Method for resource allocation of high-order multi-agent system based on event triggering mechanism

Abstract

This invention proposes a resource allocation method for high-order multi-agent systems based on an event-triggered mechanism, relating to the technical field of multi-agent resource allocation. First, a high-order multi-agent system is established. Then, a distributed resource allocation optimization model for the high-order multi-agent system is constructed based on the system. This model considers the resource requirements of each high-order agent, with the objective function being the minimization of global operating cost, and the constraints being the total network resources and total requirements of the high-order multi-agent system. Furthermore, an event-triggered mechanism is used to solve the constructed distributed resource allocation problem in a distributed manner. Finally, the high-order agents operate according to the obtained resource requirement values, ensuring the stability and convergence of the high-order multi-agent system under resource constraints. This effectively reduces the communication burden and cost of the high-order multi-agent system while ensuring optimal resource allocation.

Description

Technical Field

[0001] This invention relates to the technical field of multi-agent resource allocation, and in particular to a high-order multi-agent system resource allocation method based on an event-triggered mechanism. Background Technology

[0002] With the development of artificial intelligence and large-scale network technology, the research on resource allocation methods for high-order multi-agent systems has received increasing attention. An agent represents any entity with intelligence. Distributed resource allocation aims to ensure the balance between supply and demand of network resources and the resource constraints of the agents themselves, while minimizing the total cost of all agents in a distributed manner.

[0003] Currently, the basic idea behind RAP methods for solving the distributed resource allocation problem (RAP) is that agents share information through a network to achieve the optimal allocation scheme. Network environment and network resources are the foundation of distributed optimization. Information is transmitted between local decision-making agents through the network. Changes or instability in the network environment determine the security and integrity of information acquired by agents, affecting the effectiveness of decisions made based on that information. Therefore, changes in the network environment inevitably impact distributed optimization research. Existing technologies disclose a resource allocation method for high-order multi-agent systems. By optimizing the resource allocation algorithm, the stability and convergence of the high-order multi-agent system under resource constraints are guaranteed. However, while completing the resource allocation task, the communication burden of the high-order multi-agent system cannot be reduced; that is, the communication frequency between high-order multi-agents cannot be reduced under the premise of optimal resource allocation, resulting in the high-order multi-agent system completing the resource allocation task at a high communication cost. Summary of the Invention

[0004] To address the issues of high communication burden and cost in current resource allocation methods for high-order multi-agent systems, this invention proposes a resource allocation method for high-order multi-agent systems based on an event-triggered mechanism. This method effectively reduces the communication burden and cost of high-order multi-agent systems while ensuring optimal resource allocation.

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

[0006] A resource allocation method for a high-order multi-agent system based on an event-triggered mechanism includes the following steps:

[0007] S1. Establish a high-order multi-agent system consisting of N high-order agents;

[0008] S2. Using the resource requirements of each higher-order agent as the decision variable, minimizing the global operating cost within the higher-order multi-agent system as the objective function, and the total network resources and total requirements of the higher-order multi-agent system as constraints, construct a distributed resource allocation optimization model for the higher-order multi-agent system.

[0009] S3. An event-triggered mechanism is used to solve the constructed distributed resource allocation optimization model in a distributed manner to obtain the resource requirements of all higher-order agents when the global running cost is minimized.

[0010] S4. Based on the resource requirements of all higher-order agents obtained in S3, schedule the operation of each higher-order agent.

[0011] In this technical solution, a high-order multi-agent system is first established. Then, a distributed resource allocation optimization model for the high-order multi-agent system is constructed based on the high-order multi-agent system. The distributed resource allocation optimization model considers the decision variables of the resource requirements of each high-order agent, and takes minimizing the global operating cost within the high-order multi-agent system as the objective function, with the total network resources and total requirements of the high-order multi-agent system as constraints. This ensures that the decision variables of the high-order agents are constrained by the network resources of the system. Furthermore, an event-triggered mechanism is used to solve the constructed distributed resource allocation optimization model in a distributed manner, so that communication between high-order agents only occurs when the triggering conditions are met. Finally, the high-order agents operate according to the obtained resource requirement values, ensuring the stability and convergence of the high-order multi-agent system under resource constraints. Under the premise of ensuring optimal resource allocation, the communication burden of the high-order multi-agent system is effectively reduced, and the communication cost is reduced.

