Positive multi-agent system dynamic event trigger control method

Abstract

The invention provides a positive multi-agent system dynamic event triggering control method, and relates to the technical field of positive multi-agent system event triggering. A communication topological graph of a second-order multi-agent system and a dynamic model of a positive multi-agent system are constructed, dynamic event triggering conditions suitable for the positive multi-agent system are designed, and dynamic threshold parameters with time-varying items are adopted as upper and lower bounds of the dynamic event triggering conditions. The stability and the positivity of the system are analyzed by adopting a linear complementary positive Lyapunov function, a stable condition and a positive condition are obtained through derivation, solution simulation of controller gain is carried out according to the obtained stable condition and positive condition, and finally, a novel linear dynamic event triggering mechanism suitable for the positive multi-agent system is combined, so that the stability and the positivity of the system are improved. Simulation verification of consistency control is carried out, consistency convergence is ensured, communication and calculation burdens are reduced at the same time, and network resources are saved.

Description

Technical Field

[0001] The present invention relates to the technical field of event triggering of a multi-agent system, and in particular to a method for controlling dynamic event triggering of a multi-agent system. Background Art

[0002] In various fields of life and production, there exists a special class of systems whose states and outputs remain nonnegative. These systems are called positive systems. In real life, positive systems are often nonlinear positive systems with nonlinear characteristics. To address these nonlinear characteristics, researchers have used polynomial fuzzy modeling to model nonlinear positive systems as polynomial fuzzy positive systems. Currently, research on polynomial fuzzy positive systems is still in its infancy, with results only addressing a few specific issues. Numerous unresolved issues remain to be addressed. Consensus control of multi-agent systems is a core issue in the field of distributed collaboration. Its goal is to enable multiple agents to achieve asymptotic consistency in their states or outputs through distributed control strategies based on local interactions. This technology has broad applications in areas such as drone formations, smart grid scheduling, distributed robot collaboration, and wireless sensor networks. However, due to factors such as limited communication resources, dynamic network topology changes, and external interference, achieving consensus in multi-agent systems efficiently and stably remains a challenge. At present, the research on the consistency of positive multi-agent systems formed by the combination of positive systems and multi-agent systems is still in its infancy. It is necessary to consider both the positivity of the positive system and the stability of the multi-agent system, and then use the event triggering mechanism to control the positive multi-agent system so that the system can achieve consistency convergence. Now only a few scholars use static event triggering mechanism to control positive multi-agent systems, while the present invention focuses on consistency control of positive multi-agent systems based on dynamic event triggering mechanism.

[0003] When studying the consensus control problem of multi-agent systems, a key research topic is the design of event-triggered mechanism conditions. Optimizing communication and computing resources is crucial in the coordinated control of multi-agent systems. Currently, two event-triggered control approaches exist. The first is the static event-triggered mechanism. Traditional static event-triggered mechanisms utilize fixed cycles for communication and control updates. Their advantages lie in their simplicity, strong scheduling determinism, and suitability for systems with strict real-time requirements. However, static event-triggered mechanisms suffer from significant drawbacks, such as low resource utilization, poor dynamic adaptability, and limited scalability. The other control approach is the dynamic event-triggered mechanism. The core concept of the dynamic event-triggered mechanism is to perform communication and control updates only when the system state satisfies dynamically adjusted trigger conditions, significantly reducing unnecessary interactions. Compared to the static event-triggered mechanism, the dynamic event-triggered mechanism introduces internal dynamic variables (such as adaptive thresholds and time-varying parameters) to achieve real-time adjustment of trigger sensitivity, offering advantages such as greater resource efficiency and robustness. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention provides a method for dynamic event-triggered control of a positive multi-agent system. This method uses a dynamic event triggering mechanism to design appropriate dynamic threshold parameters. It then performs system modeling, derives stability conditions and positivity conditions, and finally implements consistency control of the positive multi-agent system.

