Cooperative countermeasure iterative learning controller design method based on communication protocol

Abstract

The invention provides a cooperative adversarial iterative learning controller design method based on a communication protocol, and belongs to the technical field of communication information processing. The method comprises the following steps: S1, constructing a cooperation-confrontation system with n nodes, wherein the dynamic characteristics of each node are described by two time scales; s2, designing a communication network based on an RAP protocol so as to avoid data conflicts caused by simultaneous data transmission between nodes and adjacent nodes; and S3, designing an iterative learning controller with a cooperation-adversarial relationship, calculating an error according to the ideal trajectory to realize tracking, designing parameters of the iterative learning controller, and realizing a convergence condition. According to the method, the dynamic tracking problem of a cooperative-adversarial relation system can be effectively solved, data conflicts in signal transmission are reduced, and the target trajectory is tracked more accurately.

Description

Technical Field

[0001] The present invention belongs to the technical field of communication information processing, and in particular relates to a design method of a cooperative adversarial iterative learning controller based on a communication protocol. Background Art

[0002] Iterative learning control (ILC) is an effective learning-based control method that can achieve high-precision tracking even without precise knowledge of the underlying system. This technique leverages available information from previous iterations during the control process. It corrects the control signal based on the error between the actual and desired system outputs, generating new control signals to improve the system's tracking performance. Typically, after a finite number of iterations, the system output approaches the desired trajectory. As an effective control design tool, ILC has been widely used in industrial applications such as robotic manipulator control, chemical processes, and hard disk drives.

[0003] A multi-agent system is a system composed of multiple autonomous or semi-autonomous agents, such as software programs, robots, and drones. Each agent can independently perceive the environment, process information, make decisions, and take actions. It can also interact and collaborate with other agents to jointly accomplish complex tasks. Multi-agent systems can collaboratively accomplish tasks in a shared environment that would be difficult for a single agent, offering greater scalability, flexibility, and robustness. Currently, research on iterative learning control techniques for multi-agent systems has largely considered the connections between agents to be cooperative. However, the information received by nodes may come from neighbors with both competitive and cooperative relationships. For example, autonomous vehicles require cooperative avoidance to ensure road safety, but also compete for road resource allocation. In a public utility area, cooperative and competitive incentives can be used to minimize mutual interference and maximize network speed within the shared spectrum of wireless networks. In recent years, research on iterative learning control techniques for multi-agent systems with cooperative and adversarial relationships has attracted considerable attention.

[0004] On the other hand, in practical applications, multi-agent systems often exhibit heterogeneous characteristics, and two timescale variables are often considered to reflect differences in system states. For example, in a hospital, patient wards and emergency departments typically operate on two different timescales: patient wards operate on a timescale of days, while the emergency department's state changes occur more rapidly, operating on a timescale of hours or even minutes. Therefore, constructing a dual-timescale model to handle heterogeneous types of information has become an important approach to studying heterogeneous systems. Introducing a dual-timescale model into node dynamics and combining iterative learning control techniques can better capture the heterogeneous characteristics of cooperative-adversarial multi-agent systems.

[0005] At the same time, with the rapid development of network technology, information transmission between nodes in large-scale networks is becoming increasingly frequent. However, due to the limited overall network bandwidth, when a large number of network nodes transmit data through shared channels, data conflicts may occur, resulting in unacceptable consequences and, in severe cases, system crashes. To avoid data conflicts, an effective strategy is to use reliable communication protocols to coordinate signal transmission across the entire network. Currently, there are three main types of communication protocols in common use: random access protocol (RAP), round-robin protocol (RRP), and one-time attempt and discard protocol (TODP). Among these three protocols, RAP assigns a uniform priority to all nodes, allowing any node to send data when a transmission channel is available. During the RAP data transmission process, there is no fixed time step or transmission order. Its lack of centralized scheduling reduces communication costs and resolves data conflicts, making it widely used in industry.

