Finite time consistency control method of leader-follower multi-agent system

Abstract

The invention belongs to the field of multi-agent system control, and relates to a finite time consistency control method of a leader-follower multi-agent system, which comprises the following steps: constructing a communication topological graph G of the leader-follower multi-agent system; the leader-following multi-agent system comprises a plurality of followers and a leader; constructing a multi-agent dynamic system; the multi-agent dynamics system comprises a leader dynamics system and a follower dynamics system. Based on the communication topological graph G and the multi-agent dynamic system, finite time consistency control is conducted on the leader-follower multi-agent system through a traction control method; according to the method, topological conditions are relaxed in traction control, traction control gains are corrected according to neighbor communication gains, followers obtain control input of the followers through information of neighbor followers, and it is ensured that even if part of followers cannot indirectly obtain leader information, convergence can still be achieved according to probabilities, the anti-interference capacity is enhanced, the convergence speed is increased, and communication resource consumption is reduced.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of multi-agent system control, and particularly relates to a finite-time consensus control method for a leader-follower multi-agent system. BACKGROUND

[0002] In actual problems, due to the influence of time, resources and cost and other factors, in many cases, the multi-agent system is required to converge to consensus in a limited time. Therefore, it is necessary to study the finite-time consensus. The finite-time consensus refers to the fact that all agents in the system can reach the same state in a certain time through an effective consensus algorithm. Due to various uncontrollable factors, such as equipment precision, natural environment and the like, the system is in various complex or dangerous environments in most cases, and is disturbed by uncertain factors, such as time delay, noise, external disturbance and the like every moment, so that the measured agent state and the actual agent state are deviated, and the stability of the system is destroyed.

[0003] In view of the above, in order to make the research more in line with the actual situation, the convergence speed is improved, the communication resources are reduced, and the anti-interference ability is improved. SUMMARY

[0004] In order to solve the above technical problems, the application adopts a finite-time consensus control method for a leader-follower multi-agent system, which comprises the following steps:

[0005] S1, a communication topology graph G of the leader-follower multi-agent system is constructed; the leader-follower multi-agent system comprises a plurality of followers and a leader;

[0006] S2, a multi-agent dynamics system is constructed; the multi-agent dynamics system comprises a leader dynamics system and a follower dynamics system;

[0007] S3, the leader-follower multi-agent system is controlled by using the traction control method based on the communication topology graph G of the leader-follower multi-agent system and the multi-agent dynamics system.

[0008] The finite-time consensus control of the leader-follower multi-agent system comprises the following steps:

[0009] S31, an assumption of a traction control node selection rule and a leader-follower finite-time consensus condition are constructed based on the communication topology graph G and the multi-agent dynamics system;

[0010] S32, a distributed finite-time observer and a control protocol are designed based on the assumption of the traction control node selection rule;

[0011] S33, controlling the leader-follower multi-agent system according to the distributed finite-time observer and control protocol;

[0012] S34, verifying that the multi-agent dynamic system can reach the finite-time consensus in probability under the control protocol based on the random Lyapunov stability theory and the leader-follower finite-time consensus condition.

[0013] Advantages:

[0014] 1. The application breaks through the traditional requirement that a spanning tree with a leader as the root must exist in the system, relaxes the topological condition in traction control, and corrects the traction control gain according to the neighbor communication gain, so that when the system has no spanning tree, each follower obtains its control input through the information of the neighbor followers, thereby expanding the application scenario of the system from a "strongly connected topology" to a weak topology of "arbitrary connectivity + partial traction", ensuring that even if some followers cannot indirectly obtain the leader information, they can still converge in probability, thereby maintaining stability when the topology changes dynamically, enhancing the anti-interference ability, reducing the convergence delay caused by topological restrictions, significantly improving the convergence speed, and at the same time, without relying on a global strongly connected structure, reducing the transmission of information across network levels, and reducing communication resource consumption.

