A data-driven multi-agent system self-triggered tracking control method

Abstract

The application discloses a data-driven multi-agent system self-triggered tracking control method, solves the consistency tracking control problem of the leader-following multi-agent system with unknown models under the directed communication topology. Firstly, a distributed data-driven self-triggered communication mechanism is proposed, which realizes the use of data to determine the next trigger time at the current trigger time, avoids continuous state detection, and saves computing and communication resources. Secondly, the scheme avoids continuous communication between agents, effectively reduces the communication load, and further saves resources on the basis of ensuring the asymptotic consistency tracking of the multi-agent system. Finally, the scheme provides a method for jointly designing the controller and the trigger matrix only by using the state-input data, eliminates the dependence of the traditional control on the system model, and realizes the self-triggered consistency tracking control for the unknown multi-agent system for the first time.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of multi-agent system cooperative control, and particularly relates to a data-driven self-triggered tracking control method for multi-agent system. BACKGROUND

[0002] Multi-agent systems (MASs), such as multi-robot systems, vehicle platoon systems and sensor networks, have attracted extensive attention from both academia and industry due to their potential to cooperatively perform complex tasks. As one of the key problems in the field of multi-agent systems, tracking control aims to design a distributed control algorithm based on local information exchange among agents, so that all follower agents track the state of a leader agent.

[0003] In practical applications, individual agents are often subject to limited communication bandwidth and energy constraints. Therefore, in view of the limited transmission resources, research on intermittent communication mechanisms has been carried out, that is, by sampling / transmitting only when necessary to prolong the life cycle of sensors and improve resource utilization efficiency. The self-triggered mechanism is a commonly used method in intermittent communication strategies, which uses the available information at the current trigger time to determine the next trigger time in advance. As can be seen, the trigger (transmission) time under the self-triggered mechanism is planned in advance, and the system's measurement values only need to be sampled at each trigger time, so during the event-triggered intermittent period, the system's sensors can switch to sleep mode. In addition, multi-agent system self-triggered control, by designing a feedback controller and a self-triggered mechanism, not only avoids continuous communication among agents, but also avoids continuous state monitoring, effectively saving communication and computing resources, and to some extent prolonging the service life of sensors and the operation time of the system.

[0004] It is worth noting that current research on self-triggered consensus control is based on models, that is, the design of the controller and the self-triggered mechanism depends on the explicit system model. However, in practical applications, it is very challenging to obtain an accurate system model. The absence of system models for different application scenarios will lead to a series of control problems, such as the difficulty of cooperative production in intelligent manufacturing processes due to the absence of production line models. For this reason, new data-driven control methods provide an end-to-end paradigm to solve the above problems, that is, only data is used to achieve control and analysis of unknown systems, and no intermediate steps such as system identification are needed to estimate the system model. Although extensive research has been conducted on data-driven control of a single unknown system, there is currently no research considering consensus tracking control of unknown multi-agent systems under limited transmission resources. Therefore, under the self-triggered communication mechanism, it has become an urgent problem to achieve distributed data-driven consensus tracking control of multi-agent systems with a leader-follower structure. SUMMARY

[0005] The technical solution of the present application is to overcome the shortcomings of the prior art and provide a data-driven multi-agent system self-triggered tracking control method.

[0006] The technical solution of the present application is:

[0007] A data-driven multi-agent system self-triggered tracking control method comprises the steps of:

[0008] S100, a distributed self-triggered consensus tracking control strategy is designed for the multi-agent system, and the control strategy comprises a state feedback controller and a model-based distributed self-triggered communication mechanism;

[0009] S200, state data and input data of the multi-agent system are collected through offline experiments, a closed-loop promotion system of tracking error is established, and a parameterized representation of the data-driven promotion system is constructed;

[0010] S300, a data-driven distributed self-triggered communication mechanism is designed according to the model-based distributed self-triggered communication mechanism in step S100 and the parameterized representation of the data-driven promotion system constructed in step S200, so as to realize prediction of the next trigger time only by using data at the current trigger time;

[0011] S400, a data-based stability criterion is established, and the gain matrix in the state feedback controller in step S100 is designed according to the established data-based stability criterion, and the trigger matrix of the data-driven distributed self-triggered communication mechanism obtained in step S300 is also designed, so as to realize data-driven multi-agent system self-triggered tracking control.