[0006] Therefore, introducing a dual-time-scale model to capture heterogeneous features in a multi-agent system with cooperative-adversarial relationships and designing an iterative learning controller based on the RAP protocol can provide a feasible solution for achieving asymptotic stability of tracking trajectories within a limited time. Summary of the Invention

[0007] The present invention aims to provide a design method for a cooperative adversarial iterative learning controller based on a communication protocol. This method introduces a dual-time-scale model to describe the heterogeneous states of nodes in a system and a random access communication protocol to avoid data conflicts, ultimately achieving relatively accurate tracking of the system's trajectory. This method addresses the existing technical problem of data conflicts that can occur when a large number of network nodes transmit data over a shared channel.

[0008] In order to solve the above technical problems, the present invention proposes a design method of cooperative adversarial iterative learning controller based on communication protocol, such as Figure 1 As shown, the following steps are included:

[0009] Step S1: Construct a cooperative-adversarial system with n nodes, where the dynamic characteristics of each node are described by two time scales.

[0010] Step S2: Design a communication network based on the RAP protocol to avoid data conflicts caused by simultaneous data transmission between a node and its adjacent nodes.

[0011] Step S3: Design an iterative learning controller with a cooperative-adversarial relationship, calculate the error according to the ideal trajectory to achieve tracking, design the parameters of the iterative learning controller, and achieve convergence conditions.

[0012] Furthermore, in step S1, the cooperation-adversary system modeling process includes the cooperation-adversary relationship design and the node dynamics description in the cooperation-adversary system.

[0013] The cooperation-confrontation system is designed as follows:

[0014] The cooperation-confrontation system has n nodes. The topological relationship of n nodes in the cooperation-confrontation system is described as a signed directed graph, that is, a topological relationship graph. The topological relationship graph is represented as Topology diagram From the node set Θ={1,2,…,n}, the edge set Weight Matrix Composition. ij is the weight matrix The element in the i-th row and j-th column of represents the connection coefficient between node i and node j, i,j∈{1,2,…,n}, represents the set of real numbers.

[0015] For any two nodes i and j in the cooperative-antagonistic system, if node i can send data to node j, it means there is an edge X(i,j)∈X between node i and node j. The neighbor node set of node i is expressed as

[0016] Weight Matrix The following conditions must be met: 1) 2) When the connection relationship between the i-th node and the j-th node is a cooperative relationship, q ij >0(i≠j,i,j∈{1,2,…,n}); 3) When the connection relationship between the i-th node and the j-th node is an adversarial competition relationship, q ij <0(i≠j,i,j∈{1,2,…,n}).

[0017] Weight Matrix The Laplace matrix L is defined as Among them, l ij represents the element in the i-th row and j-th column of the Laplacian matrix, represents the degree matrix, is a diagonal matrix, expressed as: represents the diagonal elements in the i-th row and i-th column, and there is Right now:

[0018]

[0019] The node dynamics in the cooperative-adversarial system can be described as follows:

[0020] In the above cooperative-adversarial system, the dynamic characteristics of each node are described by the following two-time-scale system:

[0021]

[0022] Among them, i=1,2,…,n,y i,l (t+1) represents the slow state of the i-th node at the l-th iteration t+1 time step;

[0023] z i,l (t+1) represents the fast state of the i-th node at the l-th iteration t+1 time step; They represent the slow state and fast state of the i-th node at the l-th iteration t time step, respectively, m y Indicates the number of dimensions of the slow state, m z The number of dimensions representing the fast state. i,l (t) and the fast state z i,l (t) depends on two independent variables: the time step t(t∈

[0024] {0,1,2,…,T}) and the number of iterations l (l=1,2,…), where T is the maximum iteration time step of each iteration. ε represents the time scale adjustment factor, which is a small positive number that affects the speed difference between the slow state and the fast state. A 1i ,B 1i ,A 2i ,B 2i is the number of slow state dimensions m of the cooperative-antagonistic system y and the number of fast state dimensions m z The constant matrix of . and are the control inputs of the slow state and fast state of the i-th node at the t-th time step of the l-th iteration. C1 and C2 are the control matrices that adapt to the number of dimensions of the slow state and fast state control inputs, respectively.

