Optimization control method for human-in-loop multi-agent system under FDI attack

Abstract

The invention provides an optimal control method for a human-in-loop multi-agent system under FDI attack, and belongs to the technical field of multi-agent system control. According to the control method, a non-completely autonomous leader system is constructed, and FDI attacks from a follower controller to an actuator end are considered. In view of a contrary relationship between an attacker and a defender, under a unified design framework of a zero-sum game and an adaptive dynamic programming theory, constructing a performance function and obtaining a Nash equilibrium point, namely an optimal strategy of the attacker and the defender; meanwhile, in order to reduce the consumption of network resources, a dynamic event triggering mechanism is designed; and a Nash optimal solution is obtained by combining a single evaluation network structure based on a neural network. According to the control method disclosed by the invention, dynamic event triggering game optimization control under the influence of FDI attacks is realized, a method for simultaneously designing optimal strategies of attackers and defenders under a unified framework is constructed, and communication resources are saved while game performance optimization is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-agent system control, and in particular relates to an optimization control method for a human-in-the-loop multi-agent system under FDI attack. Background Art

[0002] With the rapid development of technologies such as artificial intelligence, the Internet of Things, and big data, multi-agent systems have been widely used in automation, intelligent transportation, robot collaboration, smart grids, financial market analysis, and other fields. Exploring them has important strategic significance and positive economic prospects. Since the security and reliability of fully autonomous systems cannot be fully guaranteed, the control of human-in-the-loop multi-agent systems is of great significance. In the network communication topology composed of agents, malicious network attacks represented by false data injection attacks (FDI attacks) can have a huge impact on the accurate transmission of information of agents. At the same time, in the existing human-in-the-loop multi-agent control results (CN202410193921.8, CN202410031096.1), there is no solution for designing the strategies of attackers and defenders under FDI attacks, and it is impossible to achieve a compromise in system optimization performance when subjected to FDI attacks. In addition, effectively reducing the overhead of network communication resources is also an inevitable requirement for the complexity of the multi-agent system network.

[0003] Therefore, under the trend of high informatization, collaboration and intelligence, it is of practical significance to design a dynamic event-triggered game optimization method for human-in-the-loop multi-agent systems under FDI attacks. Summary of the invention

[0004] In view of the problems existing in the background technology, the purpose of the present invention is to provide an optimization control method for a human-in-the-loop multi-agent system under FDI attack. The control method constructs a non-fully autonomous leader system and considers that the follower controller to the actuator end is attacked by FDI. In view of the antagonistic relationship between the attacker and the defender, under the unified design framework of zero-sum game and adaptive dynamic programming theory, a performance function is constructed and the Nash equilibrium point, that is, the optimal strategy of the attacker and the defender, is obtained; at the same time, in order to reduce the consumption of network resources, a dynamic event triggering mechanism is designed; combined with a single evaluation network structure based on a neural network, the Nash optimal solution is obtained. The control method of the present invention realizes the dynamic event-triggered game optimization control under the influence of FDI attack, constructs a method for simultaneously designing the optimal strategies of the attacker and the defender under a unified framework, and saves communication resources while achieving game performance optimization.

[0005] To achieve the above object, the technical solution of the present invention is as follows:

[0006] An optimization control method for a human-in-the-loop multi-agent system under FDI attack includes the following steps:

[0007] Step 1: Construct a dynamic model of a non-fully autonomous multi-agent system, including the dynamic equations of the externally controlled leader and follower, where the external human expert command signal is an unknown quantity;

[0008] Step 2: Based on the dynamic model of the multi-agent system constructed in step 1, consider the FDI attack on the follower controller to the actuator end, and construct a dynamic model of the agent system attacked by FDI;

[0009] Step 3: Based on the dynamic model of the intelligent agent system attacked by FDI obtained in step 2, design the performance function and find the Nash equilibrium point for each intelligent agent, that is, the Nash optimal strategy of the attacker and the defender;

[0010] Step 4: Based on the Nash equilibrium point in step 3, design the HJI equation and Nash optimal strategy based on dynamic event triggering;

[0011] Step 5: According to the HJI equation based on dynamic event triggering obtained in step 4, a dynamic event triggering mechanism is designed to save network resource overhead;

[0012] Step 6: Design a single evaluation network model based on a neural network to approximate the performance function in step 3, and obtain an approximate solution to the Nash equilibrium point triggered by dynamic events;

[0013] Step 7: Based on the Bellman residual generated in the approximation process in step 6, the gradient descent method is used to generate the weight change law of the single evaluation network in step 6 until convergence, and the control input can be obtained based on the weight result.