[0005] A method for controlling dynamic event triggering of a multi-agent system, comprising the following steps:

[0006] Step 1: Construct the communication topology diagram of the second-order multi-agent system;

[0007] Step 1.1: Assume that the multi-agent system consists of N agents, numbered 1, 2, ..., N; define the agent set as , where N is the total number of agents;

[0008] Step 1.2: Define the edge set Describe the communication relationship between agents; if , indicating that agent i can pass information to agent j;

[0009] Step 1.3: Based on graph theory, define the communication topology graph as , where G is a directed or undirected graph used to describe the communication structure of all agents:

[0010] Step 1.4: Define the adjacency matrix A and Laplace matrix L of the communication topology graph, and describe the communication relationship between intelligent agents through the adjacency matrix A and Laplace matrix L;

[0011] The adjacency matrix , defined as follows:

[0012] (1)

[0013] The Laplace matrix is , the relationship between the Laplace matrix L and the adjacency matrix A is ,in is the degree matrix;

[0014] Step 2: Construct a dynamic model of the multi-agent system;

[0015] Step 2.1: Combine the velocity and position states of each agent to establish a second-order dynamics model;

[0016] Specifically, assume that there are N agents in the multi-agent system and the communication topology is a connected undirected graph; for agent i, its state dynamics is expressed as:

[0017] (2)

[0018] in is the system membership function, and , r is the number of rules, i=1,2,…,N, N is the total number of agents; is the premise variable, t represents the continuous time, are the system state vector and the control input vector respectively; are the known polynomial system matrix and input matrix, Represents the real number field dimensional matrix;

[0019] Step 2.2: Construct a consistency objective function based on the linear copositive Lyapunov function, so that the states of all agents converge to a consistent state within a predefined time;

[0020] Specifically, the linear cosine Lyapunov function is:

[0021] (3)

[0022] in is a Lyapunov function variable whose elements are all positive; System status abbreviation of; For the integral item The representation of is transposed; is the sampling period; according to the system stability, it is necessary to ensure that the derivative of the linear copositive Lyapunov function with respect to time is less than 0, and the stability condition and the positivity condition are obtained;

[0023] The stability conditions are as follows:

[0024] (4)

[0025] in:

[0026]

[0027] The positive conditions are as follows:

[0028] (5)

[0029] Step 3: Design dynamic event triggering conditions suitable for the multi-agent system, and use dynamic threshold parameters with time-varying terms as the upper and lower bounds of the dynamic event triggering conditions;

[0030] Step 3.1: Improve the dynamic event triggering conditions applicable to general systems. The dynamic event triggering conditions of general systems are as follows:

[0031] (6)

[0032] in is the basic threshold scalar of the ith agent, Determine the basic threshold scalar The degree of change and , is the actual threshold parameter of the ith agent, is a weighted matrix, Determine the basic threshold scalar of changing direction, is a scalar and is the state of agent i at the time of event triggering, Represents the formation-keeping behavior, Represents position-keeping behavior, is the measurement error of agent i, is the transpose, is the mth sampling moment of agent i, m is the number of sampling moments of agent i, is the number of sampling moments of agent j;

[0033] Defining Artificial Time Delay , substituted into formula (6), we get the overall expression with all agents:

[0034] (7)

[0035] in, is continuous time, is a scalar, is the overall representation of the measurement error, is the transpose, is the identity matrix, is the overall expression of the system state, 、 is the matrix related to the multi-agent formation, The specific form is as follows;

[0036]

[0037] Step 3.2: Improve the square term in the dynamic event triggering condition of Equation (6) to obtain the dynamic event triggering condition suitable for the positive multi-agent system:

[0038] (8)

[0039] Right now:

[0040] (9)

[0041] Step 4: Based on the measurement error term at the triggering moment, a distributed dynamic event triggering controller is constructed so that the states of all agents can converge to a consistent state;

[0042] Step 4.1: Based on the measurement error term at the trigger time, construct a distributed dynamic event-triggered controller and calculate the control input value calculated by the controller ;

[0043] The distributed dynamic event triggering controller is as follows:

[0044] (10)

[0045] in is the control input of the system, is the controller membership function, and , , r is the number of rules, is the controller gain to be determined;

[0046] Step 4.2: Conduct simulation verification based on the dynamic event triggering conditions in step 3 to ensure that the multi-agent system meets the consistency convergence, that is, and are the states of agents i and j respectively.