[0025] set up and Represent the slow state y i,l (t) and the fast state z i,l The expected trajectory of (t) and the tracking error in the slow state are expressed as The tracking error in the fast state is expressed as Represents the transpose operation of a matrix.

[0026] set up x i,l (t) represents the lth iteration t

[0027] The joint state of the i-th node at time step, u i,l (t) represents the joint control input of the i-th node at the l-th iteration t time step.

[0028] The expected trajectory of the joint state is expressed as: The joint state tracking error is expressed as:

[0029]

[0030] The two-time-scale system can be rewritten as:

[0031] Dx i,l (t+1)=E i x i,l (t)+Cu i,l (t) (3)

[0032] Where D represents the joint state time scale adjustment factor matrix, E i represents the constant matrix that adapts to the number of dimensions of the joint state, C represents the control matrix that adapts to the number of dimensions of the joint state control input, Indicates the dimension is m y The identity matrix, Indicates the dimension is m z The identity matrix of .

[0033] Wait a minute state y i,l (t) and the fast state z i,l (t) satisfies the following initial value conditions:

[0034]

[0035] Where i = 1, 2, ..., n, y i,l (0) indicates the initial value of the slow state, z i,l (0) indicates the initial value of the fast state, and represent the initial constants of the slow state and the fast state respectively.

[0036] From the above, there are That is:

[0037]

[0038] Among them, x i,l (0) represents the initial value of the joint state.

[0039] Furthermore, in step S2, the communication network based on the RAP protocol is designed as follows:

[0040] At each transmission moment, for each node i, only the set of neighboring nodes from node i is allowed An adjacent node in transmits data to node i. The RAP protocol is used to determine the node that transmits data at each transmission moment. Definition It is represented as the selected neighboring node that transmits data to node i at the tth time step of the lth iteration. can be considered as a series of independent random variables. The probability of is given by:

[0041]

[0042] Among them, Prob{·} represents the probability value, is the probability that node j is selected to transmit data to node i via the communication network at the tth time step of the lth iteration, and Without loss of generality,

[0043] Furthermore, in step S3, an iterative controller for the cooperation-adversarial relationship is designed as follows:

[0044] Considering the dual-time-scale system designed in Equation (3), the iterative control law of each node should be designed based on its own measurement data and the data from its neighbors. The iterative learning controller with cooperative-adversarial relationship based on the RAP protocol is designed as follows:

[0045] u i,l+1 (t) = u i,l (t)+Δu i,l (t) (8)

[0046]

[0047] Among them, u i,l+1 (t) represents the joint control input of the i-th node at the l+1th iteration t time step, Δu i,i (t) represents the control increment of each iteration, is the control function to be designed, and node i and its neighbor nodes information about .

[0048] Control Function The design is as follows:

[0049] Considering the cooperation-antagonism relationship between neighboring nodes, design the control function Right now:

[0050]

[0051] Among them, q ij Represents the connection coefficient between node i and node j in the weight matrix Q.

[0052] The RAP protocol is introduced to prevent data conflicts caused by multiple neighboring nodes transmitting data to node i at the same time. The following update method of the iterative learning controller is designed:

[0053]

[0054] Where l = 1, 2, ..., t∈ {1, 2, ..., T}, is the weight matrix at time step t+1 The connection coefficient between node i and the selected adjacent nodes, Represents the tracking error of the adjacent node selected at the lth iteration t+1 time step, ∈ i ≥0 is a non-negative control parameter, r>0 is a positive control parameter; Indicates whether the node that transmits data to node i at the lth iteration t+1 time step is node j. If it is node j, then If it is not node j, then δ(·) is the Kronecker function, e j,l (t+1) represents the tracking error of node j at the lth iteration t+1 time step, e i,l (t+1) represents the tracking error of node i at the lth iteration t+1 time step.

[0055] From formula (11), we can see that Δu i,l The value of (t) is affected by the selected neighboring node that transmits data to node i at the tth time step of the lth iteration In order to solve the difficulties caused by its randomness, the following two lemmas are given to convert the random variable sequence and its probability distribution mapped to the form in the lemma.