[0015] 2. The application proposes a distributed finite-time observer, which enables each follower to autonomously estimate the leader state only through the estimation error of the finite-time observer of the neighbor followers and the estimation error of the finite-time observer of the leader state of itself, avoids each follower directly obtaining the global state of the leader, improves the anti-interference ability of the system, significantly reduces the communication resource occupation, improves the energy efficiency ratio and real-time performance, thereby realizing complete distributed autonomy, breaking the dependence on the global state of the leader, and adapting to dynamic, large-scale and high-risk scenarios.

[0016] 3. Because the system contains noise, the application uses the Itô formula to decompose the Lyapunov function into a combination of "position error terms" and "velocity error terms", and then derives the stochastic differential of the error, which can accurately depict the cooperative evolution law of the position and velocity errors, avoid the convergence asynchronization problem caused by single error term analysis, and improve the overall convergence speed. By specifically processing the random interference of the position and velocity errors, the application reduces the communication resource consumption without transmitting redundant global information for error correction. At the same time, the accurate decomposition and compensation of the noise term by the Itô formula can effectively offset the influence of random interference on error convergence, and in combination with the positive definite property of the Lyapunov function, the anti-interference ability of the system is significantly improved, and finally the position and velocity of the second-order system can simultaneously converge in probability to the leader state in finite time. BRIEF DESCRIPTION OF DRAWINGS

[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, constructing assumptions of the traction control node selection rule and the leader-follower finite time consensus condition based on the communication topology graph G and the multi-agent dynamic system;

[0038] The assumptions of the traction control node selection rule include:

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

[0040] That is, for any follower i, the state of the leader can directly or indirectly affect the state of the follower.

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

[0042]

[0043] Where x i , x j are the independent variables of the function g(·), and ζ>0 is a Lipschitz constant.

[0044] Assumption 3: There exists a function f(y): R→R that satisfies the following condition:

[0045]

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

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

[0048] The leader-follower finite time consensus condition is that for any initial condition, there exists a random rest time T0≥0 that satisfies the probability P{T0<∞} = 1, such that It is expected that E[T(x0, ω)] ≤ T0; wherein, T(x0, ω) is the rest time of the multi-agent dynamic system, ω is the sample path of the multi-agent dynamic system, and x0 is the initial state of the multi-agent dynamic system.

[0049] The sample path of the multi-agent dynamic system refers to the record of the trajectory of the state (such as position and speed) of each agent in the system changing over time in a specific random evolution process. Different sample paths ω correspond to different noise interference, which will cause the system to converge to different consistent times. When the consistent time is defined in probability, it is necessary to ensure that the rest time is limited for almost all sample paths ω.

[0050] S32, designing a distributed finite-time observer and control protocol according to the assumption of the control node selection rule;

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

[0052] From the distributed demand, a state equation conforming to the second-order kinematics is constructed In the state equation conforming to the second-order kinematics, the traction control gain and the nonlinear power term are introduced to obtain the distributed finite-time observer; wherein, the nonlinear power term includes: the estimation error of the finite-time observer of the follower and its neighbor follower And the estimation error of the finite-time observer of the follower to the state of the leader

[0053] The distributed finite-time observer is:

[0054]

[0055] wherein, is the estimation of the position change rate of the i-th follower to the leader, is the estimation of the speed change rate of the i-th follower to the leader, respectively represent the estimation of the position x0(t) and the speed v0(t) of the i-th follower to the leader, 0 < α1 < 1, α1 is a design parameter, the nonlinear term is defined as a linear growth characteristic, α2 is a design parameter, When the position error and the speed error are matched, is the corrected traction control gain,

[0056] If assumption 1 is established, the influence of the leader on each follower can be reached, which provides a topological basis for the information transmission of the observer, so that the Lyapunov derivative of the observer satisfies the finite-time convergence condition, and therefore the finite-time observer can realize finite-time observation.

