Multi-agent output feedback safety control method based on average subsequence reduction algorithm

Abstract

The invention discloses a multi-agent output feedback safety control method based on an average subsequence reduction algorithm, and belongs to the technical field of safety consistency control of a multi-agent system. The multi-agent control method solves the problem that an existing multi-agent control method is poor in safety and stability. According to the method, a strict feedback nonlinear multi-agent system mathematical model with unstructured uncertainty, time-varying disturbance, stateless measurement and Byzantine attack is established, the influence of Byzantine agents is eliminated by adopting a mean value subsequence reduction algorithm, and a fuzzy state observer which approaches an unknown nonlinear term and observes a state which cannot be measured is constructed. A virtual control law and an actual control law of a backstepping controller are designed based on a state estimation result of the fuzzy state observer and the apunov stability theory, and safe and stable consistency control of the multi-agent system under the Byzantine attack is achieved. The method can be applied to consistency control of multiple agents under the Byzantine attack.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-agent system security consistency control, and specifically relates to a multi-agent output feedback security control method based on an average subsequence reduction algorithm. Background Art

[0002] With the rapid development of distributed control technology, multi-agent systems have demonstrated significant advantages in areas such as drone fleets, smart grids, and the Industrial Internet of Things. Through local information exchange and collaborative decision-making, multi-agent systems can efficiently complete complex tasks. However, in open network environments, these systems face a serious threat from Byzantine attacks. In such attacks, malicious nodes can mislead healthy nodes from their target state by forging, tampering, or selectively discarding data, leading to a breakdown in system consistency and even global failure. Especially in critical infrastructure areas such as power grid scheduling and traffic coordination, Byzantine attacks can have catastrophic consequences, necessitating the design of control methods that are both secure and robust.

[0003] While some progress has been made in the prior art regarding consensus control for multi-agent systems, significant deficiencies remain in addressing Byzantine attacks and state estimation. For example, patent application publication number CN106802564A discloses a model-agnostic multi-agent consensus collaborative control method. This method uses a fuzzy logic control algorithm 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 implemented to update the position and velocity information of each agent in the system within a specified timeframe. However, this method lacks an integrated state observer and is unable to handle the nonlinear dynamics and external disturbances commonly found in the system, resulting in limited control accuracy. Furthermore, various types of attack signals are not considered, limiting the safety control of the multi-agent system. Patent application publication number CN109557818A discloses a linear multi-agent fault-tolerant control method that focuses on addressing sensor and actuator failures. 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, incorporating disturbance compensation techniques to mitigate 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 fails to consider the arbitrariness of Byzantine node attacks. Furthermore, traditional linear observers have limited approximation capabilities for nonlinear systems, limiting their application scenarios.

[0004] In summary, while 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 and Byzantine attacks exist. Therefore, developing a control method that integrates a high-precision nonlinear state observer and can handle Byzantine attacks and ensure the safe and stable operation of multi-agent systems is a challenge currently facing the field of multi-agent secure consensus control. Summary of the Invention

[0005] The purpose of the present invention is to solve the problems of poor security and stability of existing multi-agent control methods, and to propose a multi-agent output feedback safety control method based on an average subsequence reduction algorithm.

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

[0007] Step S1: Establish a nonlinear multi-agent system consisting of 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 of step S2, healthy agents are selected from neighboring agents with non-fixed followers;

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

[0011] Step S5: For the non-stationary follower, design a virtual control law and an actual control law according to the screening result in step S3 and the system state observed by the fuzzy state observer in step S4, and obtain an adaptive law of the control law;

[0012] For the fixed follower, a virtual control law and an actual control law are designed according to 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:

[0014]

[0015] in, is the state vector consisting of the 1st state to the lth state of the i-th follower agent, x i,1 ,xi,2 ,...,x i,l are the 1st, 2nd, ..., 1st states of the ith follower agent, R is a real number, is x i,l The first derivative of x i,l+1 is the l+1th state of the i-th follower agent, d i,l is the external disturbance of the lth state of the ith follower agent, x i is the state vector consisting of all states of the ith follower agent, l i is the number of states of the i-th follower agent, g i,l (·) represents an unknown smooth nonlinear function, is the lth follower agent of the i-th i The external disturbance of the state, u i represents the control input of the i-th follower agent, y i 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 is a constant, ξ and ξ′ are function variables, |·| means taking the absolute value, and ||·|| means calculating the 2-norm.