[0047] The beneficial effects of adopting the above technical solution are:

[0048] The present invention provides a method for controlling dynamic event triggering in a positive multi-agent system. This method designs improved dynamic event triggering conditions for positive multi-agent systems. Due to the unique positivity of positive systems, which differs from general systems, the use of linear copositive Lyapunov functions and the exclusion of square terms in the triggering conditions allow the improved dynamic event triggering conditions to be used in positive multi-agent systems. The dynamic event triggering conditions designed in this invention feature variable dynamic threshold parameters, which can reduce the number of triggers, thereby increasing system robustness, conserving network resources, and enabling the system to achieve better consistency convergence. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a flow chart of a method for controlling dynamic events triggered by a multi-agent system provided in an embodiment of the present invention;

[0050] Figure 2 is the convergence curve of the positions of the three agents in the embodiment of the present invention;

[0051] Figure 3is the convergence curve of the speed of the three agents in the embodiment of the present invention;

[0052] Figure 4 This is a trigger response diagram of three agents in an embodiment of the present invention;

[0053] Figure 5 is the triggering rate of the three agents in the embodiment of the present invention. DETAILED DESCRIPTION

[0054] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0055] A dynamic event-triggered control method for multi-agent systems, such as Figure 1 As shown, the following steps are included:

[0056] Step 1: Construct the communication topology diagram of the second-order multi-agent system;

[0057] Step 1.1: Assume that the multi-agent system consists of N agents, numbered 1, 2, ..., N; define the agent set as , where N is the total number of agents;

[0058] Step 1.2: Define the edge set Describe the communication relationship between agents; if , indicating that agent i can pass information to agent j;

[0059] Step 1.3: Based on graph theory, define the communication topology graph as , where G is a directed or undirected graph used to describe the communication structure of all agents:

[0060] Step 1.4: Define the adjacency matrix A and Laplace matrix L of the communication topology graph, and describe the communication relationship between intelligent agents through the adjacency matrix A and Laplace matrix L;

[0061] The adjacency matrix , defined as follows:

[0062] (1)

[0063] The Laplace matrix is , the relationship between the Laplace matrix L and the adjacency matrix A is ,in is the degree matrix;

[0064] Step 2: Construct a dynamic model of the multi-agent system;

[0065] Step 2.1: Combine the velocity and position states of each agent to establish a second-order dynamics model;

[0066] Specifically, assume that there are N agents in the multi-agent system and the communication topology is a connected undirected graph; for agent i, its state dynamics is expressed as:

[0067] (2)

[0068] in is the system membership function, and , r is the number of rules, i=1,2,…,N, N is the total number of agents; is the premise variable, t represents the continuous time, are the system state vector and the control input vector respectively; are the known polynomial system matrix and input matrix, Represents the real number field dimensional matrix;

[0069] Step 2.2: Construct a consistency objective function based on the linear copositive Lyapunov function so that the states of all agents converge to a consistent state within a predefined time.

