A method and system for achieving inclusive control of a second-order multi-agent system under network prediction

Abstract

The application discloses a kind of second-order multi-agent system under network prediction realizes inclusive control method and system, it is related to networked multi-agent system technical field.The technical points of the present application include: establishing discrete-time second-order multi-agent system dynamic model with network delay and data packet loss;State prediction is carried out according to the dynamic model to establish prediction model;Predictive controller is designed using the predicted state obtained by prediction model;The expression of position estimation error and speed estimation error is obtained by substituting predictive controller into the dynamic model;The feedback gain constant of predictive controller and the condition that sampling period satisfies are obtained by solving position estimation error and speed estimation error;The feedback gain constant that satisfies condition is substituted into the predictive controller designed, and inclusive control is realized using predictive controller.The present application overcomes the influence of communication delay and data packet loss on inclusive control, with the advantages of easy solution, easy implementation, etc.

Description

Technical Field

[0001] This invention relates to the field of networked multi-agent systems technology, specifically to a method and system for achieving inclusive control of a second-order multi-agent system under network prediction. Background Technology

[0002] With the rapid development of computer science and intelligent control technology, complex real-world tasks have been considered, such as cooperative transportation by vehicle platoons, collaborative operations between naval vessels, and drone-based collaborative rescue and disaster relief. These tasks cannot be accomplished by a multi-agent system with a single leader; therefore, it is necessary to consider cooperation among multiple leaders through information transmission. The reason why a system needs multiple leaders is that a multi-agent system with leaders can reduce communication costs and the time spent on information exchange between individuals, saving network bandwidth compared to a leaderless multi-agent system.

[0003] Therefore, the inclusive control problem of multi-agent systems has been extensively studied by scholars both domestically and internationally. For example, in robot cooperative combat systems, some robots carrying sensors are considered leaders. These leaders detect the surrounding environment and establish a safe zone, while the remaining agents are considered followers, entering the safe zone and following the leader's movement. This ensures that individuals in the system avoid dangerous areas and successfully complete the mission. Compared with traditional problems, inclusive control better highlights the advantages of distributed cooperative control and can be widely applied in practical tasks such as obstacle avoidance in UAV swarms, reconnaissance missions, and rescue missions.

[0004] Networked predictive control uses information from the past to predict information from the present and future. If the agent's trajectory and state information are not updated in time during communication, networked multi-agent systems will be unable to achieve inclusive control and will be unable to predict the agent's next state of motion in the event of communication delays and data packet loss. Summary of the Invention

[0005] To address this, the present invention proposes a method and system for inclusive control of a second-order multi-agent system under network prediction, which proactively predicts the current and future states to solve the inclusive control problem of networked multi-agent systems.

[0006] According to one aspect of the present invention, a method for achieving inclusive control of a second-order multi-agent system under network prediction is proposed, the method comprising the following steps:

[0007] Step 1: Use a directed topology graph to describe the communication relationships between multiple agents and establish a dynamic model of a discrete-time second-order multi-agent system with network latency and packet loss; the multi-agent system includes multiple leaders and multiple followers;

[0008] Step 2: Establish a prediction model based on the dynamic model and perform state prediction;

[0009] Step 3: Design a predictive controller using the predicted state obtained from the prediction model;

[0010] Step 4: Substitute the predictive controller into the dynamic model to obtain the expressions for the position estimation error and velocity estimation error;

[0011] Step 5: Solve for the position estimation error and velocity estimation error to obtain the feedback gain constant of the predictive controller and the conditions that the sampling period must satisfy;

[0012] Step 6: Substitute the feedback gain constant that meets the conditions into the designed predictive controller, and use the predictive controller to realize the inclusive control of the discrete-time second-order multi-agent system with network delay and packet loss under network prediction.

[0013] Furthermore, the dynamic model described in step one is represented as follows:

[0014] X i (k+1)=AX i (k)+Bu i (k)

[0015] y i (k)=CX i (k)

[0016] In the formula, C = [c1 c2], X i (k) represents the state of agent i at time k, including position. and speed A, B, and C represent the system matrix, input matrix, and output matrix, respectively. and Let c1, c2, a, and b represent the measurement output and control input of agent i, respectively. T > 0 is the sampling period, and c1, c2, a, and b are constants. It is the set of real numbers.

