Consistency output feedback control method for fractional order multi-agent system

Abstract

The invention discloses a consistency output feedback control method for a fractional order multi-agent system. The method comprises the following steps: establishing a second-order model of the fractional order multi-agent system without external interference; constructing a second-order model of the fractional order multi-agent system without a leader; designing a distributed state feedback control scheme corresponding to the second-order model of the fractional-order multi-agent system; constructing a Lyapunov function corresponding to the distributed state feedback control scheme, and determining a consistency condition for realizing the fractional order multi-agent system; and the consistency of the fractional order multi-agent system without the leader is controlled. The invention belongs to the field of multiple agents. According to the method, the problem that the integer order agent system cannot accurately describe the system physical model can be solved, and the key influence of the second major characteristic value of the coupling matrix on the consistency of the multi-agent system is realized.

Description

Technical Field

[0001] The present invention relates to the field of multi-agents, and in particular to a consistent output feedback control method for a fractional-order multi-agent system. Background Art

[0002] Multi-agent systems involve how to design and implement control strategies for robotic systems so that robots can complete designated tasks or achieve specific goals. This field covers a variety of technologies and methods. Robot control methods mainly include open-loop control, closed-loop feedback control, trajectory tracking control, motion planning and control, collaborative control and multi-robot systems, and perception and decision-making. In practical applications, robot control is usually a comprehensive engineering problem that requires engineers and researchers to comprehensively consider knowledge and technologies from multiple fields such as mechanical design, control theory, electronic technology, and computer science to achieve efficient operation and task execution capabilities of robots in various complex environments.

[0003] Consistency behavior is the most typical behavior of cooperative control of multi-agent systems such as robots, that is, all agents achieve a common goal by adjusting their own behaviors, so that a certain state tends to be the same. However, integer-order agent systems cannot accurately describe the physical model of the system, and due to the complex working environment and other reasons, external factors such as noise interference and sensor vibration will inevitably appear, which will greatly affect the convergence effect of traditional consistency control methods. Therefore, for multi-agent systems such as robots, how to achieve consistency control is an urgent problem to be solved. Summary of the invention

[0004] The embodiment of the present invention solves the technical problem in the prior art that the integer-order agent system cannot accurately describe the physical model of the system by providing a consistent output feedback control method for a fractional-order multi-agent system, thereby achieving the technical effect of enabling the integer-order agent system to accurately describe the physical model of the system.

[0005] In a first aspect, the present invention provides a method for consistent output feedback control of a fractional-order multi-agent system, the method comprising:

[0006] Establish a second-order model of the fractional-order multi-agent system with and without external interference, including a second-order model of the fractional-order multi-agent system with and without external interference;

[0007] Construct a second-order model of a leaderless fractional-order multi-agent system;

[0008] Design a distributed state feedback control scheme corresponding to the second-order model of the fractional-order multi-agent system;

[0009] Construct the Lyapunov function corresponding to the distributed state feedback control scheme and determine the consistency conditions for realizing the fractional-order multi-agent system;

[0010] Under the consensus condition, the leaderless fractional-order multi-agent system is controlled to achieve consensus.

[0011] Furthermore, the second-order model of the fractional-order multi-agent system with external interference and the second-order model of the fractional-order multi-agent system without external interference include:

[0012]

[0013] Where D = {1, 2, ..., w}, D represents the set of agents, m∈(0, 1), m is the order of the fractional order, k = 1, 2, ..., w, w is the number of agents, a k (t) is the position information of the kth agent at time t, b k (t) is the speed information of the kth agent at time t, u k (t) is the control input of the kth agent at time t, d k (t) is the external interference of the kth agent at time t, t is the time variable, g(t,)∈R h And g(t,) is a nonlinear function.

[0014] Furthermore, the second-order model of the leaderless fractional-order multi-agent system includes:

[0015]

[0016]

[0017] in, is the expected position of the agent at time t, is the expected speed of the agent at time t, is the error between the actual position and the expected position of the kth agent at time t, is the error between the actual speed and the expected speed of the kth agent, and and satisfy:

[0018]

[0019] in, is the transpose of the error between the actual position and the expected position of the w-th agent, is the transpose of the error between the actual speed and the expected speed of the w-th agent.