[0012] Preferably, the high-order multi-agent system is represented by an undirected graph G, and the N high-order agents are set on the undirected graph, with each node in the undirected graph representing a high-order agent.

[0013] Preferably, the objective function is calculated as follows:

[0014]

[0015] Among them, f i (x i Let f(x) represent the operating cost function of the i-th higher-order agent, and let f(x) represent the global operating cost function of the higher-order multi-agent system. Let i represent the resource requirement of the i-th higher-order agent, i∈V, where V represents the vertex set of all higher-order agents in the undirected graph;

[0016] The specific expression for the total network resources and total demand of a high-order multi-agent system, constrained by these conditions, is as follows:

[0017]

[0018] in, This represents the total resource requirements of a high-order multi-agent system. This represents the total network resources of a high-order multi-agent system.

[0019] Preferably, based on the premise that each higher-order agent autonomously completes the resource allocation task, each higher-order agent in the undirected graph is described by the following expression:

[0020]

[0021] in, x represents i The nth derivative of (t), x i (t) represents the resource requirement of the i-th higher-order agent at time t. This represents the dynamics of the i-th higher-order agent at time t, reflecting the interaction relationships between the internal components of the higher-order agent.

[0022] Preferably, a characteristic equation is used to describe the high-order multi-agent system. The roots of the characteristic equation of the high-order multi-agent system are defined to be in the left half of the root plane. The characteristic equation of the high-order multi-agent system is represented by a characteristic polynomial p(t), and the specific expression of p(t) is as follows:

[0023] p(t):=t n-1 +k n-1 t n-2 +...+k2t+k1 (4)

[0024] Wherein, the coefficients k1, k2, ..., k of the characteristic polynomial n-1 It satisfies the Hurwitz criterion.

[0025] Preferably, a distributed algorithm from an event-triggered mechanism is used to solve the constructed distributed resource allocation problem in a distributed manner, wherein the distributed algorithm is denoted as:

[0026]

[0027]

[0028]

[0029] in, Indicates y i The derivative of (t), y i (t) represents the transitive variable when the i-th higher-order agent transmits common information at time t. Z represents i The derivative of (t), Z i(t) represents the constraint variables of the network resource constraints of the high-order multi-agent system at time t, where l∈{1,...,n}, m i(n-1) Let represent the element in the i-th row and (n-1)-th column of matrix M. Matrix M satisfies the following formula:

[0030] MH+H T M = -I n-1 (8)

[0031] The specific expression for matrix H is:

[0032]

[0033] The parameter ε satisfies the following relationship:

[0034]

[0035] Where L is the Laplace matrix, λ2 represents the eigenvalue of the Laplace matrix L, μ represents a parameter in the Lyapunov function, ω represents the scaling parameter, and m1 represents the error parameter for event triggering;

[0036] The calculation expression is:

[0037]

[0038] Preferably, before adopting an event-triggered mechanism, define Measurement error The calculation expression is:

[0039]

[0040] For y i Measurement error of (t) The calculation expression is:

[0041]

[0042] For z i Measurement error of (t) The calculation expression is:

[0043]

[0044] in, Denotes the decision variables when the i-th higher-order agent transmits information. The state value, y i (t) represents the variable y transferred when the i-th higher-order agent transmits information. i The state value of (t), z represents the network resource constraint variable when the i-th higher-order agent transmits information.i The state value of (t); when the i-th higher-order agent has not transmitted information, let the initial triggering time sequence state of the i-th higher-order agent be... The initial trigger time series state of the j-th higher-order agent, which is a neighbor of the i-th higher-order agent, is: When the i-th higher-order agent transmits information, the triggering condition of the triggering time sequence for the i-th higher-order agent to transmit information is denoted as:

[0045]

[0046] in, These are all trigger functions for distributed algorithms.

[0047] Preferably, the trigger function The calculation expressions are as follows:

[0048]

[0049]

[0050]

[0051] Where, α i β i γ and γ are the trigger functions respectively. Positive parameters; and Both refer to information transmission between higher-order intelligent agents.