[0017] Furthermore, the prediction model described in step two is expressed as follows:

[0018]

[0019]

[0020]

[0021] In the formula, This means that based on the information of agent i up to time k-τ, the predicted state of agent i at time k-τ+1 is obtained; This means that based on the information of agent i up to time k-τ-1, the predicted state of agent i at time k-τ is obtained; τ represents the predicted output; L represents the observation gain matrix; τ = d + p, where d is the upper bound of the communication delay and p is the upper bound of the number of lost data packets; This indicates that the predicted state of agent i at time k-τ+s is obtained based on information up to time k-τ. i (k-τ+s-1) represents the control input of agent i at time k-τ+s-1;

[0022] The expression for state prediction using a prediction model is:

[0023]

[0024] In the formula, This indicates that based on the information of agent i up to time k-τ, the predicted state of agent i at time k is obtained; e i (k-τ+1) represents the state estimation error at time k-τ+1;

[0025] Furthermore, the predictive controller described in step three is represented as:

[0026]

[0027] In the formula, α1 and α2 are the feedback gain constants to be solved, and N i Let R be the set of neighboring vertices of agent i; R = {1,2,…,M} is the leader indicator set, and F = {M+1,M+2,…,N} is the follower indicator set. For location prediction bias, For speed prediction deviation, It is the weighted sum of the position prediction deviations of agent i and its neighboring agents; It is the weighted sum of the velocity prediction deviations of agent i and its neighboring agents.

[0028] Furthermore, the expressions for the position estimation error and velocity estimation error mentioned in step four are as follows:

[0029]

[0030] E(k+1)=ΨE(k)

[0031] In the formula, e x (k) is the position estimation error vector of the follower at time k, e v (k) represents the velocity estimation error vector of the follower at time k; E xF (k-τ+1) represents the position estimation error vector of the follower at time k-τ+1, E xR(k-τ+1) represents the error vector for estimating the leader's position at time k-τ+1; E vF (k-τ+1) is the velocity estimation error vector of the follower at time k-τ+1, E vR (k-τ+1) represents the velocity estimation error vector of the leader at time k-τ+1;

[0032]

[0033]

[0034]

[0035] L fr L is the Laplace matrix corresponding to the leader. ff Let I be the Laplace matrix corresponding to the follower. N-M Let I be an NM-dimensional identity matrix. M Let N be an M-dimensional identity matrix; M is the total number of leaders; N is the total number of agents.

[0036] Furthermore, in step five, the bilinear transform and Schur stability test are used to solve the problem. The feedback gain constants α1 and α2 and the sampling period T obtained from the solution satisfy the following conditions:

[0037]

[0038] m i =α1μ i -a

[0039] n i =α2μ i -b

[0040]

[0041]

[0042]

[0043] In the formula, μ i It is matrix L ff The eigenvalues; Re(·) denotes finding the real part, and Im(·) denotes finding the imaginary part.

[0044] According to another aspect of the present invention, a system for implementing inclusive control of a second-order multi-agent system under network prediction is provided, the system comprising:

[0045] A multi-agent model building module is configured to use a directed topological graph to describe the communication relationships between multiple agents, and to build a dynamic model of a discrete-time second-order multi-agent system with network latency and packet loss; wherein the multi-agent system includes multiple leaders and multiple followers; the dynamic model is represented as:

[0046] X i (k+1)=AX i (k)+Bu i (k)

[0047] y i (k)=CX i (k)

[0048] In the formula, C = [c1 c2], X i (k) represents the state of agent i at time k, including position. and speed A, B, and C represent the system matrix, input matrix, and output matrix, respectively. and Let c1, c2, a, and b represent the measurement output and control input of agent i, respectively. T > 0 is the sampling period, and c1, c2, a, and b are constants. It is the set of real numbers;

[0049] A predictive controller establishment module is configured to establish a predictive model based on the dynamic model and perform state prediction; design a predictive controller using the predicted state obtained from the predictive model; substitute the predictive controller into the dynamic model to obtain expressions for position estimation error and velocity estimation error; solve for the position estimation error and velocity estimation error to obtain the feedback gain constant of the predictive controller and the conditions satisfied by the sampling period.

[0050] The inclusive control module is configured to substitute a feedback gain constant that meets certain conditions into the designed predictive controller, and use the predictive controller to realize inclusive control of a discrete-time second-order multi-agent system with network latency and packet loss under network prediction.

[0051] Furthermore, the prediction model in the prediction controller establishment module is represented as follows:

[0052]

[0053]

[0054]

[0055] In the formula, This means that based on the information of agent i up to time k-τ, the predicted state of agent i at time k-τ+1 is obtained; This means that based on the information of agent i up to time k-τ-1, the predicted state of agent i at time k-τ is obtained; τ represents the predicted output; L represents the observation gain matrix; τ = d + p, where d is the upper bound of the communication delay and p is the upper bound of the number of lost data packets; This indicates that the predicted state of agent i at time k-τ+s is obtained based on information up to time k-τ. i (k-τ+s-1) represents the control input of agent i at time k-τ+s-1, where s=2,3,…,τ;

[0056] The expression for state prediction using a prediction model is:

[0057]

