Second-order multi-agent system consensus control method with noise and adversarial information

Abstract

The application discloses a kind of second-order multi-agent system consistency control method with noise and counter information, the method comprises: according to the cooperation-antagonism information between second-order nonlinear multi-agent determines the topology structure of second-order nonlinear multi-agent system;Establish the dynamics model of second-order nonlinear multi-agent system;Under the compound noise interference of simultaneously considering additive noise and multiplicative noise, design consistency control protocol;The control protocol is brought into dynamics model, the consistency problem of this multi-agent system is converted into the stability problem of stochastic differential equation, stability analysis is carried out, and position error and speed error are guaranteed to converge.The application designs the consistency control protocol with cooperation-antagonism information under the compound noise interference of simultaneously existing additive noise and multiplicative noise, can greatly improve the anti-interference ability of system, and through stability analysis consistency condition, so that the controlled system is adjusted more easily, reduces control operation complexity.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent control technology, specifically relating to a consensus control method for a nonlinear second-order multi-agent system with composite communication noise and cooperative-adversarial information. Background Technology

[0002] Multi-agent systems (MAS) are inspired by the collective behavior of organisms and are currently mainly applied in areas such as UAV swarms, unmanned vehicle deployment, and air-to-ground heterogeneous combat tracking. In the future, they will show great potential for application development in military, aerospace, intelligent transportation, and intelligent robotic systems. The consensus problem in MAS occurs during the coordination and control process among multiple agents. Agents need to exchange information with neighboring agents to complete a predetermined task or achieve a common goal, thereby reaching a consensus on certain properties. A consensus protocol refers to the rules governing the information exchange between agents, neighboring agents, or the leader. In addressing the consensus problem, designing a high-quality consensus protocol is a crucial factor determining whether the system can achieve consensus and the speed of convergence.

[0003] Current research on consensus in multi-agent systems largely focuses on deterministic systems with cooperation between agents, and this approach is becoming increasingly mature. However, multi-agent systems in the context of big data often operate in complex environments, and local communication between agents is subject to various uncertainties, such as time delays, noise, and communication topology switching. For example, the invention patent CN111781822A discloses a privacy-preserving group consensus control method for multi-agent systems. This method, targeting heterogeneous multi-agent systems, optimizes and groups the location information sent by agents using Laplace-distributed noise. The consensus control protocol considers communication delays in actual communication networks and input delays caused by controllers and sensors within the system to enhance anti-interference capabilities. However, besides group cooperation, real-world multi-agent systems also exhibit various operational modes, such as adversarial cooperation. The simultaneous existence of cooperative and adversarial information complicates the system's communication structure and couples it with cooperative control objectives and communication uncertainties, rendering traditional cooperative control research methods inapplicable. Furthermore, the simultaneous presence of two types of communication noise interference means that considering only a single Laplace-distributed noise is insufficient to effectively improve the system's anti-interference capabilities, thus limiting the practical significance of consensus control. Summary of the Invention

[0004] In view of this, the present invention proposes a consensus control method and system for a second-order multi-agent system with noise and adversarial information, which is used to solve the problem of poor anti-interference performance of multi-agent systems with cooperative-adversarial information interaction.

[0005] In a first aspect, this invention discloses a consensus control method for a second-order multi-agent system with noise and adversarial information, the method comprising:

[0006] The topology of the second-order nonlinear multi-agent system is determined based on the cooperative-adversarial information of the interactions between the second-order nonlinear multi-agents.

[0007] Establish a dynamic model for a second-order nonlinear multi-agent system;

[0008] Considering the combined noise interference of additive and multiplicative noise, a consensus control protocol is designed by introducing a random time-varying control gain function using relative position and velocity measurement information combined with a sign function.

[0009] The control protocol is incorporated into the dynamic model, and error terms are designed to transform the consistency problem of the multi-agent system into a stability problem of stochastic differential equations under composite noise. Stability analysis is performed to ensure that the position and velocity errors of all agents converge in the mean-square bisection consistency sense.