[0014] Furthermore, in step 1, a non-fully autonomous multi-agent system is established, including a leader and N followers. The multi-agent system is specifically:

[0015] Leaders:

[0016] Followers:

[0017] in, represents the derivative, the subscript i is the number of a single agent system, i = 1, 2, ..., N, represents the system state of agent i, represents the control input of agent i, represents the internal dynamics of agent i, represents the output dynamics of agent i; represents the system state of the leader, represents an unknown and non-zero command signal sent by an external human expert to the leader, Represents the internal dynamics of the leader, Represents the output dynamics of the leader.

[0018] Furthermore, in step 2, the specific process of establishing the dynamic model of the i-th agent system attacked by FDI is as follows:

[0019] Considering the FDI attack on the channel from the controller of agent i to the actuator, the control input of agent i under FDI attack is:

[0020]

[0021] Among them, u i for u i (t) is the abbreviation of i Input for FDI attack;

[0022] The dynamic model of the i-th agent attacked by FDI can be expressed as:

[0023]

[0024] in, It is the state of the system being attacked.

[0025] Furthermore, the attacker should meet the following conditions:

[0026] (1) All actuators may be attacked by attackers at any time.

[0027] (2) State variables can be monitored in real time and provided as information to attackers.

[0028] (3) False data and control signals can be injected into the actuator synchronously.

[0029] (4) The attacker’s energy is limited.

[0030] Furthermore, the specific process of step 3 is:

[0031] The dynamic equation defining the bipartite consistency error of the ith agent is:

[0032]

[0033] in, a ij is the connection weight between agent i and agent j, if a ij >0 means that agent i and agent j are in a cooperative relationship. ij <0 means that agent i and agent j are in a competitive relationship; b i is the connection weight between agent i and the leader, if b i>0 means that there is a cooperative relationship between agent i and the leader, otherwise, there is a competitive relationship; represents the degree matrix and

[0035] According to game theory, the expected performance of control input is improved while the expected performance of external FDI attack is reduced. There is an antagonistic relationship between the two, and when the performance of the two reaches the optimal equilibrium, a Nash equilibrium point can be formed. Therefore, the design performance function is in the following form:

[0036]

[0037] Among them, γ i represents the expected attack attenuation level, γ i >0, Q ii , R ij , R ii , P ii and P ij are all symmetric positive definite matrices with matching dimensions, represents the neighboring agent of the ith agent;

[0038] According to Pontryagin's maximum-minimum principle, the Nash equilibrium point The following inequality is satisfied:

[0039]

[0040] The Hamiltonian function is constructed as follows:

[0041]

[0042] in, represents the partial derivative of the performance function with respect to the bipartite consensus error;

[0043] The corresponding HJI (Hamilton-Jacobi-Isaacs) equation can be expressed as:

[0044] According to the theory of adaptive dynamic programming, the specific form of the Nash equilibrium point is:

[0045]

[0046] Furthermore, the specific process of step 4 is:

[0047] definition is the kth triggering moment, and satisfies The current status With sampling status The error between them can be expressed as:

[0048]

[0049] The two-part consistency error based on dynamic event triggering has the following form:

[0050]

[0051] Then the dynamic event trigger error is expressed as:

[0052]

[0053] Considering that FDI attack is an external output and uncontrollable, the specific forms of the optimal control strategy based on dynamic event triggering and the optimal FDI attack strategy based on time triggering are:

[0054]

[0055] Combining the above results with the HJI equation, the specific form of the HJI equation based on dynamic event triggering is obtained as follows:

[0056]

