A multi-agent output feedback security control method based on average sub-sequence reduction algorithm

Abstract

The application discloses a multi-agent output feedback security control method based on an average sub-sequence reduction algorithm, and belongs to the technical field of safety consensus control of multi-agent systems.The application solves the problem of poor safety and stability of existing multi-agent control methods.A strict feedback nonlinear multi-agent system mathematical model with unstructured uncertainty, time-varying disturbance, stateless measurement and Byzantine attack is established, an average sub-sequence reduction algorithm is used to eliminate the influence of Byzantine agents, a fuzzy state observer is constructed to approximate unknown nonlinear terms and observe unmeasurable states, a virtual control law and an actual control law of a backstepping controller are designed based on the state estimation result of the fuzzy state observer and the Lyapunov stability theory, and safety, stable and consistent control of the multi-agent system under the Byzantine attack is realized.The method can be applied to the consistent control of the multi-agent under the Byzantine attack.

Description

Technical Field

[0001] This invention belongs to the field of security and consistency control technology for multi-agent systems, specifically relating to a multi-agent output feedback security control method based on the average subsequence reduction algorithm. Background Technology

[0002] With the rapid development of distributed control technology, multi-agent systems have demonstrated significant advantages in fields such as drone swarming, smart grids, and the Industrial Internet of Things (IIoT). Through local information interaction and collaborative decision-making, multi-agent systems can efficiently complete complex tasks. However, in open network environments, these systems face a serious threat of Byzantine attacks. In such attacks, malicious nodes can forge, tamper with, or selectively discard data, misleading healthy nodes away from the target state, leading to system consistency collapse or even global failure. Especially in critical infrastructure areas such as power grid dispatching and transportation coordination, Byzantine attacks can have catastrophic consequences, thus necessitating the design of control methods that combine security and robustness.

[0003] While some progress has been made in consensus control of multi-agent systems in the prior art, significant shortcomings remain in addressing Byzantine attacks and state estimation. For example, patent application CN106802564A discloses a multi-agent consensus cooperative control method with an unknown model. This method uses fuzzy logic control algorithms to estimate the unknown components and external disturbances in the multi-agent system. Based on the time scale function, the unknown components, and external disturbances, a second-order consensus control protocol is set to update the position and velocity information of each agent within a specified time. However, this method does not integrate a state observer and cannot handle the prevalent nonlinear dynamics and external disturbances in the system, resulting in limited control accuracy. Furthermore, various types of attack signals are not considered, limiting the security control of the multi-agent system. Patent application CN109557818A discloses a linear multi-agent fault-tolerant control method, focusing on solving sensor and actuator failure problems. This method first establishes a fault model and estimates the system state and fault parameters using a distributed observer. Subsequently, an adaptive fault-tolerant controller is designed based on sliding mode control, combined with disturbance compensation techniques to suppress external disturbances. Experiments show that this method can maintain system stability even under sensor failures. However, its core assumption is that node failures are deterministic, and it does not consider the arbitrary nature of Byzantine node attack methods. Furthermore, traditional linear observers have limited approximation capabilities for nonlinear systems, limiting their application scenarios.

[0004] In summary, although existing technologies have made some progress in multi-agent consensus control, they still suffer from poor security and stability when faced with situations where the system state cannot be measured or by Byzantine attacks exist. Therefore, developing a control method that integrates a high-precision nonlinear state observer capable of handling Byzantine attacks and ensuring the safe and stable operation of multi-agent systems is a problem that needs to be solved in the field of safe consensus control for multi-agent systems. Summary of the Invention

[0005] The purpose of this invention is to address the poor security and stability of existing multi-agent control methods by proposing a multi-agent output feedback security control method based on the average subsequence reduction algorithm.

[0006] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a multi-agent output feedback security control method based on the average subsequence reduction algorithm, the method specifically includes the following steps:

[0007] Step S1: Establish a nonlinear multi-agent system comprising one leader agent and N follower agents, and establish a dynamic model of the follower agents;

[0008] Step S2: Establish a communication topology model for a Byzantine attack;

[0009] Step S3: Based on the improved average subsequence reduction algorithm and the communication topology graph model in step S2, select healthy agents from the neighbor agents of non-fixed followers.

