A finite time coordination method for fractional order swarm of agents under input constraints

Abstract

The application relates to a finite time cooperation method for a fractional intelligent agent group under input restriction, comprising the following steps: describing a fractional intelligent agent and information flow among the rest of the agents in the system as a directed graph with a time-varying signal, and characterizing information interaction as an algebraic form by using algebraic graph theory; establishing a fractional dynamics model of the time-varying signal, and using a finite time estimation method to enable each agent to obtain real-time estimation of the assigned time-varying signal; based on the constructed directed graph and the obtained real-time estimation of the time-varying signal, using a finite time distributed estimation method to enable each agent to obtain real-time estimation of the average time-varying signal; based on the obtained real-time estimation of the average time-varying signal, designing a finite time input-restricted control strategy to realize distributed average tracking. Compared with the prior art, the control method provided by the application is applicable to a fractional system, eliminates the restrictive relationship between time constraints and input restrictions, and guarantees distributed average tracking.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of distributed cooperative control of multi-agent systems, and in particular to a finite-time cooperation method for fractional-order agent groups under input constraints. BACKGROUND

[0002] In recent years, multi-agent cooperation has been highly valued and concerned in many fields due to its strong robustness, high reliability, and good scalability. Distributed average tracking is one of the important problems in multi-agent cooperation, which means that each agent is assigned a time-varying signal, and the agent is required to track the average value of the time-varying signal. Most existing researches are only applicable to integer-order systems, while fractional-order dynamics can more accurately describe the characteristics of physical systems in harsh environments. However, not all important properties in integer-order theory are applicable to fractional-order systems. Therefore, it is meaningful to consider the distributed average tracking cooperation of fractional-order agent groups.

[0003] On the basis of achieving the basic control goal of distributed average tracking, further improvement of control performance is considered. On the one hand, considering the external engineering application index constraint, it is usually required that the regulation time of the agent group to complete the cooperation task should have an analytical upper bound. On the other hand, due to the limitation of internal structure physical size, the control input of the agent should evolve within the rated range. At present, the completely distributed anti-windup tracking control method proposed in the invention patent CN113589694B can realize the cooperation of integer-order agent groups under input constraints, but it has not solved the problem of finite-time cooperation control of fractional-order agent groups. The finite-time formation control method based on multi-agent systems proposed in the invention patent CN109144047B can achieve the cooperation of integer-order agent groups in finite time, but it has not solved the problem of finite time and input constraints of fractional-order agent groups. The fundamental reason is that the former requires a larger control input as a drive, which is contradictory to the requirement of the latter. However, neglecting one aspect will reduce the practicality of the algorithm. SUMMARY

[0004] The purpose of the present application is to focus on fractional-order agent groups and consider the problem of distributed average tracking under input constraints and finite-time constraints, and to provide a finite-time cooperation method for fractional-order agent groups under input constraints. This method is applicable to fractional-order dynamics and overcomes the restrictive relationship between finite time and input constraints. The most important part of the present application is to construct a finite-time time-varying signal estimator and a distributed average time-varying signal estimator applicable to fractional-order dynamics, and to design a finite-time input-constrained control strategy based on the estimation results, thereby comprehensively improving the control quality of distributed average tracking.

[0005] The purpose of the present application can be achieved by the following technical solutions:

[0006] A finite-time cooperation method for fractional-order agent groups under input constraints, comprising the following steps:

[0007] Step 1) The fractional-order agent is described as a directed graph with time-varying signals and information flow between the remaining agents in the system, and the information interaction is characterized in algebraic form by using algebraic graph theory;

[0008] Step 2) A fractional-order dynamic model of the time-varying signal is established, and a finite-time estimation method is used to enable each agent to obtain a real-time estimate of the assigned time-varying signal;

[0009] Step 3) Based on the directed graph constructed in step 1) and the real-time estimate of the time-varying signal obtained in step 2), a finite-time distributed estimation method is used to enable each agent to obtain a real-time estimate of the average time-varying signal;

[0010] Step 4) Based on the real-time estimate of the average time-varying signal obtained in step 3), a finite-time input-constrained control strategy is designed to achieve distributed average tracking.