[0056] Lemma 1: In the RAP protocol, the sequence of random variables Can be mapped to a random sequence Ω represents the value space set. The mapping Γ(·) is defined as follows:

[0057]

[0058] Among them, l (t) represents the communication network transmission state at the lth iteration t time step, represents the node that transmits data to node i at the lth iteration t time step, In addition, given η l (t), then:

[0059]

[0060] in, is related to l,i,η l (t) is the relational function related to node i, which represents the selected adjacent nodes that transmit data to node i at the t-th time step of the l-th iteration, and mod represents the modulo operation.

[0061] By Lemma 1, ζ l (t) and ηl (t) have a one-to-one correspondence, so ζ l The probability distribution of (t) can be calculated by Lemma 2.

[0062] Lemma 2: For t∈{1,2,…,T} and l=1,2,…, the random sequence η l (t)(η l The transmission probability of (t) = k, k∈Ω) (i.e., the probability of the kth communication network transmission state occurring at the lth iteration t time step) can be calculated by the following formula:

[0063]

[0064] in, As given in Lemma 1, η in l (t) takes the value k, It represents the probability that the selected neighboring node transmits data to node j via the communication network at the tth time step of the lth iteration.

[0065] Iterative learning controller designed by the present invention According to Lemma 1 and Lemma 2, η l The probability distribution of (t) achieves the following convergence:

[0066]

[0067] in, is the expectation of the random variable f. According to e i,l (t), condition (15) is equivalent to

[0068]

[0069] Based on the above iterative learning controller, the parameter design of the communication network based on the RAP protocol is considered under the conditions of known and unknown transmission probabilities.

[0070] Combined with the definition in formula (11) Supplementary definition: When i∈{1,2,…,n}, when hour,

[0071] Formula (11) can be rewritten as

[0072]

[0073] in, and is the degree matrix, At the same time

[0074]

[0075] in, represents the Laplace matrix of the mapped communication network, express The element in row i and column j, represents the weight matrix of the mapped communication network, express The element in row i and column j of

[0076] 1) Probability of delivery in RAP When the number of control matrices C1 and C2 of the slow-state and fast-state control input dimensions is known, the positive control parameter r and the non-negative control parameter ∈ i (i=1,2,…,n), satisfying the following conditions:

[0077]

[0078] Where t∈{0,1,…,T}, l∈{1,2,…}, Λ(k) represents the communication state function,

[0079] Indicates whether the node transmitting data to node i at the lth iteration t time step is node j; the probability of the kth communication network transmission state occurring at the lth iteration t+1 time step As given in Lemma 2, Represents the matrix and The θth eigenvalue of , θ=1,2,…,n, is the matrix D -1 The i-th eigenvalue of C, i = 1, 2, ..., m y +m z . Positive control parameter r and non-negative control parameter ∈ i Choice and and Related, need to be based on the transmission probability value to adjust. represents the Hadamard product, and |·| represents the complex modulus of the eigenvalue product.

[0080] 2) When the RAP transmission probability is partially unknown, that is:

[0081]

[0082] in, represents a known probability, and “?” represents an unknown probability. represents the set of neighbor nodes with known transmission probabilities of node i; represents the set of neighbor nodes with unknown transmission probability of node i; and Obviously,

[0083]

[0084] definition and That is, S K ∪S UK =χ, χ is the set of all edges. Another assumption is that the random variable There is a positive lower bound θ, namely:

[0085]

[0086] Where i∈{1,2,…,n}.

[0087] Combined with Lemma 2, we can get Lemma 3.

[0088] Lemma 3: For t∈{1,2,…,T} and l=1,2,…, the random variable η l (t)(η l The transmission probability of (t) = k, k∈Ω) Satisfy the following formula

[0089]

[0090] in, Represents the transmission probability The lower limit of Represents the transmission probability Upper limit,

[0091]

[0092] num(S K ) and num(S UK ) represent S K and S UK The number of edges in , represents the positive lower bound of the product of all unknown transmission probabilities, Represents a positive upper bound on the product of all unknown transmission probabilities.

