Distributed optimization method, device, and storage medium for multi-agent systems triggered by dynamic elastic events under DoS attacks

Abstract

The present invention discloses a distributed optimization method, device, and storage medium for a multi-agent system triggered by dynamic elastic events under DoS attacks. The distributed optimization method for a multi-agent system triggered by dynamic elastic events under DoS attacks includes: obtaining elastic event triggering data, using the elastic event triggering data to trigger a heterogeneous linear multi-agent system model to perform distributed optimization of the multi-agent system, and obtaining an optimal solution for the distributed optimization method; and introducing auxiliary variables to resolve imbalance problems caused by directed unbalanced topological graphs. The present invention discloses a distributed optimization method, device, and storage medium for a multi-agent system triggered by dynamic elastic events under DoS attacks. Based on a heterogeneous linear multi-agent system, the method introduces a dynamic elastic event triggering mechanism to save communication resources, thereby improving the efficiency of solving distributed optimization problems while ensuring system security.

Description

Technical Field

[0001] The present invention relates to the technical field of distributed optimization of multi-agent systems, and in particular to a distributed optimization method, device, and storage medium for a multi-agent system triggered by dynamic elastic events under DoS attacks. Background Art

[0002] In existing technologies, multi-agent systems are composed of numerous independent agents, each with its own goals and decision-making autonomy. These agents collaborate to complete diverse and complex tasks. In distributed optimization problems in multi-agent systems, each agent has a local objective function and certain constraints. The sum of all local objective functions is the global objective function. The distributed optimization problem that the system needs to solve is to ensure that all agents converge to the optimal solution that minimizes the global objective function while satisfying the constraints.

[0003] Furthermore, as industrial networks evolve from closed local area networks to the open Industrial Internet, the openness of network environments continues to increase. In these open communication networks, the risk of data being illegally intercepted, accidentally lost, or maliciously tampered with by agents while performing data transmission tasks increases significantly. This not only threatens the independent operation of agents but also poses unprecedented challenges to the stability and security of the entire multi-agent system. For example, DoS attacks can disrupt communication between agents, causing system topology switching, and impacting the convergence speed and stability of designed distributed optimization methods, as well as the quality of the optimal solution.

[0004] Furthermore, agents need to exchange state information across a communication network to calculate and update their own states. Generally speaking, continuous communication between agents is impractical. Traditional MASs typically perform control tasks using a weekly triggering method to periodically sample and transmit state data, which is then used to update control strategies and agent states. However, such frequent data transmission and control updates still place significant pressure on the limited bandwidth of communication networks and result in excessive computational overhead for control and actuators. Summary of the Invention

[0005] The present invention overcomes the shortcomings of the existing technology and provides a distributed optimization method, device, and storage medium for a multi-agent system triggered by dynamic elastic events under DoS attacks. Based on a heterogeneous linear multi-agent system, a dynamic elastic event triggering mechanism is introduced to save communication resources, thereby improving the efficiency of solving distributed optimization problems while ensuring system security.

[0006] In a preferred embodiment of the present invention, a distributed optimization method for a multi-agent system triggered by dynamic elastic events under DoS attacks includes:

[0007] Get elastic event trigger data,

[0008] The elastic event triggering data triggers the heterogeneous linear multi-agent system model to perform distributed optimization of the multi-agent system to obtain the optimal solution of the distributed optimization method;

[0009] The elastic event triggering data includes, when the communication network is subjected to a DoS attack, the DoS attack causes the heterogeneous linear multi-agent system to switch between an undirected topology and a directed unbalanced topology;

[0010] In the heterogeneous linear multi-agent system model, auxiliary variables are introduced by optimizing the controller to solve the imbalance problem caused by the directed unbalanced topology graph; and through the dynamic elastic event triggering mechanism, a distributed optimization method based on dynamic elastic event triggering is obtained.

[0011] In a preferred embodiment of the present invention, the heterogeneous linear multi-agent system model comprising N agents includes:

[0012] ;

[0013] Where t is the time, the state of agent i is , control input and output , , and Respectively , and -dimensional real vector; , and are the constant matrices of agent i, , and Respectively , and dimensional real matrix.

[0014] In a preferred embodiment of the present invention, the consistency distributed optimization problem that needs to be solved in the heterogeneous linear multi-agent system model is the output value of each agent Uniformly converge to the optimal solution of the optimization problem Department;

[0015] The following algorithms are included:

[0016] ; ;

[0017] in, is the local objective function of agent i, ; is the global objective function of the system, ; is the consistency constraint in the distributed optimization problem, is the stack of N agent outputs, i.e. the output of the entire system, where the superscript T represents the transpose operation; is the abbreviation for satisfying the constraint; is the Laplace matrix, is the Kronecker product, is the q-dimensional identity matrix;

[0018] When the heterogeneous linear multi-agent system model converges uniformly to the optimal solution of the optimization problem When , the global objective function reaches its minimum, then the system solves the distributed optimization problem.