[0010] Step S4: Design a fuzzy state observer, and use the fuzzy state observer to estimate the system state and compensate for unknown nonlinear terms;

[0011] Step S5: For non-fixed followers, design virtual control laws and actual control laws based on the screening results in step S3 and the system state observed by the fuzzy state observer in step S4, and obtain the adaptive law of the control law.

[0012] For a fixed follower, virtual control laws and actual control laws are designed based on the system state observed by the fuzzy state observer in step S4, and an adaptive law of the control law is obtained.

[0013] Furthermore, the dynamic model of the follower agent is as follows:

[0014]

[0015] in, It is the state vector consisting of the first to the lth states of the i-th follower agent. x i,1 ,xi,2 ,...,x i,l Let R represent the 1st, 2nd, ..., 1st states of the i-th follower agent, respectively, and R be a real number. For x i,l The first derivative, x i,l+1 For the (l+1)th state of the i-th follower agent, d i,l For the external disturbance of the i-th follower agent in the l-th state, x i It is a state vector consisting of all the states of the i-th follower agent. l i Let g be the number of states of the i-th follower agent. i,l (·) represents an unknown smooth nonlinear function. For the i-th follower agent, the l-th... i External disturbances in each state, u i y represents the control input of the i-th follower agent. i This represents the control output of the i-th follower agent, i = 1, ..., N, l = 1, ..., l i -1.

[0016] Furthermore, the nonlinear function satisfies the Lipschitz condition |g i,l (ξ)-g i,l (ξ′)|≤Y i,l ||ξ-ξ′||,Y i,l Let ξ be a constant, and ξ and ξ′ be the independent variables of the function. |·| represents taking the absolute value, and ||·|| represents calculating the 2-norm.

[0017] Furthermore, the communication topology graph model of the Byzantine attack is strongly robust to a fixed set of followers X (2f+1), and the number of Byzantine agents present in the incoming neighbors of each agent does not exceed f, i.e., it satisfies...

[0018] in, Let be the set of incoming neighbors of the i-th agent. This refers to the set of Byzantine agents in the communication topology graph model. Indicates intersection The number of elements in the array.

[0019] Furthermore, the specific process of step S3 is as follows:

[0020] Step S31: Collect the data received by the i-th non-fixed follower agent from all incoming neighbors. Status information y j And store the state information received by the i-th non-fixed follower agent into the set.

[0021] in, A set of non-fixed followers;

[0022] Step S32, set Δ i The state values ​​in the data are respectively related to y i Compare and put the set Δ i Less than or equal to y i The set of state values ​​is denoted as Set Δ i The greater than y i The set of state values ​​is denoted as

[0023] Among them, y i The state information of the i-th non-fixed follower agent;

[0024] Step S33: Calculate the dynamically adjusted filtering threshold and

[0025]

[0026] Where f is the upper bound on the number of Byzantine nodes in the communication topology graph model. Represents a set The number of elements in the middle. Represents a set The number of elements in the middle;

[0027] Step S34: Sort the state information received by the i-th non-fixed follower agent in ascending order, and remove the smallest value from the sorted results. Each state information and the largest One status information;

[0028] Step S35: Set Δ i The neighboring agents whose state information has been deleted are marked as κ. i,j =0, set Δ i The state information in the data is retained and labeled as κ by the neighboring agents. i,j =1;

[0029] Marked as κ i,j The set of neighboring agents whose value is 1 is denoted as . gather The agent within is the healthy neighbor that the i-th non-fixed follower agent needs to track.

[0030] Furthermore, the specific process of step S4 is as follows:

[0031] Step S41: Reconstruct the dynamic model of equation (1) as follows:

[0032]

[0033] in, yes The estimate, They are x i,1 ,x i,2 ,...,x i,l The estimate, It is x i The estimate, They are The estimate, l = 1, 2, ..., l i , For x i,l The first derivative, for The first derivative;

[0034] Step S42: Construct a fuzzy logic system:

[0035]

[0036] in, This indicates a method used to approximate an unknown nonlinear function. Fuzzy logic system Let l represent the l-th fuzzy membership function of the fuzzy logic system, and satisfy the following conditions: δ is a positive design constant. i,l Indicates to The approximation error, θ i,l Let l be the l-th adaptive rate of the i-th follower agent, and the superscript T indicates transpose;

[0037] Step S43: Design the fuzzy state observer as follows:

[0038]

[0039] in, for The first derivative, K i Let be the gain matrix of the i-th follower agent. K i,1 For K i The first element in For K i The l in i There are elements, A i It is the Herwitz matrix, and the vector B i,l =[0,...,1 l,...,0] T Matrix B i =[0,0,...,1] T , for The estimate, It is y i The estimate, C i These are the design parameters for the observer.