[0012] The multi-agent system comprises N+1 agents, wherein one agent is a leader and N agents are followers, and the dynamic model of the leader is:

[0013] x0(t+1)=A tr x0(t)

[0014] The dynamic model of the follower is:

[0015] x i (t+1)=A tr x i (t)+B tr u i (t),i=1,2,…,N

[0016] Wherein, a state of a leader; and respectively represent a state vector and a control input of a follower i, a real system matrix A tr ,B tr are constant, stabilizable and unknown; a connection relationship between the intelligent agents is described by a directed spanning tree with the leader as a root node

[0017] In the step S100, the state feedback controller and a model-based distributed self-triggered communication mechanism are specifically designed as follows:

[0018] S111, a state feedback controller is designed by using local intermittent information, specifically:

[0019]

[0020] wherein, is a feedback gain matrix to be designed; is a time of the kth triggering of the follower i; a ij is an element of the i-th row and the j-th column of an adjacency matrix

[0021] S112, the design of the model-based distributed self-triggered communication mechanism is as follows:

[0022] Without loss of generality, it is assumed that the leader is not configured with a triggering device, so for the follower i, it is assumed that is the first triggering time, and a sequence of triggering times is determined by the following formula:

[0023]

[0024] wherein, a triggering function is designed as:

[0025]

[0026] wherein, is a positive definite symmetric matrix to be designed; σ is a normal number; is a kth event-triggered interval of the follower i; represents a state error between and ; a symbol T represents a transpose of a matrix;

[0027] In the step S200, a data-driven lifting system parameterization representation is constructed as:

[0028] wherein,

[0029] ​​

[0030] Δ i :=[δ i (0) δ i (1)…δ i (ρ-1)], Moreover, E 1 :=E, when s=1 and E s :=I, is the state-input data collected at discrete time points T∈[0,ρ]. The data and is calculated according to the definition of tracking error δ i (t):=x i (t)-x0(t) after collection, and are known matrices of appropriate dimensions;

[0031] The step S300, the data-driven distributed self-triggered communication mechanism, specifically comprises:

[0032]

[0033] The data-driven trigger function is designed as:

[0034]

[0035] wherein,

[0036]

[0037] α>0, M>0.

[0038] Specifically, the construction step of the data-driven lifting system parameterized representation comprises:

[0039] S211, within the time interval T∈{0,1,…,ρ}, the state data and input data of the multi-agent system are measured by the following disturbed open-loop system through open-loop experiments:

[0040] x i (T+1)=A tr x i (T)+B tr u i (T)+Ew i (T)

[0041] wherein, is a known matrix for simulating the noise w i(t) the impact on the system;

[0042] S212, define the tracking error δ of the follower i and the leader i (t) := x i (t) - x0(t), according to the feedback controller designed in step S111, the dynamic equation of the tracking error closed-loop system satisfies:

[0043]

[0044] Then, at the triggering moment, the state of the closed-loop system is controlled by the following switching system:

[0045]

[0046] wherein, is the promotion controller gain; and is the promotion system matrix; the above system is the tracking error closed-loop promotion system.

[0047] S213, according to the pre-collected input-state data of each agent i Further, the definition of tracking error calculates and collects tracking error data Stacked in the following way to form a matrix:

[0048]

[0049] S214, define the data that can explain the agent i All promotion matrices A of s , B s The set in which it is located is

[0050]

[0051] Wherein, when s = 1, E 1 : = E, When s = 0, E s : = I.

[0052] S215, by constructing a noise model, the upper bound of unknown noise is limited, specifically:

[0053]

[0054] Wherein, and are known matrices of appropriate dimensions. When s = 1, When s = 0,

[0055] S216, based on the above steps S211, S212, S213, S214, S215, obtaining

[0056] The data-driven promotion system parameterization representation is:

[0057]

[0058] wherein,

[0059] In the step S400, the data-based stability criterion is based on:

[0060] Considering the topological graph And the multi-agent system with leader-follower structure, for a given positive σ>0 and ∈, for all [A B]∈∑ i If there exists a parameter β>0, and matrix P>0, Φ>0, G and K G If i=1, 2, …, N satisfy the following linear matrix inequality, then under the action of the distributed feedback controller and the distributed self-triggered communication mechanism, all follower states in the network asymptotically track the leader state for any initial state;

[0061] The gain matrix is designed as K=K G G -1 ;

[0062]