[0019] In a preferred embodiment of the present invention, DoS attacks are modeled by constraining the number and duration of attacks;

[0020] The number of DoS attack constraints on the heterogeneous linear multi-agent system model includes: ;

[0021] The duration constraints of the DoS attack on the heterogeneous linear multi-agent system model include:

[0022] ;

[0023] in, and Respectively indicate the time period The number and duration of internal attacks, and are the corresponding constraint parameters, and are the initial values ​​of the corresponding number of attacks and duration respectively.

[0024] In a preferred solution of the present invention, a DoS attack may destroy the communication channels between agents, causing the communication topology of the system to switch;

[0025] Since the communication topology of heterogeneous linear multi-agent systems is an undirected graph and a directed unbalanced graph, Indicates the occurrence signal of DoS attack, that is, the switching signal of system topology; is a piecewise function, when When , the heterogeneous linear multi-agent system does not suffer from DoS attack. When >0, the heterogeneous linear multi-agent system is subjected to DoS attack;

[0026] use represents the communication topology of a heterogeneous linear multi-agent system at time t, is the topological set of the system, where is the original topology of the heterogeneous linear multi-agent system before it suffers a DoS attack. It is the topology type p that the heterogeneous linear multi-agent system switches to when it suffers a DoS attack.

[0027] In a preferred embodiment of the present invention, the optimization controller adopts a distributed optimization controller constructed by combining a consistency control method and a gradient-based optimization method;

[0028] When the topology of a heterogeneous linear multi-agent system is an undirected graph, a distributed optimization controller is constructed by combining the consistency control method with the gradient-based optimization method. The distributed optimization controller includes the following algorithms: ;

[0029] in, , and are the control input, state and output of agent i respectively; and are the auxiliary states of agent i; and is the output state of agents i and j at the triggering moment; α and β are both positive control parameters; is the local objective function The gradient, is the connection weight between agent i and agent j, Indicates that a DoS attack will cause the connection weight between agents i and j to switch between 0 and 1. is the parameter gain control matrix;

[0030] , , is the gain matrix of agent i. The matrix equality conditions that need to be satisfied include: ,in and represent and dimensional zero matrix.

[0031] In a preferred embodiment of the present invention, when the topology of the heterogeneous linear multi-agent system is a directed unbalanced graph, an auxiliary variable is introduced into the distributed optimization controller. An improved distributed optimization controller is obtained to solve the distributed optimization problem of heterogeneous multi-agent systems caused by directed unbalanced topology graphs:

[0032] The improved distributed optimization controller includes:

[0033] ;

[0034] in, is the auxiliary state variable of the j-th agent.

[0035] In a preferred embodiment of the present invention, the output value of each agent is used to design a dynamic elastic event triggering mechanism to determine the trigger value of each agent. , including the following steps:

[0036] Using the output value error of agent i at the trigger time and time t The error value between the neighbor agent j and the neighbor agent j at the triggering time Get the dynamic elastic event triggering mechanism, where is the adjacency index set of agent i; the triggering time sequence of each agent is determined by the dynamic elastic event triggering mechanism:

[0037] ;

[0038] in, and are the output values ​​of agents i and j at the triggering moment, and as well as These are all trigger parameters;

[0039] is an auxiliary dynamic variable, and the initial condition satisfies , the corresponding dynamic equation is:

[0040] ;

[0041] Among them, there are two trigger conditions, when , the system does not use trigger parameters when it is attacked and ; ; Indicates that the system is under attack, using trigger parameters and ; to increase the event triggering frequency during the attack period to reduce the impact of DoS attacks on the speed at which the system converges to the optimal solution.

[0042] In a preferred embodiment of the present invention, a distributed optimization device for a multi-agent system under DoS attack based on dynamic elastic event triggering is used to implement a distributed optimization method for a multi-agent system under DoS attack based on dynamic elastic event triggering; the method comprises:

[0043] An acquisition unit, configured to acquire elastic event triggering data;

[0044] a processing unit configured to trigger a heterogeneous linear multi-agent system model according to the elastic event trigger data to perform distributed optimization of the multi-agent system and obtain an optimal solution of the distributed optimization method;

[0045] The elastic event triggering data includes, when the communication network is subjected to a DoS attack, the DoS attack causes the heterogeneous linear multi-agent system to switch between an undirected topology and a directed unbalanced topology;

[0046] In the heterogeneous linear multi-agent system model, auxiliary variables are introduced into the optimization controller to solve the imbalance problem caused by the directed unbalanced topology graph; and a distributed optimization method based on dynamic elastic event triggering is obtained through the dynamic elastic event triggering mechanism.