[0011] The step 1) comprises the following steps:

[0012] Step 1-1) Assuming that the initial agent group contains N agents, the time-varying signal assigned to agent i is marked as the N+i agent; the initial agent group and the time-varying signal are reorganized and split to extract N agents and time-varying signals N+i to form a new agent group S i , thereby obtaining N new agent groups;

[0013] Step 1-2) Based on algebraic graph theory, the new agent group S i and the information flow inside it are described as a directed graph , wherein represents the set of agents in S i , and represents the information interaction relationship in S i , (i,j)∈ε i represents that the information of agent i can flow to agent j, is an adjacency matrix, wherein

[0014]

[0015] Step 1-3) Based on the adjacency matrix , the Laplacian matrix is defined, wherein

[0016]

[0017] Step 1-4) Repeat steps 1-2) to 1-3) N times to cumulatively obtain N directed graphs and its corresponding Laplacian matrix is expressed as:

[0018]

[0019] is an N x N matrix, is an N x 1 matrix, 0 N is an N x 1 all-zero vector.

[0020] The agent group and its corresponding time-varying signal both have Caputo fractional order dynamics, wherein the definition of the Caputo fractional order is:

[0021]

[0022] wherein f(t) is a time-varying function with respect to time t, q is a Caputo fractional order, n-1 < q ≤ n, n is a predefined positive integer, Γ(δ) is a gamma function, D q f(t) is a form of q-order differentiation of f(t), f (n) (μ) is an n-order derivative of f(μ).

[0023] The step 2) comprises the following steps:

[0024] Step 2-1) establishing a fractional order dynamics model of the time-varying signal:

[0025] D q x N+i =u N+i ,0<q<1

[0026] wherein q is a Caputo fractional order, x N+i and u N+i are a system state and an input of the time-varying signal N+i respectively, D q x N+i is a form of q-order differentiation of x N+i ;

[0027] Step 2-2) designing a finite time estimator suitable for fractional order dynamics:

[0028]

[0029] wherein z i and v i are estimated values of x N+i and u N+i , is a gain, satisfying and sign(z i -x N+i ) is a sign function;

[0030] Step 2-3) Based on the finite-time estimator, the estimation value z of the time-varying signal N+i is obtained i .

[0031] The step 2) further comprises a verification process and an estimation process of the time-varying signal estimation time,

[0032] Wherein, the verification process is specifically: fusing Caputo fractional derivative property and Lyapunov stability theory, constructing Lyapunov function

[0033] Verify whether the estimation error can converge to zero in finite time, that is:

[0034] z i -x N+i = 0, v i -u N+i = 0

[0035] The estimation process of the time-varying signal estimation time is specifically: analytically obtaining the adjustment time T1 required for time-varying signal estimation, which satisfies:

[0036]

[0037] Wherein,

[0038]

[0039] λ max (H i ) represents the maximum eigenvalue of H i , and λ min (M i ) represents the minimum eigenvalue of M i , is the value of Lyapunov function

[0040] at the initial moment.

[0041] The step 3) comprises the following steps:

[0042] Step 3-1) Based on the directed graph obtained in step 1) According to the estimation value of the time-varying signal N+i obtained in step 2), a finite-time distributed estimator suitable for fractional order dynamics is designed:

[0043]

[0044] Wherein,

[0045] ​​is an auxiliary variable, ρ N+i,k and γ N+i,k are the estimation of the kth agent for the ith time-varying signal, c1>0, c2>0 and c3≥|u N+i | are the estimator gains, σ, ε are the estimator parameters, 0<σ<1<ε;

[0046] Step 3-2) Repeat step 3-1) so that each agent obtains the distributed estimation value of N time-varying signals, and average them to obtain the average time-varying signal estimation value:

[0047]

[0048] where, and are the system state and input estimation of the average time-varying signal, respectively.

[0049] The step 3) further comprises a verification process and an estimation process of the average time-varying signal estimation time,

[0050] wherein the verification process is specifically: combining Caputo fractional derivative properties with Lyapunov stability theory to construct Lyapunov function and to verify whether the estimation error can converge to zero in finite time, i.e.:

[0051] ρ N+i,k -z i = 0, γ N+i,k -v i = 0

[0052] wherein z i and v i are the estimation values of x N+i and u N+i , respectively;

[0053] The estimation process of the average time-varying signal estimation time is specifically: analytically obtaining the adjustment time T2 required for the average time-varying signal estimation, which satisfies:

[0054]

[0055] wherein q is Caputo fractional order, Γ(·) is the gamma function,

[0056] P i = diag{p N+i,1 ,p N+i,2 ,...,p N+i,N} so that is a positive definite matrix, p N+i,k is a constant greater than 0, is the Laplacian matrix corresponding to the directed graph is the element in min (Q i ) is the minimum eigenvalue of Q i , λ max (P i ) is the maximum eigenvalue of P i .