[0010] Based on the above technical solutions, preferably, the step of determining the topology of the second-order nonlinear multi-agent system based on the adversarial information of the second-order nonlinear multi-agent system specifically includes:

[0011] Suppose a second-order nonlinear multi-agent system contains N agents. Let G = {V, E, A} denote the directed symbolic topology of this agent system, and V = {v1, ..., v...} N} represents a set of nodes. Let A be the edge set of the graph, A = [a ij ]∈R N×N Represent the adjacency matrix of graph G;

[0012] a ij =1 indicates that the j-th agent can receive the cooperation information of the i-th agent, a ij =-1 indicates that the j-th agent can receive adversarial information from the i-th agent, a ij =0 indicates that the j-th agent cannot receive information from the i-th agent;

[0013] Based on adversarial information, node V is divided into two node sets, V1 and V2, where V1∪V2=V. If a ij ≥0, have or If a ij ≤0, have Or v i ∈V1,

[0014] Based on the above technical solutions, preferably, the establishment of the dynamic model of the second-order nonlinear multi-agent system specifically includes:

[0015] Suppose a second-order nonlinear multi-agent system contains N agents, and its dynamic model is expressed as:

[0016]

[0017] Where i = 1, ..., N, p i (k) represents the position of the i-th agent at time k, q i (k) represents the velocity of the i-th agent at time k, u i (k) represents the control protocol of the i-th agent at time k, f(p) i (k),q i (k),k) is a nonlinear function.

[0018] Based on the above technical solutions, preferably, the expression for the consensus control protocol with adversarial information designed under the combined noise interference of additive and multiplicative noise is as follows:

[0019]

[0020] Among them, h pji (·) and h qji (·) represent the multiplicative noise intensity functions for position and velocity, respectively, σ pji and σ qji These represent the additive noise intensity coefficients for position and velocity, respectively.

[0021] ω 1pji (t), ω 2pji (t) represents Gaussian independent white noise at the location, ω 1qji (t), ω 2qji (t) are Gaussian independent white noise with velocity, satisfying:

[0022] Eω zgji (s)=0,E|ω zgji (s)| 2 =1,E|ω zgji (s)ω zgji (t)|=0

[0023] Where g = p, q, s, t ≥ 0 and s ≠ t; sign(·) is the sign function, and E represents the expectation;

[0024] c1(k) > 0 is the position control gain function, c2(k) > 0 is the velocity control gain function, and satisfies:

[0025]

[0026] Where z = 1, 2.

[0027] Based on the above technical solutions, preferably, the stability analysis includes: solving the bipartite consistency condition of a second-order nonlinear multi-agent system with adversarial information under composite noise interference with both additive and multiplicative noise.

[0028] Based on the above technical solutions, preferably, the step of incorporating the control protocol into the dynamic model, designing error terms, and transforming the consistency problem of the multi-agent system into a stability problem of stochastic differential equations under composite noise, and performing stability analysis, specifically includes:

[0029] The variables of a second-order multi-agent system are uniformly represented by column vectors, and error terms and invertible matrices satisfying constraints are defined.

[0030] The consensus control protocol is incorporated into the dynamic model, and the formula of the dynamic model is rewritten according to the relationship between the error term, the invertible matrix and the variables of the second-order multi-agent system. The second-order multi-agent system is then transformed into a stochastic differential equation.

[0031] The specific process of designing the binary consistency condition of a second-order nonlinear multi-agent system with adversarial information under composite noise interference with both additive and multiplicative noise.

[0032] A semi-decoupling method is used to solve the bipartite consistency condition of a second-order nonlinear multi-agent system with adversarial information under composite noise interference with both additive and multiplicative noise.

[0033] Based on the above technical solutions, the preferred solution, obtained under composite noise interference with both additive and multiplicative noise, specifically includes the following binary consistency conditions for a second-order nonlinear multi-agent system with adversarial information:

[0034] The selection of coefficients for the multiplicative noise intensity function must meet certain conditions;

[0035] The selection of the additive noise intensity coefficient must meet certain conditions;

[0036] Nonlinear function f(p) i (k),q i The selection of coefficients (k),k) must satisfy certain conditions;

[0037] The selection of position control gain function and velocity control gain function must meet certain conditions.

[0038] A second aspect of the present invention discloses a consensus control device for a second-order multi-agent system with noise and adversarial information, the device comprising:

[0039] Topology establishment module: used to determine the topology of a second-order nonlinear multi-agent system based on the adversarial information of the system.

[0040] Dynamics Model Building Module: Used to build dynamics models of second-order nonlinear multi-agent systems;

[0041] Control Protocol Design Module: Used to design a consensus control protocol with cooperative-adversarial information under composite noise interference where additive and multiplicative noise coexist.