[0047] An output unit is used to output the optimal solution of the distributed optimization method obtained by the heterogeneous linear multi-agent system model.

[0048] In a preferred embodiment of the present invention, a storage medium for distributed optimization of a multi-agent system triggered by dynamic elastic events under DoS attacks is used to implement the steps of a distributed optimization method for a multi-agent system triggered by dynamic elastic events under DoS attacks.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] The present invention discloses a distributed optimization method, device, and storage medium for a multi-agent system triggered by dynamic elastic events under DoS attacks. Based on a heterogeneous linear multi-agent system, a dynamic elastic event triggering mechanism is introduced to save communication resources, thereby improving the efficiency of solving distributed optimization problems while ensuring system security.

[0051] To better address distributed optimization problems in real-world physical environments, this paper examines heterogeneous linear multi-agent systems, demonstrating their greater challenges and research value. Furthermore, given the vulnerability of communication networks, which are often subject to cyberattacks, DoS attacks can even cause the system's communication topology to switch, impacting the system's convergence performance and ability to solve distributed optimization problems, potentially preventing the optimal solution.

[0052] This paper considers both undirected and directed unbalanced graph communication environments, designing and improving the controller to achieve consistent system convergence to the optimal solution to the distributed optimization problem. Furthermore, to mitigate the impact of DoS attacks on system performance, reduce communication costs, and minimize the waste of communication resources, a dynamic elastic event triggering mechanism is incorporated into the optimization controller. This mechanism improves upon the existing dynamic event triggering mechanism and, compared to the dynamic event triggering mechanism, enhances system robustness and improves communication resource utilization. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] The present invention will be further described below with reference to the accompanying drawings and examples.

[0054] Figure 1 This is a flow chart of an embodiment of a multi-agent distributed optimization method based on dynamic elastic event triggering under DoS attack in a preferred embodiment of the present invention;

[0055] Figure 2 A DoS attack occurrence signal diagram in a preferred embodiment of the present invention;

[0056] Figure 3 The undirected network topology diagram of the heterogeneous linear multi-agent system and the topology switching diagram caused by DoS attack in the preferred embodiment of the present invention;

[0057] Figure 4 A directed unbalanced network topology diagram of a heterogeneous linear multi-agent system and a topology switching diagram resulting from a DoS attack in a preferred embodiment of the present invention;

[0058] Figure 5 The output error trajectory graph and the trajectory graph of the global objective function of the intelligent agent in the undirected topological graph in the preferred embodiment of the present invention are shown in FIG.

[0059] Figure 6 A triggering time distribution diagram of an intelligent agent in an undirected topological graph in a preferred embodiment of the present invention;

[0060] Figure 7 The output error trajectory graph of the intelligent agent and the trajectory graph of the global objective function under the directed unbalanced topology graph in the preferred embodiment of the present invention;

[0061] Figure 8 A triggering time distribution diagram of intelligent agents in a directed unbalanced topology diagram in a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0062] The technical solution of the present invention is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations on the technical solution of the present invention. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0063] The term "and / or" simply describes a relationship between related objects, indicating that three possible relationships exist. For example, "A and / or B" can mean: A exists alone, A and B exist simultaneously, or B exists alone. Additionally, the character " / " generally indicates an "or" relationship between the related objects.

[0064] Embodiment 1, a distributed optimization method for a multi-agent system triggered by dynamic elastic events under DoS attacks, comprising:

[0065] Get elastic event trigger data,

[0066] The elastic event triggering data triggers the heterogeneous linear multi-agent system model to perform distributed optimization of the multi-agent system to obtain the optimal solution of the distributed optimization method;

[0067] The elastic event triggering data includes, when the communication network is subjected to a DoS attack, the DoS attack causes the heterogeneous linear multi-agent system to switch between an undirected topology and a directed unbalanced topology;

[0068] In the heterogeneous linear multi-agent system model, auxiliary variables are introduced by optimizing the controller to solve the imbalance problem caused by the directed unbalanced topology graph; and through the dynamic elastic event triggering mechanism, a distributed optimization method based on dynamic elastic event triggering is obtained.

[0069] In a preferred embodiment of the present invention, the heterogeneous linear multi-agent system model comprising N agents includes:

[0070] ;

[0071] Among them, the state of agent i , control input and output , , and Respectively , and is a real vector; , and are the constant matrices of agent i, , and Respectively , and dimensional real matrix.

[0072] In a preferred embodiment of the present invention, the consistency distributed optimization problem that needs to be solved in the heterogeneous linear multi-agent system model is the output value of each agent Uniformly converge to the optimal solution of the optimization problem Department;

[0073] The following algorithms are included:

[0074] ; ;

[0075] in, is the local objective function of agent i, ; is the global objective function of the system, ; is the consistency constraint in the distributed optimization problem, is the stack of N agent outputs, i.e. the output of the entire system, where the superscript T represents the transpose operation; is the abbreviation for satisfying the constraint; is the Laplace matrix, is the Kronecker product, is the q-dimensional identity matrix;

[0076] When the heterogeneous linear multi-agent system model converges uniformly to the optimal solution of the optimization problem When , the global objective function reaches its minimum, then the system solves the distributed optimization problem.