[0057] The step 4) comprises the following steps:

[0058] Step 4-1) establishing fractional-order dynamics model of the agent:

[0059] D q x i = u i +f i (x i ,t)

[0060] wherein q is Caputo fractional order, 0 < q < 1, x i and u i are system state and input of the agent i respectively, f i (x i ,t) is a bounded nonlinear function, and u i satisfies the condition are upper limit and lower limit of the agent input respectively;

[0061] Step 4-2) determining error between each agent state and average time-varying signal estimation value:

[0062]

[0063] Step 4-3) constructing finite-time input limited control strategy based on error e i and average time-varying signal estimation value obtained in step 3):

[0064]

[0065] wherein a i , b i , α, s i are set constants, satisfying a i < 0 < b i , 0 < α < 1, gain g i > 0, r i ≥ f i (x i ,t) |, The saturation function and are defined as:

[0066]

[0067] sign(e i ) is a sign function,

[0068] Step 4-4) realizes distributed control based on a finite-time input limited control strategy.

[0069] The step 4) further comprises a verification process and an estimation process of distributed control time,

[0070] The verification process is specifically: fusing Caputo fractional derivative property and Lyapunov stability theory, constructing Lyapunov function verifying whether the error can converge to zero in a finite time;

[0071] The estimation process of distributed control time is specifically: analytically obtaining the adjustment time T3 required for distributed control, and the adjustment time T3 satisfies:

[0072]

[0073] wherein, is the Lyapunov function at the initial moment, and Γ(·) is a gamma function.

[0074] The total control adjustment time of the method satisfies: T=T1+T2+T3, wherein T1, T2 and T3 are respectively the adjustment time required for time-varying signal estimation, the adjustment time required for average time-varying signal estimation and the adjustment time required for distributed control.

[0075] Compared with the prior art, the present application has the following beneficial effects:

[0076] (1) The present application faces fractional order intelligent agent groups, introduces Caputo fractional derivative property of composite functions, combines the property with Lyapunov stability theorem, avoids invalid Leibniz formula in the proof process, and guarantees that the intelligent agent groups realize distributed average tracking. The considered objects include conventional integer order intelligent agent groups as special cases, and the application range is wide.

[0077] (2) The present application discloses state evolution rules of intelligent agents under limited and unlimited control input conditions, takes into account the adjustment time constraint and control input constraint of intelligent agent groups, i.e. overcomes the mutual restriction problem, and gives an analytical expression of the required adjustment time, which can assist in advance estimation and limitation of the adjustment time, and has practicability in engineering application fields.

[0078] (3) The distribution interaction in the agent group designed in the application is described by a directed graph. The Lyapunov function is constructed by skillfully using algebraic graph theory, so as to overcome the challenge brought by the asymmetric Laplacian matrix in the directed graph to the control design and verification. BRIEF DESCRIPTION OF DRAWINGS

[0079] Figure 1 The flow chart of the method of the application is shown in Figure 1.

[0080] Figure 2 The directed graph of the information interaction of the agent in the simulation of the application is shown in Figure 2.

[0081] Figure 3 The numerical simulation graph of the finite-time time-varying signal estimation based on the Matlab platform is shown in Figure 3.

[0082] Figure 4 The numerical simulation graph of the average time-varying signal estimation based on the Matlab platform is shown in Figure 4.

[0083] Figure 5 The numerical simulation graph of the state evolution of the agent based on the Matlab platform is shown in Figure 5.

[0084] Figure 6 The numerical simulation graph of the control input evolution of the agent based on the Matlab platform is shown in Figure 6. DETAILED DESCRIPTION

[0085] The application will be described in detail below in combination with the drawings and specific embodiments. The embodiments are implemented on the premise of the technical solution of the application, and detailed implementation modes and specific operation processes are given, but the protection scope of the application is not limited to the following embodiments.

