A finite time consensus control method for leader-follower multi-agent system

Abstract

The application belongs to the field of multi-agent system control, and relates to a finite time consensus control method for a leader-follower multi-agent system, comprising the following steps: constructing a communication topology graph G of the leader-follower multi-agent system; the leader-follower multi-agent system comprises a plurality of followers and a leader; constructing a multi-agent dynamics system; the multi-agent dynamics system comprises a leader dynamics system and a follower dynamics system; performing finite time consensus control on the leader-follower multi-agent system by using a traction control method based on the communication topology graph G and the multi-agent dynamics system; in the traction control, the topological condition is relaxed, the traction control gain is corrected according to the neighbor communication gain, the follower obtains its control input through the information of the neighbor follower, the probability convergence is ensured even if part of the followers cannot indirectly obtain the leader information, the anti-interference ability is enhanced, the convergence speed is improved, and the communication resource consumption is reduced.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent system control technology, specifically relating to a finite-time consistency control method for a leader-follower multi-agent system. Background Technology

[0002] In practical problems, due to factors such as time, resources, and cost, multi-agent systems are often required to converge to consensus within a finite time. Therefore, research on finite-time consensus is essential. Finite-time consensus refers to the ability of all agents in a system to reach the same state within a certain time using an effective consensus algorithm. Due to various uncontrollable factors, such as equipment accuracy and the natural environment, systems are often in complex or dangerous environments and are constantly affected by uncertainties such as latency, noise, and external interference. This leads to discrepancies between the measured agent states and the actual states, compromising system stability.

[0003] Taking all the above into consideration, in order to make the research more in line with reality, we will consider improving the convergence speed, reducing communication resources, and improving anti-interference capabilities. Summary of the Invention

[0004] To address the aforementioned problems in the prior art, this invention employs a finite-time consistency control method for a leader-follower multi-agent system, comprising:

[0005] S1. Construct the communication topology G of the leader-follower multi-agent system; the leader-follower multi-agent system includes: multiple followers and one leader;

[0006] S2. Construct a multi-agent dynamic system; the multi-agent dynamic system includes: a leader dynamic system and a follower dynamic system;

[0007] S3. Based on the communication topology G of the leader-follower multi-agent system and the multi-agent dynamics system, the leader-follower multi-agent system is subjected to finite-time consistency control using the traction control method.

[0008] Finite-time consistency control for leader-follower multi-agent systems includes:

[0009] S31. Assumptions and leader-follower finite-time consistency conditions for constructing traction control node selection rules based on communication topology graph G and multi-agent dynamics system;

[0010] S32. Design a distributed finite-time observer and control protocol based on the assumption of traction control node selection rules;

[0011] S33. Control the leader-follower multi-agent system based on a distributed finite-time observer and control protocol;

[0012] S34. Based on stochastic Lyapunov stability theory and leader-follower finite-time consistency condition, it is verified that multi-agent dynamics systems can achieve probability-dependent finite-time consistency under control protocols.

[0013] Beneficial effects:

[0014] 1. This invention breaks through the traditional requirement that "the system must have a spanning tree rooted in the leader". It relaxes the topology conditions in traction control and corrects the traction control gain according to the neighbor communication gain. When the system has no spanning tree, each follower obtains its control input through the information of its neighbor followers. This expands the applicable scenarios of the system from "strongly connected topology" to weak topology of "arbitrary connectivity + partial traction". It ensures that even if some followers cannot indirectly obtain the leader's information, they can still converge according to probability. This keeps the system stable when the topology changes dynamically, enhances anti-interference ability, reduces convergence delay caused by topology restrictions, and significantly improves convergence speed. At the same time, it does not rely on a global strongly connected structure, reduces cross-network layer information transmission, and reduces communication resource consumption.

[0015] 2. This invention proposes a distributed finite-time observer, which allows each follower to autonomously estimate the leader's state using only the estimation errors of its neighboring followers' finite-time observers and the estimation errors of its own finite-time observers. This avoids each follower directly obtaining the leader's global state, improves the system's anti-interference capability, significantly reduces communication resource consumption, and improves energy efficiency and real-time performance. As a result, it achieves fully distributed autonomy, gets rid of dependence on the leader's global state, and adapts to dynamic, large-scale, and high-risk scenarios.