[0077] In a preferred embodiment of the present invention, DoS attacks are modeled by constraining the number and duration of attacks;

[0078] The number of DoS attack constraints on the heterogeneous linear multi-agent system model includes: ;

[0079] The duration constraints of DoS attacks on heterogeneous linear multi-agent system models include: ;

[0080] in, and Respectively indicate the time period The number and duration of internal attacks, and are the corresponding constraint parameters, and are the initial values ​​of the corresponding number of attacks and duration respectively.

[0081] In a preferred solution of the present invention, a DoS attack may destroy the communication channels between agents, causing the communication topology of the system to switch;

[0082] Since the communication topology of heterogeneous linear multi-agent systems is an undirected graph and a directed unbalanced graph, Indicates the occurrence signal of DoS attack, that is, the switching signal of system topology; is a piecewise function, when When , the heterogeneous linear multi-agent system does not suffer from DoS attack. When , the heterogeneous linear multi-agent system suffers from DoS attack;

[0083] use represents the communication topology of a heterogeneous linear multi-agent system at time t, is the topological set of the system, where is the original topology of the heterogeneous linear multi-agent system before it suffers a DoS attack. It is the topology type p that the heterogeneous linear multi-agent system switches to when it suffers a DoS attack.

[0084] In a preferred embodiment of the present invention, the optimization controller is a distributed optimization controller constructed by combining a consistency control method and a gradient-based optimization method.

[0085] When the topology of a heterogeneous linear multi-agent system is an undirected graph, a distributed optimization controller is constructed by combining the consistency control method with the gradient-based optimization method. The distributed optimization controller includes the following algorithms: ;

[0086] in, , and are the control input, state and output of agent i respectively. and are the auxiliary states of agent i; and is the output state of agents i and j at the triggering moment; α and β are both positive control parameters; is the local objective function The gradient, is the connection weight between agent i and agent j, Indicates that a DoS attack will cause the connection weight between agents i and j to switch between 0 and 1. is the parameter gain control matrix; , , is the gain matrix of agent i. The matrix equality conditions that need to be satisfied include: ,in and represent and dimensional zero matrix.

[0087] In a preferred embodiment of the present invention, when the topology of the heterogeneous linear multi-agent system is a directed unbalanced graph, an auxiliary variable is introduced into the distributed optimization controller. An improved distributed optimization controller is obtained to solve the distributed optimization problem of heterogeneous multi-agent systems caused by directed unbalanced topology graphs:

[0088] The improved distributed optimization controller includes:

[0089] ;

[0090] in, is the auxiliary state variable of the j-th agent.

[0091] In a preferred embodiment of the present invention, the output value of each agent is used to design a dynamic elastic event triggering mechanism to determine the trigger value of each agent. , including the following steps:

[0092] Using the output value error of agent i at the trigger time and time t The error value between the neighbor agent j and the neighbor agent j at the triggering time Get the dynamic elastic event triggering mechanism, where is the set of adjacent indexes of agent i. The triggering time sequence of each agent is determined by the dynamic elastic event triggering mechanism:

[0093] ;

[0094] in, and are the output values ​​of agents i and j at the triggering moment, and as well as These are all trigger parameters; is an auxiliary dynamic variable, and the initial condition satisfies , the corresponding dynamic equation is:

[0095] ;

[0096] Among them, there are two trigger conditions, when , the system does not use trigger parameters when it is attacked and ; ; Indicates that the system is under attack, using trigger parameters and ; to increase the event triggering frequency during the attack period to reduce the impact of DoS attacks on the speed at which the system converges to the optimal solution.

[0097] Example 2, see Figure 1 As shown, this embodiment discloses a multi-agent distributed optimization method based on dynamic elastic event triggering under DoS attack, including the following steps:

[0098] Step S1: Construct a model of a heterogeneous linear multi-agent system and design the consistent distributed optimization problem that the system needs to solve;

[0099] Step S2: Considering that the system's communication network may be subject to a DoS attack, the attack causes the heterogeneous linear multi-agent system to switch between an undirected topology and a directed unbalanced topology; combining the consistency control method with the gradient-based optimization method to construct an optimized controller, and further introducing an additional window top;

[0100] Step S3: Combining the consistency control method with the gradient-based optimization method to construct an optimized controller, further introducing additional auxiliary variables to solve the imbalance problem caused by the directed unbalanced topology graph;

[0101] Step S4: Introduce a dynamic elastic event triggering mechanism and propose a distributed optimization method based on dynamic elastic event triggering.