[0057] Furthermore, the specific process of step 5 is: according to the HJI equation based on dynamic event triggering in step 4, the dynamic event triggering mechanism is designed as follows:

[0058]

[0059] Among them, T DED is the dynamic trigger threshold, and

[0060]

[0061] λ min (Q ii ) represents the matrix Q ii The smallest eigenvalue of i,1 is the design parameter, 0<ν i,1 <1,

[0062] Design dynamic parameters The change law is as follows:

[0063]

[0064] in,

[0065]

[0066] Furthermore, the specific process of step 6 is:

[0067] A single evaluation network model based on a neural network is designed to approximate the performance function in step 3. The specific expression of the single evaluation network model based on a neural network is:

[0068]

[0069] in, is the ideal weight vector, h ci is the number of neurons in the hidden layer, S c (∈ i ) is a differentiable continuous activation function, o(∈ i ) is the approximation error;

[0070] The performance function gradient is expressed as:

[0071]

[0072] in, is the gradient value of the activation function, is the gradient of the approximation error.

[0073] Considering that the ideal weight vector is an unknown quantity and cannot be directly obtained, the estimated form of the approximate value of the gradient value of the construction performance function is:

[0074]

[0075] in, W ci The estimated form.

[0076] Furthermore, the estimated value of the optimal control strategy based on dynamic event triggering and the approximate value of the optimal FDI attack strategy based on time triggering in step 4 is obtained as follows:

[0077]

[0078] Combining the above results with the HJI equation based on dynamic event triggering in step 4, the estimated form of its approximate value is:

[0079]

[0080] in,

[0081]

[0082] Furthermore, the specific process of step 7 is:

[0083] The Bellman residual generated in the approximation process in step 6 is The Bellman residual is defined as:

[0084]

[0085] The design optimization objective function is:

[0086]

[0087] Based on this function, using the gradient descent method, the specific form of the change law of the weight of the single evaluation network in step 6 can be obtained as follows:

[0088]

[0089] Among them, 0<μ i <1 is the design parameter;

[0090] Substitute the obtained weight value into the expression form of control input,

[0091]

[0092] The control input of the system can be obtained.

[0093] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0094] The method of the present invention uses the trajectory adjustment command signal sent by external human experts to the leader to respond to sudden dangerous situations in real time, thereby improving the safety and reliability of the system; at the same time, considering the FDI attack between the controller and the actuator of the intelligent body, a system model under attack is established; based on this model, in view of the antagonistic relationship between the attacker and the defender, under the unified design framework of zero-sum game and adaptive dynamic programming theory, a performance function is constructed and the Nash equilibrium point, that is, the optimal strategy of the attacker and the defender, is obtained, which effectively achieves the balance of the system game optimization performance. More importantly, considering the need to save communication resource consumption in practical applications, a dynamic event triggering mechanism is designed to ensure that communication resource consumption is saved while achieving game performance optimization, effectively improving the control quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 is a flow chart of the control method of the present invention.

[0096] Figure 2 A schematic diagram of the communication topology adopted by the present invention.

[0097] Figure 3 It is a curve diagram of the state consistency of the intelligent agent of the present invention.

[0098] Figure 4 Graph showing the bipartite consistency error of the agent of the present invention.

[0099] Figure 5 It is the FDI attack curve diagram of the intelligent agent of the present invention.

[0100] Figure 6 is the optimal control input curve diagram of the intelligent agent of the present invention,

[0101] Among them, (a) is the optimal control input curve diagram of agent 1, (b) is the optimal control input curve diagram of agent 2, (c) is the optimal control input curve diagram of agent 3, (d) is the optimal control input curve diagram of agent 4, and (e) is the optimal control input curve diagram of agent 5.

[0102] Figure 7 It is a curve chart of the weight changes of the single evaluation neural network of the intelligent agent of the present invention.

[0103] Figure 8 A curve chart of the triggering interval of the intelligent agent dynamic event triggering of the present invention. DETAILED DESCRIPTION

[0104] In order to make the objectives, technical solutions and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with the implementation modes and the accompanying drawings.