[0020] Furthermore, the distributed state feedback control scheme includes:

[0021]

[0022] Among them, M 1 ∈R h×h is a symmetric and positive definite matrix, A=(A KP ) w×w ∈R w×w is the communication weight matrix between agents, and the communication weight matrix satisfies:

[0023]

[0024] Among them, A KP is the communication weight matrix between the kth agent and the pth agent, represents an undirected communication line between agents. If there is communication between agent k and agent p, then 0 KP =A PK ∈R; otherwise 0=A KP =A PK ∈R, in addition,

[0025] Furthermore, the steps of constructing the Lyapunov function to ensure the consistency of the multi-agent system include:

[0026] Construct the following Lyapunov function:

[0027]

[0028] in, λ 2 (A) is A=(A KP ) w×w ∈R w×w The second largest eigenvalue of the matrix, V 1 (t) is the Lyapunov function, A is the communication topology matrix between agents, I w is the identity matrix of order w, Matrix B 2 satisfy:

[0029]

[0030] Among them, I wh ∈R w×h is the identity matrix, I h is the identity matrix.

[0031] Scaling the Lyapunov function inequality, we get Right now ​or

[0032] Furthermore, the steps of constructing the Lyapunov function to ensure the consistency of the multi-agent system include:

[0033] Construct the following Lyapunov function:

[0034]

[0035] Among them, V 2 (t) is the Lyapunov function, and A is the communication topology matrix between agents.

[0036] By scaling the Lyapunov function and combining it with the fractional differential equation, we can get

[0037]

[0038] Among them, I m is the mth power of the identity matrix, V 2 (0) is the Lyapunov function and t = 0, for The square of is the transpose of the external disturbance vector of the kth agent, k=1,2,…,w,t≥0∈R,V 2 (t)≥0∈R,

[0039] One or more technical solutions provided in the embodiments of the present invention have at least the following technical effects or advantages:

[0040] The present invention provides a consistent output feedback control method for a fractional-order multi-agent system, the method comprising: a second-order model of a fractional-order multi-agent system with or without external interference, wherein the second-order model of the fractional-order multi-agent system with or without external interference and the second-order model of the fractional-order multi-agent system without external interference are included; the second-order model of the fractional-order multi-agent system without a leader is constructed; a distributed state feedback control scheme corresponding to the second-order model of the fractional-order multi-agent system is designed; a Lyapunov function corresponding to the distributed state feedback control scheme is constructed, and the consistency condition of the fractional-order multi-agent system is determined; under the consistency condition, the fractional-order multi-agent system without a leader is controlled to achieve consistency. The present invention solves the problem that the integer-order agent system cannot accurately describe the physical model of the system by proposing a second-order model of the fractional-order multi-agent system with or without external interference without a leader, and by establishing a fractional-order robot multi-agent system model, the dynamic characteristics of the controlled system and the controller are described more realistically, and the system situation can be more truly reflected and the control performance can be improved, and the key influence of the second largest eigenvalue of the coupling matrix on achieving the consistency of the multi-agent system is realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. 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 creative work.

[0042] Figure 1 A flow chart of a consistent output feedback control method for a fractional-order multi-agent system provided by the present invention;

[0043] Figure 2 A schematic diagram of the simulation of the speed and position of the intelligent agent system without external interference provided by the present invention;

[0044] Figure 3 A schematic diagram of the simulation of the position and speed of the intelligent system with external interference provided by the present invention. DETAILED DESCRIPTION

[0045] The embodiment of the present invention solves the technical problem in the prior art that an integer-order agent system cannot accurately describe the physical model of the system by providing a consistent output feedback control method for a fractional-order multi-agent system.

[0046] The technical solution of the embodiment of the present invention is to solve the above technical problems, and the overall idea is as follows:

[0047] A consistent output feedback control method for a fractional-order multi-agent system, the method comprising: establishing a second-order model of the fractional-order multi-agent system with and without external interference, wherein the second-order model of the fractional-order multi-agent system with and without external interference is included; constructing a second-order model of the fractional-order multi-agent system without a leader; designing a distributed state feedback control scheme corresponding to the second-order model of the fractional-order multi-agent system; constructing a Lyapunov function corresponding to the distributed state feedback control scheme, and determining a consistency condition for realizing the fractional-order multi-agent system;

[0048] Under the consensus condition, the leaderless fractional-order multi-agent system is controlled to achieve consensus.

[0049] In order to better understand the above technical solution, the above technical solution will be described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0050] First of all, the term "and / or" in this article is only a description of the association relationship of the associated objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in this article generally indicates that the associated objects before and after are in an "or" relationship.

[0051] The present invention provides Figure 1 A consistent output feedback control method for a fractional-order multi-agent system is shown, comprising steps S11-S15:

[0052] Step S11, establishing a second-order model of the fractional-order multi-agent system with and without external interference, including a second-order model of the fractional-order multi-agent system with and without external interference.