[0102] The optimized controller is integrated into the multi-agent system to solve the given distributed optimization problem. The following is the detailed design process:

[0103] Consider a heterogeneous linear multi-agent system with N agents. The dynamic equation of the i-th agent is:

[0104] ;

[0105] Where t is the time, the state of agent i is , control input and output , , and Respectively , and -dimensional real vector; , and are the constant matrices of agent i, , and Respectively , and dimensional real matrix.

[0106] Assumption 1: For , the matrix pair is controllable, and the following equations are satisfied: ;in, yes A matrix whose dimensions are all zero, , and q are positive integers related to the dimensions of the state vector, input vector, and output vector of agent i, respectively.

[0107] Next, the distributed optimization problem that needs to be solved in the system design is considered in this paper. The consistency distributed optimization problem is considered, that is, each agent needs to satisfy the consistency constraint and have its own output value. The sum of the local objective functions of N agents is the global objective function, and the distributed optimization problem that needs to be solved is that the output values ​​of all agents can converge to the optimal solution of the optimization problem. The optimal solution The global objective function can be minimized, and the following is the designed distributed optimization problem:

[0108] ; ;in, is the local objective function of agent i, ; is the global objective function of the system, ; is the consistency constraint in the distributed optimization problem, is the stack of N agent outputs, i.e. the output of the entire system, where the superscript T represents the transpose operation; is the abbreviation for satisfying the constraint; is the Laplace matrix, is the Kronecker product, is the q-dimensional identity matrix; when the system converges uniformly to the optimal solution of the optimization problem When , the global objective function reaches its minimum, which means that the system solves the distributed optimization problem. In order to ensure the uniqueness of the optimal solution, the local objective function needs to assume the strong convexity of the two conditions and the Lipschitz continuity of its gradient.

[0109] Assumption 2: Local objective function is continuously differentiable and strongly convex, for constant ; then the inequality holds: ;

[0110] Each local objective function The gradient is Lipschitz continuous, for constant , then the inequality holds:

[0111] Considering that DoS attacks may cause the switching of the communication topology of the multi-agent system, a piecewise constant function is introduced. To describe the moment when the DoS attack occurs and the type of system topology switched to: ;in It represents a set of positive natural numbers, and also represents the set of communication topology types that may appear when an attack occurs, while 0 represents the original communication topology of the system when the attack occurs. For a more intuitive representation, the present invention considers two communication environments: undirected topology graph and directed unbalanced topology graph. Figure 2 middle During the time period, the system's communication topology will switch from the original topology to topology 1. At time t, the system's communication topology is represented as , then the possible topological graph set is expressed as , accordingly, its Laplace matrix set is expressed as Since DoS attacks cannot be sustained for a long time, it is necessary to restrict the number of DoS attacks and their duration. The number and duration of attacks within a time period need to satisfy assumption 3.

[0112] Assumption 3: In any period of time , there exists a positive constant and ; Not attacked Communication topology and attacks Number of switches between topologies The following constraints are met: ; and the duration of the attack The following constraints are met: ;in, and Respectively indicate the time period The number and duration of internal attacks, and are the corresponding constraint parameters, and are the initial values ​​of the corresponding number of attacks and duration respectively.

[0113] When the system's communication topology is an undirected graph and is attacked, the following distributed optimization controller is constructed by combining the consistency control method with the gradient-based optimization method:

[0114] ;

[0115] in, , and are the control input, state and output of agent i respectively; and are the auxiliary states of agent i; and is the output state of agents i and j at the triggering moment; α and β are both positive control parameters; is the local objective function Since DoS attacks randomly interrupt the communication channels between agents, they will affect the connection weights between agents. is the connection weight between agent i and agent j, Indicates that a DoS attack will cause the connection weight between agents i and j to switch between 0 and 1. Indicates that the communication channel between agents i and j is interrupted by DoS attack, and It means that they can communicate normally and are not affected by the attack. is the parameter gain control matrix; , , is the gain matrix of agent i. In order to ensure the effectiveness of the distributed optimization controller, the matrix equality conditions that need to be satisfied include: ;in and represent and dimensional zero matrix.

[0116] By introducing this controller into a heterogeneous linear multi-agent system, we can obtain the following compact form of the closed-loop system:

[0117] ;

[0118] in, , , which represent the states of N agents respectively , auxiliary status , and output A stack of , i=1,2,...,N. is the constant matrix of the system, It is represented by N constant matrices The diagonal elements are composed of the matrix, while the other matrices are constant matrices , control matrix and the gain matrix The same is true for diagonal matrices of this class, and , equalize the system to 0, and the equilibrium point of the system is , is the equilibrium state of the system, and are all auxiliary variables of the system's equilibrium. Then, by assuming And use Multiplying the last two equations of the closed-loop system on the left, we can get the equilibrium point and The equation holds, where is the transpose of the N-dimensional unit vector. From the fact that the global objective function is equal to 0 at the equilibrium point, we can know that the optimal solution to the distributed optimization problem is At the balance point Then, using the matrix equality conditions mentioned above, the equilibrium point can be rewritten as: Then the distributed optimization problem of heterogeneous linear multi-agent systems can be transformed into the problem of system consistency and stability.

