Predetermined time proportion consistency control method of multi-agent system

Abstract

According to the method, the problem of the preset time proportion consistency of the multi-agent system under the disturbance condition is researched, two preset time proportion consistency control protocols are provided, the proportion consistency of the multi-agent system within the preset time can be achieved, the convergence time boundary of the system does not depend on the initial state of the system, and the system reliability is improved. The upper bound of the convergence time of the system can be set by selecting a single time parameter instead of a complex setting function, the setting property is good, the actual convergence time of the system is closer to the preset convergence time, the actual demand is better facilitated, the condition of topology switching is considered, and the method is more practical in actual application and has a wide application prospect. The correctness of the two control protocols is proved through an algebraic graph theory and a Lyapunov theory, and the effectiveness and superiority of the proposed protocols are verified through a simulation contrast experiment.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-agent collaborative control, and specifically relates to a method for controlling a multi-agent system's predetermined time ratio consistency. Background Art

[0002] In recent years, the collaborative control of multi-agent systems has been deeply applied in the fields of multi-robot formation control, collaborative drones, etc. The consistency control problem is the basis of the collaborative control problem. It is to make each agent in the multi-agent system achieve state consistency through information exchange under the action of the consistency control protocol. The consistency can be divided into leader-follower consistency, binary consistency, proportional consistency, etc. according to the effect achieved. It has many applications in the fields of robot collaborative control and power system distributed control.

[0003] In the design of consistency protocols, convergence speed is a very important performance indicator. Usually, the control protocol obtains asymptotic convergence results. Finite-time control can achieve consistency within a finite time, which can produce better system performance, such as anti-interference and robustness to uncertainty. Therefore, it is considered to be one of the most ideal design goals of the consistency algorithm. In some technical research, the finite-time consistency control problem of first-order uncertain nonlinear MAS is studied, and the leader-containing and leaderless consistency control protocols are specifically designed; the finite-time tracking control problem of MAS under directed topology under the condition of communication changes is studied.

[0004] However, the stabilization time of the finite-time consistency control protocol depends on the initial state conditions of the system. The change of the initial state conditions makes it difficult to distinguish the convergence performance of the finite-time consistency control protocol from the asymptotic consistency control protocol. To this end, Polyakov A proposed a fixed-time consistency control protocol, in which the convergence time bound can be obtained from the algorithm parameters, thereby eliminating the dependence on the initial state conditions of the system. Later, some scholars studied the fixed-time leader-follower consistency problem of the second-order multi-agent system under the influence of input delay; considered the control problem of the next-order time-delay nonlinear MAS under the adversarial network, and realized the fixed-time bisection consistency; studied the collaborative control of MAS under the influence of disturbances, and realized the fixed-time ratio consistency of the system.

[0005] Although the fixed-time control protocol overcomes the shortcomings of the finite-time control protocol, there are still aspects that need to be improved. One is that the convergence time bound determined by the Lyapunov stability analysis is too different from the actual system convergence time, which is not conducive to the experimenter's estimation of the system convergence time; the other is that its upper bound of convergence time is a complex function constructed by the algorithm parameters. If the user wants to set the upper bound of the system convergence time, multiple parameters need to be debugged, which is not convenient for tuning. The scheduled time control protocol proposed by Sánchez-Torres JD optimizes the two shortcomings of the fixed-time control protocol. Under the action of the scheduled time control protocol, the system convergence time bound is only related to one parameter in the designed control protocol, which solves the problem of poor tuning; the system convergence time estimate under this algorithm is closer to the actual convergence time, which improves the problem of high conservatism.

[0006] At present, there are technical studies on the problem of scheduled time consistency control and binary consistency control. However, there is little research on proportional consistency, which can be applied to many fields, such as compartment mass action systems, web page sorting algorithms, water distribution systems, and multi-proportional coordination control between spacecraft and ground simulation vehicles. Therefore, there is still a lot of room for development in proportional consistency control.