[0070] Specifically, the linear cosine Lyapunov function is:

[0071] (3)

[0072] in is a Lyapunov function variable whose elements are all positive; System status abbreviation of; For the integral item The representation of is transposed; is the sampling period; according to the system stability, it is necessary to ensure that the derivative of the linear copositive Lyapunov function with respect to time is less than 0, and the stability condition and the positivity condition are obtained;

[0073] The stability conditions are as follows:

[0074] (4)

[0075] in:

[0076]

[0077] The positive conditions are as follows:

[0078] (5)

[0079] Step 3: Design dynamic event triggering conditions suitable for the multi-agent system, and use dynamic threshold parameters with time-varying terms as the upper and lower bounds of the dynamic event triggering conditions;

[0080] Step 3.1: Improve the dynamic event triggering conditions applicable to the general system so that they can be used in the positive system. The dynamic event triggering conditions of the general system are as follows:

[0081] (6)

[0082] in is the basic threshold scalar of the ith agent, Determine the basic threshold scalar The degree of change and , is the actual threshold parameter of the ith agent, is a weighted matrix, Determine the basic threshold scalar of changing direction, is a scalar and is the state of agent i at the time of event triggering, Represents the formation-keeping behavior, Represents position-keeping behavior, is the measurement error of agent i, is the transpose, is the mth sampling moment of agent i, m is the number of sampling moments of agent i, is the number of sampling moments of agent j;

[0083] Defining Artificial Time Delay , substituted into formula (6), we get the overall expression with all agents:

[0084] (7)

[0085] in, is continuous time, is a scalar, is the overall representation of the measurement error, is the transpose, is the identity matrix, is the overall expression of the system state, 、 is the matrix related to the multi-agent formation, The specific form is as follows;

[0086]

[0087] Step 3.2: Improve the square term in the dynamic event triggering condition of Equation (6) to obtain the dynamic event triggering condition suitable for the positive multi-agent system so that it can be used in the positive system:

[0088] (8)

[0089] Right now:

[0090] (9)

[0091] Step 4: Based on the measurement error term at the triggering moment, a distributed dynamic event triggering controller is constructed so that the states of all agents can converge to a consistent state;

[0092] Step 4.1: Based on the measurement error term at the trigger time, construct a distributed dynamic event-triggered controller and calculate the control input value calculated by the controller ;

[0093] The distributed dynamic event triggering controller is as follows:

[0094] (10)

[0095] in is the control input of the system, is the controller membership function, and , , r is the number of rules, is the controller gain to be determined;

[0096] Step 4.2: Conduct simulation verification based on the dynamic event triggering conditions in step 3 to ensure that the multi-agent system meets the consistency convergence, that is, and are the states of agents i and j respectively.

[0097] The present invention verifies the effectiveness of the proposed method through a numerical simulation example. The simulation results are as follows Figure 2-5 As shown. Figure 2 、 Figure 3 They are the convergence diagrams of the states (speed and position) of the three agents. It can be seen from the diagram that the method for consistent control of a positive multi-agent system based on dynamic event triggering proposed in the present invention is capable of performing consistent control on the positive multi-agent system so that the state of the agent converges to 0. Figure 4 , Figure 5 These are the trigger response diagrams and trigger rates of the three agents. It can be seen that the reduction in the number of triggers and the reduction in the trigger rate have achieved good consistency control.

[0098] The above description is merely an illustration of the preferred embodiments of the present disclosure and the technical principles employed. Those skilled in the art should understand that the scope of the invention encompassed by the embodiments of the present disclosure is not limited to technical solutions formed by specific combinations of the aforementioned technical features. It also encompasses other technical solutions formed by any combination of the aforementioned technical features or their equivalents, without departing from the aforementioned inventive concept. For example, a technical solution formed by replacing the aforementioned features with (but not limited to) technical features with similar functions disclosed in the embodiments of the present disclosure.

Claims

1. A method for controlling dynamic event triggering of a multi-agent system, characterized in that: The following steps are involved: Step 1: Construct the communication topology diagram of the second-order multi-agent system; Step 2: Construct a dynamic model of the multi-agent system; Step 3: Design dynamic event triggering conditions suitable for the multi-agent system, and use dynamic threshold parameters with time-varying terms as the upper and lower bounds of the dynamic event triggering conditions; Step 4: Based on the measurement error term at the triggering moment, a distributed dynamic event triggering controller is constructed so that the states of all agents can converge to a consistent state.