[0053] Step S12, constructing a second-order model of a leaderless fractional-order multi-agent system.

[0054] Step S13, designing a distributed state feedback control scheme corresponding to the second-order model of the fractional-order multi-agent system.

[0055] Step S14, construct the Lyapunov function corresponding to the distributed state feedback control scheme, and determine the consistency conditions for realizing the fractional-order multi-agent system.

[0056] Step S15, under the consistency condition, controlling the leaderless fractional-order multi-agent system to achieve consistency.

[0057] Regarding step S11, a second-order model of the fractional-order multi-agent system with and without external interference is established, including a second-order model of the fractional-order multi-agent system with external interference and a second-order model of the fractional-order multi-agent system without external interference.

[0058] It can be understood that the second-order model of the fractional-order multi-agent system with external interference and the second-order model of the fractional-order multi-agent system without external interference provided by the present invention can be collectively referred to as the second-order model of the leaderless fractional-order multi-agent system with and without external interference. The present invention fully explains the second-order model of the leaderless fractional-order multi-agent system with and without external interference by respectively describing the second-order model of the fractional-order multi-agent system with external interference and the second-order model of the fractional-order multi-agent system without external interference.

[0059] The second-order model refers to a mathematical model that contains second-order dynamic characteristics, that is, the response of the fractional-order multi-agent system is affected by the description of the second-order differential equation. By adopting the second-order model, the present invention can more accurately reflect the inertia, damping and dynamic response characteristics of the fractional-order multi-agent system.

[0060] The second-order model of the fractional-order multi-agent system with external interference and the second-order model of the fractional-order multi-agent system without external interference include:

[0061]

[0062] Where D = {1, 2, ..., w}, D represents the set of agents, m∈(0, 1), m is the order of the fractional order, k = 1, 2, ..., w, w is the number of agents, a k (t) is the position information of the kth agent at time t, b k (t) is the speed information of the kth agent at time t, u k (t) is the control input of the kth agent at time t, d k (t) is the external interference of the kth agent at time t, t is the time variable, g(t,)∈R h is a nonlinear function.

[0063] Here, we assume that t≥0∈R such that d k (t)Satisfy:

[0064] I m ‖d k (t)‖ 2 <+∞

[0065] Among them, I m is the mth power of the identity matrix.

[0066] g(t,)∈R hIt is a nonlinear function, assuming that g(t,) satisfies:

[0067] (γ 1 -γ 2 +(κ 1 -κ 2 ))(g(t,γ 1 ,κ 1 )-g(t,γ 2 ,κ 2 ))

[0068] ≤δ 1 (γ 1 -γ 2 ) T (γ 1 -γ 2 )+δ 2 (κ 1 -κ 2 ) T (κ 1 -κ 2 )

[0069] For any constant y 1 ,y 2 ,κ 1 ,κ 2 ∈R,δ 1 ,δ 2 Is a normal number.

[0070] Regarding step S12, a second-order model of a leaderless fractional-order multi-agent system is constructed.

[0071] The second-order model of a leaderless fractional-order multi-agent system refers to a system in which there are multiple autonomous working units or robots that can make autonomous decisions and schedule according to task requirements and system status. The system structure without a central leader can be modeled as a distributed control system in which tasks are allocated and executed through collaboration and communication between components.

[0072] For any given initial state, if the following equation holds, the leaderless FMSs (fractional multi-agent systems) with or without external interference are said to achieve consensus.

[0073]

[0074] in, is the expected position of the agent, is the expected speed of the agent, k=1,2,…,w.

[0075] For any given initial state, if the following equation holds, the leaderless FMSs with or without external interference are said to achieve H∞ consistency:

[0076]

[0077] Where t≥0∈R,V 2 (t)≥0∈R,

[0078] For the second-order model of the fractional-order multi-agent system with external interference and the second-order model of the fractional-order multi-agent system without external interference obtained in step S11, the above-mentioned expected model (including expected position and expected speed) is introduced to obtain the second-order model of the fractional-order multi-agent system without a leader, which specifically includes:

[0079]

[0080] in, is the expected position of the agent at time t, is the expected speed of the agent at time t, is the error between the actual position and the expected position of the kth agent at time t, is the error between the actual speed and the expected speed of the kth agent, and and satisfy:

[0081]

[0082] in, is the transpose of the error between the actual position and the expected position of the w-th agent, is the transpose of the error between the actual speed and the expected speed of the w-th agent.