[0007] To this end, the technical problem to be solved by the present invention is that the prior art lacks research on the consistency problem of the predetermined time ratio, and the existing controller has a large convergence error and is not suitable for situations where communication conditions are changeable. Summary of the invention

[0008] In order to solve the technical problems that there is a lack of research on the problem of consistency of predetermined time ratio in the prior art, and that the existing controller has large convergence error and is not suitable for situations where communication conditions are changeable, the present invention provides a predetermined time ratio consistency control method for a multi-agent system.

[0009] The specific plan is as follows:

[0010] Step 1: Use the undirected graph in graph theory to establish the communication topology of the intelligent system;

[0011] The communication topology of a multi-agent system is defined as an undirected graph G = (V, ε, A), where V = {v 1 ,v 2 ,…,v m} is a node set, represents the edge set, A=[a ij ] m×m is an adjacency matrix, each node v i Represents an agent i, the edge set (v i ,v j )∈ε exists, indicating that agents j and i can communicate with each other. For the undirected graph G, the adjacency matrix A=[aij ] m×m , when (v j ,v i )∈ε, i≠j, a ij =1, otherwise a ij = 0, the Laplacian matrix L of the undirected graph G is defined as L = DA, where D = diag{d 1 ,d 2 ,…,d m} is a diagonal matrix,

[0012] Step 2: The nonlinear MAS model under disturbance conditions is given as:

[0013]

[0014] Among them, x i ∈R n ,u i ∈R n are the state and control input of agent i, i∈Γ n ={1,2,…,n},d i (t)∈R n represents unknown disturbances and noise;

[0015] Step 3: According to the MAS consistency problem under fixed topology conditions, a distributed scheduled time ratio consistency control protocol is designed;

[0016] In order to achieve the predetermined time ratio consistency of nonlinear MAS (7), the control protocol is designed as follows:

[0017]

[0018] in, 0<α<1, β≥D is the system parameter, s ij =s i / s j is the proportional coefficient between agent i and agent j, λ 2 (L) is the non-zero minimum eigenvalue of the Laplacian matrix L of the MAS, T is the preset convergence time, and the sign function sign(x) satisfies that when x≠0, sign(x)=x / |x|; otherwise sign(x)=0;

[0019] Step 4: According to the MAS consistency problem under the switching topology condition, a distributed scheduled time ratio consistency control protocol is designed;

[0020] In order to achieve the predetermined time ratio consistency of nonlinear MAS (7) under the switching topology condition, the control protocol is designed as follows:

[0021]

[0022] in, The rest of the parameter settings are the same as those in step 3 under fixed topology conditions.

[0023] In the step 1, the multi-agent system includes N agents having the same linear dynamic model.

[0024] In step 2, an assumption is set as follows:

[0025] Assumption 1: Bounded external disturbance d i (t) Satisfaction

[0026]

[0027] in, D≥0.

[0028] In step 4, suppose the MAS communication topology set G c = {G 1 ,G 2 ,…,G N}, switching signal c(t):[0,+∞)→Π, Π={1,2,…,N} is the atlas G c Index set, definition The sampling time is t 0 The corresponding Laplacian matrix is

[0029] The beneficial effects of the present invention are:

[0030] (1) Compared with the existing asymptotically convergent controller and finite-time convergent controller, the controller proposed in the present invention can make the convergence time bound of the system independent of the initial state of the system, and can quickly achieve system stability;

[0031] (2) Under the action of the proposed controller, the system convergence time limit is simple to set and can be directly pre-set by a single time parameter. The actual convergence time of the system is closer to the preset value than the result of the fixed time algorithm, which enables the system to achieve proportional consistency within the preset time.