[0042] A control stability analysis module is used to incorporate the control protocol into the dynamic model, design error terms, transform the consistency problem of a multi-agent system into a stability problem of stochastic differential equations under composite noise, perform stability analysis, and ensure that the position and velocity errors of all agents converge under the mean-square bipartite consistency principle. A third aspect of this invention discloses an electronic device comprising: at least one processor, at least one memory, a communication interface, and a bus;

[0043] The processor, memory, and communication interface communicate with each other through the bus.

[0044] The memory stores program instructions that can be executed by the processor, which invokes the program instructions to implement the method as described in the first aspect of the present invention.

[0045] In a fourth aspect, the present invention discloses a computer-readable storage medium storing computer instructions that cause a computer to perform the method described in the first aspect of the present invention.

[0046] The present invention has the following advantages over the prior art:

[0047] 1) This invention addresses the practical problem in real-world communication systems where each agent inevitably encounters communication noise when obtaining information from its neighboring agents, and this noise is often multiplicative and additive. A consensus control protocol with adversarial information is designed and implemented under composite noise interference involving both additive and multiplicative noise. This significantly improves the system's anti-interference capability and enhances the robustness of multi-agent systems. Considering composite noise is therefore of greater practical significance.

[0048] 2) This invention utilizes matrix theory, graph theory and other knowledge to transform a second-order nonlinear multi-agent system into a discrete-time stochastic equation, and establishes an algebraic consistency condition with explicit mathematical parameters and matrix expressions related to the multiplicative noise figure, additive noise figure, nonlinear coefficient and control gain function through stability analysis, which makes the controlled system easier to adjust and reduces the complexity of control operation;

[0049] 3) This invention reveals that the mathematical expectation of the final convergence value is related to the initial state and the canonical matrix of the agent, and that the convergence state of the agent system can be changed by appropriate adjustment; at the same time, it proves that nonlinear terms with small Lipschitz constants do not destroy the consistency of stochastic multi-agent systems with additive and multiplicative noise. Attached Figure Description

[0050] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0051] Figure 1 This is a flowchart of the consensus control method for a second-order multi-agent system with noise and adversarial information according to the present invention.

[0052] Figure 2 This is an example of the topology diagram of a second-order multi-agent system with adversarial information according to the present invention;

[0053] Figure 3 The position and state curves of each agent obtained from the simulation experiment;

[0054] Figure 4 The velocity state curves of each intelligent agent obtained from the simulation experiment;

[0055] Figure 5 The position error curves of each agent obtained from the simulation experiment;

[0056] Figure 6 The velocity error curves of each intelligent agent obtained from the simulation experiment are shown. Detailed Implementation

[0057] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0058] Please see Figure 1 This invention discloses a consensus control method for a second-order multi-agent system with noise and adversarial information, the method comprising:

[0059] S1. Determine the topology of the second-order nonlinear multi-agent system based on the adversarial information of the second-order nonlinear multi-agent system.

[0060] Suppose a second-order nonlinear multi-agent system contains N agents. Let G = {V, E, A} denote the directed symbolic topology of this agent system, and V = {v1, ..., v...} N} represents a set of nodes, i = 1, ..., N. Let A be the edge set of the graph, A = [a ij ]∈R N×N Let represent the adjacency matrix of graph G. ij =1 indicates that the j-th agent can receive the cooperation information of the i-th agent, a ij =-1 indicates that the j-th agent can receive adversarial information from the i-th agent, a ij =0 indicates that the j-th agent cannot receive information from the i-th agent.

[0061] Based on adversarial information, node V is divided into two node sets, V1 and V2, where V1∪V2=V. If a ij ≥0, have or If a ij ≤0, have Or v i ∈V1, In this case, only cooperative information exists between agents within a node set V1 or V2, while adversarial information exists between the two node sets V1 and V2. A unified opinion is reached within the group, but differing opinions exist between different groups. This aligns with natural laws and practical applications. This invention addresses the binary consensus problem in second-order nonlinear multi-agent systems.