[0063] wherein,

[0064] L κ :=[0 n×(κ-1)n ,I n ,0 0×(3-κ)n ],κ=1,2,3,

[0065] U i :=[u i (1) u i (2) … u i (ρ-1)],Δ i+ :=[δ i (1) δ i (2) … δ i (ρ)]

[0066] Beneficial effects

[0067] The application solves the problem of unknown model leader-following multi-agent system consistent tracking control under directed communication topology. First, a distributed self-triggered consistent tracking control strategy is proposed, including a state feedback controller and a self-triggered mechanism based on the model; further, the state-input data and the closed-loop tracking error are used to improve the system, and the parameterization of the data-driven improved system is constructed; by combining the model-based self-triggered mechanism and the parameterization of the data-driven improved system, a distributed data-driven self-triggered mechanism is designed; finally, by constructing the parameterization of the data-driven original system, a joint design method of the controller and the trigger matrix is proposed, and a data-based consistent condition is obtained, realizing the asymptotic tracking of the leader state by all followers. In summary, the main contributions of the application can be summarized as follows: first, the designed distributed data-driven self-triggered communication mechanism only uses data to determine the next trigger time at the current trigger time, avoiding continuous state detection and saving computing and communication resources; second, the scheme avoids continuous communication between agents on the basis of ensuring the asymptotic consistency of the multi-agent system, effectively reducing the communication load and further saving resources; finally, the scheme provides a data-driven method for designing the controller and the trigger matrix only using state-input data, eliminating the dependence of traditional control on the system model, and realizing the self-triggered consistent tracking control for unknown multi-agent systems for the first time.

[0068] The application discloses a data-driven multi-agent system self-triggered tracking control method, which solves the problem of unknown model leader-following multi-agent system consistent tracking control under directed communication topology. First, a distributed data-driven self-triggered communication mechanism is proposed, which realizes the determination of the next trigger time only by using data at the current trigger time, avoids continuous state detection, saves computing and communication resources; second, the scheme avoids continuous communication between agents on the basis of ensuring the asymptotic consistent tracking of the multi-agent system, effectively reduces the communication load, and further saves resources; finally, the scheme provides a method for jointly designing the controller and the trigger matrix only using state-input data, eliminates the dependence of traditional control on the system model, and realizes the self-triggered consistent tracking control for unknown multi-agent systems for the first time. BRIEF DESCRIPTION OF DRAWINGS

[0069] Figure 1 is a structural schematic diagram of the data-driven multi-agent system self-triggered tracking control method provided by the application;

[0070] Figure 2 is a flowchart of the data-driven multi-agent system self-triggered tracking control method provided by the application;

[0071] Figure 3is a state trajectory graph of a multi-agent system under the data-driven self-triggered control strategy in an embodiment of the present application;

[0072] Figure 4 is a trigger time graph of a multi-agent system under the data-driven trigger control strategy in an embodiment of the present application. DETAILED DESCRIPTION

[0073] Embodiments of the present application will be described in detail below with reference to the accompanying drawings and embodiments.

[0074] As Figure 1 shown is a system structure schematic diagram of the present application, which includes a controlled object (an unknown model leader-follower multi-agent system), a sensor, an actuator, a state feedback controller and a distributed self-triggering decision maker. Among them, the distributed self-triggering decision maker predicts the next trigger time at the current departure time and broadcasts the predicted value to its neighbors. If the neighbor triggers the event, the agent immediately receives the latest state of the neighbor and rechecks its self-triggering function; otherwise, the agent will verify the trigger condition only when it reaches its scheduled trigger time. Through the pre-collected system state-input data, a data-driven feedback controller and a self-triggering mechanism are designed to achieve unknown system asymptotic tracking consistency control.

[0075] As Figure 2 shown is a flowchart of the present application, a data-driven multi-agent system self-triggering tracking control method, comprising the following steps:

[0076] S100, considering a linear multi-agent system with a leader-follower structure, a distributed self-triggering consistency tracking control strategy is designed, which includes a state feedback controller and a distributed model-based self-triggering communication mechanism.

[0077] In an embodiment, a discrete-time linear multi-agent system composed of N followers and 1 leader is considered, and the dynamic model of each agent is:

[0078]

[0079] wherein, represents the state of the leader; and respectively represent the state vector and the control input of the follower i. The real system matrix A tr ,B tr is constant, stabilizable and unknown. The connection relationship between the agents in the system can be described by a directed spanning tree with the leader as the root node.