[0032] (3) The controller convergence error is small;

[0033] (4) Considering the communication changes of various intelligent agents in practical applications, a predetermined time ratio consistency control protocol under switching topology conditions is provided, which is more suitable for situations with changeable communication conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is the communication topology diagram under the fixed topology condition of Experiment 1;

[0035] Figure 2a It is a schematic diagram of the state trajectory of the agent in the nonlinear uncertain MAS in Experiment 1 when the initial state of the system is x(0) under the action of controller 10;

[0036] Figure 2b It is a schematic diagram of the state trajectory of the agent in the nonlinear uncertain MAS in Experiment 1 when the initial state of the system is x'(0) under the action of controller 10;

[0037] Figure 3a It is a schematic diagram of the Lyapunov function trajectory of the nonlinear uncertain MAS in Experiment 1 with the initial state of the system being x(0) under the action of controller 10;

[0038] Figure 3b It is a schematic diagram of the Lyapunov function trajectory of the nonlinear uncertain MAS in Experiment 1 with the initial state of the system being x'(0) under the action of controller 10.

[0039] Figure 4 It is the communication topology diagram under the switching topology condition in Experiment 2;

[0040] Figure 5a It is a schematic diagram of the state trajectory of the agent in Experiment 2 when the nonlinear uncertain MAS is under the action of controller 20 and the initial state of the system is x(0);

[0041] Figure 5b It is a schematic diagram of the state trajectory of the agent in Experiment 2 when the nonlinear uncertain MAS is under the action of controller 20 and the initial state of the system is x'(0);

[0042] Figure 6a It is a schematic diagram of the Lyapunov function trajectory of the nonlinear uncertain MAS in Experiment 2 with the initial state of the system being x(0) under the action of controller 20;

[0043] Figure 6b It is a schematic diagram of the Lyapunov function trajectory of the nonlinear uncertain MAS in Experiment 2 with the initial state of the system being x'(0) under the action of controller 20.

[0044] Figure 7a It is a schematic diagram of the SCKM simulation results of the nonlinear uncertain MAS in Experiment 3 with the initial state of the system being x(0) under the action of three control protocols;

[0045] Figure 7b This is a schematic diagram of the SCKM simulation results of the nonlinear uncertain MAS in Experiment 3 with the initial state of the system being x'(0) under the action of three control protocols. DETAILED DESCRIPTION

[0046] The following will be combined with the accompanying drawings in the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the implementation of the present invention, not all of the implementations. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0047] The present invention provides a method for controlling a predetermined time ratio consistency of a multi-agent system, which specifically comprises the following steps:

[0048] Step 1: Use the undirected graph in graph theory to establish the communication topology of the multi-agent system;

[0049] Step 2: Give a nonlinear MAS model under disturbance conditions;

[0050] Step 3: According to the MAS consistency problem under fixed topology conditions, a distributed scheduled time ratio consistency control protocol is designed;

[0051] The present invention provides a proof of the stability of the system under a fixed topology condition under the action of a distributed predetermined time ratio consistency controller;

[0052] Step 4: According to the MAS consistency problem under the switching topology condition, a distributed scheduled time ratio consistency control protocol is designed;

[0053] The present invention provides a proof of the stability of the system under switching topology conditions under the action of a distributed predetermined time ratio consistency controller.

[0054] The detailed description is given below.

[0055] Step 1: Use the undirected graph in graph theory to establish the communication topology of the multi-agent system;

[0056] A nonlinear MAS with N intelligent agents has a communication topology represented by an undirected graph G = (V, ε, A), where V = {v 1 ,v 2 ,…,v m} is a node set, represents the edge set, A=[a ij ] m×m is an adjacency matrix, each node v i Represents an agent i, the edge set (v i ,v j )∈ε exists, indicating that agents j and i can communicate with each other. For the undirected graph G, the adjacency matrix A=[a ij ] m×m , when (v j ,v i )∈ε,i≠j, a ij=1, otherwise a ij = 0, the Laplacian matrix L of the undirected graph G is defined as L = DA, where D = diag{d 1 ,d 2 ,…,d m} is a diagonal matrix, An undirected graph G is connected if there is at least one path between any two nodes.