[0017] Furthermore, the communication topology model of the Byzantine attack is strongly 2f+1-robust with respect to a fixed follower set X, and the number of Byzantine agents in the incoming neighbors of each agent does not exceed f, that is,

[0018] in, is the neighbor set of the ith agent, is the set of Byzantine agents in the communication topology graph model, Represents intersection The number of elements in .

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

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

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

[0022] Step S32: Set Δ i The state values ​​in y are respectively i Compare and set Δ i is less than or equal to y i The set of state values ​​is recorded as The set Δ i is greater than y i The set of state values ​​is recorded as

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

[0024] Step S33: Calculate the dynamic adjustment filtering threshold and

[0025]

[0026] Where f is the upper bound of the number of Byzantine nodes in the communication topology model, Representing a collection The number of elements in Representing a collection The number of elements in

[0027] Step S34: Arrange the state information received by the i-th non-fixed follower agent in ascending order, and remove the smallest one in the arrangement result. Status information and the maximum Status information;

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

[0029] Marked as κ i,j = 1 is denoted as gather The agents in are the healthy neighbors that the i-th non-stationary follower agent needs to track.

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

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

[0032]

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

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

[0035]

[0036] in, Represents the function used to approximate unknown nonlinear functions The fuzzy logic system, Represents the lth fuzzy membership function of the fuzzy logic system, and satisfies is a positive design constant, δ i,l Express The approximation error, θ i,l is the lth adaptation rate of the i-th follower agent, and the superscript T indicates transposition;

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

[0038]

[0039] in, for The first derivative of K i is the gain matrix of the ith follower agent, K i,1 K i The first element in K i The first i elements, A i is the Hurwitz matrix, vector B i,l =[0,...,1 l,...,0] T , matrix B i =[0,0,...,1] T , for Estimates, It is y i The estimate of C i are the design parameters of the observer.

[0040] Furthermore, the Hurwitz 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 represents the tracking error of the ith follower agent to the first state, represents the incoming neighbor set of the ith follower agent. When the ith follower agent directly receives the leader information, a i,0 = 1, when the i-th follower agent does not directly receive information from the leader a i,0 =0,y d represents the output signal of the leader, z i,l represents the tracking error of the i-th follower agent to the l-th state, i=1,2,...,N,l=2,...,l i , α i,l-1 is the virtual control signal, τ i Representing a collection The number of elements in ;

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

[0047]

[0048] Among them, γ i,1 with γ j,1 is a positive design parameter; ν i =τ i -a i,0 τ i +a i,0 >0, is θ i,l The estimation error of

[0049] The virtual control law is designed as:

[0050]

[0051] Among them, p i,1 is a positive design parameter, y d The first derivative of ;

[0052] Adaptive Law and They are:

[0053]

[0054] Among them, λ i,1 and λ j,1 is a positive design parameter, for The first derivative of for The first derivative of ;

[0055] Step S53, initializing l=2;

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

[0057]

[0058] Among them, γ i,l is a positive design parameter;

[0059] Virtual control law α i,l for:

[0060]

[0061] Among them, p i,l is a positive design parameter;

[0062]

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

[0064] Adaptive Law Designed to:

[0065]

[0066] Among them, λ i,l is a positive design parameter;

[0067] Step S55: whether l=l is satisfied i -1:

[0068] If l=l i -1, then execute step S56;

[0069] If l=l is not satisfied i -1, then set l=l+1 and return to step S54;

[0070] Step S56: Design Lyapunov function

[0071]

[0072] in, is a positive design parameter;

[0073] Actual control law u i Designed to:

[0074]

[0075] in, is a positive design parameter;

[0076]

[0077] Actual adaptive law Designed to:

[0078]

[0079] in, is a positive design parameter.

[0080] Furthermore, the observation error is:

[0081]

[0082] Among them, e i is the observation error of the i-th follower agent, for e i The first derivative of

[0083] Construct Lyapunov function V i,0 :

[0084]

[0085] Among them, given the matrix Matrix P i T =P i >0, and satisfies

[0086] From Young's inequality we get:

[0087]

[0088] Among them, ||·|| means calculating the 2-norm;

[0089]

[0090] in, represents the vector consisting of the upper bound of the approximation error, represents the vector consisting of the upper bound of external interference, Respectively The upper bound of

[0091]

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

[0093]

[0094] Among them, λ min (Q i ) represents the matrix Q i The minimum eigenvalue of .