[0093] In conditions (18) and (19), in order to solve the uncertainty caused by the unknown transmission probability, the matrix When the transmission probability is unknown, it is required to be symmetric, and the following Lemma 4 is given.

[0094] Lemma 4: For any symmetric non-negative n-dimensional matrices X and Y, let That is, all eigenvalues ​​of the matrix XZ are non-negative real numbers. Let are the eigenvalues ​​of the matrix XZ, and satisfy λ1≤λ2≤…≤λ i ≤…≤λ n , μ1≤μ2≤…≤μ i ≤…≤μ n . The following inequality holds:

[0095]

[0096] Where i = 1, 2,…, n.

[0097] According to the parameter design in 1) and Lemma 4, the parameter design under the condition of partially unknown transmission probability is obtained: design the control matrices C1 and C2 that adapt to the number of dimensions of the slow state and fast state control input, the positive control parameter r, the non-negative control parameter ∈ i (i=1,2,…,n) satisfies the following conditions:

[0098]

[0099] Among them, Λ(k) represents the communication state function, is symmetrical, represents the Hadamard product, Represents the Laplace matrix of the mapped communication network, probability and As given in Lemma 3, is the matrix D -1 The i-th eigenvalue of C, i = 1, 2, ..., m y +m z , ρ(·) is the spectral radius of the matrix.

[0100] Compared with the existing technology, the present invention has the following beneficial technical effects: the present invention introduces RAP into the design of the iterative learning controller, which consists of a series of random variables with known and unknown probabilities, and can effectively prevent data conflicts during signal transmission; it uses a dual-time scale model to describe the node state, and can effectively process heterogeneous types of information; it fully restores the cooperation-adversary relationship in the real network, designs a cooperation-adversary type iterative learning controller, and provides sufficient conditions for realizing network tracking, with high tracking performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0101] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0102] Figure 1 It is a structural diagram of the cooperative adversarial iterative learning controller based on the communication protocol of the present invention.

[0103] Figure 2 Schematic diagram of the cooperation-antagonism relationship among six nodes in the cooperation-antagonism system of the present invention.

[0104] Figure 3 is the tracking error e when the cooperative-antagonistic system of the present invention has no controller i,l (t) trajectory diagram.

[0105] Figure 4 The cooperative-antagonistic system of the present invention has a controller when l = 300 and the transmission probability When the tracking error e is known i,l (t) trajectory diagram.

[0106] Figure 5 The cooperative-antagonistic system of the present invention has a controller l = 500 and the transmission probability When the tracking error e is known i,l (t) trajectory diagram.

[0107] Figure 6 The cooperative-antagonistic system of the present invention has a controller when l = 300 and the transmission probability Tracking error e when part is unknown i,l (t) trajectory diagram.

[0108] Figure 7 The cooperative-antagonistic system of the present invention has a controller l = 500 and the transmission probability Tracking error e when part is unknown i,l (t) trajectory diagram. DETAILED DESCRIPTION

[0109] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0110] The following describes in detail a design method of a cooperative adversarial iterative learning controller based on a communication protocol proposed by the present invention using a specific embodiment.

[0111] In step S1, consider the following system:

[0112] The S1-1 node cooperation-confrontation relationship is designed as follows:

[0113] There are 6 nodes in the system, and the connection relationship is as follows Figure 2 As shown. Figure 2 In the example, the three relationships between nodes 1 and 5, nodes 2 and 6, and nodes 3 and 4 are adversarial, and the other relationships are collaborative. For simplicity, in the weight matrix Define q in ij =1 or q ij =-1. According to Figure 2 , the Laplace operator can be rewritten as follows:

[0114]

[0115] The S1-2 node dynamics description, the dual time scale system is as follows:

[0116]

[0117] in, The number of nodes n = 6, i.e., i = 1, 2, ..., 6, the parameter ε = 0.2, and the maximum iteration time step T = 15. Matrix A 1i ,B 1i ,A 2i ,B 2i as follows:

[0118]

[0119]

[0120] set up The two-time-scale system can be rewritten as follows:

[0121] Dx i,l (t+1)=E i x i,l (t)+Cu i,l (t)

[0122] in,

[0123]

[0124] Define the initial value of the joint state and the joint state expected trajectory

[0125] In step S2, according to the weight matrix The Laplace matrix L of the known transmission probability The RAP definition is shown in Table 1.