[0057] The distributed finite-time observer enables each follower i to autonomously estimate the leader state by only using the estimation error of the finite-time observer of its neighbor follower and the estimation error of the finite-time observer of the follower itself on the state of the leader, supports the control protocol, avoids each follower from directly obtaining the global state of the leader, improves the anti-interference capability of the system, significantly reduces the occupation of communication resources, improves the energy efficiency ratio and real-time performance, and thus realizes complete distributed autonomy, gets rid of the dependence on the global state of the leader, and adapts to dynamic, large-scale and high-risk scenarios.

[0058] The designed control protocol comprises:

[0059] By processing the position difference and the speed difference between the follower and the neighbor;

[0060] By processing the estimation difference between the follower and the leader;

[0061] wherein, is a traction gain, and the traction gain can strengthen the tracking strength of the follower on the leader; the distributed observer are respectively the local estimation values of each follower i on the state (i.e., the position x0 and the speed v0) of the leader, the estimation results of the observer are directly used to design the traction term, the fusion of the local estimation of the observer on the state of the leader and the traction of the control protocol on the follower is realized, and the follower can track the leader only through local interaction without global communication.

[0062] The nonlinear power term is introduced to accelerate the convergence:

[0063] By introducing the nonlinear power term such as |x j (t)-x i (t)| p , |v j (t)-v i (t)| p-1 , etc., the control is not overloaded when the error is large, and the convergence is more sensitive when the error is small, so that the system converges to “all agent states consistent” is accelerated, and the requirement of “finite time” is supported.

[0064] The variance term and the random term of the random disturbance are introduced to offset the random disturbance:

[0065] The variance compensation term: is used to offset the average interference of the system caused by the “quadratic variation” of the noise.

[0066] The random term: σ ij g(v j (t)-v i (t))η ij(t), directly adapt the random fluctuation form of white noise η, and actively cope with the destruction of consistency by noise.

[0067] Finally, introduce the sign function and the linear feedback term The control protocol is obtained.

[0068] The control protocol is expressed as:

[0069]

[0070] where k1≥ζ, ζ>0 is the Lipschitz constant, k1and k2are the gain parameters of noise compensation, the core role is to offset the interference of random noise on the system, which is derived through random Lyapunov stability analysis, p is the nonlinear power parameter, the core role is to regulate the convergence characteristics of the system, ρ is the feedback strength, sign is the sign function, is the white noise variance between the followers i and j, is the white noise variance between the follower i and the leader, and the fluctuation amplitude of the noise is obtained through experimental statistics or given by theoretical modeling, η ij (t) is the standard white noise function between the followers i and j, η i0 is the standard white noise function between the follower i and the leader, which is randomly generated, respectively represent the position x0(t) and velocity v0(t) of the leader estimated by the i-th follower of the distributed finite-time observer output.

[0071] The control protocol breaks through the traditional requirement that the system needs to exist with the leader as the root of the spanning tree, relaxes the topology condition in traction control, and modifies the traction control gain according to the neighbor communication gain. Then when the system has no spanning tree, each follower obtains its control input through the information of the neighbor followers, thereby expanding the application scenario of the system from "strongly connected topology" to "arbitrary connected + partial traction" weak topology, ensuring that even if some followers cannot indirectly obtain the leader information, they can still converge with probability, thereby maintaining stability when the topology changes dynamically, enhancing the anti-interference ability, reducing the convergence delay caused by topology restrictions, significantly improving the convergence speed, and at the same time, without relying on global strong connectivity structure, reducing the transmission of information across network levels, and reducing communication resource consumption.

[0072] S33, control the leader-follower multi-agent system according to the distributed finite-time observer and the control protocol.

[0073] Specifically, the control of the leader-follower multi-agent system according to the distributed finite-time observer and the control protocol comprises: outputting, by the distributed finite-time observer, an estimation of the position and speed of the leader by each follower, substituting the estimation of the position and speed of the leader by each follower into the control protocol to obtain a control input of each follower, and controlling each follower according to the control input.