[0119] When the system topology is a directed unbalanced graph, additional auxiliary variables are introduced to solve the imbalance problem caused by the directed unbalanced topology. The following improved distributed optimization controller is further obtained to solve the distributed optimization problem of heterogeneous multi-agent systems under directed unbalanced topology:

[0120] ;in, is the auxiliary state variable of the jth agent; in the gradient part of the local objective function, , yes The i-th element of the vector, Needs to be satisfied and The controller can solve the distributed optimization problem of the design only when . Its role is: due to the influence of the directed unbalanced topology, its corresponding Laplace matrix There is no eigenvector corresponding to an eigenvalue of 0 such that , which causes the original controller to make the system unable to search for the optimal solution. However, there is a left eigenvector make established, and , represents a positive real number, is the transpose of the left eigenvector.

[0121] pass get: ,in , from which we can know Can be used to estimate the left eigenvector of agent i , in order to eliminate the impact of imbalance problems on finding the optimal solution. The closed-loop system formed by multiplying the controller on the left is:

[0122] ;

[0123] in, is an N-order diagonal matrix, , For the diagonal matrix constructor, the equilibrium point is the optimal solution, and the distributed optimization problem of heterogeneous linear multi-agent system can be transformed into the consistency stability problem of the system.

[0124] In order to reduce the communication burden, the output value of each agent is used to design a dynamic elastic event triggering mechanism to determine the trigger value of each agent. , and then use the output value error of agent i at the trigger time and time t The error value between the neighbor agent j and the neighbor agent j at the triggering time Get two trigger functions and To determine the two trigger conditions, is the set of adjacent indexes of agent i, then the triggering time sequence of each agent can be determined by the following formula:

[0125] ;

[0126] in, and are the output values ​​of agents i and j at the triggering moment, , and These are trigger parameters. is an auxiliary dynamic variable, and the initial condition satisfies , and its dynamic equation is:

[0127] ;

[0128] The dynamic elastic event trigger mechanism is improved on the basis of the general dynamic event trigger mechanism. Considering that the system may be subject to DoS attacks, two trigger conditions and two auxiliary dynamic variable dynamic equations are designed. That is, when the system is not under attack, use the trigger parameter and , Indicates that the system is under attack, using trigger parameters and ; to increase the event triggering frequency during the attack period to reduce the impact of DoS attacks on the speed at which the system converges to the optimal solution.

[0129] By combining the dynamic elastic event triggering mechanism with the distributed optimization controller and transforming the distributed optimization problem into the system consistency stability problem, the Lyapunov stability theorem can be designed to obtain the state of the system. The exponential convergence to the equilibrium point shows that the designed distributed optimization controller based on the dynamic elastic event triggering mechanism can enable the heterogeneous linear multi-agent system to converge consistently to the optimal solution of the distributed optimization problem in the presence of DoS attacks, effectively and successfully solving the distributed optimization problem.

[0130] Example 3, a distributed optimization device for a multi-agent system triggered by dynamic elastic events under DoS attacks, comprising:

[0131] An acquisition unit, configured to acquire elastic event triggering data;

[0132] a processing unit configured to trigger a heterogeneous linear multi-agent system model according to the elastic event trigger data to perform distributed optimization of the multi-agent system and obtain an optimal solution of the distributed optimization method;

[0133] The elastic event triggering data includes, when the communication network is subjected to a DoS attack, the DoS attack causes the heterogeneous linear multi-agent system to switch between an undirected topology and a directed unbalanced topology;

[0134] In the heterogeneous linear multi-agent system model, auxiliary variables are introduced into the optimization controller to solve the imbalance problem caused by the directed unbalanced topology graph; and a distributed optimization method based on dynamic elastic event triggering is obtained through the dynamic elastic event triggering mechanism.

[0135] An output unit is used to output the optimal solution of the distributed optimization method obtained by the heterogeneous linear multi-agent system model.

[0136] Example 4, a storage medium for distributed optimization of a multi-agent system triggered by dynamic elastic events under DoS attacks, is used to implement the steps of a distributed optimization method for a multi-agent system triggered by dynamic elastic events under DoS attacks in Example 1 or Example 2.

[0137] In the fifth embodiment, the distributed optimization method of a multi-agent system based on dynamic elastic event triggering under a DoS attack of the second embodiment of the present invention is simulated, and the implementation of the present invention is described in detail.