[0062] A directed symbolic topological graph G is a structurally balanced graph if and only if there exists a canonical matrix D satisfying DLD = |L|, where L is a Laplace matrix, and D = diag{ζ1,ζ2,...,ζ} N}and ζ i ∈{±1}. The degree matrix of a directed symbolic topological graph G is represented by Υ=[γ ij ]∈R N×N It means that, among them:

[0063]

[0064] L = Υ - A = [l] ij ]∈R N×N

[0065]

[0066] N0 = {1,2,…,N} is the set of IDs for N agents.

[0067] S2. Establish a dynamic model of a second-order nonlinear multi-agent system.

[0068] Suppose a second-order nonlinear multi-agent system contains N agents, and its dynamic model is expressed as:

[0069]

[0070] Where i = 1, ..., N, p i (k) represents the position of the i-th agent at time k, q i (k) represents the velocity of the i-th agent at time k, u i (k) represents the control protocol of the i-th agent at time k, f(p) i (k),q i (k),k) is a nonlinear function.

[0071] S3. Considering the combined noise interference of additive and multiplicative noise, a consistency control protocol is designed by combining relative position and velocity measurement information with a sign function and introducing a random time-varying control gain function.

[0072] Based on different statistical characteristics and the characteristics of the medium transmitting information, communication noise can be divided into additive noise and multiplicative noise. This invention analyzes and simulates additive noise independent of the signal and multiplicative noise coupled with the agent's state, and designs an effective consensus control protocol. The expression of this control protocol is as follows:

[0073]

[0074] Among them, h pji (·) and h qji (·) represent the multiplicative noise intensity functions for position and velocity, respectively, σ pji and σ qji These represent the additive noise intensity coefficients for position and velocity, respectively.

[0075] ω 1pji ω 2pji All are Gaussian independent white noise at position, ω 1qji ω 2qji All are Gaussian independent white noise with velocity, satisfying:

[0076] Eω zgji (s)=0,E|ω zgji (s)| 2 =1,E|ω zgji (s)ω zgji (t)|=0

[0077] Where g = p, q, s, t ≥ 0 and s ≠ t, sign(·) is the sign function, and E represents the expectation;

[0078] c1(k) and c2(k) are both stochastic time-varying control gain functions, where c1(k) > 0 is the position control gain function and c2(k) > 0 is the velocity control gain function, and they satisfy the following:

[0079]

[0080] Where z = 1, 2.

[0081] In practical communication systems, each agent is inevitably affected by communication noise when obtaining information from its neighboring agents, and multiplicative and additive noise are likely to coexist. The main additive noise includes thermal noise generated within electronic components (e.g., semiconductor components and resistors), which is independent of the signal and interferes with the signal in a superimposed form. Multiplicative noise is noise caused by random variations in channel characteristics; it is correlated with the signal and impairs the communication process. Therefore, this invention analyzes and simulates additive noise independent of the signal and multiplicative noise coupled with the agent's state, and designs a consensus control protocol with cooperative-adversarial information under composite noise interference with both additive and multiplicative noise. Based on this consensus control, the system's anti-interference capability can be significantly improved, the robustness of multi-agent systems can be enhanced, and considering composite noise is of greater practical significance.

[0082] S4. Incorporate the control protocol into the dynamic model, design error terms, and transform the consistency problem of the multi-agent system into a stability problem of stochastic differential equations under composite noise. Perform stability analysis to ensure that the position and velocity errors of all agents converge under the mean square bisection consistency principle.

[0083] The purpose of stability analysis is to solve the bipartite consistency condition of a nonlinear second-order nonlinear multi-agent system with cooperative-adversarial information under the combined noise interference of additive and multiplicative noise.

[0084] The stability analysis in step S4 specifically includes the following sub-steps:

[0085] S41. Design appropriate error terms and invertible matrices, and use column vectors to uniformly represent the variables of the second-order multi-agent system and define error terms and invertible matrices that satisfy the constraints.

[0086] Let column vectors uniformly represent the variables of a second-order multi-agent system.

[0087] Let J N =D1 N θ T D, where 1 N =[1,...,1] N T θ=[θ1,...,θ N],θ i >0, Define the error term as Then δ g (k)=(I N -J N )g(k),g=p,q,I N It is an N-dimensional identity matrix.

[0088] There exists an invertible matrix T such that And T -1 LT = diag(0, Λ), Λ∈R (N -1)×(N-1), Λ=diag(λ2,λ3,…,λ N ). λ2,λ3,…,λ N Let L be an eigenvalue. and If g = p, q, then

[0089] S42. Incorporate the consensus control protocol into the dynamic model and rewrite the formulas of the dynamic model based on the relationship between the error term, the invertible matrix, and the variables of the second-order multi-agent system.