[0016] 3. Because the system contains noise, this invention utilizes Itoh's formula to decompose the Lyapunov function into a combination of "position error term" and "velocity error term," and then derives the stochastic differential of the error. This accurately characterizes the co-evolution law of position and velocity errors, avoiding the convergence asynchrony problem caused by single error term analysis and improving the overall convergence speed. By specifically handling the random interference of position and velocity errors, there is no need to transmit redundant global information for error correction, reducing communication resource consumption. At the same time, Itoh's formula's accurate decomposition and compensation of the noise term can effectively offset the impact of random interference on error convergence. Combined with the positive definite characteristic of the Lyapunov function, it significantly improves the system's anti-interference capability. Finally, it rigorously and efficiently proves that the position and velocity of the second-order system can simultaneously converge to the leader state in a probabilistic finite time. Attached Figure Description

[0017] Figure 1A flowchart of a finite-time consistency control method for a leader-follower multi-agent system provided in an embodiment of the present invention;

[0018] Figure 2 A schematic diagram of a second-order multi-agent system containing three followers and one leader under different topologies G1, G2 and G3 provided in the embodiments of the present invention;

[0019] Figure 3 This is a schematic diagram of the trajectories of all agents under the topology G1 provided in an embodiment of the present invention;

[0020] Figure 4 This is a schematic diagram of the trajectories of all agents under the topology G2 provided in this embodiment of the invention;

[0021] Figure 5 This is a schematic diagram of the trajectories of all agents under the topology G3 provided in an embodiment of the present invention. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] like Figure 1 As shown, this embodiment of the invention employs a finite-time consistency control method for a leader-follower multi-agent system, comprising:

[0024] S1. Construct the communication topology of the leader-follower multi-agent system; the leader-follower multi-agent system includes: n followers and one leader;

[0025] The communication topology of a leader-follower multi-agent system is G = (V, E, A); where V = {v1, v2, ..., v...}. n Let} be a set of nodes, and let v be a node in the set of nodes. i Let E represent a follower or leader, E∈V×V be the edge set, and the edges in the edge set represent the communication relationship between nodes. A is the weighted adjacency matrix of graph G, A[1:n,1:n] is the weighted adjacency matrix between followers of graph G, and A[0] is the connection weight vector between followers and leader.

[0026] If follower i and follower j can communicate with each other, then follower j and follower i are neighboring agents, N. i ={j|(v i ,v jLet E represent the set of all neighboring followers of follower i.

[0027] Weighted adjacency matrix A[1:n,1:n]=[a ij ]∈R n×n When j∈N i When i, j = 1, 2, ..., n, a ij =a ji >0; otherwise, a ij =a ji =0, and a ii =0.

[0028] Connect the weight vector A[0] = [w1(t), w2(t), ..., w n (t)] T Among them, w i (t) represents the connection weight between follower i and leader, i.e., when follower i and leader can communicate, w i (t)>0, otherwise, w i (t) = 0.

[0029] S2. Construct a multi-agent dynamic system; the multi-agent dynamic system includes: a leader dynamic system and a follower dynamic system;

[0030] The follower dynamics system is as follows:

[0031]

[0032] The leader dynamics system is as follows:

[0033]

[0034] Among them, u i (t), x i (t) and v i (t) represents the control input, position, and velocity of follower i∈[1,n] at time t, respectively, and u0(t), x0(t), and v0(t) represent the control input, position, and velocity of leader at time t, respectively. Let i represent the rate of change of position and velocity of follower i∈[1,n] at time t, respectively. Let represent the rate of change of the leader's position and velocity at time t, respectively.

[0035] S3. Based on the communication topology G of the leader-follower multi-agent system and the multi-agent dynamics system, the leader-follower multi-agent system is subjected to finite-time consistency control using the traction control method.