[0083] Regarding step S13, a distributed state feedback control scheme corresponding to the second-order model of the fractional-order multi-agent system is designed.

[0084] The distributed state feedback control scheme designed by the present invention includes:

[0085]

[0086] Among them, M 1 ∈R h×h is a symmetric and positive definite matrix, A=(A KP ) w×w ∈R w×w is the communication weight matrix between agents, and the communication weight matrix satisfies:

[0087]

[0088] Among them, A KPis the communication weight matrix between the kth agent and the pth agent, represents an undirected communication line between agents. If there is communication between agent k and agent p, then 0 KP =A PK ∈R; otherwise 0=A KP =A PK ∈R, in addition,

[0089] Combining the distributed state feedback control scheme with the second-order model of the fractional-order multi-agent system, the following model is obtained, including:

[0090]

[0091] Regarding step S14, a Lyapunov function corresponding to the distributed state feedback control scheme is constructed, and the consistency conditions for realizing the fractional-order multi-agent system are determined.

[0092] in:

[0093]

[0094] is the transpose of the error between the actual position and the desired position of the agent, is the transpose of the error between the actual speed of the agent and the expected speed, and d(t) is the error between the actual error and the expected error of the agent.

[0095] In order to achieve the consistency of the leaderless fractional-order multi-agent system, the positive definite matrix A = (A KP ) w×w ∈R w×w and M 1 ∈R h×h The following conditions are established:

[0096]

[0097] Among them, it also includes:

[0098] W 1 =λ 2 (A)M 1 +δ 1 I h ,W 2 =λ 2 (A)M 1 +(1+δ 2 )I h

[0099]

[0100] Among them, B​1 and B 4 are matrices, I w is the identity matrix of order w, I wh ∈R w×h is the identity matrix, λ 2 (A) is A=(A KP ) w×w The second largest eigenvalue of .

[0101] Based on the above formula, the Lyapunov function is constructed, including:

[0102]

[0103] in, λ 2 (A) is A=(A KP ) w×w ∈R w×w The second largest eigenvalue of the matrix, V 1 (t) is the Lyapunov function, A is the communication topology matrix between agents, I w is the identity matrix of order w, Matrix B 2 satisfy:

[0104]

[0105] Among them, I wh ∈R w×h is the identity matrix, I h is the identity matrix.

[0106] Regarding step S15, under the consistency condition, the leaderless fractional-order multi-agent system is controlled to achieve consistency.

[0107] The present invention combines Theorem 1 to Theorem 4 to derive the consistency of the leaderless fractional-order multi-agent system.

[0108] Theorem 1: For any function f(t)∈C 1 (0,+∞),R n ),exist:

[0109] D m (f T (t)Pf(t))≤2f(t)PD m f(t),

[0110] Among them, 0 <m<1,P≥0∈R n×n Is a normal number.

[0111] Theorem 2: For The Laplace transform of can be expressed as:

[0112]

[0113] Where m1, m2 are positive constants, v∈R. L is the Laplace transform symbol, and Re(s) is the real part of the complex number s in the Laplace transform.

[0114] Theorem 3: If is a symmetric matrix and irreducible, Then we can get:

[0115]

[0116] in,

[0117] Theorem 4: For any function φ(t)∈C 1 (0,+∞),R), we can get:

[0118] I m D m φ(t)=φ(t)-φ(0)

[0119] Among them, 0 <m<1。

[0120] 【1】Combining the second-order model of the fractional-order multi-agent system without external interference obtained in the above steps with Theorem 1, we can obtain:

[0121]

[0122]

[0123] because Then we can get:

[0124]

[0125] Combined with Theorem 3, we can get:

[0126]

[0127] Combined with step S11, we can get:

[0128]

[0129] In summary, we can get:

[0130]

[0131] make v(t)=cV 1 (t)-D m V 1(t)≥0, we can get D m V 1 (t) = cV 1 (t)-v(t). According to Theorem 2, we can get:

[0132] L{D m V 1 (t)}=s m V 1 (s)-s m-1 V 1 (0) = cV 1 (s)-(s)

[0133] Among them, V 1 (s) = L{V 1 (t)},(s)=L{v(t)}.

[0134] but Combined with Theorem 2, we can get:

[0135] V 1 (t) = V 1 (0)E m (ct m )-v(t)*t m-1 E m,m (ct m )≤V 1 (0)E m (ct m )

[0136] That is The equation becomes The division can be obtained:

[0137]

[0138] Therefore, the leaderless fractional-order multi-agent system without external interference achieves consensus.