[0090] Substituting the control protocol into the dynamic model formula, that is, substituting (2) into (1), we get:

[0091]

[0092] in:

[0093]

[0094] f(p(k),q(k),k)=[f1(p1(k),q1(k),k),…f i (p i (k),q i (k),k),…,f N (p N (k),q N (k),k)]

[0095] Γ N,i Let i represent an N-dimensional column vector where the i-th element is 1 and all other elements are 0. This is the Kronecker product symbol.

[0096] According to step S41, formula (3) can be rewritten as:

[0097]

[0098] in:

[0099]

[0100]

[0101]

[0102] h p >0 and h q >0 represents the coefficients of the multiplicative noise intensity function.

[0103] S43. Transform a second-order multi-agent system into a stochastic differential equation.

[0104] Formula (4) can be rewritten as:

[0105]

[0106] in:

[0107]

[0108]

[0109]

[0110]

[0111] S44. Prove the stability of the stochastic differential equation, i.e., formula (5), and obtain the specific process of the bipartite consistency condition of a second-order nonlinear multi-agent system with adversarial information under the combined noise interference of additive and multiplicative noise.

[0112] Suppose there exists an invertible matrix P such that It is the Jordan canonical form of the Laplace matrix and

[0113]

[0114] The eigenvalue is The corresponding if blocks, J = 1,...,l. λ1,...,λ l For J Λ Eigenvalues, n1,…,n l As a dimension, J represents Λ If the block,

[0115] make Then formula (5) can be expressed as:

[0116]

[0117]

[0118]

[0119]

[0120] make Represents eigenvalues. If we represent the dimension, then formula (6) can be written as:

[0121]

[0122] in:

[0123]

[0124]

[0125] S45. Using a semi-decoupling method and the convergence theorem combined with Lyapunov functions, solve the bipartite consistency condition of a second-order nonlinear multi-agent system with cooperative-adversarial information under composite noise interference with both additive and multiplicative noise.

[0126] The solution yields the bipartite consistency condition for a second-order nonlinear multi-agent system with adversarial information under combined noise interference of additive and multiplicative noise. This condition includes the conditions that the coefficients of the multiplicative noise intensity function must satisfy, the conditions that the coefficients of the additive noise intensity function must satisfy, and the conditions that the nonlinear function f(p) must satisfy. i (k),q i The selection of coefficients (k),k) must meet certain conditions, as must the selection of position control gain function and velocity control gain function, etc.

[0127] The semi-decoupling method and the seedling convergence theorem are used to solve the conditions required to satisfy consistency.

[0128] like

[0129]

[0130] like

[0131]

[0132] Where, let g = p, q,

[0133] In order to make Combining the conditions in S3 Choose the control gain function c z (k), z = 1, 2, in the form of γ∈(1 / 2,1],b>0 and a>0.

[0134] Next, we will design a suitable Lyapunov function based on formula (5) in S43. in Where μ(k) is the coefficient function. Then we can obtain:

[0135]

[0136] Formula (10) algebraizes the matrix. Combining this with Lyapunov's stability theorem, expanding formula (10) and setting each term in formula (10) to be less than 0, we can obtain the additive noise intensity coefficient σ. p and σ q Multiplicative noise intensity coefficient h p and h q Control gain function c z The selection of coefficients τ1 and τ2 of (k), z = 1, 2 and the nonlinear function f(p(k), q(k), k) needs to satisfy the following conditions:

[0137]

[0138]

[0139]

[0140]

[0141]

[0142] 0 < Θ < 1

[0143] Where λ min T represents -1 The smallest eigenvalue of matrix Λ obtained by LT = diag(0, Λ) is λ. max T represents -1 The largest eigenvalue of matrix Λ is obtained by LT = diag(0, Λ); τ1 and τ2 are the coefficients of the nonlinear function f(p(k), q(k), k); I N Let σ represent an N-dimensional identity matrix. p and σ q Indicates the selected additive noise intensity coefficient; h p and h q The coefficients represent the multiplicative noise intensity function.