[0058] In the formula, This indicates that based on the information of agent i up to time k-τ, the predicted state of agent i at time k is obtained; e i (k-τ+1) represents the state estimation error at time k-τ+1;

[0059] Furthermore, the predictive controller in the predictive controller establishment module is represented as:

[0060]

[0061] In the formula, α1 and α2 are the feedback gain constants to be solved, and N i Let R be the set of neighboring vertices of agent i; R = {1,2,…,M} is the leader indicator set, and F = {M+1,M+2,…,N} is the follower indicator set. For location prediction bias, For speed prediction deviation, It is the weighted sum of the position prediction deviations of agent i and its neighboring agents; It is the weighted sum of the velocity prediction deviations of agent i and its neighboring agents;

[0062] The expressions for the position estimation error and velocity estimation error are as follows:

[0063]

[0064] E(k+1)=ΨE(k)

[0065] In the formula, e x (k) is the position estimation error vector of the follower at time k, e v(k) represents the velocity estimation error vector of the follower at time k; E xF (k-τ+1) represents the position estimation error vector of the follower at time k-τ+1, E xR (k-τ+1) represents the error vector for estimating the leader's position at time k-τ+1; E vF (k-τ+1) is the velocity estimation error vector of the follower at time k-τ+1, E vR (k-τ+1) represents the velocity estimation error vector of the leader at time k-τ+1;

[0066]

[0067]

[0068]

[0069] L fr L is the Laplace matrix corresponding to the leader. ff Let I be the Laplace matrix corresponding to the follower. N-M Let I be an NM-dimensional identity matrix. M Let N be an M-dimensional identity matrix; M is the total number of leaders; N is the total number of agents.

[0070] Furthermore, the predictive controller establishment module utilizes bilinear transformation and Schur stability determination to solve for the feedback gain constants α1 and α2, and the sampling period T obtained from the solution satisfy the following conditions:

[0071]

[0072] m i =α1μ i -a

[0073] n i =α2μ i -b

[0074]

[0075]

[0076]

[0077] In the formula, μ i It is matrix L ff The eigenvalues; Re(·) denotes finding the real part, and Im(·) denotes finding the imaginary part.

[0078] The beneficial technical effects of this invention are:

[0079] This invention considers the impact of communication delay and data packet loss on the containment control of discrete-time second-order multi-agent systems. It utilizes a networked prediction method to comprehensively consider effective delay information. Compared to existing methods that directly use outdated position and velocity information to design controllers, this invention can proactively compensate for the negative impact of communication delay and data packet loss, providing a unified prediction process for all followers and overcoming the influence of these factors on containment control. Using graph theory and stability theory, it provides the necessary and sufficient conditions for ensuring containment control in discrete-time second-order multi-agent systems. Based on the bilinear transform method, it provides conditions for the feedback gain constant and sampling period to ensure that followers move into the convex hull formed by the leader, thus achieving containment control. This invention also has advantages such as ease of solution and implementation, and its main features are strong practicality and wide applicability. Attached Figure Description

[0080] The above and other objects, features, and advantages of exemplary embodiments of the present invention will become readily apparent from the following detailed description taken in conjunction with the accompanying drawings. Several embodiments of the invention are illustrated in the drawings by way of example, not limitation, in which:

[0081] Figure 1 This is a flowchart of a method for achieving inclusive control of a second-order multi-agent system under network prediction, as described in this invention.

[0082] Figure 2 This is a communication topology diagram of a discrete-time second-order multi-agent system in an embodiment of the present invention;

[0083] Figure 3 This is an example diagram illustrating the implementation of inclusive control of the position of a second-order multi-agent system under a network predictive controller in an embodiment of the present invention;

[0084] Figure 4 This is an example diagram illustrating the implementation of inclusive control of the velocity of a second-order multi-agent system under a network predictive controller in an embodiment of the present invention;

[0085] Figure 5 This is an example diagram showing that the positional error trajectory of the follower reaches zero in an embodiment of the present invention;

[0086] Figure 6 This is an example diagram showing that the speed error trajectory of the follower reaches zero in an embodiment of the present invention. Detailed Implementation

[0087] The principles and spirit of the invention will now be described with reference to several exemplary embodiments. It should be understood that these embodiments are given merely to enable those skilled in the art to better understand and implement the invention, and are not intended to limit the scope of the invention in any way. Rather, these embodiments are provided to make this disclosure more thorough and complete, and to fully convey the scope of this disclosure to those skilled in the art.

[0088] Those skilled in the art will recognize that embodiments of the present invention can be implemented as a system, apparatus, device, method, or computer program product. Therefore, this disclosure can be specifically implemented in the following forms: entirely hardware, entirely software (including firmware, resident software, microcode, etc.), or a combination of hardware and software. It should be understood herein that any number of elements in the accompanying drawings is for illustrative purposes only and not as a limitation, and any naming is for distinction only and has no limiting meaning.