[0139] [2] Further, for the second-order model of the fractional-order multi-agent system with external interference without a leader in step S13, using the inequality, we can obtain:

[0140]

[0141] Combined with Theorem 4, we can get:

[0142]

[0143] in, We can get:

[0144]

[0145] Therefore, the leaderless fractional-order multi-agent system with external interference achieves consistency. Figure 2-Figure 3 , explaining how to achieve system consistency.

[0146] {1} The second-order model of the fractional-order multi-agent system with 5 agents without external interference is as follows:

[0147] D 0.8 a k (t) = b k (t)

[0148] D 0.8 b k (t) = g(t,a k (t),b k (t))+u k (t)

[0149] in:

[0150] g(t,a k (t),b k (t)) = (cos(a k1 (t))-b k1 (t),2a k2 (t)+3sin(b k2 (t))) T ,k=1,2,…5. Obviously, this formula satisfies the assumption:

[0151] (γ 1 -γ 2 +(κ 1 -κ 2 ))(g(t,γ 1 ,κ 1 )-g(t,γ 2 ,κ 2 ))

[0152] ≤δ 1 (γ 1 -γ 2 ) T (γ 1 -γ 2 )+δ 2 (κ 1 -κ 2 ) T (κ 1 -κ 2 )

[0153] For any constant y 1 ,y 2 ,κ1 ,κ 2 ∈R,δ 1 ,δ 2 Is a normal number.

[0154] Select δ 1 =4.5,δ 2 =5.5,M 1 =diag(3.1,2.8)

[0155]

[0156] Using the MATLAB YALMIP toolbox, we can get λ 2 (A)≤-2.8991 satisfies:

[0157] {2} Verify the consistency of five fractional-order multi-agent systems with external interference without a leader:

[0158] D 0.9 a k (t) = b k (t)

[0159] D 0.9 b k (t) = g(t,a k (t),b k (t))+u k (t)+d k (t)

[0160] in,

[0161] in:

[0162] g(t,a k (t),b k (t))=(2sin(a k1 (t))-3b k1 (t),2cos a k2 (t)+2b k2 (t)) T ,k=1,2,…5. Obviously, this formula satisfies the assumption:

[0163] (γ 1 -γ 2 +(κ 1 -κ 2 ))(g(t,γ 1 ,κ 1 )-g(t,γ 2 ,κ 2 ))

[0164] ≤δ 1 (γ1 -γ 2 ) T (γ 1 -γ 2 )+δ 2 (κ 1 -κ 2 ) T (κ 1 -κ 2 )

[0165] For any constant y 1 ,y 2 ,κ 1 ,κ 2 ∈R,δ 1 ,δ 2 Is a normal number.

[0166] Select δ 1 =4.5,δ 2 =4,M 1 =diag(2.5,2.6).

[0167]

[0168] Using the MATLAB YALMIP toolbox, we can get 2 (A)≤-3.2559, satisfy:

[0169]

[0170] Figure 2 It is a simulation diagram of the position and speed states of a five-agent system without external interference by a state feedback controller as an example in an embodiment of the present invention.

[0171] Depend on Figure 2 It can be seen that given different initial states for the five agents, after the intervention of the controller, they gradually tend toward consistency from 1s, and finally achieve full system consistency at 2.2-2.3s. Figure 2 It includes Figure A and Figure B. The horizontal axis of Figure A represents time, and the vertical axis represents position; the horizontal axis of Figure B represents time, and the vertical axis represents speed.

[0172] Figure 3 It is a state simulation diagram of position error and velocity error of a five-agent system with external interference by a state feedback controller as an example in an embodiment of the present invention. Figure 3 It includes Figure C and Figure D. The horizontal axis of Figure C represents time, and the vertical axis represents position error; the horizontal axis of Figure D represents time, and the vertical axis represents speed error.

[0173] Depend on Figure 3It can be seen that given different initial states for the five agents, after the intervention of the controller, they gradually tend to consistency from 1s, and finally the error tends to 0, that is, H∞ consistency is achieved under interference. a1 and a5 in Figure C almost coincide, and b1 and b5 in Figure D almost coincide.