[0057] Step 2: The nonlinear MAS model under disturbance conditions is given as:

[0058]

[0059] Among them, x i ∈R n ,u i ∈R n are the state and control input of agent i, i∈Γ n ={1,2,…,n},d i (t)∈R n represents unknown disturbances and noise.

[0060] Let’s assume a condition:

[0061] Assumption 1: Bounded external disturbance d i (t) Satisfaction

[0062]

[0063] in, D≥0.

[0064] Definition: For the nonlinear MAS equation (7) with disturbance, there exists a predefined time constant T, which satisfies when t ≥ T, so that the system has

[0065]

[0066] The system can then achieve a predetermined time ratio consistency.

[0067] Step 3: According to the MAS consistency problem under fixed topology conditions, a distributed scheduled time ratio consistency control protocol is designed;

[0068] In order to achieve the predetermined time ratio consistency of nonlinear MAS (7), the control protocol is designed as follows:

[0069]

[0070] in, 0<α<1, β≥D is the system parameter, s ij =s i / s j is the proportional coefficient between agent i and agent j, λ 2 (L) is the non-zero minimum eigenvalue of the Laplacian matrix L of the MAS, and T is the preset convergence time. The sign function sign(x) satisfies that when x≠0, sign(x)=x / |x|; otherwise sign(x)=0.

[0071] The present invention provides a proof of the stability of the system under a fixed topology condition under the action of a distributed predetermined time ratio consistency controller;

[0072] When Assumption 1 is satisfied, the controller (10) can be used to ensure that the nonlinear MAS achieves the predetermined time ratio consistency under fixed topology conditions. Proof: Construct the following Lyapunov function

[0073]

[0074] Taking the derivative of V(x), we get

[0075]

[0076] Following the trajectory of equation (7), substituting into equation (7), the derivative of V(x) is

[0077]

[0078] Substituting the proposed controller equation (10) into equation (13), we get

[0079]

[0080] According to hypothesis 1, we can get

[0081]

[0082] Since β ≥ D,

[0083]

[0084] Given 0<α<1, then 0<1-α<1, 1<1+α<2. According to Lemma 3, we have

[0085]

[0086] Lemma 3: For a real number ε 1 ,ε 2 ,K,ε m ∈R + ,have

[0087]

[0088] Substituting into equation (17) and equation (18), according to Lemma 2, equation (16) can be transformed into

[0089]

[0090] Lemma 2: For a connected undirected graph G, its Laplacian matrix L is semi-positive definite and its eigenvalues ​​satisfy

[0091]

[0092] For x=(x 1 ,x 2 ,...,x m ) T ∈R n ,have

[0093]

[0094] Therefore, if 1 T x=0, that is When λ 2 (L)x T x≤x T Lx≤λ m (L)x T x.

[0095] From Lemma 1, we can get Therefore, when t≥T, V(x)=0, and MAS achieves proportional consistency.

[0096] Lemma 1: If there exists a positive definite function V(x):R m →R, and So that the following formula holds

[0097]

[0098] Among them, the constant T>0, 0<α<1, then the system is stable within the predetermined time T.

[0099] Therefore, Theorem 1 can be obtained: under the action of the distributed scheduled time ratio consistency controller (10), the system can achieve scheduled time ratio consistency under fixed topology conditions.

[0100] Step 4: According to the MAS consistency problem under the switching topology condition, a distributed scheduled time ratio consistency control protocol is designed;

[0101] Since there may be communication changes in practical applications, the present invention considers the consistency of the predetermined time ratio under the switching topology. c = {G 1 ,G 2,...,G N}, switching signal c(t):[0,+∞)→Π, Π={1,2,...,N} is the atlas G c Index set, definition The sampling time is t 0 The corresponding Laplacian matrix is

[0102] In order to achieve the predetermined time ratio consistency of nonlinear MAS (7) under the switching topology condition, the control protocol is designed as follows:

[0103]

[0104] in, The rest of the parameter settings are the same as those in step 3 under fixed topology conditions.