[0080] Further, the distributed self-triggered consensus tracking control strategy in step S100 includes a state feedback controller and a distributed self-triggered communication mechanism, and is specifically designed as follows:

[0081] S111, a distributed state feedback controller is designed by using local intermittent information, and is specifically designed as follows:

[0082]

[0083] wherein, is the feedback gain matrix to be designed; is the time of the kth trigger of the follower i; a ij is the element in the i-th row and the j-th column of the adjacent matrix .

[0084] S112, the distributed self-triggered communication mechanism is designed as follows:

[0085] Without loss of generality, it is assumed that the leader is not configured with a trigger device. Then, for the follower i, it is assumed that is the first trigger time, and the trigger time sequence is determined by the following formula:

[0086]

[0087] wherein, the trigger function is designed as:

[0088]

[0089] wherein, is the positive definite symmetric matrix to be designed; σ is a normal number; is the kth event trigger interval of the follower i; represents the state error between and ; the symbol T represents the transpose of the matrix.

[0090] S200, state data and input data of an open-loop system are collected through offline experiments, a closed-loop promotion system of tracking error is established, and a parameterized representation of a data-driven promotion system is constructed;

[0091] In one embodiment, the parameterized representation of the data-driven promotion system in step S200 is expressed as:

[0092]

[0093] wherein,

[0094]

[0095] Δ i :=[δi (0) δ i (1)…δ i (ρ-1)], Moreover, E 1 := E when s = 1. s := I. The state-input data is collected at discrete time points T ∈ [0, ρ]. The data and can be collected after the definition of the tracking error δ i (t):= x i (t) - x0(t). and are known matrices of appropriate dimensions.

[0096] In particular, the data-driven lifting system parameterization construction step is:

[0097] S211, the state data x and input data u of the system are measured by open-loop experiments on the following disturbed open-loop system:

[0098] x i (T+1) = A tr x i (T) + B tr u i (T) + Ew i (T)

[0099] where, E is a known matrix modeling the effect of the noise w i (t) on the system.

[0100] S212, define the tracking error δ i (t):= x i (t) - x0(t) for the follower i and the leader, and according to the feedback controller designed in step S111, the dynamics of the tracking error closed-loop system satisfies:

[0101]

[0102] Then, at the triggering time, the state of the closed-loop system is controlled by the following switched system:

[0103]

[0104] where, is the lifting controller gain; and To enhance the system matrix. The above system is a closed-loop enhanced system of tracking error.

[0105] S213, according to the pre-collected input-state data of each agent i Further, the definition of tracking error calculates and collects tracking error data Stacked in the following way to form a matrix:

[0106] Δ i :=[δ i (0) δ i (1)…δ i (ρ-1)],

[0107]

[0108] S214, define the data that can explain agent i All enhanced matrices A s , B s The set where it is located is

[0109]

[0110] Where, when s=1, E 1 : = E, When E s : = I.

[0111] S215, by constructing a noise model, the upper bound of unknown noise is limited, specifically:

[0112]

[0113] Where, And are known matrices of appropriate dimensions. When s=1 When

[0114] S216, based on the above steps S211, S212, S213, S214, S215, the data-driven enhanced system parameterization can be obtained as:

[0115]

[0116] Where,

[0117] S300, combined with the model-based self-triggering mechanism and the data-based enhanced system parameterization, a distributed data-driven self-triggering communication mechanism is designed to predict the next trigger time only at the current trigger time.

[0118] In one embodiment, the distributed data-driven self-triggered communication mechanism described in step S300 is specifically:

[0119]

[0120] wherein the data-driven trigger function is designed as:

[0121]

[0122] wherein,

[0123]

[0124] α>0, M>0.

[0125] Specifically, the design step of the distributed data-driven self-triggered communication mechanism is:

[0126] S311, rewriting the model-based distributed self-triggered communication mechanism described in step S100 into the following quadratic matrix inequality:

[0127]

[0128] S312, introducing a positive definite matrix M, and rewriting the data-driven promotion system parameterization described in step S200 into

[0129]

[0130] S312, combining S311 and S312, and using the S-lemma, the distributed data-driven self-triggered communication mechanism can be obtained, which is expressed as:

[0131] Considering the topological graph a multi-agent system with a leader-follower structure, and a feedback controller. For a given positive constant σ>0, a controller gain K, a trigger matrix Φ>0, and the latest transmitted state of agent i If there exists a parameter α>0 and a matrix M>0, then the following linear matrix inequality holds for i=1,2,…,N and

[0132]

[0133] S400, establishing a data-based stability criterion for jointly designing the controller gain matrix and the trigger matrix to achieve data-driven self-triggered consensus tracking control of the unknown model multi-agent system.