[0036] Finite-time consistency control for leader-follower multi-agent systems includes:

[0037] S31. Assumptions and leader-follower finite-time consistency conditions for constructing traction control node selection rules based on communication topology graph G and multi-agent dynamics system;

[0038] The assumptions underlying the traction control node selection rules include:

[0039] Assumption 1: Traction control matrix P(t) = [p1(t), p2(t), ..., p n (t)] T Traction control gain p of agent i i (t) satisfies the following condition: when controlling agent i, the traction control gain p of agent i is... i (t)>0; otherwise, p i (t) = 0;

[0040] In other words, for any follower i, the leader's state can always directly or indirectly affect the follower's state.

[0041] Assumption 2: There exists a continuously differentiable function g(·):R→R that satisfies the following conditions:

[0042]

[0043] Where, x i x j Let ζ be the independent variable of the function g(·), and ζ > 0 be the Lipschitz constant;

[0044] Assumption 3: There exists a function f(y):R→R satisfying the following conditions:

[0045]

[0046] Where y is the independent variable of the function f(y), γ>0, and γ is the gain coefficient of the lower bound of the function, which is used to ensure the lower limit of the control strength and support the scaling of Lyapunov analysis; The ratio is an odd integer, used to ensure y q It is defined everywhere in the real number field, q<1 is a sublinear growth, used to balance the control effect of large / small errors; q1 and q2 are both positive odd integers, and R is the real number field;

[0047] Assumption 4: The communication topology G of the leader-follower multi-agent system is a connected graph.

[0048] The leader-follower finite-time consistency condition is: for any initial conditions, there exists a random rest period T0 ≥ 0 satisfying the probability P{T0 < ∞} = 1, such that... We expect E[T(x0,ω)]≤T0; where T(x0,ω) is the resting time of the multi-agent dynamics system, ω is the sample path of the multi-agent dynamics system, and x0 is the initial state of the multi-agent dynamics system.

[0049] In a multi-agent dynamics system, a sample path refers to the trajectory record of the state (such as position and velocity) of each agent in the system as it changes over time during a specific stochastic evolution. Different sample paths ω correspond to different noise disturbances, which will lead to different convergence times for the system. When defining probability-finite-time convergence, it is necessary to ensure that the resting time is finite for almost all sample paths ω.

[0050] S32. Design a distributed finite-time observer and control protocol based on the assumptions of the control node selection rules.

[0051] Designing a distributed finite-time observer includes:

[0052] Starting from distributed requirements, construct state equations that conform to second-order kinematics. By introducing traction control gain and nonlinear power terms into the state equations conforming to second-order kinematics, a distributed finite-time observer is obtained; wherein, the nonlinear power terms include: the estimation errors of the finite-time observers of the follower and its neighboring followers. And the estimation error of the leader's state by the follower's finite-time observer.

[0053] The distributed finite-time observer is:

[0054]

[0055] in, Let be the estimate of the rate of change of the leader's position for the i-th follower. Let be the estimate of the rate of change of the leader's velocity for the i-th follower. Let αi represent the i-th follower's estimates of the leader's position x0(t) and velocity v0(t), respectively, where 0 < α1 < 1, α1 is a design parameter defining the sublinear growth characteristic of the nonlinear term, and α2 is a design parameter. At that time, the convergence characteristics of position error and velocity error are matched in tandem. This is the corrected traction control gain.

[0056] If Assumption 1 holds, then the leader’s influence on each follower is attainable, providing a topological basis for the information transmission of the observer, and enabling the Lyapunov derivative of the observer to satisfy the finite-time convergence condition. Therefore, the finite-time observer can achieve finite-time observation.

[0057] The distributed finite-time observer allows each follower i to autonomously estimate the leader's state using only the estimation errors of its neighboring followers' finite-time observers and the estimation errors of its own finite-time observer. This supports the control protocol, avoids each follower directly obtaining the leader's global state, improves the system's anti-interference capability, significantly reduces communication resource consumption, and improves energy efficiency and real-time performance. As a result, it achieves fully distributed autonomy, gets rid of dependence on the leader's global state, and adapts to dynamic, large-scale, and high-risk scenarios.