[0144] From ΨΛ+Λ T Ψ = I N-1 We can obtain Ψ, λ max (Ψ) is the largest eigenvalue of Ψ. From step S41 achievable express The i-th column, t i t j These respectively represent step S41 middle The i-th and j-th columns.

[0145] Furthermore, for any distinct (j,i), f(0,0,t), there exist constants τ1≥0, τ2≥0 (Lipschitz constants) such that for any constants x, y, All

[0146] The above constraints are mutually restrictive and together form the binary consistency condition for a second-order nonlinear multi-agent system.

[0147] S46. Based on the established discrete-time nonlinear second-order multi-agent system model, control protocol, system error, and parameter conditions, enable the system to achieve mean-square bipartite consistency control, requiring that the position and velocity errors between any agents within each group satisfy the following:

[0148]

[0149]

[0150] That is, under the control protocol, the position and velocity errors between the agents in the two groups gradually decrease to 0, and the final stable positions of the two groups are opposites of each other, and the final stable velocities of the two groups are also opposites of each other. Then, the second-order nonlinear agent system (1) in step S2 is said to have achieved mean-square bisection consensus control under the control protocol (2), that is, the position and velocity errors of all agents in the system converge in the mean-square bisection consensus sense. Introducing α i The operator shows that the mathematical expectation of the final convergence value is related to the initial state and the canonical matrix of the agent.

[0151] The stability analysis of this invention reveals that the mathematical expectation of the final convergence value is related to the initial state and canonical matrix of the agent, and that the convergence state of the agent system can be changed through appropriate adjustments. It also reveals that nonlinear terms with small Lipschitz constants do not disrupt the consistency of stochastic multi-agent systems with additive and multiplicative noise.

[0152] This invention establishes consistency conditions with explicit mathematical parameters and matrix expressions related to multiplicative noise figure, additive noise figure, nonlinear coefficient and control gain function through stability analysis, making the controlled system easier to adjust and reducing the complexity of control operation.

[0153] S47. Perform binary search consistency control.

[0154] The additive noise intensity coefficient σ is analyzed in step S4. p and σ q Multiplicative noise intensity coefficient h p and h q Control gain function c z The selection of coefficients for (k), z = 1, 2 and the nonlinear function f(p(k), q(k), k) must satisfy certain conditions. The specific parameters of the consensus control protocol are determined. Then, the motion of the second-order nonlinear multi-agent system is controlled. The position error and velocity error between the agents in the two adversarial groups are calculated respectively. The position error and velocity error between the agents in the two adversarial groups are substituted into the dynamic model. Under the action of the consensus control protocol, iterative control of the position error and velocity error is carried out until the position error and velocity error converge, thus realizing the bipartite consensus control.

[0155] The effectiveness of the invention is verified through simulation examples below:

[0156] Eight second-order agents were selected, with agents 1-4 (black circles) forming one group and agents 5-8 (dashed circles) forming another group. Their topology diagram is shown below. Figure 2 As shown, black connecting lines represent cooperative information, and black arrows represent adversarial information. The adjacency matrix and Laplace matrix of this topology graph are expressed as follows:

[0157]

[0158]

[0159] Then λ min =0.3759,λ max =4.2369, let the multiplicative noise intensity function h pji (k)=0.2k,h qji (k) = 0.1k; let the additive noise intensity coefficient σ p =0.2, σ q =0.5; Let the nonlinear function f(p(k), q(k), k) = 0.01sink + 0.0037cosk; then the control gain function is chosen as c1(k) = (1 + k) 0.8 c2(k) = (1.5 + k). Then 0 < Θ = 0.1537 < 1 satisfies the condition. The initial value of the position state is set to [-30, 30, -24, -3, -12, 8, 25, 10], and the initial value of the velocity state is set to [-150, 150, -140, -80, -100, 80, 60, 90].

[0160] Figure 3 and Figure 4The figures show the position and velocity state curves of each agent obtained using the control method designed in this invention. Agents 1 to 8 represent eight agents. Experimental results show that under the control protocol, after selecting coefficients that satisfy the control conditions, each group of agents reaches a stable state after a period of time. Furthermore, the final stable positions of the two groups are opposites of each other, and their final stable velocities are also opposites. This demonstrates that this invention can achieve bipartite consistent control of a nonlinear second-order multi-agent system with cooperative-adversarial information under additive noise and multiplicative environments. Figure 5 and Figure 6 The position error curves and velocity error curves of each agent were plotted based on the simulation results, and observed. Figure 5 and Figure 6 It can be seen that after a period of time, the errors between the positions and velocities of the agents in the two groups tend to 0, indicating that the algorithm has a good convergence effect.