[0089] To overcome the impact of communication delays and packet loss on inclusive control in multi-agent systems, this invention proposes a method for achieving inclusive control in a second-order multi-agent system under network prediction, such as... Figure 1 As shown, the specific steps of this method include:

[0090] Step 1: Use a directed topology graph to describe the communication relationships between multiple agents and establish a dynamic model of a discrete-time second-order multi-agent system with network latency and packet loss; the multi-agent system includes multiple leaders and multiple followers;

[0091] Step 2: Establish a prediction model based on the dynamic model and perform state prediction;

[0092] Step 3: Design a predictive controller using the predicted state obtained from the prediction model;

[0093] Step 4: Substitute the predictive controller into the dynamic model to obtain the expressions for the position estimation error and velocity estimation error;

[0094] Step 5: Solve for the position estimation error and velocity estimation error to obtain the feedback gain constant of the predictive controller and the conditions that the sampling period must satisfy;

[0095] Step 6: Substitute the feedback gain constant that meets the conditions into the designed predictive controller, and use the predictive controller to realize the inclusive control of the discrete-time second-order multi-agent system with network delay and packet loss under network prediction.

[0096] The present invention will now be described in detail.

[0097] In step one, a directed topological graph is first used to describe the communication relationships between multiple agents, and a dynamic model of a discrete-time second-order multi-agent system with network latency and packet loss is established.

[0098] According to an embodiment of the present invention, agents are considered as vertices of a graph, and a directed topological graph G = (V, E, A) is defined to describe the communication relationships between N agents, where the vertex set V = {v1, v2, ..., v...} N} represents N intelligent agents, and the edge set e represents the communication structure between intelligent agents ij It is a connection of ordered pairs (v j ,v i an edge of ) v j It's the starting point, v i The endpoint is i,j=1,2,…,N,v j Called v i The set of neighboring vertices, N i ={v j ∈V|e ij =(v j ,v i )∈E,j≠i} means v i The set of neighboring vertices; Let a represent the adjacency matrix of a directed graph G. ij >0 indicates that agent j can send information to agent i; otherwise, a ij =0. In this embodiment, let the first M agents out of N agents be leaders and the last NM agents be followers. Let R = {1,2,…,M} and F = {M+1,M+2,…,N} represent the leader indicator set and the follower indicator set, respectively.

[0099] The established dynamic model of the discrete-time second-order multi-agent system is described as follows:

[0100] X i (k+1)=AX i (k)+Bu i (k)

[0101] y i (k)=CX i (k), i = 1, 2, ..., N (1)

[0102] In the formula, C = [c1 c2], X i (k) represents the state of agent i at time k, including position. and speed A, B, and C represent the system matrix, input matrix, and output matrix, respectively. and Let c1, c2, a, and b represent the measurement output and control input of agent i, respectively. T > 0 is the sampling period, and c1, c2, a, and b are constants. It is the set of real numbers.

[0103] In step two, a prediction model is established based on the dynamic model, and state prediction is performed.

[0104] According to an embodiment of the present invention, in order to reduce the negative impacts caused by the communication network (such as network latency and packet loss), an active compensation rule is proposed by predicting the state of neighboring agents. For agent i, a state observer is constructed as follows:

[0105]

[0106]

[0107] in, and These represent the predicted state, predicted position, predicted velocity, and predicted output of agent i at time k-τ, obtained based on information up to time k-τ-1. i (k-τ) and y i (k-τ) represents the control input and measurement output of agent i at time k-τ, L is the observer gain matrix, τ = d + p, where d is the upper bound of the communication delay and p is the upper bound of the number of lost data packets.

[0108] Based on the predicted state for the next step obtained from the state observer (2) The prediction model is established as follows:

[0109]

[0110]

[0111]

[0112] Thus, the predicted state of agent i from time k-τ+2 to time k is obtained. In the formula, This indicates that the predicted state of agent i at time k-τ+s is obtained based on information up to time k-τ. i (k-τ+s-1) is the control input of agent i at time k-τ+s-1, where s=2,3,...,τ.

[0113] Iterating over equation (3), we obtain the expression for the predicted state of agent i at time k:

[0114]

[0115] in, and Let $\mathbf$ represent the predicted state, predicted position, and predicted velocity of agent $i$ at time $k$, respectively. yes The function, is u i The function, f3(y) i ) = A τ-1 Ly i (k-τ) is y i The function.

[0116] Similarly, by iterating over equation (1), we can obtain the state expression of the system as follows:

[0117] X i (k)=A τ X i (k-τ)+f2(u i (5)

[0118] Among them, X i (k) and X i (k-τ) represent the states of agent i at time k and time k-τ, respectively.