[0052] Preferably, if the triggering function When the triggering condition is met, the higher-order agents communicate with each other and update their information through the information transmission part of the distributed algorithm. and If the value is not specified, continue running the higher-order agent and monitor the next trigger time; otherwise, continue running the higher-order agent and monitor the next trigger time.

[0053] Preferably, during the distributed solution of the constructed distributed resource allocation problem, the form of the distributed algorithm is transformed into a compact form. It is then calculated whether the compact form converges to an equilibrium point corresponding to the minimization of global running cost. If so, the distributed algorithm corresponding to the compact form converges to that equilibrium point, and the coordinates of that equilibrium point are obtained. The optimal values ​​of the decision variables of the higher-order agent are then obtained from the coordinates of that equilibrium point. Otherwise, the compact form of the distributed algorithm is used for calculation until the compact form calculation converges to an equilibrium point corresponding to the minimization of global running cost.

[0054] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0055] This invention proposes a resource allocation method for high-order multi-agent systems based on an event-triggered mechanism. First, a high-order multi-agent system is established. Then, a distributed resource allocation optimization model is constructed based on the high-order multi-agent system. This model considers the decision variables of each high-order agent's resource requirements and uses minimizing the global operating cost within the high-order multi-agent system as the objective function, with the total network resources and total requirements of the high-order multi-agent system as constraints. This ensures that the decision variables of the high-order agents are constrained by the system's network resources. Furthermore, the distributed resource allocation optimization model is solved in a distributed manner using an event-triggered mechanism, ensuring that communication between high-order agents only occurs when the triggering conditions are met. Finally, the high-order agents operate according to the obtained resource requirement values, guaranteeing the stability and convergence of the high-order multi-agent system under resource constraints. This effectively reduces the communication burden and cost of the high-order multi-agent system while ensuring optimal resource allocation. Attached Figure Description

[0056] Figure 1 This is a flowchart illustrating a resource allocation method for a high-order multi-agent system based on an event-triggered mechanism proposed in an embodiment of the present invention.

[0057] Figure 2 This is a graph showing the change in output power of the power generation system proposed in this embodiment of the invention.

[0058] Figure 3 This is a graph showing the variation of the total output power of the power generation system proposed in the embodiments of the present invention.

[0059] Figure 4 This is a graph showing the variation of the error values ​​of the state variables of the power generation system proposed in the embodiments of the present invention.

[0060] Figure 5 This shows the communication triggering timing diagram of the power generation system proposed in the embodiments of the present invention. Detailed Implementation

[0061] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent.

[0062] To better illustrate this embodiment, some parts of the accompanying drawings may be omitted, enlarged, or reduced, and do not represent actual dimensions. The descriptions of directions such as "up" and "down" are not intended to limit this patent.

[0063] It is understandable to those skilled in the art that some well-known details may be omitted from the accompanying drawings;

[0064] The positional relationships depicted in the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent.

[0065] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0066] Example 1

[0067] like Figure 1 As shown, this embodiment proposes a resource allocation method for a high-order multi-agent system based on an event-triggered mechanism, including the following steps:

[0068] S1. Establish a high-order multi-agent system consisting of N high-order agents;

[0069] In step S1, the high-order multi-agent system is represented by an undirected graph G, where the N high-order agents are set on the undirected graph, and each node in the undirected graph represents a high-order agent.

[0070] S2. Using the resource requirements of each higher-order agent as the decision variable, minimizing the global operating cost within the higher-order multi-agent system as the objective function, and the total network resources and total requirements of the higher-order multi-agent system as constraints, construct a distributed resource allocation optimization model for the higher-order multi-agent system.

[0071] In step S2, the calculation expression of the objective function is:

[0072]

[0073] Among them, f i (x i Let f(x) represent the operating cost function of the i-th higher-order agent, and let f(x) represent the global operating cost function of the higher-order multi-agent system. Let i represent the resource requirement of the i-th higher-order agent, i∈V, where V represents the vertex set of all higher-order agents in the undirected graph;

[0074] The specific expression for the total network resources and total demand of a high-order multi-agent system, constrained by these conditions, is as follows:

[0075]

[0076] in, This represents the total resource requirements of a high-order multi-agent system. This represents the total network resources of a high-order multi-agent system.