[0058] The design control protocol includes:

[0059] pass Handling the position and speed differences between followers and neighbors;

[0060] pass Handling the estimation discrepancy between followers and leaders;

[0061] in, It's the traction gain, added It can enhance the followers' ability to track the leader; distributed observers For each follower i, a local estimate of the leader's state (i.e., position x0, velocity v0) is given. The traction term is designed directly using the observer's estimation results, realizing the fusion of the observer's local estimation of the leader's state and the control protocol to traction the follower. This allows the follower to track the leader without global communication, only through local interaction.

[0062] Introducing nonlinear power terms accelerates convergence:

[0063] By introducing |x j (t)-x i (t)| p 、|v j (t)-v i (t)| p-1 Nonlinear power terms, etc., enable control to avoid overload under large errors and converge more sensitively under small errors, thereby accelerating the system to converge to "consistent state of all agents" and supporting the requirement of "finite time".

[0064] The variance term, which introduces random disturbance, cancels out the random disturbance with the random term:

[0065] Variance compensation term: Used to counteract the average interference of noise "second variation" on the system.

[0066] Random item: σ ij g(v j (t)-v i (t))η ij(t) directly adapts to the random fluctuation form of white noise η, and actively responds to the disruption of consistency caused by noise.

[0067] Finally, we introduce the symbolic function. and linear feedback term Obtain the control protocol.

[0068] The control protocol is represented as follows:

[0069]

[0070] Where k1≥ζ, ζ>0 is the Lipsitz constant, k1 and k2 are the gain parameters for noise compensation, whose core function is to cancel the interference of random noise on the system. They are derived through stochastic Lyapunov stability analysis. p is a nonlinear power parameter, whose core function is to regulate the convergence characteristics of the system. ρ is the feedback strength, and sign is the sign function. Let $\mathbf{i}$ be the variance of white noise between followers $i$ and $j$. The variance of white noise between follower i and leader i is determined by experimentally statistically analyzing the fluctuation amplitude of the noise, or by theoretical modeling, given η. ij (t) is the standard white noise function between followers i and j, η i0 The standard white noise function between follower i and leader i is randomly generated. Let x0(t) and v0(t) be the estimates of the leader's position x0(t) and velocity v0(t) by the i-th follower, respectively, as output by the distributed finite-time observer.

[0071] This control protocol breaks through the traditional requirement that "the system must have a spanning tree rooted in the leader." It relaxes the topology conditions in traction control and adjusts the traction control gain according to the neighbor communication gain. When the system has no spanning tree, each follower obtains its control input through the information of its neighbor followers. This expands the applicable scenarios of the system from "strongly connected topology" to weak topology of "arbitrary connectivity + partial traction". It ensures that even if some followers cannot indirectly obtain the leader's information, they can still converge according to probability. This keeps the system stable when the topology changes dynamically, enhances anti-interference ability, reduces convergence delay caused by topology constraints, and significantly improves convergence speed. At the same time, it does not rely on a global strongly connected structure, reduces cross-network layer information transmission, and reduces communication resource consumption.

[0072] S33. Control the leader-follower multi-agent system based on a distributed finite-time observer and control protocol.

[0073] Specifically, controlling the leader-follower multi-agent system based on the distributed finite-time observer and control protocol includes: using the output of the distributed finite-time observer to estimate the position and velocity of each follower relative to the leader; substituting each follower's estimate of the leader's position and velocity into the control protocol to obtain the control input for each follower; and controlling each follower based on the control input.

[0074] S34. Based on stochastic Lyapunov stability theory and leader-follower finite-time consistency condition, it is verified that multi-agent dynamics systems can achieve probability-dependent finite-time consistency under control protocols.

[0075] The multi-agent dynamics system is transformed using Itō's formula according to the control protocol, resulting in the transformed multi-agent dynamics system.

[0076] The specific transformation process is as follows: Substitute the control protocol into the stochastic second-order multi-agent dynamics system, and use the Iton formula to decompose the stochastic second-order multi-agent dynamics system into drift term (dt) and diffusion term (dω), thus obtaining the Iton expansion of the stochastic second-order multi-agent dynamics system.