[0119] Subtracting equation (5) from equation (4) yields the expression for state prediction:

[0120]

[0121] In the formula, This indicates that based on the information of agent i up to time k-τ, the predicted state of agent i at time k is obtained; e i (k-τ+1) represents the state estimation error at time k-τ+1;

[0122] Then, the predicted position of agent i at time k can be obtained from equation (6). and prediction speed With position estimation error e xi (k) and velocity estimation error e vi The relationship of (k) is:

[0123]

[0124]

[0125] In step three, using the predicted state obtained from the prediction model, a prediction controller is designed as follows:

[0126]

[0127] in, For location prediction bias, For speed prediction deviation, It is the weighted sum of the position prediction deviations of agent i and its neighboring agents; It is the weighted sum of the velocity prediction deviations of agent i and its neighboring agents, α1 and α2 are the feedback gain constants to be solved, R = {1,2,…,M} is the leader indicator set, F = {M+1,M+2,…,N} is the follower indicator set, and N i Let be the set of neighboring vertices of agent i.

[0128] In step four, the predictive controller is substituted into the dynamic model to obtain expressions for the position estimation error and velocity estimation error.

[0129] According to an embodiment of the present invention, the expressions for the position estimation error and the velocity estimation error are as follows:

[0130] E(k+1)=ΨE(k) (8)

[0131]

[0132] In the formula,

[0133]

[0134]

[0135] L fr L is the Laplace matrix corresponding to the leader. ff Let I be the Laplace matrix corresponding to the follower. N-M Let I be an NM-dimensional identity matrix. M It is an M-dimensional identity matrix. x (k)=[e xM+1 (k),e xM+2 (k),…e xM+N (k)] T To estimate the error vector of the follower's position at time k, e v (k)=[e vM+1 (k),e vM+2 (k),…e vM+N (k)] T E is the velocity estimation error vector of the follower at time k. xR (k-τ+1)=[e x1 (k-τ+1),e x2 (k-τ+1),…,e xM (k-τ+1)] T E is used to estimate the error vector of the leader's position at time k-τ+1. vR (k-τ+1)=[e v1 (k-τ+1),ev2 (k-τ+1),…,e vM (k-τ+1)] T E represents the velocity estimation error vector of the leader at time k-τ+1. xF (k-τ+1)=[e xM+1 (k-τ+1),e xM+2 (k-τ+1),…,e xN (k-τ+1)] T E is used to estimate the error vector of the follower's position at time k-τ+1. vF (k-τ+1)=[e vM+1 (k-τ+1),e vM+2 (k-τ+1),…,e vN (k-τ+1)] T The error vector for estimating the velocity of the follower at time k-τ+1.

[0136] Based on the expressions for position estimation error and velocity estimation error, the following conclusion can be drawn: For a discrete-time second-order multi-agent system with network delay and packet loss, i.e., Equation (1), the necessary and sufficient condition for the designed predictive controller to achieve inclusive control is that Γ1 and Γ3 are Schur stable, i.e., their characteristic roots are all located inside the unit circle.

[0137] In step five, the position estimation error and velocity estimation error are solved to obtain the feedback gain constant of the predictive controller and the conditions that the sampling period must satisfy.

[0138] According to an embodiment of the present invention, by using the bilinear transform and Schur stability determination method, the feedback gain constants α1 and α2 can be obtained, and the condition satisfied by the sampling period T is as follows:

[0139]

[0140] in,

[0141] m i =α1μ i -a

[0142] n i =α2μ i -b

[0143]

[0144]

[0145]

[0146]

[0147]

[0148] Re(n i )=α2Re(μ i )-b

[0149]

[0150]

[0151] In the formula, μ i It is matrix L ff The eigenvalues ​​are denoted by Re(·), which is used to find the real part, and Im(·), which is used to find the imaginary part.

[0152] In step six, the feedback gain constant that meets the conditions is substituted into the designed predictive controller, and the predictive controller is used to realize the inclusive control of the discrete-time second-order multi-agent system with network delay and packet loss under network prediction.

[0153] The technical effects of the present invention were further verified through simulation experiments.

[0154] The simulation experiment considers a multi-agent system consisting of 2 leaders and 8 followers, where N = 10, M = 2, R = {1, 2} and F = {3, 4, ..., 10}. The system parameters are: C = [1 1] Network communication topology G such as Figure 2 As shown. Without loss of generality, the connection weights of all edges in the network topology are considered to be 1. Assume that the sum of the upper bounds of delays and packet losses incurred by the agent during communication is τ = 4.