[0174] In summary, the present invention provides a method for consistent output feedback control of a fractional-order multi-agent system, the method comprising: a second-order model of a fractional-order multi-agent system with or without external interference, wherein the second-order model of the fractional-order multi-agent system with or without external interference and the second-order model of the fractional-order multi-agent system without external interference are included; a second-order model of the fractional-order multi-agent system without a leader is constructed; a distributed state feedback control scheme corresponding to the second-order model of the fractional-order multi-agent system is designed; a Lyapunov function corresponding to the distributed state feedback control scheme is constructed, and the consistency conditions for realizing the fractional-order multi-agent system are determined; under the consistency conditions, the fractional-order multi-agent system without a leader is controlled to realize consistency. The present invention solves the problem that the integer-order agent system cannot accurately describe the physical model of the system by proposing a second-order model of the fractional-order multi-agent system with or without external interference without a leader, and by establishing a fractional-order robot multi-agent system model, the dynamic characteristics of the controlled system and the controller are described more realistically, and the system conditions can be more truly reflected and the control performance can be improved, and the key influence of the second largest eigenvalue of the coupling matrix on realizing the consistency of the multi-agent system is realized.

Claims

1. A consistent output feedback control method for a fractional-order multi-agent system, characterized in that: The method comprises: Establish a second-order model of the fractional-order multi-agent system with and without external interference, including a second-order model of the fractional-order multi-agent system with and without external interference; Construct a second-order model of a leaderless fractional-order multi-agent system; Design a distributed state feedback control scheme corresponding to the second-order model of the fractional-order multi-agent system; Constructing a Lyapunov function corresponding to the distributed state feedback control scheme and determining a consistency condition for realizing the fractional-order multi-agent system; Under the above-mentioned consistency conditions, the leaderless fractional-order multi-agent system is controlled to achieve consistency.

2. A method for consistent output feedback control of a fractional-order multi-agent system as claimed in claim 1, characterized in that: The second-order model of the fractional-order multi-agent system with external interference and the second-order model of the fractional-order multi-agent system without external interference include: Where D = {1, 2, ..., w}, D represents the set of agents, m∈(0, 1), m is the order of the fractional order, k = 1, 2, ..., w, w is the number of agents, a k (t) is the position information of the kth agent at time t, b k (t) is the speed information of the kth agent at time t, u k (t) is the control input of the kth agent at time t, d k (t) is the external interference of the kth agent at time t, t is the time variable, g(t,)∈R h And g(t,) is a nonlinear function.

3. A method for consistent output feedback control of a fractional-order multi-agent system as claimed in claim 2, characterized in that: Second-order model of leaderless fractional-order multi-agent systems, including: in, is the expected position of the agent at time t, is the expected speed of the agent at time t, is the error between the actual position and the expected position of the kth agent at time t, is the error between the actual speed and the expected speed of the kth agent, and and satisfy: in, is the transpose of the error between the actual position and the expected position of the w-th agent, is the transpose of the error between the actual speed and the expected speed of the w-th agent.

4. A method for consistent output feedback control of a fractional-order multi-agent system as claimed in claim 3, characterized in that: Distributed state feedback control scheme, including: Where M1∈R h×h is a symmetric and positive definite matrix, A=(A KP ) w×w ∈R w×w is the communication weight matrix between agents, and the communication weight matrix satisfies: Among them, A KP is the communication weight matrix between the kth agent and the pth agent, represents an undirected communication line between agents. If there is communication between agent k and agent p, then 0 KP =A PK ∈R; otherwise 0=A KP =A PK ∈R, in addition, ​ 5. A consistent output feedback control method for a fractional-order multi-agent system as claimed in claim 4, characterized in that: The steps to construct the Lyapunov function and ensure the consistency of the multi-agent system include: Construct the following Lyapunov function: in, λ2(A) is A=(A KP ) w×w ∈R w×w The second largest eigenvalue of the matrix, V1(t) is the Lyapunov function, A is the communication topology matrix between agents, I w is the identity matrix of order w, The matrix B2 satisfies: Among them, I wh ∈R w×h is the identity matrix, I n is the identity matrix; Scaling the Lyapunov function inequality, we get Right now or 6. A method for consistent output feedback control of a fractional-order multi-agent system as claimed in claim 4, characterized in that: The steps to construct the Lyapunov function and ensure the consistency of the multi-agent system include: Construct the following Lyapunov function: Among them, V2(t) is the Lyapunov function, and A is the communication topology matrix between agents; By scaling the Lyapunov function and combining it with the fractional differential equation, we can get Among them, I m is the mth power of the identity matrix, V2(0) is the Lyapunov function, and t=0, for The square of is the transpose of the external disturbance vector of the kth agent, k=1,2,…,w,t≥0∈R,V2(t)≥0∈R,

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