[0095] Furthermore, the virtual control law and the actual control law are such that:

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

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

[0098] The beneficial effects of the present invention are:

[0099] The present invention establishes a mathematical model of a strict feedback nonlinear multi-agent system with unstructured uncertainty, time-varying disturbances, stateless measurement and Byzantine attacks, adopts a mean subsequence reduction algorithm to eliminate the influence of the Byzantine agent, constructs a fuzzy state observer that approximates unknown nonlinear terms and observes unmeasurable states, and designs a virtual control law and an actual control law of the backstepping controller based on the state estimation results of the fuzzy state observer and the Yapunov stability theory. This realizes safe and stable consistency control of the multi-agent system under Byzantine attacks, has strong robustness to flexible node attack methods, and has the ability to estimate unmeasurable states and cope with external interference. Experiments have shown that the control method of the present invention can realize intelligent adaptive tracking control, so that all signals of the controlled system have boundaries and the tracking error can be arbitrarily small. Under Byzantine attacks, the control method of the present invention can still ensure safety and stability, which is of great practical significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0100] Figure 1 It is a flow chart of a multi-agent output feedback safety control method based on an average subsequence reduction algorithm of the present invention;

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

[0102] Figure 3 Graph showing the controller signal of a healthy follower agent under attack according to an embodiment of the present invention. DETAILED DESCRIPTION

[0103] Specific implementation method 1: Combination Figure 1 This embodiment describes a multi-agent output feedback safety control method based on an average subsequence reduction algorithm, and 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, which includes one leader agent and N (N≥3) follower agents, and a dynamic model of the follower agents is 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 of step S2, healthy agents are selected from neighboring agents with non-fixed followers;

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

[0108] Step S5: For the non-stationary follower, design a virtual control law and an actual control law according to the screening result in step S3 and the system state observed by the fuzzy state observer in step S4, and obtain an adaptive law of the control law;

[0109] For the fixed follower, a virtual control law and an actual control law are designed according to 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 the present invention is highly robust against flexible node attack methods and is applicable to situations where the system contains nonlinear terms and unmeasurable system states.

[0111] Specific embodiment 2: This embodiment differs from specific embodiment 1 in that the dynamic model of the follower agent is:

[0112]

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

[0114] Other steps and parameters are the same as those in the first embodiment.

[0115] Specific embodiment 3: This embodiment differs from specific embodiment 1 or 2 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 is a constant, ξ and ξ′ are function variables, |·| means taking the absolute value, and ||·|| means calculating the 2-norm.

[0116] Other steps and parameters are the same as those in the first or second embodiment.

[0117] Specific embodiment 4: This embodiment differs from the specific embodiments 1 to 3 in that the communication topology model of the Byzantine attack is about a fixed follower set. Strong 2f+1-robustness, and the number of Byzantine agents in the incoming neighbors of each agent does not exceed f, that is, it satisfies

[0118] in, is the neighbor set of the ith agent, is the set of Byzantine agents in the communication topology graph model, Represents intersection The number of elements in .

[0119] The other steps and parameters are the same as those in the first to third embodiments.

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

[0121] (1) Not following the preset control law to update the state;

[0122] (2) Having the ability to tamper with state values ​​independently;

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

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

[0125] In the present invention, the intelligent agent that can directly receive the leader's information is called a fixed follower, and the intelligent agent that cannot directly receive the leader's information is called a non-fixed follower.

[0126] Specific embodiment 5: This embodiment differs from any one of specific embodiments 1 to 4 in that the specific process of step S3 is as follows:

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

[0128] in, 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 valid for the control process of healthy agents;

[0129] Step S32: Set Δ i The state values ​​in y are respectively i Compare and set Δ i is less than or equal to y i The set of state values ​​is recorded as The set Δ i is greater than y i The set of state values ​​is recorded as

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

[0131] Step S33: Calculate the dynamic adjustment filtering threshold and

[0132]

[0133] Where f is the upper bound of the number of Byzantine nodes in the communication topology model, Representing a collection The number of elements in Representing a collection The number of elements in

[0134] Step S34: Arrange the state information received by the i-th non-fixed follower agent in ascending order, and remove the smallest one in the arrangement result. Status information and the maximum Status information;

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

[0136] Marked as κ i,j = 1 is denoted as gather The agents in are the healthy neighbors that the i-th non-stationary follower agent needs to track.

[0137] The other steps and parameters are the same as those in the first to fourth embodiments.