[0077] Since each higher-order agent autonomously completes the resource allocation task, the dynamics of the higher-order agents need to be considered. Each higher-order agent in the undirected graph can be described by the following expression:

[0078]

[0079] in, x represents i The nth derivative of (t), x i (t) represents the resource requirement of the i-th higher-order agent at time t. This represents the dynamics of the i-th higher-order agent at time t, reflecting the interactions between its internal components; each higher-order agent needs to find a suitable decision variable x. i This minimizes the global cost function f(x) under the network resource constraints of the high-order multi-agent system.

[0080] S3. An event-triggered mechanism is used to solve the constructed distributed resource allocation optimization model in a distributed manner to obtain the resource requirements of all higher-order agents when the global running cost is minimized.

[0081] S4. Based on the resource requirements of all higher-order agents obtained in S3, schedule the operation of each higher-order agent.

[0082] In this embodiment, a high-order multi-agent system is first established. Then, a distributed resource allocation optimization model for the high-order multi-agent system is constructed based on the high-order multi-agent system. The distributed resource allocation optimization model considers the decision variables of the resource requirements of each high-order agent, and takes minimizing the global operating cost within the high-order multi-agent system as the objective function, with the total network resources and total requirements of the high-order multi-agent system as constraints. This ensures that the decision variables of the high-order agents are constrained by the network resources of the system. Furthermore, an event-triggered mechanism is used to solve the constructed distributed resource allocation optimization model in a distributed manner, so that communication between high-order agents only occurs when the triggering conditions are met. Finally, the high-order agents operate according to the obtained resource requirement values, ensuring the stability and convergence of the high-order multi-agent system under resource constraints. Under the premise of ensuring optimal resource allocation, the communication burden of the high-order multi-agent system is effectively reduced, and the communication cost is reduced.

[0083] Example 2

[0084] See Figure 1 In step S1, this embodiment uses a characteristic equation to describe a high-order multi-agent system. The root of the characteristic equation of a high-order multi-agent system is defined as being in the left half of the root plane, indicating that the high-order multi-agent system is stable. The characteristic equation of the high-order multi-agent system is represented by a characteristic polynomial p(t), and the specific expression of p(t) is as follows:

[0085] p(t):=t n-1 +k n-1 t n-2 +...+k2t+k1 (4)

[0086] Wherein, the coefficients k1, k2, ..., k of the characteristic polynomial n-1The system must satisfy the Hurwitz criterion, an important criterion for determining the stability of a system. It provides a necessary and sufficient condition for a real-coefficient polynomial to have roots with non-negative real parts.

[0087] In step S3, the distributed algorithm in the event-triggered mechanism is used to solve the constructed distributed resource allocation problem in a distributed manner. The distributed algorithm is denoted as:

[0088]

[0089]

[0090]

[0091] in, Indicates y i The derivative of (t), y i (t) represents the transitive variable when the i-th higher-order agent transmits common information at time t. Z represents i The derivative of (t), Z i (t) represents the constraint variable of the network resource constraints of the high-order multi-agent system at time t. l∈{1,…,n},m i(n-1) This represents the element in the i-th row and (n-1)-th column of matrix M, where matrix M:=[m ij ] (n-1)×(n-1) Satisfy the following formula:

[0092] MH+H T M = -I n-1 (8)

[0093] The specific expression for matrix H is:

[0094]

[0095] The parameter ε satisfies the following relationship:

[0096]

[0097] Where L is the Laplace matrix, λ2 represents the eigenvalue of the Laplace matrix L, μ represents a parameter in the Lyapunov function, ω represents the scaling parameter, and m1 represents the error parameter for event triggering;

[0098] The calculation expression is:

[0099]

[0100] Before adopting an event-triggered mechanism, define Measurement error The calculation expression is:

[0101]

[0102] For y i Measurement error of (t) The calculation expression is:

[0103]

[0104] For z i Measurement error of (t) The calculation expression is:

[0105]

[0106] in, Denotes the decision variables when the i-th higher-order agent transmits information. The state value, y i (t) represents the variable y transferred when the i-th higher-order agent transmits information. i The state value of (t), z represents the network resource constraint variable when the i-th higher-order agent transmits information. i The state value of (t); when the i-th higher-order agent has not transmitted information, let the initial triggering time sequence state of the i-th higher-order agent be... The initial trigger time series state of the j-th higher-order agent, which is a neighbor of the i-th higher-order agent, is: When the i-th higher-order agent transmits information, the triggering condition of the triggering time sequence for the i-th higher-order agent to transmit information is denoted as:

[0107]

[0108] in, These are all trigger functions for distributed algorithms.

