time of the actual controller, υ ξ ∈(0,1),k ξ >0,λ ξ >k ξ / (1-υ ξ ).

[0225] When t∈(t k ,t k+1 ),u ξ =B ξ (t k ),like t1=0 holds, then the control signal is u ξ t k+1 .

[0226] There is a parameter π ξ,1 (t) and π ξ,2 (t), satisfying And π ξ,1 (t) and π ξ,2 The absolute value of (t) does not exceed 1, and we get:

[0227]

[0228] B(t) satisfies:

[0229]

[0230] Here, tanh represents the hyperbolic tangent function.

[0231] Example 2

[0232] This embodiment provides a pendulum system as an example, and applies the method described in Example 1. The topology diagram of the pendulum system is as follows: Figure 2 As shown, it includes 1 leader and 4 followers. Figure 2 0 in the middle represents the leader.

[0233] In this embodiment, the Nussbaum-type function adopts cos(ξ)ξ 2 . Each agent is represented as:

[0234]

[0235] Among them, m represents the mass, q ξrepresents the counterclockwise direction, l is the length of the rod, g is the acceleration due to gravity, u ξ is the torque, k is the friction coefficient, ξ=1,...,4. In this embodiment, g=10, m=1, k=0.1, l=1.

[0236] Each interconnected pendulum agent is represented as:

[0237]

[0238] Among them, x ξ,1 =q ξ ,

[0239] In this embodiment, the preset accuracy is set to ν = 0.01, and the expected trajectory is set to y dg =0.5sin(t), and the initial state values ​​are all set to 0. The actual controller parameters constructed are l ξ,1 = l ξ,2 =10, l m,1 = l m,2 =200(m=1,2,3),l 4,1 = l 4,2 =400,h ξ,1 =h ξ,2 =1,β ξ,1 =β ξ,2 =1,ω ξ,1 =ω ξ,2 =1,θ ξ,1 =θ ξ,2 =1,λ ξ =30, k ξ =3.5, υ ξ =0.2,

[0240] The simulation results are as follows Figure 3-6 As shown in the figure: the output trajectories of the four followers can all follow the expected trajectory; the tracking errors of the four followers can all converge to within the preset accuracy of 0.01; the input signals of the four followers are verified to be bounded signals; the input signals of the four followers are discontinuous signals based on event triggering technology. This shows that the control method ensures that the tracking error of the multi-agent system converges to the preset accuracy range, eliminates the boundary layer error in each step of the backstepping method, and improves the stability of the multi-agent system. At the same time, resource consumption is reduced through event triggering technology.

[0241] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0242] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0243] These computer program instructions may also be stored in a computer readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0244] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0245] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for output feedback consistency control of a nonlinear multi-agent system, characterized in that: include: Obtain a multi-agent system including a leader and a number of followers; constructing a state observer based on the estimated values ​​of the state variables of the follower in the multi-agent system; Acquire an auxiliary function pre-constructed according to a tracking error of a follower in the multi-agent system and a dynamic surface with a nonlinear filter pre-constructed according to a boundary error of a follower in the multi-agent system; Based on the state observer, the auxiliary function and the dynamic surface with nonlinear filter, the actual controller of the multi-agent system is constructed and updated by backstepping method; Wherein, in the process of constructing the actual controller, an event triggering technology is adopted to control the update frequency of the actual controller.

2. The output feedback consistency control method for a nonlinear multi-agent system according to claim 1, characterized in that: The dynamic equation of the ξth follower in the multi-agent system is expressed as: Where ξ represents the serial number of the follower in the multi-agent system, ξ=1,...,N, N represents the total number of followers, Indicates the follower's order, σ represents the total order of followers, Indicates the ξth follower The state variable vector of order, Indicates the ξth follower The state variables of order, express The derivative of ξ represents the input signal of the ξth follower, y ξ represents the output trajectory of the ξ-th follower, represents an unknown smooth and continuous function, represents an unknown smooth internal function, y represents all output signals of the ξth follower, 3. The output feedback consistency control method for a nonlinear multi-agent system according to claim 1, characterized in that: The state observer is used to observe the state variables that cannot be measured in the multi-agent system; The state observer is expressed as: in, and denotes the estimated value of the state variable of the ξth follower, express The derivative of represents a positive constant; Constructing the observation vector error in, represents the observation vector error of the ξth follower of the σth order; Observation vector error It is then expressed as: in, represents the Hurwitz matrix, which satisfies: For any positive definite matrix J ξ , we can get the matrix K ξ >0, satisfying: Where I represents the identity matrix.

4. The output feedback consistency control method for a nonlinear multi-agent system according to claim 1, characterized in that: The auxiliary function is used to set the preset accuracy of the tracking error, which includes the auxiliary function and Respectively expressed as: Where ν represents the preset accuracy, z represents the tracking error, and sgn(·) represents the step function.

5. The output feedback consistency control method for a nonlinear multi-agent system according to claim 4, characterized in that: The dynamic surface with nonlinear filter is used to eliminate the boundary error of each order in the multi-agent system. The dynamic surface with nonlinear filter is expressed as: in, Indicates the ξth follower The boundary error of order, Indicates the ξth follower Virtual controller of the first order, Indicates the ξth follower The filter virtual controller of order express The initial value of represents a constant, express The derivative of express The initial value of represents a constant, and Represents an adaptive variable.