[0086] Embodiment 1

[0087] The embodiment provides a finite-time cooperation method for a fractional-order agent group under input restriction, as shown in Figure 1, which comprises the following steps. Figure 1

[0088] Step 1) The information flow between the fractional-order agent and the time-varying signal and the rest of the agents in the system is described as a directed graph, and the information interaction is characterized in an algebraic form by using algebraic graph theory.

[0089] Step 1) comprises the following steps.

[0090] Step 1-1) assumes that the initial agent group contains N agents, and the time-varying signal allocated to the agent i is marked as the N+i agent; the initial agent group and the time-varying signal are recombined and split to extract N agents and N+i time-varying signals to form a new agent group S i , thereby obtaining N new agent groups.​

[0091] Step 1-2) Based on algebraic graph theory, a new group of agents S i and the information flow inside it are depicted as a directed graph Wherein represents the set of agents in S i , and characterizes the information interaction relationship in S i , (i,j)∈ε i characterizes that the information of agent i can flow to agent j, is an adjacency matrix, wherein

[0092]

[0093] Step 1-3) Based on the adjacency matrix Define the Laplacian matrix Wherein

[0094]

[0095] Step 1-4) Repeat steps 1-2) to 1-3) N times to obtain N directed graphs and their corresponding Laplacian matrices are expressed as:

[0096]

[0097] is an N×N matrix, is an N×1 matrix, 0 N is an N×1 all-zero vector.

[0098] The group of agents and their corresponding time-varying signals have Caputo fractional order dynamics, wherein the definition of Caputo fractional order is:

[0099]

[0100] Wherein f(t) is a time-varying function with respect to time t, q is Caputo fractional order, n-1<q≤n, n is a predefined positive integer, Γ(δ) is the gamma function, D q f(t) is the form of taking q-order differential of f(t), f (n) (μ) is the n-order derivative of f(μ).

[0101] Step 2) Establish a fractional order dynamics model of the time-varying signal, and use the finite time estimation method to make each agent obtain the real-time estimation of the assigned time-varying signal.

[0102] Step 2) includes the following steps:

[0103] Step 2-1) Establish the fractional-order dynamic model of the time-varying signal:

[0104] D q x N+i = u N+i , 0 < q < 1 (5)

[0105] where q is the Caputo fractional order, x N+i and u N+i are the system state and input of the time-varying signal N+i, respectively, D q x N+i is the qth-order differential form of x N+i .

[0106] Step 2-2) Design a finite-time estimator for each time-varying signal suitable for fractional-order dynamics:

[0107]

[0108] where z i and v i are the estimates of x N+i and u N+i , respectively, is the gain satisfying and sign(z i -x N+i ) is the sign function.

[0109] Step 2-3) Obtain the estimate z i of the time-varying signal N+i based on the finite-time estimator.

[0110] Step 2-4) Verification process: combine the Caputo fractional derivative property with Lyapunov stability theory to construct the Lyapunov function

[0111]

[0112] where and are based on the Caputo fractional derivative property of a composite function

[0113]

[0114] and Lyapunov stability theory, we obtain:

[0115]

[0116] Verify that the estimation error can converge to zero in finite time, i.e.: z i -x N+i= 0, v i - u N+i = 0

[0117] Step 2-5) Estimation of the estimation time of the time-varying signal: According to equation (9), the adjustment time T1 required for the estimation of the time-varying signal is obtained analytically and satisfies:

[0118]

[0119]

[0120]

[0121] λ max (H i ) represents the maximum eigenvalue of H i , and λ min (M i ) represents the minimum eigenvalue of M i , is the Lyapunov function

[0122] the value of the Lyapunov function at the initial time.

[0123] Step 3) Based on the directed graph constructed in step 1) and the real-time estimation of the time-varying signal obtained in step 2), each agent obtains a real-time estimation of the average time-varying signal using a finite-time distributed estimation method.

[0124] Step 3) includes the following steps:

[0125] Step 3-1) Based on the directed graph obtained in step 1) and the estimation value of the time-varying signal N+i obtained in step 2), a finite-time distributed estimator suitable for fractional-order dynamics is designed:

[0126]

[0127] wherein,

[0128] is an auxiliary variable, ρ N+i,k and γ N+i,k are the estimation of the kth agent for the ith time-varying signal, c1>0, c2>0 and c3≥|u N+i | are the estimator gains, σ, ε are the estimator parameters, 0<σ<1<ε.