[0105] Figure 1 is a flow chart of the control method of the present invention, such as Figure 1 As shown, the present invention discloses an optimization control method for a human-in-the-loop multi-agent system under FDI attack, which specifically includes the following steps:

[0106] Step 1: Establish a dynamic model of a non-fully autonomous multi-agent system. The specific process is as follows:

[0107] Leaders:

[0108] Followers:

[0109] Among them, the subscript i is the number of a single follower agent system, represents the system state of agent i, represents the control input of agent i, represents the internal dynamics of agent i, Represents the output dynamics of agent i. represents the system state of the leader, represents an unknown and non-zero command signal sent by an external human expert to the leader, Represents the internal dynamics of the leader, Represents the output dynamics of the leader;

[0110] Step 2: Considering the FDI attack on the follower controller to the actuator end, a dynamic model of the intelligent system attacked by FDI is constructed. The specific process is as follows:

[0111] For model building, the attacker is assumed to have the following capabilities:

[0112] (1) All actuators may be attacked by attackers at any time.

[0113] (2) State variables can be monitored in real time and provided as information to attackers.

[0114] (4) The attacker’s false data and control signals can be injected into the actuator synchronously.

[0115] (4) The attacker’s energy is limited.

[0116] The control input of agent i under FDI attack becomes:

[0117]

[0118] Among them, χ i Input for FDI attack;

[0119] Then the dynamic model of the i-th agent attacked by FDI can be expressed as

[0120]

[0121] in, is the state of the system being attacked;

[0122] Step 3: Based on the attacked system model obtained in step 2, design a performance function and find the Nash equilibrium point for each agent, that is, the Nash optimal strategy of the attacker and the defender. The specific process is as follows:

[0123] Define the bipartite consistency error of the i-th agent as:

[0124]

[0125] Among them, a ij is the connection weight between agent i and agent j, if a ij >0 means that agent i and agent j are in a cooperative relationship. ij <0 means that agent i and agent j are in a competitive relationship; b i is the connection weight between agent i and the leader, if b i >0 means that there is a cooperative relationship between agent i and the leader, otherwise, there is a competitive relationship; represents the degree matrix and

[0126] Then the dynamic equation of the bipartite consistency error of the i-th agent is:

[0127]

[0128] in,

[0129] According to game theory, the expected performance of control input is improved while the expected performance of external FDI attack is reduced. There is an antagonistic relationship between the two. The point where the two reach a balance of performance is the Nash equilibrium point. The performance at the Nash equilibrium point is the Nash optimal.

[0130] Control input u i Not only must consistent final bounded stability be guaranteed, but also L2 gain must be satisfied, that is, the attack energy is limited, which can be specifically expressed as:

[0131]

[0132] Among them, γ i >0 indicates the desired attack attenuation level;

[0133] Therefore, the design performance function is as follows:

[0134]

[0135] Among them, Q ii , R ij , R ii , P ii and P ij are all symmetric positive definite matrices with matching dimensions, represents the neighboring agent of the ith agent;

[0136] According to Pontryagin's maximum-minimum principle, the Nash equilibrium point The following inequality is satisfied:

[0137]

[0138] The Hamiltonian function is constructed as follows:

[0139]

[0140] in, represents the partial derivative of the performance function with respect to the bipartite consensus error;

[0141] Then the corresponding HJI equation can be expressed as:

[0142] According to the theory of adaptive dynamic programming, the specific form of the Nash equilibrium point is:

[0143]

[0144] Based on the expression of Nash equilibrium point, the HJI equation can be specifically expressed as:

[0145]

[0146] in,

[0147] Step 4: Based on the design of the Nash equilibrium point in step 3, design the HJI equation and optimal Nash strategy based on dynamic event triggering. The specific process is as follows:

[0148] definition is the kth triggering moment and satisfies The current status With sampling status The error between them can be expressed as:

[0149]

[0150] Furthermore, the bipartite consistency error triggered by dynamic events has the following form:

[0151]

[0152] Then the dynamic event trigger error is expressed as:

[0153]

[0154] Considering that FDI attack is an external output and uncontrollable, the specific forms of the optimal control strategy based on dynamic event triggering and the optimal FDI attack strategy based on time triggering are:

[0155]

[0156] Combining the above results with the HJI equation in step 3, the specific form of the HJI equation based on dynamic event triggering is obtained as follows:

[0157]

[0158] Step 5: The specific process of designing a dynamic event trigger mechanism is as follows:

[0159] According to the HJI equation based on dynamic event triggering in step 4, the dynamic event triggering mechanism is designed as follows:

[0160]

[0161] Among them, T DED is the dynamic trigger threshold, and

[0162]

[0163] Design dynamic parameters The change law is as follows:

[0164]

[0165] in,

[0166]

[0167] Step 6: Design a single evaluation network model based on a neural network to approximate the performance function in step 3, and obtain an approximate solution to the Nash equilibrium point triggered by dynamic events. The specific process is as follows:

[0168] The form of constructing a single evaluation network based on a neural network is:

[0169]

[0170] in, is the ideal weight vector, h ci is the number of neurons in the hidden layer, S c (∈ i ) is a differentiable continuous activation function, o(∈ i ) is the approximation error;

[0171] The performance function gradient is expressed as:

[0172]

[0173] in, is the gradient value of the activation function, is the gradient value of the approximation error;

[0174] Considering that the ideal weight vector is an unknown quantity and cannot be directly obtained, the estimated form of the approximate value of the gradient value of the construction performance function is:

[0175]

[0176] in, W ci The estimated form.

[0177] Then the estimated value of the optimal control strategy based on dynamic event triggering and the approximate value of the optimal FDI attack strategy based on time triggering in step 4 is:

[0178]

[0179] Combining the above results with the HJI equation based on dynamic event triggering in step 4, the estimated form of its approximate value is:

[0180]

[0181] in,

[0182]

[0183] Step 7: According to the Bellman residual generated in the approximation process in step 6, the weight change law of the single evaluation network in step 6 is trained using the gradient descent method until convergence. The specific process is as follows:

[0184] The Bellman residual generated during the approximation process in step 6 is Define it as:

[0185]

[0186] The design optimization objective function is:

[0187] Based on this function, using the gradient descent method, the specific form of the change law of the weight of the single evaluation network in step 6 can be obtained as follows:

[0188]

[0189] Among them, 0<μ i <1 is the design parameter;

[0190] Substitute the obtained weight value into the expression form of control input,

[0191]

[0192] The control input of the system can be obtained.

[0193] The system of the present invention is also stable under event triggering conditions, for the following reasons:

[0194] Define the approximation error of the neural network weights as Then the dynamic equation of the error system is:

[0195]

[0196] in, Used to ensure continuous motivation of the neural network learning process;

[0197] Considering that the optimal control input is sampled based on the dynamic event trigger mechanism, the continuous closed-loop system becomes a jump system; define the augmented variable The specific form of the dynamic equation of the augmented variable is:

[0198]

[0199] in,

[0200] It can be seen from the above formula that even when the system is at a jump time point, the augmented variable of the system tends to a fixed value, that is, when the control input is updated, the jump point will not make the system unstable.

[0201] Example 1

[0202] A multi-agent system consisting of five followers and one leader is adopted. Assume that the specific form of the input command of the external human expert is:

[0203]

[0204] The schematic diagram of the communication topology is as follows Figure 2 As shown in the figure, the agents are divided into cooperative and competitive relationships. Red and black represent two groups of agents, respectively. Agents of the same color are in a cooperative relationship, while agents of different colors are in a competitive relationship.

[0205] Figure 3 It is the state consistency curve of the intelligent agents. It can be seen from the figure that the states of agents 1 and 2 can be consistent with the leader, and the states of the remaining intelligent agents are consistent with the leader's state in size but opposite in sign, achieving bipartite consistency. In addition, external human experts can send instructions to the leader to adjust the leader's trajectory in time, so that the multi-agent system can avoid sudden obstacles and improve the safety and reliability of the system.

[0206] Figure 4 It is the bipartite consistency error curve of the agent. It can be seen that the bipartite consistency error can converge to a very small area near zero, thus ensuring the realization of bipartite consistency.