[0155] Depend on Figure 2 From the communication topology diagram G, the corresponding Laplace matrix can be obtained as follows:

[0156]

[0157] The initial state of the system is selected as follows:

[0158] x R (0) = [2 1] T ,v R (0) = [0.2 -0.1] T

[0159] x F (0) = [-6 -12 -7 -3 6 13 18 15] T

[0160] v F (0) = [2.1 1.5 -1.4 -2.2 0.75 0.3 -0.35 -0.7]T

[0161] Solving using equation (9), the conditions that the feedback gain constant and sampling period must satisfy are: α1 > 0.3742, α2 > 0.1871, T < 0.5. Therefore, when the feedback gain constants α1 and α2 and the sampling period T satisfy these conditions, the designed predictive controller can achieve inclusive control of a discrete-time second-order multi-agent system.

[0162] Specifically, α1 = 0.5, α2 = 0.5, and T = 0.1 are selected and substituted into the predictive controller to achieve inclusive control of the discrete-time second-order multi-agent system.

[0163] Experimental results are as follows Figures 3-6 As shown, Figure 3 For the position trajectories of all agents. Figure 4 Given the velocity trajectories of all agents, it is demonstrated that a discrete-time second-order multi-agent system can achieve inclusive control under a designed network predictive controller. Figure 5 Estimate the error trajectory for the position of the follower. Figure 6 The velocity estimation error trajectory for the follower demonstrates that the position error trajectory and velocity error trajectory of the follower will eventually tend to zero over time.

[0164] Another embodiment of the present invention proposes a system for inclusive control of a second-order multi-agent system under network prediction, the system comprising:

[0165] A multi-agent model building module is configured to use a directed topological graph to describe the communication relationships between multiple agents, and to build a dynamic model of a discrete-time second-order multi-agent system with network latency and packet loss; wherein the multi-agent system includes multiple leaders and multiple followers; the dynamic model is represented as:

[0166] X i (k+1)=AX i (k)+Bu i (k)

[0167] y i (k)=CX i (k)

[0168] In the formula, C = [c1 c2], X i (k) represents the state of agent i at time k, including position. and speed A, B, and C represent the system matrix, input matrix, and output matrix, respectively. and Let c1, c2, a, and b represent the measurement output and control input of agent i, respectively. T > 0 is the sampling period, and c1, c2, a, and b are constants. It is the set of real numbers;

[0169] A predictive controller establishment module is configured to establish a predictive model based on the dynamic model and perform state prediction; design a predictive controller using the predicted state obtained from the predictive model; substitute the predictive controller into the dynamic model to obtain expressions for position estimation error and velocity estimation error; solve for the position estimation error and velocity estimation error to obtain the feedback gain constant of the predictive controller and the conditions satisfied by the sampling period.

[0170] The inclusive control module is configured to substitute a feedback gain constant that meets certain conditions into the designed predictive controller, and use the predictive controller to realize inclusive control of a discrete-time second-order multi-agent system with network latency and packet loss under network prediction.

[0171] In this embodiment, preferably, the prediction model in the prediction controller establishment module is represented as:

[0172]

[0173]

[0174]

[0175] In the formula, This means that based on the information of agent i up to time k-τ, the predicted state of agent i at time k-τ+1 is obtained; This means that based on the information of agent i up to time k-τ-1, the predicted state of agent i at time k-τ is obtained; τ represents the predicted output; L represents the observation gain matrix; τ = d + p, where d is the upper bound of the communication delay and p is the upper bound of the number of lost data packets; This indicates that the predicted state of agent i at time k-τ+s is obtained based on information up to time k-τ. i (k-τ+s-1) represents the control input of agent i at time k-τ+s-1;

[0176] The expression for state prediction using a prediction model is:

[0177]

[0178] In the formula, This indicates that based on the information of agent i up to time k-τ, the predicted state of agent i at time k is obtained; e i (k-τ+1) represents the state estimation error at time k-τ+1;

[0179] In this embodiment, preferably, the predictive controller in the predictive controller establishment module is represented as:

[0180]

[0181] In the formula, α1 and α2 are the feedback gain constants to be solved, and N i Let R be the set of neighboring vertices of agent i; R = {1,2,…,M} is the leader indicator set, and F = {M+1,M+2,…,N} is the follower indicator set. For location prediction bias, For speed prediction deviation, It is the weighted sum of the position prediction deviations of agent i and its neighboring agents; It is the weighted sum of the velocity prediction deviations of agent i and its neighboring agents;

[0182] The expressions for the position estimation error and velocity estimation error are as follows:

[0183]

[0184] E(k+1)=ΨE(k)

[0185] In the formula, e x (k) is the position estimation error vector of the follower at time k, e v (k) represents the velocity estimation error vector of the follower at time k; E xF (k-τ+1) represents the position estimation error vector of the follower at time k-τ+1, E xR (k-τ+1) represents the error vector for estimating the leader's position at time k-τ+1; E vF (k-τ+1) is the velocity estimation error vector of the follower at time k-τ+1, E vR (k-τ+1) represents the velocity estimation error vector of the leader at time k-τ+1;

[0186]

[0187]

[0188]

[0189] L fr L is the Laplace matrix corresponding to the leader. ff Let I be the Laplace matrix corresponding to the follower. N-M Let I be an NM-dimensional identity matrix. MLet N be an M-dimensional identity matrix; M is the total number of leaders; N is the total number of agents.