[0138] Specific embodiment 6: This embodiment differs from any one of specific embodiments 1 to 5 in that the specific process of step S4 is as follows:

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

[0140]

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

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

[0143]

[0144] in, Represents the function used to approximate unknown nonlinear functions The fuzzy logic system, Represents the lth fuzzy membership function of the fuzzy logic system, and satisfies is a positive design constant (indicating the approximation error δ i,l δ i,l Express The approximation error, θ i,l is the lth adaptation rate of the i-th follower agent, and the superscript T indicates transposition;

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

[0146]

[0147] in, for The first derivative of K i is the gain matrix of the ith follower agent, K i,1 K i The first element in K i The first i elements, A i is a strict Hurwitz matrix, vector B i,l =[0,...,1 l ,...,0] T (In vector B i,l In the matrix B, except for the first element which is 1, all other elements are 0). i =[0,0,...,1] T (Only the last element is 1, the others are all 0), Estimates, It is y i The estimate of C i 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 the first to fifth embodiments.

[0149] Specific embodiment 7: This embodiment differs from any one of specific embodiments 1 to 6 in that the Hurwitz matrix A i for:

[0150]

[0151] The other steps and parameters are the same as those in the first to sixth embodiments.

[0152] Specific embodiment eight: This embodiment differs from any one of specific embodiments 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 represents the tracking error of the ith follower agent to the first state, represents the incoming neighbor set of the ith follower agent (for fixed followers, Directly enter the neighbor set; for non-fixed followers, is the set of healthy agent neighbors that have been screened out), when the i-th follower agent directly receives the leader’s information, a i,0= 1, when the i-th follower agent does not directly receive information from the leader a i,0 =0,y d represents the output signal of the leader, z i,l represents the tracking error of the i-th follower agent to the l-th state, i=1,2,...,N,l=2,...,l i , α i,l-1 is the virtual control signal, τ i Representing a collection The number of elements in ;

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

[0157]

[0158] Among them, γ i,1 with γ j,1 is a positive design parameter; ν i =τ i -a i,0 τ i +a i,0 >0, is θ i,l The estimation error of

[0159] The virtual control law is designed as:

[0160]

[0161] Among them, p i,1 is a positive design parameter, y d The first derivative of ;

[0162] Adaptive Law and They are:

[0163]

[0164] Among them, λ i,1 and λ j,1 is a positive design parameter, for The first derivative of for The first derivative of ;

[0165] Step S53, initializing l=2;

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

[0167]

[0168] Among them, γ i,l is a positive design parameter;

[0169] Virtual control law α i,l for:

[0170]

[0171] Among them, p i,l is a positive design parameter;

[0172]

[0173]

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

[0175] Adaptive Law Designed to:

[0176]

[0177] Among them, λ i,l is a positive design parameter;

[0178] Step S55: whether l=l is satisfied i -1:

[0179] If l=l i -1, then execute step S56;

[0180] If l=l is not satisfied i -1, then set l=l+1 and return to step S54;

[0181] Step S56: Design Lyapunov function

[0182]

[0183] in, is a positive design parameter;

[0184] Actual control law u i Designed to:

[0185]

[0186] in, is a positive design parameter;

[0187]

[0188] Actual adaptive law Designed to:

[0189]

[0190] in, is a positive design parameter.

[0191] The other steps and parameters are the same as those in the first to seventh embodiments.

[0192] Specific embodiment 9: This embodiment differs from any one of specific embodiments 1 to 8 in that the observation error is obtained from formula (2) and formula (4):

[0193]

[0194] Among them, e i is the observation error of the i-th follower agent, for e i The first derivative of

[0195] Construct Lyapunov function V i,0 :

[0196]

[0197] Among them, given the matrix Matrix P i T =P i >0, and satisfies

[0198] From Young's inequality we get:

[0199]

[0200] Among them, ||·|| means calculating the 2-norm;

[0201]

[0202] in, represents the vector consisting of the upper bound of the approximation error, represents the vector consisting of the upper bound of external interference, Respectively The upper bound of

[0203] Then we can get:

[0204]

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

[0206]

[0207] Among them, λ min (Q i ) represents the matrix Q i The minimum eigenvalue of .

[0208] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0209] Specific embodiment 10: This embodiment differs from any one of specific embodiments 1 to 9 in that the virtual control law and the actual control law are such that:

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

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

[0212] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

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

[0214] Construct a composite Lyapunov function:

[0215]

[0216] From Young's inequality we can get:

[0217]

[0218]

[0219] Then we can get:

[0220]

[0221] in:

[0222]

[0223] Choose appropriate parameters so that C>0 and D>0, and integrate to get:

[0224]

[0225] This ensures that all signals are uniformly bounded.