[0109] The trigger function The calculation expressions are as follows:

[0110]

[0111]

[0112]

[0113] Where, α i β i γ and γ are the trigger functions respectively. Positive parameters; and Both represent information transfer between higher-order agents to avoid excessively large error values; if the trigger function When the triggering conditions are met, higher-order agents communicate with each other through the information transmission part of the distributed algorithm, i.e. and Update separately and The value of ; otherwise, continue running the higher-order agent and monitor the next trigger time; to avoid the Zeno phenomenon and ensure that the exponential convergence of the distributed algorithms (5), (6), and (7) to the optimal solution, the exponential function e -γt Designed in the trigger function In addition, the design parameter α i and β i To control the convergence speed of distributed algorithms (5), (6), and (7).

[0114] Example 3

[0115] In the distributed solution of the constructed distributed resource allocation problem, the distributed algorithm is transformed into a compact form. It is then calculated whether the compact form converges to an equilibrium point corresponding to the minimization of global running cost. If so, the distributed algorithm corresponding to the compact form converges to that equilibrium point, and the coordinates of that equilibrium point are obtained. The optimal values ​​of the decision variables of the higher-order agent are then derived from these coordinates. Otherwise, the compact form of the distributed algorithm continues to be used until it converges to an equilibrium point corresponding to the minimization of global running cost. The specific calculation process is as follows:

[0116] First note:

[0117] x = col(x1,...,x) N ),y=col(y1,...,y N ), (19)

[0118]

[0119]

[0120]

[0121] Then and Make the following changes:

[0122]

[0123]

[0124]

[0125] By integrating distributed algorithms (3), (5), (6), and (7) using equations (19) to (25) respectively, the following compact form is obtained:

[0126]

[0127]

[0128]

[0129]

[0130]

[0131] Suppose that the undirected graph G is an undirected connected graph, then the theorem states: if (x * ,y * ,z * If x is the equilibrium point of equations (26), (27), (28), and (29), then x * This represents the resource requirements of all higher-order agents when the global operating cost is minimized. Furthermore, if x... * If y represents the resource requirements of all higher-order agents when the global operating cost is minimized, then there exists y. * and That is (x) * ,y * ,z * ) is the equilibrium point of equations (26), (27), (28) and (29); based on the above theorem, it is said that the distributed algorithm can converge to the equilibrium point during computation, and the distributed resource allocation optimization model can solve for the resource demand values ​​of all higher-order agents when the global running cost is minimized.

[0132] Example 4

[0133] In this embodiment, a power generation system consisting of 54 boilers and steam turbines is selected, that is, a high-order multi-agent system consisting of 54 boilers and steam turbines. The power generation system uses the resource demand of each boiler and steam turbine as the decision variable, the minimization of the global operating cost within the power generation system as the objective function, and the total network resources and total demand of the power generation system as constraints to construct a distributed resource allocation optimization model for the power generation system.

[0134] The objective function for minimizing the global operating cost within the power generation system is expressed as follows:

[0135]

[0136] in, Let f(x) represent the operating cost function of the i-th boiler-turbine system, and let f(x) represent the global operating cost function of the higher-order power generation system. Let V represent the output power of the i-th boiler-turbine, i∈V, where V represents the vertex set of all boiler-turbines in the undirected graph;

[0137] The constraints are:

[0138]

[0139] in, This represents the total resource requirements of the power generation system. d represents the total network resources of the power generation system. Gi This represents the network resources of the power generation system, i.e., the load demand of the generators, measured in MW, and includes P. G =col(P G1 ,...,P G54 ).