[0190] In this embodiment, preferably, the predictive controller establishment module uses bilinear transformation and Schur stability determination to solve the problem. The feedback gain constants α1 and α2 and the sampling period T obtained by the solution satisfy the following conditions:

[0191]

[0192] m i =α1μ i -a

[0193] n i =α2μ i -b

[0194]

[0195]

[0196]

[0197] In the formula, μ i It is matrix L ff The eigenvalues; Re(·) denotes finding the real part, and Im(·) denotes finding the imaginary part.

[0198] It should be noted that although several units, modules, or sub-modules are mentioned in the detailed description above, this division is merely exemplary and not mandatory. In fact, according to embodiments of the present invention, the features and functions of two or more modules described above can be embodied in one module. Conversely, the features and functions of one module described above can be further divided and embodied by multiple modules.

[0199] Furthermore, although the operations of the method of the present invention are described in a specific order in the accompanying drawings, this does not require or imply that these operations must be performed in that specific order, or that all the operations shown must be performed to achieve the desired result. Additionally or alternatively, certain steps may be omitted, multiple steps may be combined into one step, and / or one step may be broken down into multiple steps.

[0200] While the spirit and principles of the invention have been described with reference to several specific embodiments, it should be understood that the invention is not limited to the disclosed specific embodiments, and the division of aspects does not imply that features in these aspects cannot be combined for benefit; such division is merely for ease of description. The invention is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims

1. A method for achieving inclusive control of a second-order multi-agent system under network prediction, characterized in that, Includes the following steps: Step 1: Use a directed topology graph to describe the communication relationships between multiple agents and establish a dynamic model of a discrete-time second-order multi-agent system with network latency and packet loss; the multi-agent system includes multiple leaders and multiple followers; Step 2: Establish a prediction model based on the dynamic model and perform state prediction; Step 3: Using the predicted state obtained from the prediction model, design a prediction controller; the prediction controller is represented as: ； In the formula, and It is the feedback gain constant to be solved. For intelligent agents The set of neighboring vertices; For the leader indicator set, For the follower indicator set; For location prediction bias, For speed prediction deviation, It is an intelligent agent The weighted sum of the position prediction deviations of its neighboring agents; It is an intelligent agent The weighted sum of the velocity prediction deviations of its neighboring agents; Represents intelligent agents Control input; Description A directed topological graph of communication relationships between agents. and The adjacency matrix between them; Indicates time; and Representing intelligent agents respectively And agent j in Predicted location at any given time; and Representing intelligent agents respectively And agent j in Predicting speed at any given moment; Step 4: Substitute the predictive controller into the dynamic model to obtain the expressions for the position estimation error and velocity estimation error; the expressions for the position estimation error and velocity estimation error are: ； ； In the formula, For followers in The position estimation error vector at time 1. For followers in The velocity estimation error vector at time t; For followers in Time position estimation error vector For leaders in Time position estimation error vector; For followers in The velocity estimation error vector at any given time. For leaders in The velocity estimation error vector at any given time; , ， The Laplace matrix for the leader. For the Laplace matrix corresponding to the follower, for 3D identity matrix for A 3D identity matrix; M represents the total number of leaders; N represents the total number of agents; It is the sampling period; It is a constant; A represents the system matrix of the dynamic model of a discrete-time second-order multi-agent system. C represents the output matrix of the dynamic model of a discrete-time second-order multi-agent system. The observer gain matrix; Step 5: Solve for the position estimation error and velocity estimation error to obtain the feedback gain constant of the predictive controller and the conditions that the sampling period must satisfy; Step 6: Substitute the feedback gain constant that meets the conditions into the designed predictive controller, and use the predictive controller to realize the inclusive control of the discrete-time second-order multi-agent system with network delay and packet loss under network prediction.

2. The method for achieving inclusive control of a second-order multi-agent system under network prediction according to claim 1, characterized in that, The dynamic model described in step one is represented as follows: ； ； In the formula, , express Time-based intelligent agent The state, including position and speed ; These represent the system matrix, input matrix, and output matrix, respectively. and Representing intelligent agents respectively Measurement output and control input, It is the sampling period. It is a constant. It is the set of real numbers.