[0074] S34, verifying that the multi-agent dynamic system can reach the finite-time consensus in probability under the control protocol based on the random Lyapunov stability theory and the leader-follower finite-time consensus condition.

[0075] The multi-agent dynamic system is transformed according to the control protocol by using the Ito formula to obtain a transformed multi-agent dynamic system.

[0076] The specific transformation process is: substituting the control protocol into the random second-order multi-agent dynamic system, and splitting the substituted random second-order multi-agent dynamic system into a drift term (dt) and a diffusion term (dω) by using the Ito formula to obtain an Ito expansion of the random second-order multi-agent dynamic system.

[0077] The core role of the transformation process is to decompose the random system into a "deterministic drift" and a "random diffusion" term, to provide a calculable standard form for the random Lyapunov stability analysis, to support the theoretical proof of the "finite-time consensus in probability", and to facilitate the analysis of the expected stability.

[0078] The form of the transformed multi-agent dynamic system is:

[0079]

[0080] wherein ω ij (t) is a random disturbance of the interaction between the followers i and j, ω i0 (t) is a random disturbance of the interaction between the follower i and the leader.

[0081] If the assumptions 1, 2, 3 and 4 are true, and max{1,-o}<ρ<2-o is satisfied, then the multi-agent dynamic system can reach the finite-time consensus in probability under the control protocol; wherein ρ is the feedback strength, o is the scale characteristic of the noise disturbance, and is the upper and lower limit constraint on the feedback strength ρ.

[0082] max{1,-o}<ρ: to prevent the control from being too strong, and to ensure the balance between the negative feedback and the random disturbance when the feedback strength ρ is too small and the noise positive term dominates, which cannot converge;

[0083] P < 2-o: ensure that the control is strong enough, the feedback strength p is too small, the negative feedback is insufficient, the noise positive term will dominate, and it cannot converge, and strong negative feedback is the key to limited time convergence.

[0084] Proof:

[0085] Let Then dθ i1 (t) = θ i2 (t)dt;

[0086] Substitute the transformed multi-agent dynamics system dv i (t), then

[0087]

[0088] Select the following Lyapunov function:

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

[0090] Wherein, the Lyapunov function

[0091] According to the Ito formula, the differentials of V1(t) and V2(t) are as follows:

[0092]

[0093] According to formula (8) and the differentials of V1(t) and V2(t), the following can be obtained:

[0094]

[0095] According to the definition of the stochastic differential equation and formula (11), the following can be obtained:

[0096]

[0097] Because the system contains noise, the present application uses the Ito formula to decompose the Lyapunov function into a combination of "position error terms" and "velocity error terms", and then deduces the stochastic differential of the error, which can accurately depict the cooperative evolution law of the position and velocity errors, avoid the problem of different step convergence caused by single error term analysis, and improve the overall convergence speed; by processing the random interference of the position and velocity errors, it is not necessary to transmit redundant global information for error correction, thereby reducing the communication resource consumption; at the same time, the accurate decomposition and compensation of the noise term by the Ito formula can effectively offset the influence of random interference on error convergence, combined with the positive definite characteristic of the Lyapunov function, the anti-interference ability of the system is significantly improved, and finally the position and velocity of the second-order system can be strictly and efficiently proved to converge to the leader state at the same time.

[0098] Lemma 3: for there is

[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] where, is the smallest eigenvalue of the matrix 2L(A)+C , L(A)=[l ij ] = D - A ∈ R n×n denotes the Laplacian matrix of the adjacency matrix A,

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

[0114] 1. The Laplacian matrix L of an undirected graph is a symmetric semi-definite matrix, and for any vector x = [x1, x2,..., xn]T ∈ R n ] T , there is

[0115]

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

[0117] 0 = λ1(L) ≤ λ2(L) ≤... ≤ λ n n(L) = λ max

[0118] where λ max is the largest eigenvalue, λ2(L) is the second smallest eigenvalue of L, and indicates 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 the undirected graph G is a connected graph or contains a spanning tree, and the vector b = [b1, b2,..., bn]T ∈ R n ] T ≥ 0, b ≠ 0, then L + diag(b) is a positive definite matrix.