[0105] The present invention provides a proof of the stability of the system under the condition of switching topology under the action of a distributed predetermined time ratio consistency controller;

[0106] When Assumption 1 is satisfied, the controller (20) can achieve the predetermined time ratio consistency of nonlinear MAS under the switching topology. Proof: Similar to the proof of Theorem 1, the Lyapunov function can be constructed

[0107]

[0108] Taking the derivative of V(x) and simplifying it, we can get

[0109]

[0110] Therefore, according to Lemma 1, under the switching signal c(t):[0,+∞)→Π, MAS can still achieve proportional consistency within the predetermined time.

[0111] Lemma 1: If there exists a positive definite function V(x):R m →R, and So that the following formula holds

[0112]

[0113] Among them, the constant T>0, 0<α<1, then the system is stable within the predetermined time T.

[0114] Experimental verification:

[0115] In order to further verify the effectiveness and superiority of the predetermined time ratio consistency control protocol proposed in the present invention, the following three groups of experiments are designed, in which the simulation environment is MATLAB 2018a and the step size is set to 0.001;

[0116] The purpose of the first set of experiments is to verify the effectiveness of the controller (10) under fixed topology conditions;

[0117] The purpose of the second set of experiments is to verify the effectiveness of the controller (20) under switching topology conditions;

[0118] The purpose of the third group of experiments is to verify the superiority of controller (10) compared with the finite time controller and the fixed time controller.

[0119] The specific experiments are as follows:

[0120] Experiment 1: To verify the effectiveness of the preset time ratio consistency control protocol proposed by the present invention under fixed topology conditions, that is, the system can achieve ratio consistency within a preset time under the action of the controller (10), a nonlinear MAS is set to contain 6 agents, and the communication topology between the agents under fixed topology conditions is as follows: Figure 1 As shown, the Laplacian matrix is

[0121]

[0122] The eigenvalue λ is easily obtained from the Laplacian matrix 2 (L) = 1, and the initial states of the two groups of intelligent systems are set to x(0) = [15, 7, -1, -6, 9, 5] T , x'(0) = 2x(0), and the external disturbance is set to d i (x i (t),t)=sin(it), the proportional parameter is set to: s 1 =-1,s 2 =-1,s 3 =1.5,s 4 =1.5,s 5 =2,s 6 =2, the other parameters are α=0.5, β=0.5, the convergence time limit of the system is set to T=5, and the simulation results are shown in Figures 2 and 3.

[0123] Figure 2a and Figure 2b It shows the changes of the agent states of the two systems under different initial conditions under the action of the controller (10). Figure 3a and Figure 3bIt shows the Lyapunov function trajectories of two groups of systems under the action of the controller (10) under different initial state conditions. As can be seen from FIGS. 2 and 3, under the fixed topology condition, although the initial states of the two groups of systems are different, under the action of the controller (10) at a predetermined time, both groups of systems can achieve the proportional consistency of the system states within the set convergence time of 5 s. In addition, the present invention gives the constructed Lyapunov function trajectory. As can be seen from FIG. 3, this function trajectory can approach zero within 5 s. Combining Lemma 1, it further verifies the conclusion that the convergence time bound of the system is independent of the initial state under the action of the proposed predetermined time controller.

[0124] Experiment 2: To verify the effectiveness of the proposed predetermined time proportional consistency control protocol of the present invention under the switching topology condition, that is, the system can achieve proportional consistency within a preset time under the action of the controller (20), the communication topology under the switching topology condition is as Figure 4 shown.

[0125] It is set that when 0 < t < 2 s, the topology graph G1 of Figure 4 (a) is adopted, when 2 s ≤ t < 4 s, the topology graph G2 of Figure 4 (b) is adopted, and when 4 s ≤ t ≤ 10 s, the topology graph G3 of Figure 4 (c) is adopted. From this, the remaining parameters are set the same as those under the fixed topology. The experimental results are shown in FIGS. 5 and 6.