[0129] Step 3-2) Repeat step 3-1) so that each agent obtains a distributed estimation value of N time-varying signals, and average them to obtain an average time-varying signal estimation value:

[0130]

[0131] where, and are the system state and input estimates of the mean time-varying signal, respectively.

[0132] Step 3-3) Verification procedure: Fusion Caputo fractional derivative property and Lyapunov stability theory to construct Lyapunov function and

[0133]

[0134] where, P i = diag{p N+i,1 ,p N+i,2 ,...,p N+i,N} such that is a positive definite matrix. Based on Caputo fractional derivative property of a composite function and Lyapunov stability theory, we obtain

[0135]

[0136] λ min (Q i ) is the minimum eigenvalue of Q i , λ max (P i ) is the maximum eigenvalue of P i , it is verified that the estimation error can converge to zero in finite time, i.e., ρ N+i,k -z i = 0, γ N+i,k -v i = 0.

[0137] Step 3-4) Estimation procedure of the estimation time of the mean time-varying signal: According to equations (13) and (14), the adjustment time T2 required for the estimation of the mean time-varying signal is analytically obtained as follows:

[0138]

[0139] where q is the Caputo fractional order, Γ(·) is the gamma function,

[0140] P i = diag{p N+i,1 ,p N+i,2 ,...,p N+i,N} such that is a positive definite matrix, p N+i,k is a constant greater than 0, is the Laplacian matrix corresponding to the directed graph where λ min is the smallest eigenvalue of Q i , λ i is the largest eigenvalue of P max . i i

[0141] Step 4) Design a finite-time input-constrained control strategy based on the real-time estimation of the average time-varying signal obtained in step 3) to achieve distributed average tracking.

[0142] Step 4) includes the following steps:

[0143] Step 4-1) Establish a fractional-order dynamic model of the agent:

[0144] D q x i = u i + f i (x i , t) (16)

[0145] where q is the Caputo fractional order, 0 < q < 1, x i and u i are the system state and input of agent i, respectively, f i (x i , t) is a bounded nonlinear function, and u i satisfies the condition and are the upper and lower limits of the agent input, respectively.

[0146] Step 4-2) Determine the error between each agent state and the average time-varying signal estimate:

[0147]

[0148] Step 4-3) Based on the error e i and the average time-varying signal estimate obtained in step 3), construct a finite-time input-constrained control strategy:

[0149]

[0150] where a i , b i , α, s i are set constants, satisfying a i < 0 < b i , 0 < α < 1, the gain g i > 0, r i ​​≥f i (x i ,t)|, is the saturation function and are defined as:

[0151]

[0152] sign(e i ) is the sign function,

[0153] Step 4-4) Distributed control is realized based on the finite-time input constraint control strategy.

[0154] Step 4-5) Verification process: Caputo fractional derivative properties and Lyapunov stability theory are fused to construct Lyapunov function

[0155]

[0156] Caputo fractional derivative properties and Lyapunov stability theory are fused to obtain that when , there is

[0157]

[0158] and when , there is

[0159]

[0160] It is verified that the error can converge to zero in finite time, that is, e i = 0.

[0161] Step 4-6) Distributed control time estimation process: the adjustment time T3 required for distributed control is analytically obtained to satisfy:

[0162]

[0163] where, is the value of Lyapunov function at the initial moment, and Γ(·) is the gamma function.

[0164] In summary, the total control adjustment time of the finite-time cooperation method provided in the embodiment satisfies: T=T1+T2+T3, where T1, T2 and T3 are respectively the adjustment time required for time-varying signal estimation, the adjustment time required for average time-varying signal estimation and the adjustment time required for distributed control.

[0165] Embodiment 2

[0166] This embodiment is to verify the designed score agent group collaboration method based on the estimator method by numerical simulation. An agent group consisting of 8 agents is considered, and each agent is assigned a time-varying signal. Based on the Matlab simulation platform, numerical simulation verification is carried out to evaluate the effectiveness of the collaboration method. Mainly includes: information flow relationship description, finite time time-varying signal estimation, average time-varying signal distributed estimation, and finite time input limited control strategy. Specifically as follows:

[0167] (1) Information flow relationship description:

[0168] This part corresponds to step 1) shown in Figure 1 . Specifically, this embodiment considers that the agent group contains 8 agents, labeled 1-8. Each agent is assigned a time-varying signal, labeled 9-16. The information flow relationship between agent i and other agents, time-varying signals is as shown in Figure 2 . The agent group and time-varying signal are recombined and split into 8 sets, based on algebraic graph theory to establish algebraic relationship, for Node set is The corresponding adjacency matrix And Laplacian matrix Is:

[0169] m i = 1 and m j = 0, j≠i, i,j = 1,2,...,8.