[0077] The core function of this transformation process is to decompose the stochastic system into "deterministic drift" and "random diffusion" terms, providing a computable standard form for stochastic Lyapunov stability analysis, supporting the theoretical proof of "probability-bounded time consistency", and facilitating the analysis of expected stability.

[0078] The transformed form of the multi-agent dynamics system is as follows:

[0079]

[0080] Where, ω ij (t) represents the random perturbation of the interaction between followers i and j, ω i0 (t) represents the random perturbation of the interaction between follower i and leader i.

[0081] If Assumptions 1, 2, 3, and 4 hold true, and max{1,-o}<ρ<2-o, then under the control protocol, the multi-agent dynamics system can achieve probability-dependent finite-time consistency; where ρ is the feedback strength, and o is the scale characteristic of the noise interference, which is the upper and lower bound constraint on the feedback strength ρ.

[0082] max{1,-o}<ρ: Prevents overly strong control. If the feedback strength ρ is too small, the negative feedback will be insufficient, and the positive noise term will dominate, making convergence impossible. This ensures a balance between negative feedback and random disturbances.

[0083] ρ < 2-o: Ensures that the control is strong enough. If the feedback strength ρ is too small, the negative feedback will be insufficient, the positive noise term will dominate, and convergence will not be possible. Strong negative feedback is the key to finite-time convergence.

[0084] prove:

[0085] make Then we have dθ i1 (t)=θ i2 (t)dt;

[0086] Substituting into the transformed multi-agent dynamics system dv i (t), then we have

[0087]

[0088] Choose the following Lyapunov function:

[0089] V(t)=V1(t)+V2(t))(9)

[0090] Among them, the Lyapunov function

[0091] From Itoh's formula, the differentials of V1(t) and V2(t) can be obtained as follows:

[0092]

[0093] According to equation (8) and the differentials of V1(t) and V2(t), we can obtain:

[0094]

[0095] From the definition of stochastic differential equations and equation (11), we can obtain:

[0096]

[0097] Because the system contains noise, this invention utilizes Itoh's formula to decompose the Lyapunov function into a combination of "position error term" and "velocity error term," and then derives the stochastic differential of the error. This accurately characterizes the co-evolution law of position and velocity errors, avoiding the convergence asynchrony problem caused by single error term analysis and improving the overall convergence speed. By specifically handling the random interference of position and velocity errors, there is no need to transmit redundant global information for error correction, reducing communication resource consumption. At the same time, Itoh's formula's accurate decomposition and compensation of the noise term can effectively offset the impact of random interference on error convergence. Combined with the positive definiteness of the Lyapunov function, this significantly improves the system's anti-interference capability. Finally, it rigorously and efficiently proves that the position and velocity of the second-order system can simultaneously converge to the leader state in a probabilistic finite time.

[0098] Lemma 3: For have

[0099]

[0100] Lemma 4: Assume the function h:R 2 →R + Satisfy h(x) i ,x j )=h(x j ,x i Given an undirected graph G and a set of numbers y1, y2, ..., yn, where i, j = 1, 2, ..., n and i ≠ j, then for any undirected graph G and a set of numbers y1, y2, ..., yn, ... n The following inequality holds.

[0101]

[0102] From Assumption 2, Lemma 3, Lemma 4, and Equation (12), we can obtain:

[0103]

[0104] Lemma 5: Suppose there exists a non-negative continuous function w(t) such that Where the parameter c > 0, the function v(s) ≥ 0, and s is the independent variable of the function v(s), then we have

[0105] From assumption 3, lemma 5, and equation (15), we can obtain:

[0106]

[0107] Where ξ=min|θ i2 | represents the state error of the multi-agent system, and γ is the gain coefficient of the lower bound, which is determined by the nonlinear characteristics of the system, noise intensity, etc., and is used to ensure the lower limit of the control strength.