[0126] Table 1: Transmission Probability Known RAP

[0127]

[0128] In the transmission probability In the partially unknown RAP, it is assumed is unknown, and according to formula (20), the unknown probability There is a non-negative lower bound θ = 0.1.

[0129] In the iterative learning scheme formula (11) with cooperative-adversarial relationship in step S3, the parameter r is defined as 0.2. For convenience, let ∈ i =0.1,

[0130] After calculation, it can be confirmed that the above assumptions satisfy the conditions (18), (19), (25) and (26) in the designed iterative learning method. That is, using the iterative learning methods (8) and (11) in the present invention in the finite time interval t∈[1,15], regardless of the transmission probability Whether it is known or partially unknown, it can be achieved Joint state tracking error e i,l The corresponding trajectory of (t)(i=1,2,…,6) is as follows Figure 3-7 shown.

[0131] from Figure 3 It can be seen that without a controller, the joint state tracking error e i,l The trajectory of (t)(i=1,2,…,6) is not convergent. Figure 4 and Figure 5 In RAP, we use the known transmission probability The designed iterative learning control methods (8) and (11) can achieve tracking for the dual-time-scale system when the number of iterations is l = 500. Figure 6 and Figure 7 In the RAP transmission probability The iterative learning control methods (8) and (11) designed for partial unknowns can also enable the dual-time-scale system to achieve tracking when the number of iterations is l = 500. Figure 5 and Figure 7 As a result, it can be seen that the joint state tracking error e i,l There is no significant relationship between the final convergence rate of (t)(i=1,2,…,6) and whether the transfer probability is known or partially unknown.

[0132] In summary, the iterative learning controller design method based on the random access communication protocol (RAP) for the cooperative-adversarial system proposed in the present invention can make the error of each iteration of the system show a gradually decreasing trend and approach 0 within a limited time, thereby realizing precise tracking of the system, and the iterative learning control achieves good results.

[0133] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A design method for cooperative adversarial iterative learning controller based on communication protocol, characterized in that: The method comprises the following steps: Step S1: Construct a cooperative-adversarial system with n nodes, where the dynamic characteristics of each node are described by two time scales; Step S2: Design a communication network based on the RAP protocol to avoid data conflicts caused by simultaneous data transmission between a node and its neighboring nodes; Step S3: Design an iterative learning controller with a cooperative-adversarial relationship, calculate the error according to the ideal trajectory to achieve tracking, design the parameters of the iterative learning controller, and achieve convergence conditions.

2. The method for designing a cooperative adversarial iterative learning controller based on a communication protocol according to claim 1, characterized in that: In step S1, the cooperation-confrontation system is designed as follows: The cooperation-confrontation system has n nodes. The topological relationship of n nodes in the cooperation-confrontation system is described as a signed directed graph, that is, a topological relationship graph. The topological relationship graph is expressed as Topology diagram From the node set Θ={1,2,…,n}, the edge set Weight Matrix Composition; q ij is the weight matrix The element in the i-th row and j-th column of represents the connection coefficient between node i and node j, i,j∈{1,2,…,n}, represents the set of real numbers; For any two nodes i and j in the cooperative-antagonistic system, if node i can send data to node j, it means that there is an edge χ(i,j)∈χ between nodes i and j; the neighbor node set of node i is expressed as In the cooperative-adversarial system, the dynamic characteristics of each node are described by the following dual-time-scale system; Among them, i=1,2,…,n,y i,l (t+1) represents the slow state of the i-th node at the l-th iteration t+1 time step; z i,l (t+1) represents the fast state of the i-th node at the l-th iteration t+1 time step; They represent the slow state and fast state of the i-th node at the l-th iteration t time step, respectively, m y Indicates the number of dimensions of the slow state, m z represents the number of dimensions of the fast state; ε represents the time scale adjustment factor; A 1i ,B 1i ,A 2i ,B 2i is the number of slow state dimensions m of the cooperative-antagonistic system y and the number of fast state dimensions m z The constant matrix of ; and are the control inputs of the slow state and fast state of the i-th node at the t-th time step of the l-th iteration respectively; C1 and C2 are the control matrices that adapt to the number of dimensions of the slow state and fast state control input respectively; set up x i,l (t) represents the lth iteration t The joint state of the i-th node at time step, u i,l (t) represents the joint control input of the i-th node at the l-th iteration t time step; the dual time scale system can be rewritten as: Dx i,l (t+1)=E i x i,l (t)+Cu i,l (t) Where D represents the joint state time scale adjustment factor matrix, E i represents the constant matrix that adapts to the number of dimensions of the joint state, C represents the control matrix that adapts to the number of dimensions of the joint state control input, Indicates the dimension is m y The identity matrix, Indicates the dimension is m z The identity matrix of .