[0226] The feasibility and control performance of the proposed method will be verified below. A directed topology 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 is the unknown nonlinear term, d i,1 (t) = 0.1sin(πt) and d i,2 (t) = 0.2cos(πt) represents external interference, and the leader’s signal is selected as y r (t) = 2sin(t).

[0229] The communication topology is subject to a 1-local Byzantine attack, and about a fixed set of followers Is strongly 3-robust. Byzantine agent Any malicious signal can be propagated to its neighbors. For time t>0, the specific attack signal of Byzantine agent 2 to its neighboring agents is selected as: 2→· =1.5, the specific attack signal of Byzantine agent 5 to its neighbor agents is chosen as: 5→· = 2t, the controller of agent 10 is changed to u by the Byzantine adversary 10 =2sin(t).

[0230] The design parameters are selected as follows: 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 other initial values ​​are set to 0.

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

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

[0234] The above examples are merely illustrative of the calculation model and process of the present invention and are not intended to limit the embodiments of the present invention. Persons skilled in the art will readily appreciate that other variations or modifications based on the above description are possible. This list of embodiments is not exhaustive; however, any obvious variations or modifications derived from the technical solution of the present invention remain within the scope of protection of the present invention.

Claims

1. A multi-agent output feedback safety control method based on average subsequence reduction algorithm, characterized in that: The method specifically comprises the following steps: Step S1: Establish a nonlinear multi-agent system consisting of one leader agent and N follower agents, and establish a dynamic model of the follower agents; Step S2: Establish a communication topology model for a Byzantine attack; Step S3: Based on the improved average subsequence reduction algorithm and the communication topology graph model of step S2, healthy agents are selected from neighboring agents with non-fixed followers; Step S4: designing a fuzzy state observer, using the fuzzy state observer to estimate the system state and compensate for unknown nonlinear terms; Step S5: For the non-stationary follower, design a virtual control law and an actual control law according to the screening result in step S3 and the system state observed by the fuzzy state observer in step S4, and obtain an adaptive law of the control law; For the fixed follower, a virtual control law and an actual control law are designed according to 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 safety control method based on the average subsequence reduction algorithm according to claim 1 is characterized in that: The dynamic model of the follower agent is: in, is the state vector consisting of the 1st state to the lth state of the i-th follower agent, x i,1 ,x i,2 ,...,x i,l are the 1st, 2nd, ..., 1st states of the ith follower agent, R is a real number, is x i,l The first derivative of x i,l+1 is the l+1th state of the i-th follower agent, d i,l is the external disturbance of the lth state of the ith follower agent, x i is the state vector consisting of all states of the ith follower agent, l i is the number of states of the i-th follower agent, g i,l (·) represents an unknown smooth nonlinear function, is the lth follower agent of the i-th i The external disturbance of the state, u i represents the control input of the i-th follower agent, y i represents the control output of the i-th follower agent, i=1,...,N,l=1,...,l i -1.

3. The multi-agent output feedback safety control method based on the average subsequence reduction algorithm according to claim 2 is characterized 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 is a constant, ξ and ξ′ are function variables, |·| means taking the absolute value, and ||·|| means calculating the 2-norm.

4. The multi-agent output feedback safety control method based on the average subsequence reduction algorithm according to claim 3 is characterized in that: The communication topology model of the Byzantine attack is about a fixed follower set Strong 2f+1-robustness, and the number of Byzantine agents in the incoming neighbors of each agent does not exceed f, that is, it satisfies in, is the neighbor set of the ith agent, is the set of Byzantine agents in the communication topology graph model, Represents intersection The number of elements in .

5. The multi-agent output feedback safety control method based on the average subsequence reduction algorithm according to claim 4 is characterized in that: The specific process of step S3 is: Step S31: Collect the information received by the i-th non-fixed follower agent from all incoming neighbors. Status information y j , and stores the state information received by the i-th non-fixed follower agent into the set in, is a set of non-fixed followers; Step S32: Set Δ i The state values ​​in y are respectively i Compare and set Δ i is less than or equal to y i The set of state values ​​is recorded as The set Δ i is greater than y i The set of state values ​​is recorded as Among them, y i is the state information of the i-th non-fixed follower agent; Step S33: Calculate the dynamic adjustment filtering threshold and Where f is the upper bound of the number of Byzantine nodes in the communication topology model, Representing a collection The number of elements in Representing a collection The number of elements in Step S34: Arrange the state information received by the i-th non-fixed follower agent in ascending order, and remove the smallest one in the arrangement result. Status information and the maximum Status information; Step S35: Set Δ i The neighboring agents whose state information is deleted are marked as κ i,j =0, the set Δ i The state information in the neighboring agent is retained and marked as κ i,j =1; Marked as κ i,j = 1 is denoted as gather The agents in are the healthy neighbors that the i-th non-stationary follower agent needs to track.