[0207] Figure 5 and Figure 6 (a)-(e) are the FDI attack curve and optimal control input curve of the intelligent agent, respectively. It can be seen that the designed optimal attack strategy is bounded and convergent, and conforms to the characteristics of time triggering; the optimal control input is in sampling form, which conforms to the characteristics of dynamic event triggering, effectively reduces the number of triggering times, and saves communication resources.

[0208] Figure 7 The graph is a graph of the weight change of the single evaluation neural network of the intelligent agent, which shows the boundedness and convergence of the gain. It shows that the convergence of the game optimization algorithm based on neural network approximation in the present invention can be guaranteed, which is also a necessary condition for the Nash equilibrium point to converge to the optimal one.

[0209] Figure 8The curve diagram of the trigger interval of the dynamic event trigger of the intelligent agent. It can be seen that the dynamic event trigger mechanism designed by the present invention can effectively reduce the number of triggers, save communication resources, and effectively avoid the Zeno phenomenon. The control scheme is still effective and superior under FDI attack.

[0210] The above description is only a specific implementation mode of the present invention. Any feature disclosed in this specification, unless otherwise stated, can be replaced by other alternative features that are equivalent or have similar purposes; all the disclosed features, or all the steps in the methods or processes, except for mutually exclusive features and / or steps, can be combined in any way.

Claims

1. An optimization control method for a human-in-the-loop multi-agent system under FDI attack, characterized in that: The following steps are involved: Step 1: Construct a dynamic model of a non-fully autonomous multi-agent system, including the dynamic equations of externally controlled leaders and followers, where the external human expert command signal is unknown; Step 2: Based on the dynamic model of the multi-agent system constructed in step 1, consider the FDI attack on the follower controller to the actuator end, and construct a dynamic model of the agent system attacked by FDI; Step 3: Based on the dynamic model of the agent system attacked by FDI obtained in step 2, design the performance function and find the Nash equilibrium point for each agent, that is, the Nash optimal strategy of the attacker and the defender; Step 4: Based on the Nash equilibrium point in step 3, design the HJI equation and Nash optimal strategy based on dynamic event triggering; Step 5: According to the HJI equation based on dynamic event triggering obtained in step 4, a dynamic event triggering mechanism is designed to save network resource overhead; Step 6: Design a single evaluation network model based on a neural network to approximate the performance function in step 3, and obtain an approximate solution to the Nash equilibrium point triggered by dynamic events; Step 7: Based on the Bellman residual generated in the approximation process in step 6, the gradient descent method is used to generate the weight change law of the single evaluation network in step 6 until convergence, and the control input can be obtained based on the weight result.

2. The optimization control method of a human-in-the-loop multi-agent system under FDI attack as claimed in claim 1, characterized in that: In step 1, a non-fully autonomous multi-agent system is established, including a leader and N followers. The multi-agent system is specifically: Leaders: Followers: in, represents the derivative, the subscript i is the number of a single agent system, i = 1, 2, ..., N, represents the system state of agent i, represents the control input of agent i, represents the internal dynamics of agent i, represents the output dynamics of agent i; represents the system state of the leader, represents an unknown and non-zero command signal sent by an external human expert to the leader, Represents the internal dynamics of the leader, Represents the output dynamics of the leader.

3. The optimization control method of a human-in-the-loop multi-agent system under FDI attack as claimed in claim 2, characterized in that: In step 2, the specific process of establishing the dynamic model of the i-th agent system attacked by FDI is as follows: Considering the FDI attack on the channel from the controller of agent i to the actuator, the control input of agent i under FDI attack is: Among them, u i for u i (t) is the abbreviation of i Input for FDI attack; The dynamic model of the i-th agent attacked by FDI can be expressed as: in, It is the state of the system being attacked.

4. The optimization control method of a human-in-the-loop multi-agent system under FDI attack as claimed in claim 3, characterized in that: The attacker must meet the following conditions: (1) All actuators may be attacked by attackers at any time. (2) State variables can be monitored in real time and provided as information to attackers. (3) False data and control signals can be injected into the actuator synchronously. (4) The attacker’s energy is limited.