[0138] Consider a heterogeneous linear multi-agent system consisting of 6 agents. The system matrix and control gain matrix of each agent are designed as follows:

[0139] ;

[0140] ;

[0141] ;

[0142] ;

[0143] ;

[0144] ;

[0145] ;

[0146] ;

[0147] like Figure 2 As shown in Figure 1, the signal graph of DoS attack is shown, and the attack will cause three signal graphs to switch. When the communication topology of the system is an undirected graph, the switching of the system topology is as follows: Figure 3 As shown. The local objective function designed for each agent is as follows:

[0148] ;

[0149] ;

[0150] Get the optimal solution to the distributed optimization problem: , using the method proposed in this invention, the control parameters of the distributed optimization controller are designed and trigger parameters such as Figure 5 As shown in the figure, the trajectory diagram of the error value between the output state of the six agents and the optimal solution and the trajectory diagram of the global objective function are obtained. It can be seen that the controller can successfully enable the system to solve the distributed optimization problem. The communication time diagram is shown in the figure. Figure 6 As shown, the dynamic elastic event triggering mechanism can effectively save communication resources.

[0151] When the communication topology of the system is a directed unbalanced graph, a similar DoS attack signal is used. The topology switching diagram caused by the attack is as follows: Figure 4 As shown, the local objective function designed for each agent is as follows:

[0152] ;

[0153] ;

[0154] The optimal solution found is: , the control parameters of the improved optimization controller are determined as: And select appropriate trigger parameters. Figure 7 The output error and global objective function trajectory of each agent in the directed imbalanced graph are shown. Figure 8 This is the communication triggering time diagram of each intelligent agent. It can be seen that the method proposed in the present invention can also successfully solve the distributed optimization problem under the directed unbalanced graph.

[0155] Working principle:

[0156] The present invention discloses a distributed optimization method, device, and storage medium for a multi-agent system triggered by dynamic elastic events under DoS attacks. Based on a heterogeneous linear multi-agent system, a dynamic elastic event triggering mechanism is introduced to conserve communication resources and improve the efficiency of solving distributed optimization problems while ensuring system security. To better address distributed optimization problems in real physical environments, the study of heterogeneous linear multi-agent systems presents a higher level of challenge and research value. Furthermore, given the vulnerability of communication networks, which are often subject to network attacks, DoS attacks can even cause system communication topology switching, impacting the system's convergence performance and ability to solve distributed optimization problems, potentially preventing the successful solution to the optimal solution. The present invention considers both undirected and directed unbalanced graph communication environments, designing and improving a controller to achieve consistent system convergence to the optimal solution for the distributed optimization problem. Furthermore, to mitigate the impact of DoS attacks on system performance, reduce communication costs, and minimize waste of communication resources, a dynamic elastic event triggering mechanism is incorporated into the optimization controller. This mechanism improves upon the existing dynamic event triggering mechanism and, compared to the dynamic event triggering mechanism, improves system robustness and communication resource utilization.

[0157] Based on the ideal embodiments of the present invention, and with reference to the above description, relevant personnel can make various changes and modifications without departing from the technical scope of the present invention. The technical scope of the present invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A distributed optimization method for a multi-agent system under DoS attack based on dynamic elastic event triggering, characterized in that: include: Get elastic event trigger data, The elastic event triggering data triggers the heterogeneous linear multi-agent system model to perform distributed optimization of the multi-agent system to obtain the optimal solution of the distributed optimization method; The elastic event triggering data includes, when the communication network is subjected to a DoS attack, the DoS attack causes the heterogeneous linear multi-agent system to switch between an undirected topology and a directed unbalanced topology; In the heterogeneous linear multi-agent system model, auxiliary variables are introduced into the optimization controller to solve the imbalance problem caused by the directed unbalanced topology graph; and a distributed optimization method based on dynamic elastic event triggering is obtained through the dynamic elastic event triggering mechanism. The heterogeneous linear multi-agent system model comprising N agents includes: ； Where t is the time, the state of agent i is , control input and output , , and Respectively , and -dimensional real vector; , and are the constant matrices of agent i, , and Respectively , and dimensional real matrix; The consistency distributed optimization problem that needs to be solved by the heterogeneous linear multi-agent system model is the output value of each agent. Uniformly converge to the optimal solution of the optimization problem Department; The following algorithms are included: ; ; in, is the local objective function of agent i, ; is the global objective function of the system, ; is the consistency constraint in the distributed optimization problem, is the stack of N agent outputs, i.e. the output of the entire system, where the superscript T represents the transpose operation; is the abbreviation for satisfying the constraint; is the Laplace matrix, is the Kronecker product, is the q-dimensional identity matrix; When the heterogeneous linear multi-agent system model converges uniformly to the optimal solution of the optimization problem When , the global objective function reaches its minimum value, then the system solves the distributed optimization problem; Modeling DoS attacks by constraining the number and duration of attacks; The number of DoS attack constraints on the heterogeneous linear multi-agent system model includes: The duration constraints of the DoS attack on the heterogeneous linear multi-agent system model include: ; in, and Respectively indicate the time period The number and duration of internal attacks, and are the corresponding constraint parameters, and are the initial values ​​of the corresponding number of attacks and duration; The optimization controller is constructed by combining a consistency control method and a gradient-based optimization method; When the topology of a heterogeneous linear multi-agent system is an undirected graph, a distributed optimization controller is constructed by combining the consistency control method with the gradient-based optimization method. The distributed optimization controller includes the following algorithms: ; in, , and are the control input, state and output of agent i respectively; and are the auxiliary states of agent i; and is the output state of agents i and j at the triggering moment; α and β are both positive control parameters; is the local objective function The gradient, is the connection weight between agent i and agent j, Indicates that a DoS attack will cause the connection weight between agents i and j to switch between 0 and 1. is the parameter gain control matrix; , , is the gain matrix of agent i. The matrix equality conditions that need to be satisfied include: ,in and represent and dimensional zero matrix; When the topology of a heterogeneous linear multi-agent system is a directed unbalanced graph, auxiliary variables are introduced into the distributed optimization controller. Obtain an improved distributed optimization controller, which can solve the distributed optimization problem of heterogeneous multi-agent systems caused by directed unbalanced topology graphs; The improved distributed optimization controller includes: ;in, is the auxiliary state variable of the j-th agent.