[0170] (2) Finite time time-varying signal estimation:

[0171] This part corresponds to step 2) shown in Figure 1 . The dynamic model of time-varying signal is:

[0172]

[0173] The parameters in equation (5) are selected to satisfy

[0174] The form of finite time time-varying estimator is:

[0175]

[0176] The parameters in equation (6) are selected to satisfy As shown in Figure 3 , the estimated value z i will be equal to the true time-varying signal x 8+i in a finite time.

[0177] (3) Average time-varying signal distributed estimation:

[0178] This part corresponds to Figure 1 Step 3) shown in the figure, the form of the distributed observer is:

[0179]

[0180] The parameter selection in formula (11) satisfies c1=5, c2=5, c3=10, As Figure 4 shown, the average time-varying signal estimation value and will be equal to the real time-varying signal in a limited time.

[0181] (4) Finite time input limited control strategy:

[0182] This part corresponds to Figure 1 Step 4) shown in the figure. The fractional order dynamic model of the agent is:

[0183]

[0184] The parameter selection in formula (16) satisfies The control input u i is limited in the range According to the error between the state of each agent and the average time-varying signal estimation value, the finite time input limited control strategy is constructed:

[0185]

[0186] The parameter selection in formula (18) satisfies g i =5, . As Figure 5 shown, under the action of the control strategy u i , the state of the agent i will converge to the average time-varying signal in a limited time. As Figure 6 shown, the control input is always kept in the range evolution.

[0187] This embodiment proposes a finite time cooperation method for fractional order agent group under input limitation based on estimator technology. Unlike traditional integer order agent group, it focuses on more general fractional order agent group, and the designed control method has wider application range. For fractional order autonomous agent group, a distributed average tracking method under the requirements of finite time and input limitation is considered, which overcomes the mutual restriction problem, and gives the analytical expression of the required adjustment time, which improves the practicality of the control method.

[0188] The preferred embodiments of the present application have been described above in detail. It should be understood that modifications and variations to the preferred embodiments could be made by those skilled in the art in light of the teachings above. It is therefore contemplated that the application can encompass other variations and modifications that fall within the scope of the claims.

Claims

1. A finite-time collaboration method for fractional-order agents under input constraints, characterized by: The following steps are involved: Step 1) Describe the information flow between the fractional-order agent, the time-varying signal, and the other agents in the system as a directed graph, and use algebraic graph theory to represent the information interaction in an algebraic form; Step 2) Establish a fractional-order dynamics model of the time-varying signal and use the finite-time estimation method to enable each agent to obtain a real-time estimate of the assigned time-varying signal; Step 3) Based on the directed graph constructed in step 1) and the real-time estimation of the time-varying signal obtained in step 2), each agent obtains a real-time estimation of the average time-varying signal using a finite-time distributed estimation method; Step 4) Based on the real-time estimation of the average time-varying signal obtained in step 3), a finite-time input-constrained control strategy is designed to achieve distributed average tracking; The step 4) includes the following steps: Step 4-1) Establish a fractional-order dynamics model of the agent: in, q is the Caputo fraction, , and Agents system status and inputs, is a bounded nonlinear function, requiring Meet the conditions and , 、 are the upper and lower limits of the agent’s input respectively; Step 4-2) Determine the error between each agent's state and the average time-varying signal estimate: Step 4-3) Based on the error and the average time-varying signal estimate obtained in step 3) , construct a finite-time input-constrained control strategy: in, , , , To set a constant, satisfy , , , gain 、 , is the input estimate of the average time-varying signal obtained in step 3), the saturation function and They are defined as: is a sign function, ; Step 4-4) Implement distributed control based on a finite-time input-constrained control strategy.