2. A method for controlling dynamic event triggering of a multi-agent system according to claim 1, characterized in that: The step 1 comprises the following steps: Step 1.1: Assume that the multi-agent system consists of N agents, numbered 1, 2, ..., N; define the agent set as , where N is the total number of agents; Step 1.2: Define the edge set Describe the communication relationship between agents; if , indicating that agent i can pass information to agent j; Step 1.3: Based on graph theory, define the communication topology graph as , where G is a directed or undirected graph used to describe the communication structure of all agents: Step 1.4: Define the adjacency matrix A and Laplace matrix L of the communication topology graph, and describe the communication relationship between intelligent agents through the adjacency matrix A and Laplace matrix L; The adjacency matrix , defined as follows: （1） The Laplace matrix is , the relationship between the Laplace matrix L and the adjacency matrix A is ,in is the degree matrix.

3. A method for controlling dynamic event triggering of a multi-agent system according to claim 1, characterized in that: The step 2 comprises the following steps: Step 2.1: Combine the velocity and position states of each agent to establish a second-order dynamics model; Specifically, assume that there are N agents in the multi-agent system and the communication topology is a connected undirected graph; for agent i, its state dynamics is expressed as: （2） in is the system membership function, and , r is the number of rules, i=1,2,…,N, N is the total number of agents; is the premise variable, t represents the continuous time, are the system state vector and the control input vector respectively; are the known polynomial system matrix and input matrix, Represents the real number field dimensional matrix; Step 2.2: Construct a consistency objective function based on the linear copositive Lyapunov function, so that the states of all agents converge to a consistent state within a predefined time; Specifically, the linear cosine Lyapunov function is: （3） in is a Lyapunov function variable whose elements are all positive; System status abbreviation of; For the integral item The representation of is transposed; is the sampling period; according to the system stability, it is necessary to ensure that the derivative of the linear copositive Lyapunov function with respect to time is less than 0, and the stability condition and the positivity condition are obtained; The stability conditions are as follows: （4） in, The positive conditions are as follows: （5）。 4. A method for controlling dynamic event triggering of a multi-agent system according to claim 1, characterized in that: The step 3 comprises the following steps: Step 3.1: Improve the dynamic event triggering conditions applicable to general systems. The dynamic event triggering conditions of general systems are as follows: （6） in is the basic threshold scalar of the ith agent, Determine the basic threshold scalar The degree of change and , is the actual threshold parameter of the ith agent, is a weighted matrix, Determine the basic threshold scalar of changing direction, is a scalar and is the state of agent i at the time of event triggering, Represents the formation-keeping behavior, Represents position-keeping behavior, is the measurement error of agent i, is the transpose, is the mth sampling moment of agent i, m is the number of sampling moments of agent i, is the number of sampling moments of agent j; Defining Artificial Time Delay , substituted into formula (6), we get the overall expression with all agents: （7） in, is continuous time, is a scalar, is the overall representation of the measurement error, is the transpose, is the identity matrix, is the overall expression of the system state, 、 is the matrix related to the multi-agent formation, The specific form is as follows; ； Step 3.2: Improve the square term in the dynamic event triggering condition of Equation (6) to obtain the dynamic event triggering condition suitable for the positive multi-agent system: （8） Right now: （9）。 5. A method for controlling dynamic event triggering of a multi-agent system according to claim 1, characterized in that: The step 4 comprises the following steps: Step 4.1: Based on the measurement error term at the trigger time, construct a distributed dynamic event-triggered controller and calculate the control input value calculated by the controller ; The distributed dynamic event triggering controller is as follows: （10） in is the control input of the system, is the controller membership function, and , , r is the number of rules, is the controller gain to be determined; Step 4.2: Conduct simulation verification based on the dynamic event triggering conditions in step 3 to ensure that the multi-agent system meets the consistency convergence, that is, and are the states of agents i and j respectively.

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