[0040] Furthermore, the Herwitz matrix A i for:

[0041]

[0042] Furthermore, the specific process of step S5 is as follows:

[0043] Step S51: Initialize the tracking error of the i-th follower agent:

[0044]

[0045] Among them, z i,1 Let represent the tracking error of the i-th follower agent for the first state. Let a represent the set of incoming neighbors of the i-th follower agent, where a is the set of incoming neighbors when the i-th follower agent directly receives information from the leader. i,0 =1, when the i-th follower agent does not directly receive information from the leader. i,0 =0, y d This represents the leader's output signal, z i,l This represents the tracking error of the i-th follower agent for the l-th state, where i = 1, 2, ..., N, l = 2, ..., l i α i,l-1 For virtual control signals, τ i Represents a set The number of elements in;

[0046] Step S52: Design the Lyapunov function V i,1 :

[0047]

[0048] Where, γ i,1 With γ j,1 A positive design parameter; ν i =τ i -a i,0 τ i +a i,0 >0, For θ i,l The estimation error,

[0049] The virtual control law is designed as follows:

[0050]

[0051] Where, p i,1 Positive design parameters For y d The first derivative;

[0052] Adaptive law and They are respectively:

[0053]

[0054] Where, λ i,1 With λ j,1 Positive design parameters for The first derivative, for The first derivative;

[0055] Step S53: Initialize l = 2;

[0056] Step S54: Design the Lyapunov function V i,l :

[0057]

[0058] Where, γ i,l Positive design parameters;

[0059] Virtual control law α i,l for:

[0060]

[0061] Where, p i,l Positive design parameters;

[0062]

[0063] Among them, e i,1 This represents the observation error of the first state of the i-th follower agent. Indicates y d The k-th derivative, express The k-th derivative, express The k-th derivative, express The k-th derivative;

[0064] Adaptive law Designed as follows:

[0065]

[0066] Where, λ i,l Positive design parameters;

[0067] Step S55: Does l = l satisfy? i -1:

[0068] If l = l i If the value is -1, then proceed to step S56;

[0069] If l = l is not satisfied i If the value is -1, then let l = l + 1 and return to step S54.

[0070] Step S56: Design Lyapunov functions

[0071]

[0072] in, Positive design parameters;

[0073] Actual control law u i Designed as follows:

[0074]

[0075] in, Positive design parameters;

[0076]

[0077] Real adaptive law Designed as follows:

[0078]

[0079] in, The design parameters are positive.

[0080] Furthermore, the observation error is:

[0081]

[0082] Among them, e i Let be the observation error of the i-th follower agent. For e i The first derivative,

[0083] Constructing the Lyapunov function V i,0 :

[0084]

[0085] Wherein, given matrix Matrix P i T =P i >0, and satisfy

[0086] From Young's inequality, we get:

[0087]

[0088] Where ||·|| denotes the calculation of the 2-norm;

[0089]

[0090] in, This represents the vector consisting of the upper bound of the approximation error. This represents the vector formed by the upper bound of external disturbances. They represent The upper bound;

[0091]

[0092] in, For V i,0 The first derivative;

[0093]

[0094] Where, λ min (Q i ) represents matrix Q i The smallest eigenvalue.

[0095] Furthermore, the virtual control law and the actual control law make:

[0096] (1) All signals in the entire closed-loop system are bounded;

[0097] (2) The tracking error converges to the neighborhood of zero.