2. The finite-time collaboration method for fractional-order agents with input constraints according to claim 1, characterized in that: The step 1) includes the following steps: Step 1-1) Assume that the initial group of agents contains intelligent agent, intelligent agent The assigned time-varying signal is labeled Agents; reorganize and split the initial agent group and time-varying signals, extract Agents and time-varying signals Form a new group of agents , thus we get A new group of agents; Step 1-2) Based on algebraic graph theory, the new group of agents The information flow inside it is depicted as a directed graph ,in represent The collection of agents in Characterization The information interaction relationship in Representing an Agent Information can flow to the agent , is the adjacency matrix, where Steps 1-3) Based on the adjacency matrix , define the Laplace matrix ,in, Steps 1-4) Repeat Step 1-2) - Step 1-3), cumulatively obtain Directed Graph and its corresponding Laplace matrix , expressed as: for dimensional matrix, for dimensional matrix, for dimensional all-zero vector.

3. The finite-time collaboration method for fractional-order agents with input constraints according to claim 2, characterized in that: The agent group and its corresponding time-varying signal both have Caputo fractional-order dynamics, where the Caputo fractional order is defined as: in, It's about time t The time-varying function of is the gamma function, , for Pick The form of the order differential, for of Derivatives.

4. The finite-time collaboration method for fractional-order agents with input constraints according to claim 1, characterized in that: The step 2) includes the following steps: Step 2-1) Establish a fractional-order dynamics model of the time-varying signal: in, and Time-varying signals system status and inputs, for Pick The form of the order differential; Step 2-2) Design a finite-time estimator suitable for fractional-order dynamics: in, and They are and The estimated value of Is gain, satisfaction ,as well as is a sign function; Step 2-3) Based on the finite time estimator, the time-varying signal is obtained Estimated value of .

5. The finite-time collaboration method for fractional-order agents with input constraints according to claim 4, characterized in that: Said step 2) also includes a verification process and an estimation process of the time-varying signal estimation time, The verification process is as follows: integrating Caputo fractional derivative properties with Lyapunov stability theory to construct Lyapunov function , verify whether the estimation error can converge to zero in a finite time, that is: The estimation process of the time-varying signal estimation time is specifically as follows: Analyze and obtain the adjustment time required for the time-varying signal estimation satisfy: in, , express The maximum eigenvalue of express The minimum eigenvalue of is the Lyapunov function The value at the initial moment.

6. The finite-time collaboration method for fractional-order agents with input constraints according to claim 1, characterized in that: The step 3) includes the following steps: Step 3-1) Based on the directed graph obtained in step 1) , according to the time-varying signal obtained in step 2) To estimate , design a finite-time distributed estimator for fractional-order dynamics: in, , , , , , is an auxiliary variable, and They are The agent is The estimation of a time-varying signal, , and is the estimator gain, 、 are the estimator parameters, ; Step 3-2) Repeat step 3-1) so that each agent obtains The distributed estimates of the time-varying signal are averaged to obtain the average time-varying signal estimate: in, and are the system state and input estimates of the average time-varying signal, respectively.

7. The finite-time collaboration method for fractional-order agents with input constraints according to claim 6, characterized in that: Said step 3) also includes a verification process and an estimation process of the average time-varying signal estimation time, The verification process is as follows: integrating Caputo fractional derivative properties with Lyapunov stability theory to construct Lyapunov function and , verify whether the estimated error can converge to zero in a finite time, that is: in, and They are and estimated value of; The specific process of estimating the average time-varying signal estimation time is as follows: Analyze and obtain the adjustment time required for the average time-varying signal estimation satisfy: in, is the gamma function, , , , , Make is a positive definite matrix, is a constant value greater than 0, for dimensional matrix, which is the Laplace matrix corresponding to the directed graph The elements in yes The minimum eigenvalue of yes The maximum eigenvalue of .

8. The finite-time collaboration method for fractional-order agents with input constraints according to claim 1, characterized in that: Said step 4) also includes a verification process and a distributed control time estimation process, The verification process is as follows: integrating Caputo fractional derivative properties with Lyapunov stability theory to construct Lyapunov function , verify whether the error can converge to zero in a finite time; The specific process of estimating the distributed control time is as follows: Analyze and obtain the adjustment time required for distributed control T 3 Satisfaction: in, is the Lyapunov function The value at the initial moment, is the gamma function.

9. The finite-time collaboration method for fractional-order agents with input constraints according to claim 1, characterized in that: The total control adjustment time of the method satisfies: T = T 1+ T 2+ T 3, among which, T 1. T 2. T 3 are the adjustment time required for time-varying signal estimation, the adjustment time required for average time-varying signal estimation and the adjustment time required for distributed control.

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