3. The method for achieving inclusive control of a second-order multi-agent system under network prediction according to claim 2, characterized in that, The prediction model described in step two is expressed as follows: ； ； ； In the formula, Indicated based on until Time-based intelligent agent Information obtained by the intelligent agent exist The predicted state at any given moment; Indicated based on until Time-based intelligent agent Information obtained by the intelligent agent exist The predicted state at any given moment; Indicates the predicted output; Represents the observation gain matrix; , It is the upper bound of communication latency. It is the upper bound of the number of lost data packets; Indicated based on until Information about the moment is obtained by the intelligent agent exist Predicted state at any given time Represents intelligent agents exist Time-based control input; The expression for state prediction using a prediction model is: ； In the formula, Indicated based on until Time-based intelligent agent Information obtained by the intelligent agent The predicted state at time k; express Error in state estimation at time step; .

4. The method for achieving inclusive control of a second-order multi-agent system under network prediction according to claim 3, characterized in that, Step five uses bilinear transformation and Schur stability determination to solve for the feedback gain constant. , and sampling period The conditions to be met are: ； ； In the formula, It is a matrix eigenvalues; Indicates the Department of Seeking Truth. This indicates the search for the imaginary part.

5. A system for inclusive control of a second-order multi-agent system under network prediction, characterized in that, include: A multi-agent model building module is configured to use a directed topological graph to describe the communication relationships between multiple agents, and to build a dynamic model of a discrete-time second-order multi-agent system with network latency and packet loss; wherein the multi-agent system includes multiple leaders and multiple followers; the dynamic model is represented as: ； ； In the formula, , express Time-based intelligent agent The state, including position and speed ; These represent the system matrix, input matrix, and output matrix, respectively. and Representing intelligent agents respectively Measurement output and control input, It is the sampling period. It is a constant. It is the set of real numbers; A predictive controller establishment module is configured to establish a predictive model based on the dynamic model and perform state prediction; design a predictive controller using the predicted state obtained from the predictive model; substitute the predictive controller into the dynamic model to obtain expressions for the position estimation error and velocity estimation error; solve for the position estimation error and velocity estimation error to obtain the feedback gain constant of the predictive controller and the condition satisfied by the sampling period; wherein, the predictive controller is expressed as: ； In the formula, and It is the feedback gain constant to be solved. For intelligent agents The set of neighboring vertices; For the leader indicator set, For the follower indicator set; For location prediction bias, For speed prediction deviation, It is an intelligent agent The weighted sum of the position prediction deviations of its neighboring agents; It is an intelligent agent The weighted sum of the velocity prediction deviations of its neighboring agents; Description A directed topological graph of communication relationships between agents. and The adjacency matrix between them; and Representing intelligent agents respectively And agent j in Predicted location at any given time; and Representing intelligent agents respectively And agent j in Predicting speed at any given moment; The expressions for the position estimation error and velocity estimation error are as follows: ； ； In the formula, For followers in The position estimation error vector at time 1. For followers in The velocity estimation error vector at time t; For followers in Time position estimation error vector For leaders in Time position estimation error vector; For followers in The velocity estimation error vector at any given time. For leaders in The velocity estimation error vector at any given time; , ， The Laplace matrix for the leader. For the Laplace matrix corresponding to the follower, for 3D identity matrix for A 3D identity matrix; M represents the total number of leaders; N represents the total number of agents; ; The observer gain matrix; The inclusive control module is configured to substitute a feedback gain constant that meets certain conditions into the designed predictive controller, and use the predictive controller to realize inclusive control of a discrete-time second-order multi-agent system with network latency and packet loss under network prediction.

6. A system for inclusive control of a second-order multi-agent system under network prediction according to claim 5, characterized in that, The prediction model in the prediction controller establishment module is represented as follows: ； ； ； In the formula, Indicated based on until Time-based intelligent agent Information obtained by the intelligent agent exist The predicted state at any given moment; Indicated based on until Time-based intelligent agent Information obtained by the intelligent agent exist The predicted state at any given moment; Indicates the predicted output; Represents the observation gain matrix; , It is the upper bound of communication latency. It is the upper bound of the number of lost data packets; Indicated based on until Information about the moment is obtained by the intelligent agent exist Predicted state at any given time Represents intelligent agents exist Time-based control input; The expression for state prediction using a prediction model is: ； In the formula, Indicated based on until Time-based intelligent agent Information obtained by the intelligent agent The predicted state at time k; express Error in state estimation at time step; .

7. A system for inclusive control of a second-order multi-agent system under network prediction according to claim 6, characterized in that, The predictive controller establishment module uses bilinear transformation and Schur stability determination to solve for the feedback gain constant. , and sampling period The conditions to be met are: ； ； In the formula, It is a matrix eigenvalues; Indicates the Department of Seeking Truth. This indicates the search for the imaginary part.

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