[0140] Furthermore, each boiler-turbine has a different efficiency, and different boiler-turbines have their own operating costs, which can be approximated by the following quadratic function:

[0141]

[0142] Where, α i β i and γ i This is the cost coefficient for the i-th boiler-turbine power generation, with the following value range:

[0143] α i ∈[6.78,74.33](M$)

[0144] β i ∈[8.3391,37.6968](M$ / MW)

[0145] γ i ∈[0.24,0.679](M$ / MW 2 )

[0146] When the pressure regulating valve is fixed, considering the power generation process, the pressure drop between the steam pipe inlet pressure and the throttling pressure, the boiler energy balance, and the rolling mill dynamics, the i-th boiler-turbine power generation has the following fourth-order dynamics:

[0147]

[0148]

[0149]

[0150]

[0151] Wherein, equation (33) represents the power generation process of the i-th boiler-turbine; equation (34) represents the pressure drop between the steam pipe inlet pressure and the throttling pressure; equation (35) represents the energy balance of the boiler; equation (36) describes the dynamics of the rolling mill; P Gi and B i These represent the control output and control input of the power generation system, respectively; P Di and D Qi Both represent state variables, C bi ,μ Ti ,k ei ,k si C ni ,k μi ,T ei ,k mi and T bi All of these represent system parameters.

[0152] The communication topology of the 54 boiler-turbine units in the power generation system is a ring graph with additional edges (1,4), (15,25), (25,35), and (45,50); local load demand d Gi Take a random value in the interval [50, 60] (MW); x i (0),y i (0) and z i The initial values ​​of (0) are all zero. The parameter values ​​in the distributed algorithms (5), (6) and (7) are k1 = 9, k2 = 14, k3 = 10 and ε = 12, respectively; the event trigger function parameters are γ = 0.00009 and α = 12. i =0.001,β i =15, i=1,2,3.

[0153] Figure 2 This represents the output power P of a power generation system consisting of 54 boilers and steam turbines. i Changes, from Figure 2 It can be seen that the output power of each generator system reaches a stable state after a period of time; Figure 3 This represents the total output power of 54 boiler-turbine power generation systems. The total load evolution, under the designed distributed algorithm (5), (6), (7) and event triggering condition (15), successfully converged to an equilibrium point corresponding to the minimization of global operating cost, that is, the total output power of the 54 power generation systems reached stability; Figure 4 This indicates that under the event-triggered mechanism, the measurement error value x in the designed trigger function... (3)The evolution of y and z shows that, as the triggering conditions are met and information is exchanged between the boiler and turbine, the measurement error values ​​gradually decrease and eventually stabilize; see [link to relevant documentation]. Figure 5 The communication trigger timing diagrams of five boiler-turbine units are randomly given. The results show that the boiler-turbine units in the power generation system transmit information only when the trigger condition (15) is met. Otherwise, the boiler-turbine units in the power generation system continue to operate, which effectively reduces the communication frequency between boiler-turbine units and the power generation cost of boiler-turbine units.

[0154] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for resource allocation in a high-order multi-agent system based on an event-triggering mechanism, characterized in that, Includes the following steps: S1. Establish a high-order multi-agent system consisting of N high-order agents; S2. Using the resource requirements of each higher-order agent as the decision variable, minimizing the global operating cost within the higher-order multi-agent system as the objective function, and the total network resources and total requirements of the higher-order multi-agent system as constraints, construct a distributed resource allocation optimization model for the higher-order multi-agent system. S3. An event-triggered mechanism is used to solve the constructed distributed resource allocation optimization model in a distributed manner to obtain the resource requirements of all higher-order agents when the global running cost is minimized. The distributed resource allocation problem is solved in a distributed manner using a distributed algorithm based on an event-triggered mechanism. This distributed algorithm is denoted as: （5） （6） （7） in, express The derivative of Indicates in t Time of the first i Transmission variables when a high-order intelligent agent transmits public information express The derivative of Indicates in t Constraint variables of network resource constraints in a high-order multi-agent system at any given time. , Representation matrix No. Line number Column elements, matrix Satisfy the following formula: （8） matrix H The specific expression is: （9） parameter The following relationship must be satisfied: （10） in, Represents the Laplace matrix, Represents the Laplace matrix eigenvalues, This represents a parameter in the Lyapunov function. This represents the scaling parameter. Indicates the error parameter that triggered the event; The calculation expression is: （11） S4. Based on the resource requirements of all higher-order agents obtained in S3, schedule the operation of each higher-order agent.