[0098] The beneficial effects of this invention are:

[0099] This invention establishes a rigorous feedback nonlinear multi-agent system mathematical model with unstructured uncertainty, time-varying disturbances, stateless measurement, and Byzantine attacks. It employs a mean subsequence reduction algorithm to eliminate the influence of Byzantine agents, constructs a fuzzy state observer to approximate unknown nonlinear terms and observe unmeasurable states, and designs virtual and actual control laws for the backstepping controller based on the state estimation results of the fuzzy state observer and Yapunov stability theory. This achieves safe and stable consensus control of the multi-agent system under Byzantine attacks, exhibiting strong robustness to flexible node attack methods and the ability to estimate unmeasurable states and cope with external disturbances. Experiments demonstrate that the control method of this invention can achieve intelligent adaptive tracking control, ensuring that all signals of the controlled system have boundaries and that the tracking error can be arbitrarily small. Under Byzantine attacks, the control method of this invention still guarantees safety and stability, possessing significant practical implications. Attached Figure Description

[0100] Figure 1 This is a flowchart of a multi-agent output feedback security control method based on the average subsequence reduction algorithm of the present invention;

[0101] Figure 2 The graph of the output signal of a healthy follower and the signal of a leader under the attack of an embodiment of the present invention;

[0102] Figure 3 This is a graph showing the signal of the health follower intelligent agent controller under an attack according to an embodiment of the present invention. Detailed Implementation

[0103] Specific implementation method one: Combining Figure 1 This embodiment describes a multi-agent output feedback safety control method based on an average subsequence reduction algorithm. The method specifically includes the following steps:

[0104] Step S1: Each node in the communication network represents an agent. For a communication network containing N+1 nodes, a strict feedback nonlinear multi-agent system is established, consisting of one leader agent and N (N≥3) follower agents. A dynamic model of the follower agents is also established.

[0105] Step S2: Establish a communication topology model for a Byzantine attack;

[0106] Step S3: Based on the improved average subsequence reduction algorithm and the communication topology graph model in step S2, select healthy agents from the neighbor agents of non-fixed followers.

[0107] Step S4: Design a fuzzy state observer, and use the fuzzy state observer to estimate the system state and compensate for unknown nonlinear terms;

[0108] Step S5: For non-fixed followers, design virtual control laws and actual control laws based on the screening results in step S3 and the system state observed by the fuzzy state observer in step S4, and obtain the adaptive law of the control law.

[0109] For a fixed follower, virtual control laws and actual control laws are designed based on the system state observed by the fuzzy state observer in step S4, and an adaptive law of the control law is obtained.

[0110] The method of this invention is highly robust to flexible attack methods on nodes and is applicable to situations where the system contains nonlinear terms and the system state cannot be measured.

[0111] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the dynamic model of the follower agent is as follows:

[0112]

[0113] in, It is the state vector consisting of the first to the lth states of the i-th follower agent. x i,1 ,x i,2 ,...,x i,l Let R represent the 1st, 2nd, ..., 1st states of the i-th follower agent, respectively, and R be a real number. For x i,l The first derivative, x i,l+1 For the (l+1)th state of the i-th follower agent, d i,l For the external disturbance of the i-th follower agent in the l-th state, x i It is a state vector consisting of all the states of the i-th follower agent. l i Let g be the number of states of the i-th follower agent. i,l (·) represents an unknown smooth nonlinear function. For the i-th follower agent, the l-th... i External disturbances in each state, u i y represents the control input of the i-th follower agent. i This represents the control output of the i-th follower agent, i = 1, ..., N, l = 1, ..., l i -1.

[0114] The other steps and parameters are the same as in Specific Implementation Method 1.

[0115] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that the nonlinear function satisfies the Lipschitz condition |g i,l(ξ)-g i,l (ξ′)|≤Y i,l ||ξ-ξ′||,Y i,l Let ξ be a constant, and ξ and ξ′ be the independent variables of the function. |·| represents taking the absolute value, and ||·|| represents calculating the 2-norm.

[0116] Other steps and parameters are the same as in specific implementation method one or two.

[0117] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the communication topology graph model of the Byzantine attack relates to a fixed set of followers. Strong 2f+1 robustness, and the number of Byzantine agents in each agent's incoming neighbors does not exceed f, i.e., satisfies

[0118] in, Let be the set of incoming neighbors of the i-th agent. This refers to the set of Byzantine agents in the communication topology graph model. Indicates intersection The number of elements in the array.