[0126] Figure 5a and Figure 5b show the changes in the agent states of two groups of systems under different initial state conditions under the action of the controller (20), Figure 6a and Figure 6b show the Lyapunov function trajectories of two groups of systems under different initial state conditions under the action of the controller (20). As can be seen from FIGS. 5 and 6, under the switching topology condition, although the initial states of the two groups of systems are different, under the action of the predetermined time controller (20), the system can still achieve the proportional consistency of the system states within 5 s, thus verifying the conclusion of Lemma 2. It can be easily seen from FIG. 5 that the actual convergence time of the system under the switching topology condition is slightly different from the preset convergence time. This is the result of selecting the minimum eigenvalue in the control protocol to meet the applicability of the control protocol under the switching topology. However, compared with the fixed-time control algorithm, the conservativeness of the predetermined time is still smaller. Experiment 2 verifies this conclusion.

[0127] Experiment 3: In Experiment 1, the present invention verifies the conclusion that the convergence time bound of the system is independent of the initial state of the system, can be set by itself, and is independent of the controller parameters. Next, based on Experiment 1, the superiority of the controller proposed by the present invention, i.e., controller (10), will be verified through specific simulation comparison experiments. In this experiment, a finite time controller and a fixed time controller are cited and compared and analyzed with them, wherein the finite time control protocol is shown in formula (23) and the fixed time control protocol is shown in formula (24).

[0128]

[0129] Among them, in formula (23), p = 0.6, q = 0.5, in formula (24), γ = 1.5, δ = 1, m = 5, r = 3, μ = 7, w = 9, η = 0.5. In order to ensure the accuracy of the experimental results, the controller parameters of the present invention are set to α = 2 / 3, β = 0.5, and T is determined by the convergence time estimation function obtained by the fixed time controller (24), which can be obtained

[0130]

[0131] After substituting the parameters, we calculated that T = 4.0457. To facilitate the comparison and analysis of the simulation results, the nonlinear MAS scale-consensus-keeping error metric (SCKM) is set to

[0132]

[0133] Using the fixed topology in Experiment 1, the initial states of the two systems are set to x(0)=[15,7,-1,-6,9,5] T ,x'(0)=[47,3,20,-9,16,1] T , the scale parameter remains unchanged. Figure 7 shows the SCKM simulation results of different system initial states under the action of three protocols.

[0134] Depend on Figure 7a and Figure 7bFrom the SCKM simulation comparison results, it can be seen that when the initial state of the system is x(0), under the action of the finite time controller (23), the system can achieve a convergence effect of SCKM value of 0.009724 in 4.737s; and when the initial state is x'(0), it can achieve a convergence effect of SCKM of 0.007567 in 7.537s. Therefore, it can be concluded that under the action of the finite time controller, the convergence time of the system changes with the change of the initial state. Similarly, it is easy to see from Figure 7 that both the fixed time controller and the scheduled time controller can achieve proportional consistency within the scheduled time T = 4.0457s regardless of the initial state of the system. Therefore, it can be concluded that under the action of the fixed time controller and the scheduled time controller, the scheduled value of the convergence time of the system is independent of the initial state.

[0135] However, it is worth noting that, as shown in FIG7 , the preset time controller of the present invention can make the convergence time of the system closer to the actual preset value, which is more in line with the situation that the system is expected to converge within its own preset time in actual applications. In addition, it can be seen from the origin of formula (25) that the preset convergence time of the controller of the present invention is independent of the controller parameters, and the upper limit of the convergence time can be directly set, which is simple to set, which is more advantageous than the fixed time controller.

[0136] In summary, simulation experiments have verified the effectiveness and superiority of the scheduled time control protocol proposed in the present invention in solving the nonlinear MAS proportional consistency problem.

[0137] The present invention studies the problem of predetermined time proportion consistency of multi-agent system under disturbance conditions, and proposes two predetermined time proportion consistency control protocols, which can enable the multi-agent system to achieve proportion consistency within a preset time. The upper bound of the convergence time of the system is independent of the initial state. The switching topology is taken into account, which is more practical in practical applications. The correctness of the two control protocols is proved by algebraic graph theory and Lyapunov theory, and the effectiveness and superiority of the proposed protocols are verified by simulation comparison experiments.