[0108] From Lemma 3 and Equation (16), we can obtain:

[0109]

[0110] Let parameter θ1(t) = (θ 11 (t),θ 21 (t),…,θ n1 (t)) T Parameter θ2(t)=(θ 12 (t),θ 22 (t),…,θ n2 (t)) T ,parameter parameter Then we have:

[0111]

[0112] in, The smallest eigenvalue of matrix 2L(A)+C The power, L(A) = [l] ij ]=DA∈R n×n Let A be the Laplace matrix of the adjacency matrix A.

[0113] Lemma 1: The Laplace matrix L has the following properties:

[0114] 1. The Laplace matrix L of an undirected graph is a symmetric positive semi-definite matrix, and for any vector x = [x1, x2, ..., xn], the value of L is constant. n ] T ,have

[0115]

[0116] 2. The Laplace matrix L is a symmetric matrix with n real eigenvalues, and its eigenvalues ​​satisfy:

[0117] 0=λ1(L)≤λ2(L)≤…≤λ n (L)=λ max

[0118] Where, λ max λ2(L) is the largest eigenvalue and L is the second smallest eigenvalue, representing the connectivity of the undirected graph; if the undirected graph is a connected graph or contains a spanning tree, then λ2(L)>0.

[0119] 3. If an undirected graph G is a connected graph or contains a spanning tree, and vector b = [b1, b2, ..., b...], then... n ] T If ≥0 and b≠0, then L+diag(b) is a positive definite matrix.

[0120] Lemma 2: If matrix S∈R n×n If is a symmetric matrix, then we have

[0121]

[0122] Where, λ min (S) is the smallest eigenvalue, λ max (S) is the largest eigenvalue, R n It is an n-dimensional vector space.

[0123] By Lemma 1, Lemma 2, and Equation (18), let λ * =λ min (2L(A)+C),ξ * =min{ξγ,γ}, then we have:

[0124]

[0125] From Lemma 3 and Equation (19), we can obtain:

[0126]

[0127] By Lemma 3, the solution of a multi-agent dynamical system converges to 0 in probability within a finite time, and the random resting time function T(x0,ω) satisfies:

[0128]

[0129] That is, the system reaches consistency in a finite amount of time with probability.

[0130] In one embodiment, such as Figure 2 As shown, consider a second-order multi-agent system with three followers and one leader under different topologies G1, G2, and G3. Under the distributed finite-time observer (5) and control protocol (6), the parameters satisfy: a ij =1, α1=0.5, ρ = 1.5, σ ij =σ i0 =2, g(x) = sinx, so the Lipschitz constant ζ ≥ 1 can be calculated. Choose parameters: ζ = 1, k1 = k2 = 2, where η is the standard white noise function. ij (t) and η i0 (t) is randomly generated.

[0131] The initial state of the follower is: x(0)=(3,-6,-7) T v(0) = (-9, 6, 5) T ;

[0132] The leader's initial state is: x0(0) = -9, v0(0) = -3;

[0133] Under topologies G1, G2, and G3, the connection weight vectors between followers and leaders in each topology G1, G2, and G3 are W1 = (0,0,0). T W2 = (0,0,0) T And W3 = (1,0,0) T Additionally, the traction control gain matrix is ​​chosen to be P1 = (1,0,0). T P2 = (1,0,0) T P3 = (0,0,0) T The corrected traction control gain matrix can then be calculated. satisfy

[0134] Figure 3 , Figure 4 and Figure 5 The position and velocity trajectories of the agents under topologies G1, G2, and G3 are presented. As can be seen from the figures, the position and velocity states of all followers converge probabilistically to those of the leader within a finite time. Therefore, the results demonstrate the validity and correctness of the theorem under different topologies.