[0161] The simulation results above fully demonstrate that the method of the present invention can achieve bipartite consensus convergence of a second-order nonlinear multi-agent system under adversarial information in a compound noise environment.

[0162] Corresponding to the above method embodiments, the present invention also proposes a consensus control device for a second-order multi-agent system with noise and adversarial information, the device comprising:

[0163] Topology establishment module: used to determine the topology of a second-order nonlinear multi-agent system based on the adversarial information of the system.

[0164] Dynamics Model Building Module: Used to build dynamics models of second-order nonlinear multi-agent systems;

[0165] Control Protocol Design Module: Used to design a consensus control protocol with cooperative-adversarial information under composite noise interference where additive and multiplicative noise coexist.

[0166] The control stability analysis module is used to incorporate the control protocol into the dynamic model, design error terms, and transform the consistency problem of the multi-agent system into a stability problem of stochastic differential equations under composite noise. Stability analysis is then performed to ensure that the position and velocity errors of all agents converge under the mean-square bisection consistency principle. The above device and method embodiments are one-to-one correspondences; for a brief description of the device embodiments, please refer to the method embodiments.

[0167] The present invention also discloses an electronic device, comprising: at least one processor, at least one memory, a communication interface, and a bus; wherein the processor, memory, and communication interface communicate with each other through the bus; the memory stores program instructions executable by the processor, and the processor calls the program instructions to implement the aforementioned method of the present invention.

[0168] The present invention also discloses a computer-readable storage medium that stores computer instructions, which cause the computer to implement all or part of the steps of the method described in the embodiments of the present invention. The storage medium includes various media capable of storing program code, such as a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0169] The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, meaning they can be distributed across multiple network units. Those skilled in the art can select some or all of the modules to achieve the purpose of this embodiment without any inventive effort, based on actual needs.

[0170] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A consensus control method for a second-order multi-agent system with noise and adversarial information, characterized in that, The method includes: Determine the topology of the second-order nonlinear multi-agent system based on the cooperation-adversarial information among the second-order nonlinear multi-agents; Establish a dynamic model for a second-order nonlinear multi-agent system; Considering the combined noise interference of additive and multiplicative noise, a consistency control protocol is designed based on relative position and velocity measurement information, combined with a sign function and a random time-varying control gain function. By incorporating the control protocol into the dynamic model and designing error terms, the consistency problem of the multi-agent system is transformed into the stability problem of stochastic differential equations under composite noise. Stability analysis is then performed to ensure that the position and velocity errors of all agents converge under the mean-square bisection consistency principle. The determination of the topology of the second-order nonlinear multi-agent system based on the cooperative-adversarial information of the second-order nonlinear multi-agent system specifically includes: Suppose a second-order nonlinear multi-agent system contains N agents, using... This represents a directed symbolic topology graph of the intelligent agent system. Represents a set of nodes. It is the edge set of the graph. Representation diagram The adjacency matrix; This indicates that the j-th agent can receive the cooperation information from the i-th agent. This indicates that the j-th agent can receive adversarial information from the i-th agent. This indicates that the j-th agent cannot receive information from the i-th agent; Based on adversarial information, nodes Divided into two sets of nodes ,and ,like ,have ;like have ; The establishment of the dynamic model of the second-order nonlinear multi-agent specifically includes: Suppose a second-order nonlinear multi-agent system contains N agents, and its dynamic model is expressed as: ； in, , Indicates the first i The position of the agent at time k, Indicates the first i The velocity of the agent at time k. Indicates the first i Control protocol of an agent at time k It is a non-linear function; The expression for the consensus control protocol with adversarial information designed under the combined noise interference of additive and multiplicative noise is as follows: ； in, and Let these represent the multiplicative noise intensity functions for position and velocity, respectively. and These represent the additive noise intensity coefficients for position and velocity, respectively. ; All are Gaussian independent white noise at their positions. All are Gaussian independent white noise with velocity, satisfying: ； in, , ; Let E be the sign function, and E represent the expectation. , All are stochastic time-varying control gain functions, where, The position control gain function, Let be the speed control gain function, and satisfy: ； in, z =1,2.