[0119] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0120] Byzantine nodes in a communication topology graph model have the following destructive characteristics:

[0121] (1) The state update does not follow the preset control law;

[0122] (2) Possesses the ability to autonomously tamper with status values;

[0123] (3) It can generate and propagate false state information to neighboring intelligent agents.

[0124] This allows Byzantine agents to easily simulate common network attack types, such as replay attacks, DoS attacks, and FDI attacks. When healthy nodes receive this false information during the consistency control process, it causes deviations in state updates, ultimately disrupting the network system's consistency convergence process.

[0125] In this invention, agents that can directly receive information from the leader are called fixed followers, and agents that cannot directly receive information from the leader are called non-fixed followers.

[0126] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that the specific process of step S3 is as follows:

[0127] Step S31: Collect the data received by the i-th non-fixed follower agent from all incoming neighbors. Status information y j And store the state information received by the i-th non-fixed follower agent into the set.

[0128] in, It is a set of non-fixed followers; it should be noted that step S3 will process each non-fixed follower agent, but when applied to subsequent processing, it is only effective for the control process of healthy agents.

[0129] Step S32, set Δ i The state values ​​in the data are respectively related to y i Compare and put the set Δ i Less than or equal to y i The set of state values ​​is denoted as Set Δ i The greater than y i The set of state values ​​is denoted as

[0130] Among them, y i The state information of the i-th non-fixed follower agent;

[0131] Step S33: Calculate the dynamically adjusted filtering threshold and

[0132]

[0133] Where f is the upper bound on the number of Byzantine nodes in the communication topology graph model. Represents a set The number of elements in the middle. Represents a set The number of elements in the middle;

[0134] Step S34: Sort the state information received by the i-th non-fixed follower agent in ascending order, and remove the smallest value from the sorted results. Each state information and the largest One status information;

[0135] Step S35: Set Δ i The neighboring agents whose state information has been deleted are marked as κ. i,j =0, set Δ i The state information in the data is retained and labeled as κ by the neighboring agents. i,j =1;

[0136] Marked as κ i,j The set of neighboring agents whose value is 1 is denoted as . gather The agent within is the healthy neighbor that the i-th non-fixed follower agent needs to track.

[0137] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0138] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that the specific process of step S4 is as follows:

[0139] Step S41: Reconstruct the dynamic model of equation (1) as follows:

[0140]

[0141] in, yes The estimate, They are x i,1 ,x i,2 ,...,x i,l The estimate, It is x i The estimate, They are The estimate, l = 1, 2, ..., l i , For x i,l The first derivative, for The first derivative;

[0142] Step S42: Construct a fuzzy logic system:

[0143]

[0144] in, This indicates a method used to approximate an unknown nonlinear function. Fuzzy logic system Let l represent the l-th fuzzy membership function of the fuzzy logic system, and satisfy the following conditions: A positive design constant (representing the approximation error δ) i,l (the upper bound of δ) i,l Indicates to The approximation error, θ i,l Let l be the l-th adaptive rate of the i-th follower agent, and the superscript T indicates transpose;

[0145] Step S43: Design the fuzzy state observer as follows:

[0146]

[0147] in, for The first derivative, K i Let be the gain matrix of the i-th follower agent. K i,1 For K i The first element in For K i The l in i There are elements, A i It is a strictly Herwitz matrix, and the vector B i,l =[0,...,1 l ,...,0] T (in vector B) i,l In matrix B, all elements except the l-th element are 0. i =[0,0,...,1] T (Only the last element is 1, and all other elements are 0). The estimate, It is y i The estimate, C i This is the design parameter of the observer (taken as 1 in this invention).