[0135] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A finite-time consistency control method for a leader-follower multi-agent system, characterized in that, include: S1. Construct the communication topology G of the leader-follower multi-agent system; A leader-follower multi-agent system consists of multiple followers and one leader. S2. Construct a multi-agent dynamic system; the multi-agent dynamic system includes: a leader dynamic system and a follower dynamic system; S3. Based on the communication topology G and multi-agent dynamics system of leader-follower multi-agent system, the leader-follower multi-agent system is subjected to finite-time consistency control using the traction control method. Finite-time consistency control for leader-follower multi-agent systems includes: S31. Assumptions and leader-follower finite-time consistency conditions for constructing traction control node selection rules based on communication topology graph G and multi-agent dynamics system; S32. Design a distributed finite-time observer and control protocol based on the assumption of traction control node selection rules; S33. Control the leader-follower multi-agent system based on a distributed finite-time observer and control protocol; S34. Based on stochastic Lyapunov stability theory and leader-follower finite-time consistency condition, it is verified that multi-agent dynamics systems can achieve probability-dependent finite-time consistency under control protocols. The assumptions underlying the traction control node selection rules include: Assume the traction control gain of agent i The following condition must be met: When controlling agent i, the traction control gain of agent i is... ;otherwise, ; Suppose there exists a continuously differentiable function g(·): The following conditions must be met: ;in, Let Lipschitz constant be _____. Let g be the independent variable of the function g(·), and R be the real number field; Assume there exists a function The following conditions must be met: Where y is a function The independent variable, , The gain coefficient is the lower bound of the function. For odd integer ratios, q1 and q2 are both positive odd integers; Assume that the communication topology G of the leader-follower multi-agent system is a connected graph; Distributed finite-time observer: ； in, Let be the estimate of the rate of change of the leader's position for the i-th follower. Let be the estimate of the rate of change of the leader's velocity for the i-th follower. These represent the positions of the i-th follower relative to the leader. and speed The estimate, It is a sign power function. , For design parameters, , For design parameters, Let J represent the connection weights between follower j and follower i in the communication topology graph G. Let G be the set of neighboring followers of follower i in the communication topology graph G. The traction control gain corrected for follower i.

2. The finite-time consistency control method for a leader-follower multi-agent system according to claim 1, characterized in that, Communication topology diagram of a leader-follower multi-agent system Where V is the set of nodes, where nodes represent followers or leaders, and E is the set of edges, where edges represent the communication relationships between nodes. For a weighted adjacency matrix, This is a weighted adjacency matrix among followers. Let n be the connection weight vector between followers and leaders, where n is the number of followers.

3. The finite-time consistency control method for a leader-follower multi-agent system according to claim 1, characterized in that, The follower dynamics system is as follows: ； The leader dynamics system is as follows: ； in, , and They represent followers respectively. The control input, position, and velocity at time t , and These represent the leader's control input, position, and velocity at time t, respectively. , They represent followers respectively. The rate of change of position and velocity at time t , Let represent the rate of change of the leader's position and velocity at time t, respectively.

4. The finite-time consistency control method for a leader-follower multi-agent system according to claim 1, characterized in that, The leader-follower finite-time consistency condition is: the existence of random rest periods. Probability of satisfaction , making ,expect ;in, The resting time of a multi-agent dynamics system. For sample paths in multi-agent dynamics systems, The initial state of the multi-agent dynamics system. and They represent followers respectively. Position and velocity at time t and These represent the leader's position and velocity at time t, respectively.

5. The finite-time consistency control method for a leader-follower multi-agent system according to claim 1, characterized in that, Follower i modified traction control gain ;in, For the traction control gain of follower i Let represent the connection weights between follower i and leader in the communication topology graph G.

6. The finite-time consistency control method for a leader-follower multi-agent system according to claim 1, characterized in that, The control protocol is as follows: ； in, For the control input of follower i, , , , Here, is the gain parameter for noise compensation, and p is the nonlinear power parameter. For feedback strength, For symbolic functions, Let $\mathbf{i}$ be the variance of white noise between followers $i$ and $j$. Let the variance of white noise between follower i and leader i be denoted as . Let i be the standard white noise function between followers i and j. Let i be the standard white noise function between the follower and the leader. and They represent followers respectively. Position and velocity at time t and They represent followers respectively. Position and velocity at time t.

7. The finite-time consistency control method for a leader-follower multi-agent system according to claim 1, characterized in that, Controlling an agent based on a distributed finite-time observer and a control protocol includes: using the output of the distributed finite-time observer to estimate the position and velocity of the leader for each follower; substituting each follower's estimate of the leader's position and velocity into the control protocol to obtain the control input for each follower; and controlling the follower based on the control input.

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