2. The consensus control method for a second-order multi-agent system with noise and adversarial information according to claim 1, characterized in that, The stability analysis includes solving the bipartite consistency condition of a second-order nonlinear multi-agent system with adversarial information under composite noise interference with both additive and multiplicative noise.

3. The consensus control method for a second-order multi-agent system with noise and adversarial information according to claim 2, characterized in that, The process involves incorporating the control protocol into the dynamic model, designing error terms, and transforming the consensus problem of a multi-agent system into a stability problem of stochastic differential equations under composite noise. Stability analysis is then performed, specifically including: The variables of a second-order multi-agent system are uniformly represented by column vectors, and error terms and invertible matrices satisfying constraints are defined. The consensus control protocol is incorporated into the dynamic model, and the formula of the dynamic model is rewritten according to the relationship between the error term, the invertible matrix and the variables of the second-order multi-agent system. The second-order multi-agent system is then transformed into a stochastic differential equation. The specific process of designing the binary consistency condition of a second-order nonlinear multi-agent system with adversarial information under composite noise interference with both additive and multiplicative noise. The bipartite consistency condition of a second-order nonlinear multi-agent system with adversarial information is solved by using semi-decoupling and the seedling convergence theorem.

4. The consensus control method for a second-order multi-agent system with noise and adversarial information according to claim 3, characterized in that, The binary consistency condition for a second-order nonlinear multi-agent system with adversarial information, obtained from the solution, under combined noise interference containing both additive and multiplicative noise, specifically includes: The selection of coefficients for the multiplicative noise intensity function must meet certain conditions; The selection of the additive noise intensity coefficient must meet certain conditions; nonlinear functions The selection of the coefficients must meet certain conditions; Position control gain function and speed control gain function The selection of [a] requires meeting certain conditions.

5. A consensus control device for a second-order multi-agent system with noise and adversarial information, characterized in that, The device includes: Topology establishment module: used to determine the topology of a second-order nonlinear multi-agent system based on its adversarial information; the determination of the topology based on the cooperative-adversarial information of the second-order nonlinear multi-agent system specifically includes: Suppose a second-order nonlinear multi-agent system contains N agents, using... This represents a directed symbolic topology graph of the intelligent agent system. Represents a set of nodes. It is the edge set of the graph. Representation diagram The adjacency matrix; This indicates that the j-th agent can receive the cooperation information from the i-th agent. This indicates that the j-th agent can receive adversarial information from the i-th agent. This indicates that the j-th agent cannot receive information from the i-th agent; Based on adversarial information, nodes Divided into two sets of nodes ,and ,like ,have ;like have ; Dynamics model building module: used to build dynamics models of second-order nonlinear multi-agent systems; the specific steps of building dynamics models of second-order nonlinear multi-agent systems include: Suppose a second-order nonlinear multi-agent system contains N agents, and its dynamic model is expressed as: ； in, , Indicates the first i The position of the agent at time k, Indicates the first i The velocity of the agent at time k. Indicates the first i Control protocol of an agent at time k It is a non-linear function; Control Protocol Design Module: Used to design a consensus control protocol with cooperative-adversarial information under combined noise interference of additive and multiplicative noise; the expression for the consensus control protocol with adversarial information under combined noise interference of additive and multiplicative noise is: ； in, and Let these represent the multiplicative noise intensity functions for position and velocity, respectively. and These represent the additive noise intensity coefficients for position and velocity, respectively. ; All are Gaussian independent white noise at their positions. All are Gaussian independent white noise with velocity, satisfying: ； in, , ; Let E be the sign function, and E represent the expectation. , All are stochastic time-varying control gain functions, where, The position control gain function, Let be the speed control gain function, and satisfy: ； in, z =1,2 Control stability analysis module: This module is used to incorporate the control protocol into the dynamic model, design error terms, transform the consistency problem of a multi-agent system into a stability problem of stochastic differential equations under composite noise, perform stability analysis, and ensure that the position and velocity errors of all agents converge in the mean-square bisection consistency sense.

6. An electronic device, characterized in that, include: At least one processor, at least one memory, a communication interface, and a bus; The processor, memory, and communication interface communicate with each other through the bus. The memory stores program instructions that can be executed by the processor, which invokes the program instructions to implement the method as described in any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that cause the computer to perform the method as described in any one of claims 1 to 4.

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