3. The method for designing a cooperative adversarial iterative learning controller based on a communication protocol according to claim 1, characterized in that: In step S2, the communication network based on the RAP protocol is designed as follows: At each transmission moment, for each node i, only the set of neighboring nodes from node i is allowed An adjacent node in transmits data to node i; RAP protocol is used to determine the node for data transmission at each transmission moment; definition It is represented as the selected neighboring node that transmits data to node i at the tth time step of the lth iteration; The probability of is given by: Among them, Prob{·} represents the probability value, is the probability that node j is selected to transmit data to node i via the communication network at the tth time step of the lth iteration, and Without loss of generality, 4. The method for designing a cooperative adversarial iterative learning controller based on a communication protocol according to claim 1, characterized in that: In step S3, an iterative learning controller with a cooperative-adversarial relationship is designed as follows: u i,l+1 (t)=u i,l (t)+Δu i,l (t) Among them, u i,l+1 (t) represents the joint control input of the i-th node at the l+1th iteration t time step, Δu i,l (t) represents the control increment of each iteration, is the control function to be designed; The RAP protocol is introduced to prevent data conflicts caused by multiple neighboring nodes transmitting data to node i at the same time. The following update method of the iterative learning controller is designed: Where l = 1, 2, ..., t∈ {1, 2, ..., T}, is the weight matrix for the t+1 time step The connection coefficient between node i and the selected adjacent nodes, represents the tracking error of the adjacent node selected at the lth iteration t+1 time step, ∈ i ≥0 is a non-negative control parameter, r>0 is a positive control parameter; Indicates whether the node that transmits data to node i at the lth iteration t+1 time step is node j. If it is node j, then If it is not node j, then e j,l (t+1) represents the tracking error of node j at the lth iteration t+1 time step, e i,l (t+1) represents the tracking error of node i at the lth iteration t+1 time step. Passing probability in RAP When the number of control matrices C1 and C2 of the slow-state and fast-state control input dimensions is known, the positive control parameter r and the non-negative control parameter ∈ i (i=1,2,…,n), satisfying the following conditions: Where t∈{0,1,…,T}, T represents the maximum iteration time step of each iteration, l∈{1,2,…}, Λ(k) represents the communication state function; It represents the probability of the kth communication network transmission state occurring at the lth iteration t+1 time step, that is, the transmission probability; Represents the matrix and The θth eigenvalue of , θ=1,2,…,n, is the matrix D -1 The i-th eigenvalue of C, i = 1, 2, ..., m y +m z ;|·| represents the complex modulus of the eigenvalue product; When the transmission probability is partially unknown, the control matrices C1 and C2 are designed to adapt to the number of slow state and fast state control input dimensions, positive control parameters r, and non-negative control parameters ∈ i (i=1,2,…,n) satisfies the following conditions: in, Represents the transmission probability The upper limit, Represents the transmission probability The lower limit of is the matrix D -1 is the i-th eigenvalue of C, and ρ(·) is the spectral radius of the matrix.

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