5. The optimization control method of a human-in-the-loop multi-agent system under FDI attack as claimed in claim 3, characterized in that: The specific process of step 3 is: The dynamic equation defining the bipartite consistency error of the ith agent is: in, a ij is the connection weight between agent i and agent j, if a ij >0 means that agent i and agent j are in a cooperative relationship. ij <0 means that agent i and agent j are in a competitive relationship; b i is the connection weight between agent i and the leader, if b i >0 means that there is a cooperative relationship between agent i and the leader, otherwise, there is a competitive relationship; represents the degree matrix and According to game theory, the expected performance of control input is improved while the expected performance of external FDI attack is reduced. There is an antagonistic relationship between the two, and when the performance of the two reaches the optimal equilibrium, a Nash equilibrium point can be formed. Therefore, the design performance function is in the following form: Among them, γ i represents the expected attack attenuation level, γ i >0, Q ii , R ij , R ii , P ii and P ij are all symmetric positive definite matrices with matching dimensions, represents the neighboring agent of the ith agent; According to Pontryagin's maximum-minimum principle, the Nash equilibrium point The following inequality is satisfied: The Hamiltonian function is constructed as follows: in, represents the partial derivative of the performance function with respect to the bipartite consensus error; The corresponding HJI (Hamilton-Jacobi-Isaacs) equation can be expressed as: According to the theory of adaptive dynamic programming, the specific form of the Nash equilibrium point is:

6. The optimization control method of a human-in-the-loop multi-agent system under FDI attack as claimed in claim 5, characterized in that: The specific process of step 4 is: definition is the kth triggering moment, and satisfies The current status With sampling status The error between them can be expressed as: The two-part consistency error based on dynamic event triggering has the following form: The dynamic event trigger error is expressed as: Considering that FDI attack is an external output and uncontrollable, the specific forms of the optimal control strategy based on dynamic event triggering and the optimal FDI attack strategy based on time triggering are: Combining the above results with the HJI equation, the specific form of the HJI equation based on dynamic event triggering is obtained as follows:

7. The optimization control method of a human-in-the-loop multi-agent system under FDI attack as claimed in claim 6, characterized in that: The specific process of step 5 is: according to the HJI equation based on dynamic event triggering in step 4, the dynamic event triggering mechanism is designed as follows: Among them, T DED is the dynamic trigger threshold, and λ min (Q ii ) represents the matrix Q ii The smallest eigenvalue of i,1 is the design parameter, 0<ν i,1 <1, Design dynamic parameter θ i The change law is as follows: in, 8. The optimization control method of a human-in-the-loop multi-agent system under FDI attack as claimed in claim 7, characterized in that: The specific process of step 6 is: A single evaluation network model based on a neural network is designed to approximate the performance function in step 3. The specific expression of the single evaluation network model based on a neural network is: in, is the ideal weight vector, h ci is the number of neurons in the hidden layer, S c (∈ i ) is a differentiable continuous activation function, o(∈ i ) is the approximation error; The performance function gradient is expressed as: in, is the gradient value of the activation function, is the gradient of the approximation error. Considering that the ideal weight vector is an unknown quantity and cannot be directly obtained, the estimated form of the approximate value of the gradient value of the construction performance function is: in, W ci estimated form.

9. The optimization control method of a human-in-the-loop multi-agent system under FDI attack as claimed in claim 8, characterized in that: The estimated form of the approximate value of the optimal control strategy based on dynamic event triggering and the optimal FDI attack strategy based on time triggering in step 4 is: Combining the above results with the HJI equation based on dynamic event triggering in step 4, the estimated form of its approximate value is: in, 10. The optimization control method of a human-in-the-loop multi-agent system under FDI attack as claimed in claim 9, characterized in that: The specific process of step 7 is: The Bellman residual generated in the approximation process in step 6 is The Bellman residual is defined as: The design optimization objective function is: Based on this function, using the gradient descent method, the specific form of the change law of the weight of the single evaluation network in step 6 can be obtained as follows: Among them, 0<μ i <1 is the design parameter; Substitute the obtained weight value into the expression form of control input, The control input of the system can be obtained.

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