[0148] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0149] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that the Herwitz matrix A... i for:

[0150]

[0151] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0152] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One to Seven in that the specific process of step S5 is as follows:

[0153] Step S51: Initialize the tracking error of the i-th follower agent:

[0154]

[0155] Among them, z i,1 Let represent the tracking error of the i-th follower agent for the first state. Let i represent the set of incoming neighbors of the i-th follower agent (for a fixed follower, ...). For inbound neighbors, the set is directly used; for non-fixed followers, (For the selected set of healthy intelligent agents as neighbors), when the i-th follower intelligent agent directly receives information from the leader, a i,0=1, when the i-th follower agent does not directly receive information from the leader. i,0 =0, y d This represents the leader's output signal, z i,l This represents the tracking error of the i-th follower agent for the l-th state, where i = 1, 2, ..., N, l = 2, ..., l i α i,l-1 For virtual control signals, τ i Represents a set The number of elements in;

[0156] Step S52: Design the Lyapunov function V i,1 :

[0157]

[0158] Where, γ i,1 With γ j,1 A positive design parameter; ν i =τ i -a i,0 τ i +a i,0 >0, For θ i,l The estimation error,

[0159] The virtual control law is designed as follows:

[0160]

[0161] Where, p i,1 Positive design parameters For y d The first derivative;

[0162] Adaptive law and They are respectively:

[0163]

[0164] Where, λ i,1 With λ j,1 Positive design parameters for The first derivative, for The first derivative;

[0165] Step S53: Initialize l = 2;

[0166] Step S54: Design the Lyapunov function V i,l :

[0167]

[0168] Where, γ i,l Positive design parameters;

[0169] Virtual control law α i,l for:

[0170]

[0171] Where, p i,l Positive design parameters;

[0172]

[0173]

[0174] Among them, e i,1 This represents the observation error (i.e., observation error e) of the first state of the i-th follower agent. i The first element in the text), Indicates y d The k-th derivative, express The k-th derivative, express The k-th derivative, express The k-th derivative;

[0175] Adaptive law Designed as follows:

[0176]

[0177] Where, λ i,l Positive design parameters;

[0178] Step S55: Does l = l satisfy? i -1:

[0179] If l = l i If the value is -1, then proceed to step S56;

[0180] If l = l is not satisfied i If the value is -1, then let l = l + 1 and return to step S54.

[0181] Step S56: Design Lyapunov functions

[0182]

[0183] in, Positive design parameters;

[0184] Actual control law u i Designed as follows:

[0185]

[0186] in, Positive design parameters;

[0187]

[0188] Real adaptive law Designed as follows:

[0189]

[0190] in, The design parameters are positive.

[0191] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0192] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that the observation error obtained from formulas (2) and (4) is:

[0193]

[0194] Among them, e i Let be the observation error of the i-th follower agent. For e i The first derivative,

[0195] Constructing the Lyapunov function V i,0 :

[0196]

[0197] Wherein, given matrix Matrix P i T =P i >0, and satisfy

[0198] From Young's inequality, we get:

[0199]

[0200] Where ||·|| denotes the calculation of the 2-norm;

[0201]

[0202] in, This represents the vector consisting of the upper bound of the approximation error. This represents the vector formed by the upper bound of external disturbances. They represent The upper bound;

[0203] Therefore, we can conclude that:

[0204]

[0205] in, For V i,0 The first derivative;

[0206]

[0207] Where, λ min (Q i ) represents matrix Q i The smallest eigenvalue.

[0208] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0209] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One to Nine in that the virtual control law and the actual control law make:

[0210] (1) All signals in the entire closed-loop system are bounded;

[0211] (2) The tracking error converges to the neighborhood of zero.

[0212] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0213] The convergence proof of the tracking error is as follows:

[0214] Constructing composite Lyapunov functions:

[0215]

[0216] From Young's inequality, we can obtain:

[0217]

[0218]

[0219] Therefore, we can conclude that:

[0220]

[0221] in:

[0222]

[0223] By choosing appropriate parameters such that C > 0 and D > 0, integration yields:

[0224]

[0225] This ensures that all signals are consistent and bounded.

[0226] The feasibility and control performance of the method proposed in this invention will be verified below. A directed topological graph of a multi-agent system consisting of 7 healthy agents and 3 Byzantine agents is established, where the dynamics of the healthy agents are:

[0227]

[0228] in, and For an unknown nonlinear term, d i,1 (t)=0.1sin(πt) and d i,2 (t) = 0.2cos(πt) represents external disturbance, and the leader's signal is selected as y. r (t) = 2sin(t).