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

[0121]

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

[0123] From 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 respectively give the position state and velocity state trajectories of the agents under the topologies G1, G2 and G3. From the figures, it can be seen that the position state and velocity state of all followers can converge to the position state and velocity state of the leader in probability in finite time. Therefore, the above results verify the effectiveness and correctness of the theorem under different topologies.

[0135] The above examples further illustrate the objects, technical solutions and advantages of the present application. It should be understood that the above examples are merely preferred embodiments of the present application, and are not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made to the present application within the spirit and principle of the present application shall be included in the protection scope of the present application.

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 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.

2. The finite-time consistency control method for a leader-follower multi-agent system according to claim 1, characterized in that, The communication topology of the leader-follower multi-agent system is G = (V, E, A); where V is the set of nodes, and the nodes in the set represent followers or leaders; E is the set of edges, and the edges in the set represent the communication relationships between nodes; A is the weighted adjacency matrix; A[1:n, 1:n] is the weighted adjacency matrix between followers; A[0] is the connection weight vector between followers and leaders; and 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: Among them, u i (t), x i (t) and v i (t) represents the control input, position, and velocity of follower i at time t, respectively, and u0(t), x0(t), and v0(t) represent the control input, position, and velocity of leader i at time t, respectively. Let i represent the rate of change of position and velocity of follower i at time t, respectively. 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, 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.

5. The finite-time consistency control method for a leader-follower multi-agent system according to claim 4, characterized in that, The leader-follower finite-time consistency condition is: there exists a random rest period T0 ≥ 0 satisfying the probability P{T0 < ∞} = 1, such that... The expected value is 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, x0 is the initial state of the multi-agent dynamics system, and x i (t) and v i x0(t) and v0(t) represent the position and velocity of follower i at time t, respectively, and x0(t) and v0(t) represent the position and velocity of leader at time t, respectively.

6. The finite-time consistency control method for a leader-follower multi-agent system according to claim 4, characterized in that, The assumptions underlying the traction control node selection rules include: Assume the 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; Suppose there exists a continuously differentiable function g(·):R→R that satisfies the following conditions: Where ζ>0 is the Lipschitz constant, x i x j Let g be the independent variable of the function g(·), and R be the real number field; Suppose there exists a function f(y): R→R that satisfies the following condition: 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. For odd integer ratios, q1 and q2 are both positive odd integers; Suppose that the communication topology G of the leader-follower multi-agent system is a connected graph.

7. A finite-time consistency control method for a leader-follower multi-agent system according to claim 6, characterized in that, 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. Let x0(t) and v0(t) represent the estimates of the leader's position and velocity by the i-th follower, respectively. It is a sign power function, 0 < α1 < 1, where α1 is the design parameter. α2 is the design parameter, a ij Let N be the connection weight between follower j and follower i in the communication topology graph G. i 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.

8. The finite-time consistency control method for a leader-follower multi-agent system according to claim 7, characterized in that, Follower i modified traction control gain Where, p i (t) represents the traction control gain of follower i, w i (t) represents the connection weight between follower i and leader in the communication topology graph G.

9. A finite-time consistency control method for a leader-follower multi-agent system according to claim 7, characterized in that, The control protocol is as follows: Among them, u i (t) represents the control input of follower i, where k1 ≥ ζ. k1 and k2 are the gain parameters for noise compensation, p is the nonlinear power parameter, ρ is the feedback strength, and sign is the sign function. Let $\mathbf{i}$ be the variance of white noise between followers $i$ and $j$. Let η be the white noise variance between follower i and leader i. ij (t) is the standard white noise function between followers i and j, η i0 Let i be the standard white noise function between the follower i and the leader i.

10. A finite-time consistency control method for a leader-follower multi-agent system according to claim 4, 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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