2. The resource allocation method for a high-order multi-agent system based on an event-triggered mechanism according to claim 1, characterized in that, The high-order multi-agent system is represented by an undirected graph G, and the N high-order agents are set on the undirected graph, with each node in the undirected graph representing a high-order agent.

3. The resource allocation method for a high-order multi-agent system based on an event-triggered mechanism according to claim 2, characterized in that, The objective function is calculated as follows: （1） in, Indicates the first i The operating cost function of a higher-order intelligent agent This represents the global operating cost function of a high-order multi-agent system. This represents the resource requirements of the i-th higher-order intelligent agent. V represents the set of vertices consisting of all higher-order agents in an undirected graph; The specific expression for the total network resources and total demand of a high-order multi-agent system, constrained by these conditions, is as follows: (2) in, This represents the total resource requirements of a high-order multi-agent system. This represents the total network resources of a high-order multi-agent system.

4. The resource allocation method for a high-order multi-agent system based on an event-triggered mechanism according to claim 3, characterized in that, Based on the premise that each higher-order agent autonomously completes the resource allocation task, each higher-order agent in the undirected graph can be described by the following expression: （3） in, express The nth derivative, Indicates in t The resource requirements of the i-th higher-order intelligent agent at time i. This represents the dynamics of the i-th higher-order agent at time t, reflecting the interaction relationships between the internal components of the higher-order agent.

5. The resource allocation method for a high-order multi-agent system based on an event-triggered mechanism according to claim 4, characterized in that, A high-order multi-agent system is described by a characteristic equation. The roots of the characteristic equation of a high-order multi-agent system are defined to lie in the left half of the root plane. The characteristic equation of a high-order multi-agent system uses a characteristic polynomial. express, The specific expression is: （4） Among them, the coefficients of the characteristic polynomial k 1, k 2…, k n-1 satisfy Guidelines.

6. The resource allocation method for a high-order multi-agent system based on an event-triggered mechanism according to claim 5, characterized in that, Before adopting an event-triggered mechanism, define Measurement error The calculation expression is: （12） right Measurement error The calculation expression is: （13） right Measurement error The calculation expression is: （14） in, , Indicates the first i Decision variables when a high-order intelligent agent transmits information The state value, Indicates the first i When a higher-order intelligent agent transmits information, it transmits variables. The state value, Indicates the first i Constraints on network resources when high-order intelligent agents transmit information The state value; in the first i When the first higher-order intelligent agent fails to transmit information, let the second... i The initial triggering time sequence state of each higher-level agent is: , and the i The first high-level intelligent agent neighbor's j The initial trigger time series state of the operation of the higher-order intelligent agent is ; in the i When a higher-order intelligent agent transmits information, the first... i The triggering conditions for the time sequence of information transmission by a higher-order intelligent agent are denoted as: （15） in, , , These are all trigger functions for distributed algorithms.

7. The resource allocation method for a high-order multi-agent system based on an event-triggered mechanism according to claim 6, characterized in that, The trigger function , , The calculation expressions are as follows: （16） （17） （18） in, It is a positive parameter; , and Both refer to information transmission between higher-order intelligent agents.

8. The resource allocation method for a high-order multi-agent system based on an event-triggered mechanism according to claim 7, characterized in that, If the trigger function , , If the triggering condition is met, the higher-order agents communicate with each other and update their information through the information transmission part of the distributed algorithm. , and If the value is not specified, continue running the higher-order agent and monitor the next trigger time; otherwise, continue running the higher-order agent and monitor the next trigger time.

9. The resource allocation method for a high-order multi-agent system based on an event-triggered mechanism according to claim 8, characterized in that, In the distributed solution of the constructed distributed resource allocation problem, the distributed algorithm is transformed into a compact form. It is then calculated whether the compact form converges to an equilibrium point corresponding to the minimization of global running cost. If so, the distributed algorithm corresponding to the compact form converges to that equilibrium point, and the coordinates of that equilibrium point are obtained. The optimal values ​​of the decision variables of the higher-order agent are then obtained from the coordinates of that equilibrium point. Otherwise, the compact form of the distributed algorithm is used for calculation until the compact form calculation converges to an equilibrium point corresponding to the minimization of global running cost.

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