[0229] The communication topology is vulnerable to a 1-local Byzantine attack, and this is related to the fixed set of followers. It is strongly 3-robust. Byzantine intelligent agents. It can propagate arbitrary malicious signals to its neighbors. For time t > 0, the specific attack signal of Byzantine agent 2 against its neighboring agents is selected as: ε 2→· =1.5, the specific attack signal of Byzantine agent 5 against its neighboring agents is selected as: ε 5→· =2t, the controller of agent 10 was changed to u by the Byzantine adversary. 10 =2sin(t).

[0230] Select the following design parameters: K k,1 =15, K k,2 =80, p k,1 =5, p k,2 =2.5, λ k,1 =λ k,2 =1,γ k,1 =γ k,2 =0.1, where k = 1, 3, 4, 6, 7, 8, 9.

[0231] The initial value is set to: x k,1 (0) = 0.1, x k,2 (0) = -0.1, Where k = 1, 3, 4, 6, 7, 8, 9, and all other initial values ​​are set to 0.

[0232] Control results such as Figure 2 and Figure 3 As shown, Figure 2 The graph of the output signal of a healthy follower and the signal of a leader under the attack of an embodiment of the present invention; Figure 3 This is a graph showing the signal of the health follower intelligent agent controller under an attack according to an embodiment of the present invention.

[0233] Depend on Figure 2 and Figure 3 As can be seen, the control method proposed in this invention can achieve good tracking performance. When a multi-agent system is subjected to a Byzantine attack, the control method of this invention can ensure the normal operation of the system and guarantee the boundedness of signals within the system, thereby achieving the control objective of safety and consistency.

[0234] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A multi-agent output feedback safety control method based on the average subsequence reduction algorithm, characterized in that, The method specifically includes the following steps: Step S1: Establish a system containing one leader agent and... A nonlinear multi-agent system with follower agents is established, and a dynamic model of the follower agents is constructed. Step S2: Establish a communication topology model for a Byzantine attack; The communication topology graph model of the Byzantine attack is based on a fixed set of followers. powerful Robustness, and the number of Byzantine agents existing in each agent's in-neighbors does not exceed One, that is, satisfying ; in, For the first The neighbor set of each agent, This refers to the set of Byzantine agents in the communication topology graph model. Indicates intersection The number of elements in; Step S3: Based on the improved average subsequence reduction algorithm and the communication topology graph model in step S2, select healthy agents from the neighbor agents of non-fixed followers. The specific process of step S3 is as follows: Step S31, collect the first A non-fixed follower agent receives data from all incoming neighbors. Status information and the first The state information received by each non-fixed follower agent is stored in a set. ; in, , A set of non-fixed followers; Step S32, set The state values ​​in the data are respectively related to... Compare, put the sets Less than or equal to The set of state values ​​is denoted as , will set greater than The set of state values ​​is denoted as ; in, For the first State information of a non-fixed follower agent; Step S33: Calculate the dynamically adjusted filtering threshold and : in, This is the upper bound on the number of Byzantine nodes in the communication topology graph model. Represents a set The number of elements in the middle. Represents a set The number of elements in the middle; Step S34, for the first The state information received by each non-fixed follower agent is sorted in ascending order, and the smallest value in the sorted result is removed. Each state information and the largest One status information; Step S35: Set The neighboring agents whose state information has been deleted are marked as , will set The state information in the data is marked by the neighboring agents. ; Marked as The set of neighboring intelligent agents is denoted as ,gather The intelligent agent within is the first A non-fixed follower agent needs to track healthy neighbors; Step S4: Design a fuzzy state observer, and use the fuzzy state observer to estimate the system state and compensate for unknown nonlinear terms; Step S5: For non-fixed followers, design virtual control laws and actual control laws based on the screening results in step S3 and the system state observed by the fuzzy state observer in step S4, and obtain the adaptive law of the control law. For a fixed follower, virtual control laws and actual control laws are designed based on the system state observed by the fuzzy state observer in step S4, and an adaptive law of the control law is obtained.