[0134] ​In one embodiment, the step S400 is based on a data-based stability criterion, specifically:

[0135] Considering the topological graph and the multi-agent system with leader-follower structure, for a given positive constant σ>0 and ∈, for all [A B]∈∑ i If there exists a parameter β>0 and matrices P>0, Φ>0, G and K G If the following linear matrix inequalities are satisfied for i=1,2,…,N, then all the follower states can asymptotically track the leader state under the distributed feedback controller and the distributed self-triggered communication mechanism for any initial state. In addition, the feedback gain matrix is designed as K=K G G -1 .

[0136]

[0137] where,

[0138] L κ :=[0 n×(κ-1)n ,I n ,0 n×(3-κ)n ],κ=1,2,3,

[0139]

[0140] U i :=[u i (1) u i (2) … u i (ρ-1)],Δ i+ :=[δ i (1) δ i (2) … δ i (ρ)]

[0141] Specifically, the joint design method of the controller gain matrix and the trigger matrix is designed as follows:

[0142] S411, for the multi-agent system, a data-based parameterized representation of the system is constructed as follows:

[0143]

[0144] where, Δ i+ :=[x(1) x(2) … x(ρ)],Δ i :=[x(1) x(2) … x(ρ-1)],U i :=[u(1) u(2) … u(ρ-1)].

[0145] S412, tracking error closed-loop system

[0146]

[0147] Let δ i (t) = Gs i (t), where is a nonsingular matrix. For The dynamics of the above tracking error system can be rewritten as:

[0148]

[0149] where, K G = KG. The above two systems have the same stability properties. For all i = 1, 2, …, N, x i (t) - x0(t) = 0 if and only if s(t) = 0, i.e., δ(t) = 0. In other words, the multi-agent system can achieve state consensus asymptotically if and only if the disagreement vector asymptotically converges to zero. Thus, the consensus problem for the multi-agent system is transformed into the stability problem of the disagreement vector.

[0150] S413, based on this, a Lyapunov function is constructed as:

[0151]

[0152] where P > 0. Taking the forward difference of the above function and scaling, the following condition is obtained:

[0153]

[0154] where,

[0155]

[0156] When γ < 0, the disagreement vector δ i (t) asymptotically converges to zero, i.e., when t → ∞, x i - x0→ 0.

[0157] S414, combining S411 and S413, using the S-lemma, the following data-based self-triggered consensus condition can be obtained, specifically:

[0158] Consider the topological graph and the multi-agent system with leader-follower structure, for a given positive constant σ > 0 and ∈, for all [A B] ∈ Σ i if there exists a parameter β > 0, and matrices P > 0, Φ > 0, G and KG , i = 1, 2, …, N, then all the follower states can asymptotically track the leader state under the distributed feedback controller and the distributed self-triggered communication mechanism for any initial state. Moreover, the feedback gain matrix is designed as K = K G G -1 .

[0159]

[0160] In one embodiment, the feasibility and effectiveness of the data-driven control strategy design method in the present application are verified by simulation experiments.

[0161] Consider a multi-inverted pendulum system consisting of six followers and one leader, and the dynamic model of each inverted pendulum is:

[0162]

[0163] where g = 9.8 m / s 2 is the gravitational acceleration constant, m and l are the mass and length of each inverted pendulum, and a i and a0 are the pendulum angles of the followers and the leader, respectively, and u i is the control torque of the follower inverted pendulum i. Let m = 1 kg, the period T k = 0.02 is selected, and the linear pendulum in continuous time domain can be described by a multi-agent system in discrete time domain, and the system matrix is:

[0164]

[0165] Further, the system control input constraint is u i (t) ∈ [-1, 1], the matrix E = 0.01I and the parameter p = 80 are selected, and the state data and the input data are collected. d The matrix Q d = -I, S T = 0, and The noise is obtained. The parameters are selected as ∈ = 2 and σ = 0.2. By solving the linear matrix inequality described in step S400, the feedback controller gain matrix K = [-3.5061 -1.4648],

[0166]

[0167] The initial state of each agent is set as x0(0) = [2, -1] T , x1(0) = [-4, 2]T x2(0) = [4, 2] T x3(0) = [2, 0] T x4(0) = [3, -1] T x5(0) = [-5, -3] T and x6(0) = [2, 0.5] T Thus, the simulation results are shown in Figs. Figure 3 and Figure 4 . Figure 3 The state evolution trajectories of all agents are shown. It can be seen that the multi-agent system achieves state consensus under the data-driven control strategy of the application, proving the effectiveness of the proposed data-driven self-triggered control method. Figure 4 The communication time diagrams of each agent under the self-triggered strategy are given, and compared with the traditional continuous sampling strategy. It can be seen that the self-triggering mechanism proposed in the application significantly reduces the communication times.