[0138] (1) A corresponding distributed scheduled time ratio consistency control protocol is proposed, which can make the system converge quickly within the preset time;

[0139] (2) Compared with the existing asymptotically convergent controller and finite-time convergent controller, the controller proposed in the present invention can make the convergence time bound of the system independent of the initial state of the system;

[0140] (3) Compared with the existing fixed-time convergence controller, the present invention can set the upper limit of the system convergence time by selecting a single time parameter instead of a complex setting function, and has good tuning performance. In addition, the present invention can make the actual convergence time of the system closer to the estimated convergence time, which is more conducive to actual needs.

[0141] (4) The situation in which each intelligent agent has communication transformation in practical applications is taken into consideration, and the proportional consistency control under communication topology transformation is solved, which is more practical.

[0142] The technical means disclosed in the scheme of the present invention are not limited to the technical means disclosed in the above-mentioned implementation mode, but also include technical schemes composed of any combination of the above-mentioned technical features. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications are also regarded as the protection scope of the present invention.

Claims

1. A method for controlling a predetermined time ratio consistency of a multi-agent system, characterized in that: The specific steps include: Step 1: Use the undirected graph in graph theory to establish the communication topology of the intelligent system; The communication topology of a multi-agent system is defined as an undirected graph G = (V, ε, A), where V = {v1, v2, …, v m } is a node set, represents the edge set, A=[a ij ] m×m is an adjacency matrix, each node v i Represents an agent i, the edge set (v i ,v j )∈ε exists, indicating that agents j and i can communicate with each other. For the undirected graph G, the adjacency matrix A=[a ij ] m×m , when (v j ,v i )∈ε, i≠j, a ij =1, otherwise a ij = 0, the Laplacian matrix L of the undirected graph G is defined as L = DA, where D = diag{d1, d2, …, d m } is a diagonal matrix, j∈{1,2,…,m}; Step 2: The nonlinear MAS model under disturbance conditions is given as: Among them, x i ∈R n ,u i ∈R n are the state and control input of agent i, i∈Γ n ={1,2,…,n}, d i (t)∈R n represents unknown disturbances and noise; Step 3: According to the MAS consistency problem under fixed topology conditions, a distributed scheduled time ratio consistency control protocol is designed; In order to achieve the predetermined time ratio consistency of nonlinear MAS (7), the control protocol is designed as follows: in, 0<α<1, β≥D is the system parameter, s ij =s i / s j is the proportional coefficient between agent i and agent j, λ2(L) is the non-zero minimum eigenvalue of the Laplacian matrix L of MAS, T is the preset convergence time, and the sign function sign(x) satisfies sign(x) = x / |x| when x≠0; otherwise sign(x) = 0; Step 4: According to the MAS consistency problem under the switching topology condition, a distributed scheduled time ratio consistency control protocol is designed; In order to achieve the predetermined time ratio consistency of nonlinear MAS (7) under the switching topology condition, the control protocol is designed as follows: in, The rest of the parameter settings are the same as those in step 3 under fixed topology conditions.

2. The method for controlling the predetermined time ratio consistency of a multi-agent system according to claim 1, characterized in that: In the step 1, the multi-agent system includes N agents having the same linear dynamic model.

3. The method for controlling the predetermined time ratio consistency of a multi-agent system according to claim 1, characterized in that: In step 2, an assumption is set as follows: Assumption 1: Bounded external disturbance d i (t) Satisfaction in, D≥0.

4. The method for controlling the predetermined time ratio consistency of a multi-agent system according to claim 1, characterized in that: In step 4, suppose the MAS communication topology set G c ={G1,G2,…,G N }, switching signal c(t):[0,+∞)→Π, Π={1,2,…,N} is the atlas G c Index set, definition represents the communication topology at sampling time t0, and its corresponding Laplacian matrix is

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