2. The multi-agent output feedback security control method based on the average subsequence reduction algorithm according to claim 1, characterized in that, The dynamic model of the follower agent is as follows: (1) in, It is the first The first state of each follower agent to the second state A state vector consisting of 10 states. , The first The first, second, ..., second follower agents One state, For real numbers, for The first derivative, For the first The first follower agent's first One state, For the first The first follower agent's first External disturbances in each state It is the first A state vector consisting of all the states of each follower agent. , For the first The number of states of each follower agent. Represents an unknown, smooth, nonlinear function. For the first The first follower agent's first External disturbances in each state Representing the Control input for a follower agent Representing the The control output of a follower agent .

3. The multi-agent output feedback security control method based on the average subsequence reduction algorithm according to claim 2, characterized in that, The nonlinear function satisfies the Lipschitz condition. , It is a constant. and The independent variable of the function, This indicates taking the absolute value. This indicates the calculation of the 2-norm.

4. The multi-agent output feedback security control method based on the average subsequence reduction algorithm according to claim 3, characterized in that, The specific process of step S4 is as follows: Step S41: Reconstruct the dynamic model of equation (1) as follows: (2) in, yes The estimate, , They are The estimate, yes The estimate, , They are The estimate, , , , for The first derivative, for The first derivative; Step S42: Construct a fuzzy logic system: (3) in, This indicates a method used to approximate an unknown nonlinear function. Fuzzy logic system The first fuzzy logic system A fuzzy membership function, and satisfying , A positive design constant. Indicates to The approximation error, For the first The first follower agent's first An adaptive rate, where the superscript T indicates transpose; Step S43: Design the fuzzy state observer as follows: (4) in, for The first derivative, For the first Gain matrix of each follower agent , for The first element in for The first in One element, It is a Herwitz matrix, a vector ,matrix , , for The estimate, yes The estimate, These are the design parameters for the observer.

5. A multi-agent output feedback security control method based on the average subsequence reduction algorithm according to claim 4, characterized in that, The Herwitz matrix for: 。 6. A multi-agent output feedback security control method based on the average subsequence reduction algorithm according to claim 5, characterized in that, The specific process of step S5 is as follows: Step S51, Initialize the first Tracking error of each follower agent: (5) in, Indicates the first The tracking error of the follower agent for the first state. Indicates the first The set of neighbors of a follower agent, when the first... When a follower agent directly receives information from the leader When the first When a follower agent does not directly receive information from the leader , This indicates the leader's output signal. Indicates the first The follower agent has the first The tracking error for each state, , , For virtual control signals, Represents a set The number of elements in; Step S52: Design Lyapunov functions : (6) in, and Positive design parameters; , for The estimation error, ; The virtual control law is designed as follows: (7) in, Positive design parameters for The first derivative; Adaptive law and They are respectively: (8) (9) in, and Positive design parameters for The first derivative, for The first derivative; Step S53, Initialization ; Step S54: Design Lyapunov functions : (10) in, Positive design parameters; Virtual control law for: (11) in, Positive design parameters; (12) (13) in, Indicates the first The observation error of the first state of a follower agent. express of First derivative, express of First derivative, express of First derivative, express of Derivative order; Adaptive law Designed as follows: (14) in, Positive design parameters; Step S55, Is it satisfied? : If satisfied Then proceed to step S56; If not satisfied Then let Return to step S54; Step S56: Design Lyapunov functions : (15) in, Positive design parameters; Actual control law Designed as follows: (16) in, Positive design parameters; (17) (18) Real adaptive law Designed as follows: (19) in, The design parameters are positive.

7. A multi-agent output feedback security control method based on the average subsequence reduction algorithm according to claim 6, characterized in that, The observation error is: (20) in, For the first The observation error of a follower agent , for The first derivative, ; structure function : (21) Wherein, given matrix ,matrix And satisfy ; Depend on The inequality yields: (22) in, This indicates the calculation of the 2-norm; (23) (24) (25) in, This represents the vector consisting of the upper bound of the approximation error. , This represents the vector formed by the upper bound of external disturbances. , They represent The upper bound; (26) in, for The first derivative; (27) (28) in, Representation matrix The smallest eigenvalue.

8. A multi-agent output feedback security control method based on the average subsequence reduction algorithm according to claim 7, characterized in that, The virtual control law and the actual control law make: (1) All signals in the entire closed-loop system are bounded; (2) The tracking error converges to the neighborhood of zero.

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