[0168] The above is only a preferred embodiment of the application, and the application includes but is not limited to the content disclosed in the embodiment and the drawings. Any equivalent or modification made without departing from the disclosed spirit of the application falls within the protection scope of the application.

Claims

1. A data-driven multi-agent system self-triggered tracking control method, characterized in that The method comprises the steps of: S100, designing a distributed self-triggered consensus tracking control strategy for the multi-agent system, the control strategy comprising a state feedback controller and a model-based distributed self-triggered communication mechanism; S200, collecting state data and input data of the multi-agent system through offline experiments, establishing a closed-loop promotion system of tracking error, and constructing a parameterized representation of the data-driven promotion system; S300, designing a data-driven distributed self-triggered communication mechanism according to the model-based distributed self-triggered communication mechanism in step S100 and the parameterized representation of the data-driven promotion system constructed in step S200; S400, establishing a data-based stability criterion, and designing a gain matrix in the state feedback controller in step S100 and a trigger matrix of the data-driven distributed self-triggered communication mechanism obtained in step S300 according to the established data-based stability criterion, so as to realize self-triggered tracking control of the data-driven multi-agent system; The multi-agent system comprises N+1 agents, wherein one agent is a leader and N agents are followers, the dynamic model of the leader is: x0(t+1) = A tr x0(t) The dynamic model of the follower is: x i (t+1) = A tr x i (t) + B tr u i (t), i = 1, 2,..., N wherein, denotes the state of the leader; and denote the state vector and control input of the follower i, respectively, the real system matrix A tr ,B tr are constant, stabilizable and unknown; the connectivity between the agents is described by a directed spanning tree with the leader as the root node ; In step S100, the state feedback controller is specifically designed as follows: S111, a state feedback controller is designed by using local intermittent information, specifically: wherein, is the feedback gain matrix to be designed; is the time of the kth trigger of the follower i;a ij is the adjacency matrix is the element of the ith row, jth column of In step S100, the model-based distributed self-triggered communication mechanism is designed as follows: S112, assuming the leader is not configured with a trigger device, for the follower i, assuming is the first trigger time, the sequence of trigger times is determined by the following equation: The trigger function is designed as: wherein, is a positive definite symmetric matrix to be designed; σ is a normal number; is the kth event-triggered interval of the follower i; denotes the state error between the time and the time ; the symbol denotes the transpose of a matrix; In step S300, the data-driven distributed self-triggered communication mechanism is specifically: The data-driven trigger function is designed as: wherein In step S200, the construction steps of the parameterized representation of the data-driven promotion system are as follows: S211, within a time interval T e {0, 1,..., p}, state data of the multi-agent system and input data are measured by open-loop experiments from the following disturbed open-loop system: x i (T+1) = A tr x i (t) + B tr u i (T) + Ew i (T) wherein is a known matrix modeling the noise w i (t) the impact on the system; S212, define the tracking error δ of the follower i and the leader i (t): = x i (t) - x0(t), according to the feedback controller designed in step S111, the dynamic equation of the tracking error closed-loop system satisfies: At the trigger time, the state of the closed-loop system is controlled by the following switching system: wherein, for increasing the controller gain; and for increasing the system matrix; S213, collect per-agent i input-state data in advance Define the tracking error, and collect tracking error data Stacked in the following way to form a matrix: Δ i :=[δ i (0) δ i (1)…δ i (ρ-1)] W i 1 :=[w i (0) w i (1)…w i (ρ-1)] S214, defining data capable of explaining the agent i all lifting matrices A of s ,B s the set in which where s = 1 when E 1 : = E, when E s : = I; S215, the upper bound of the unknown noise is limited by constructing a noise model, specifically: wherein and are known matrices of appropriate dimension, s = 1 when S216, the parameterized representation of the data-driven promotion system is obtained as: wherein,

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