2. The distributed optimization method for a multi-agent system under DoS attack based on dynamic elastic event triggering according to claim 1, characterized in that: DoS attacks can destroy the communication channels between agents and cause the communication topology of the system to switch; Since the communication topology of heterogeneous linear multi-agent systems is an undirected graph and a directed unbalanced graph, Indicates the occurrence signal of DoS attack, that is, the switching signal of system topology; is a piecewise function, when When , the heterogeneous linear multi-agent system does not suffer from DoS attack. When , the heterogeneous linear multi-agent system suffers from DoS attack; use represents the communication topology of a heterogeneous linear multi-agent system at time t, is the topological set of the system, where is the original topology of the heterogeneous linear multi-agent system before it suffers a DoS attack. It is the topology type p that the heterogeneous linear multi-agent system switches to when it suffers a DoS attack.

3. The distributed optimization method for a multi-agent system under DoS attack based on dynamic elastic event triggering according to claim 2, characterized in that: Use the output value of each agent to design a dynamic elastic event triggering mechanism and determine the trigger value of each agent , including the following steps: Using the output value error of agent i at the trigger time and time t The error value between the neighbor agent j and the neighbor agent j at the triggering time Get the dynamic elastic event triggering mechanism, where is the adjacency index set of agent i; The triggering time sequence of each agent is determined by the dynamic elastic event triggering mechanism: ； in, and are the output values ​​of agents i and j at the triggering moment, and as well as These are all trigger parameters; is an auxiliary dynamic variable, and the initial condition satisfies , the corresponding dynamic equation is: ； Among them, there are two trigger conditions, when , the system does not use trigger parameters when it is attacked and ; ; Indicates that the system is under attack, using trigger parameters , and , ; to increase the event triggering frequency during the attack period to reduce the impact of DoS attacks on the speed at which the system converges to the optimal solution.

4. A distributed optimization device for a multi-agent system triggered by dynamic elastic events under DoS attacks, characterized in that: The steps for implementing a distributed optimization method for a multi-agent system triggered by dynamic elastic events under a DoS attack according to any one of claims 1 to 3 include: An acquisition unit, configured to acquire elastic event triggering data; a processing unit configured to trigger a heterogeneous linear multi-agent system model according to the elastic event trigger data to perform distributed optimization of the multi-agent system and obtain an optimal solution of the distributed optimization method; The elastic event triggering data includes, when the communication network is subjected to a DoS attack, the DoS attack causes the heterogeneous linear multi-agent system to switch between an undirected topology and a directed unbalanced topology; In the heterogeneous linear multi-agent system model, auxiliary variables are introduced into the optimization controller to solve the imbalance problem caused by the directed unbalanced topology graph; and a distributed optimization method based on dynamic elastic event triggering is obtained through the dynamic elastic event triggering mechanism. An output unit is used to output the optimal solution of the distributed optimization method obtained by the heterogeneous linear multi-agent system model.

5. A distributed optimized storage medium for a multi-agent system triggered by dynamic elastic events under DoS attacks, characterized in that: Steps for implementing a distributed optimization method for a multi-agent system triggered by dynamic elastic events under a DoS attack according to any one of claims 1-3.

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