6. The multi-agent output feedback safety control method based on the average subsequence reduction algorithm according to claim 5 is characterized in that: The specific process of step S4 is as follows: Step S41: Reconstruct the dynamic model of formula (1) as follows: in, yes Estimates, They are x i,1 ,x i,2 ,...,x i,l Estimates, is x i Estimates, They are Estimates, is x i,l The first derivative of for The first derivative of ; Step S42: construct a fuzzy logic system: in, Represents the function used to approximate unknown nonlinear functions The fuzzy logic system, Represents the lth fuzzy membership function of the fuzzy logic system, and satisfies is a positive design constant, δ i,l Express The approximation error, θ i,l is the lth adaptation rate of the i-th follower agent, and the superscript T indicates transposition; Step S43: Design the fuzzy state observer as follows: in, for The first derivative of K i is the gain matrix of the ith follower agent, K i,1 K i The first element in K i The first i elements, A i is the Hurwitz matrix, vector B i,l =[0,...,1 l ,...,0] T , matrix B i =[0,0,...,1] T , for Estimates, It is y i The estimate of C i are the design parameters of the observer.

7. The multi-agent output feedback safety control method based on the average subsequence reduction algorithm according to claim 6 is characterized in that: The Hurwitz matrix A i for:

8. The multi-agent output feedback safety control method based on the average subsequence reduction algorithm according to claim 7 is characterized in that: The specific process of step S5 is as follows: Step S51: Initialize the tracking error of the i-th follower agent: Among them, z i,1 represents the tracking error of the ith follower agent to the first state, represents the incoming neighbor set of the ith follower agent. When the ith follower agent directly receives the leader information, a i,0 = 1, when the i-th follower agent does not directly receive information from the leader a i,0 =0,y d represents the output signal of the leader, z i,l represents the tracking error of the i-th follower agent to the l-th state, i=1,2,...,N,l=2,...,l i , α i,l-1 is the virtual control signal, τ i Representing a collection The number of elements in ; Step S52: Design the Lyapunov function V i,1 : Among them, γ i,1 with γ j,1 is a positive design parameter; ν i =τ i -a i,0 τ i +a i,0 >0, is θ i,l The estimation error of The virtual control law is designed as: Among them, p i,1 is a positive design parameter, y d The first derivative of ; Adaptive Law and They are: Among them, λ i,1 and λ j,1 is a positive design parameter, for The first derivative of for The first derivative of ; Step S53, initializing l=2; Step S54: Design the Lyapunov function V i,l : Among them, γ i,l is a positive design parameter; Virtual control law α i,l for: Among them, p i,l is a positive design parameter; Among them, e i,1 represents the observation error of the first state of the i-th follower agent, represents y d The k-th derivative of express The k-th derivative of express The k-th derivative of express The k-th derivative of Adaptive Law Designed to: Among them, λ i,l is a positive design parameter; Step S55: whether l=l is satisfied i -1: If l=l i -1, then execute step S56; If l=l is not satisfied i -1, then set l=l+1 and return to step S54; Step S56: Design Lyapunov function in, is a positive design parameter; Actual control law u i Designed to: in, is a positive design parameter; Actual adaptive law Designed to: in, is a positive design parameter.

9. The multi-agent output feedback safety control method based on the average subsequence reduction algorithm according to claim 8, characterized in that: The observation error is: Among them, e i is the observation error of the i-th follower agent, for e i The first derivative of Construct Lyapunov function V i,0 : Among them, given the matrix matrix and satisfy From Young's inequality we get: Among them, ||·|| means calculating the 2-norm; in, represents the vector consisting of the upper bound of the approximation error, represents the vector consisting of the upper bound of external interference, Respectively The upper bound of in, V i,0 The first derivative of ; Among them, λ min (Q i ) represents the matrix Q i The minimum eigenvalue of .

10. The multi-agent output feedback safety control method based on the average subsequence reduction algorithm according to claim 9, characterized in that: The virtual control law and the actual control law are such that: (1) All signals in the entire closed-loop system are bounded; (2) The tracking error converges to a neighborhood of zero.

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