6. The output feedback consistency control method for a nonlinear multi-agent system according to claim 1, characterized in that: The method of constructing and updating the actual controller of the multi-agent system by using the backstepping method includes: Define error variables and use radial basis neural network to transform unknown functions in error variables into known functions; A Lyapunov function is constructed based on the state observer, and a virtual controller of each order is constructed using a backstepping method.

7. The output feedback consistency control method for a nonlinear multi-agent system according to claim 6, characterized in that: The step of defining the error variable and converting the unknown function in the error variable into a known function by using the radial basis neural network includes: The error variable is expressed as: Among them, y dg represents the expected trajectory, y g represents the output trajectory of the g-th follower, Indicates the ξth follower Order error variable, s ξg Indicates the communication relationship between followers, s ξ0 A scalar representing the communication weight between the leader and the follower; Based on the above formula, the radial basis neural network function is used Estimate the unknown terms in the error variable, where 8. The output feedback consistency control method for a nonlinear multi-agent system according to claim 7, characterized in that: The constructing of the Lyapunov function based on the state observer comprises: Construct Lyapunov function V ξ,0 , expressed as: Lyapunov function V ξ,0 Derivative satisfy: Among them, λ min (J ξ ) represents the positive definite matrix J ξ The smallest eigenvalue of ξ represents the state variable of the ξth follower; Using radial basis function neural network Approximation k ξ (x ξ ), approximation error Φ ξ,n0 (H ξ,0 )satisfy in get: in, represents a compact set; represents the weights of the radial basis neural network, i=1,...,r, r represents the total number of nodes of the radial basis neural network weights, ι ξ,0i =[ι ξ,0i1 ,...,ι ξ,0iφ ] T represents the center of the receiving field, e>0 represents the width of the Gaussian function, n=1,...,φ; Based on the above formula, we get: Among them, F ξ,0 (H ξ,0 )=[Φ ξ,10 (H ξ,0 ),...,Φ ξ,φ0 (H ξ,0 )] T , Based on the above formula, we get but ||Γ ξ,0 || 2 ≤γ ξ,1 / r established; get:

9. The output feedback consistency control method of a nonlinear multi-agent system according to claim 7, characterized in that: The method of constructing a virtual controller of each order by using the backstepping method includes: The first-order Lyapunov function V1 is expressed as: Among them, β ξ,1 , ξ,1 and θ ξ represent positive real numbers, and Represent the variable γ ξ,1 ,φ ξ,1 and The error of First-order virtual controller α ξ,1 It is expressed as: Among them, X(χ ξ,1 ) indicates that the first-order variable of the ξth follower is χ ξ,1 Nussbaum-type function of ; Adaptive Law and Respectively expressed as: Among them, l ξ,1 、h ξ,1 , β ξ,1 and ω ξ,1 All represent positive numbers, and Respectively represent χ ξ,1 , γ ξ,1 and φ ξ,1 The estimated value of represents the neural network radial basis function, x *,1 =[x 1,1 ,...,x N,1 ] T , Then there exists a positive constant c ξ , so that the variable It is expressed as: No. Lyapunov function of order It is expressed as: in, and represent positive real numbers, and Respectively represent variables and The error of No. Virtual Controller It is expressed as: in, Indicates the ξth follower The variables in the order are Nussbaum-type function of ; Adaptive Law Respectively expressed as: in, and All represent positive numbers, and Respectively and The estimated value of represents the radial basis neural network function, The Lyapunov function V of order σ σ It is expressed as: Among them, β ξ,σ and λ ξ,σ represent positive real numbers, and φ ξ,σ Represent the variable γ ξ,σ and φ ξ,σ The error of The virtual controller α of the σth order ξ,σ It is expressed as: Among them, X(χ ξ,σ ) indicates that the variable in the σth order of the ξth follower is χ ξ,σ Nussbaum-type function of ; Adaptive Law and Respectively expressed as: Among them, l ξ,σ 、h ξ,σ , β ξ,σ and ω ξ,σ All represent positive numbers, and Respectively represent χ ξ,σ , γ ξ,σ and φ ξ,σ The estimated value of represents the radial basis neural network function, 10. The output feedback consistency control method for a nonlinear multi-agent system according to claim 1, characterized in that: The event triggering technology is adopted in the construction process of the actual controller, including: The event triggering technique is represented as follows: u ξ (t)=B ξ (t k ),t∈[t k ,t k+1 ]; t k+1 =inf{t∈R||e ξ (t)|≥θ ξ |u ξ (t)|+k ξ },t1=0; Among them, e ξ (t) = B ξ (t)-u ξ (t) represents an event trigger error, t k represents the update time of the actual controller, k=1,2,...,θ ξ >0,υ ξ ∈(0,1),k ξ >0,λ ξ >k ξ / (1-υ ξ ); When t∈(t k ,t k+1 ),u ξ =B ξ (t k ), if t k+1 = inf{t∈R||e ξ (t)|≥θ ξ |u ξ (t)|+k ξ }, t1=0 holds, then the control signal is u ξ t k+1 ; There is a parameter π ξ,1 (t) and π ξ,2 (t), satisfying B ξ (t)=1+π ξ,1 (t)θ ξ , and π ξ,1 (t) and π ξ,2 The absolute value of (t) does not exceed 1, and we get: you ξ (t)=(B ξ (t)-π ξ,2 (t)) / (1+π ξ,1 (t)θ ξ ); B(t) satisfies: Here, tanh represents the hyperbolic tangent function.

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