A Multi-Agent Event-Triggered Fixed-Time Consistency Control Method

Abstract

This invention relates to the fields of multi-agent control and motor control technology, and discloses a multi-agent event-triggered fixed-time consistency control method. The method establishes a multi-agent system model and communication network topology, quantifies the local interaction strength between agents using an adjacency matrix, and globally describes the system's dynamic behavior using a Laplace matrix. A measurement error and fixed-time consistency controller are established, sampling states are obtained through sensors, and estimated states are estimated using a state estimator. Based on the fixed-time consistency controller, event triggering functions and conditions are designed. If an event is triggered, the sampling states are input into the fixed-time consistency controller, and the output values ​​of each agent's fixed-time consistency controller are obtained. This method, based on event triggering and state estimation based on the real-time system state, reduces the number of triggers, avoids continuous communication between agents, improves system efficiency, and extends controller lifespan.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent control and motor control technology, specifically relating to a multi-agent event-triggered fixed-time consistency control method. Background Technology

[0002] In recent years, the cooperative control problem of multi-agent systems has attracted widespread attention and has been widely applied in practical systems such as robot formation, spacecraft attitude synchronization, and smart grids. As the foundation of cooperative control, the consensus problem has been discussed in depth. The main task of consensus in multi-agent systems is to design controllers that cause all agents in the system to converge to the same state.

[0003] In multi-agent system research, convergence speed is a key indicator for evaluating controller performance, reflecting the time required for the system to reach a consistent state from its initial state. Traditional research on consensus control in multi-agent systems is mostly based on asymptotic consensus. Therefore, researchers have proposed finite-time consensus to improve the convergence speed. However, finite-time control methods depend on the system's initial state; the greater the difference in the initial state, the longer the convergence time. Moreover, for large-scale real-world network systems, the initial values ​​are often difficult to obtain. Fixed-time control can improve the convergence speed while remaining unaffected by the initial state, ensuring that the system reaches the set state within a fixed time regardless of the initial state. Fixed-time control is particularly suitable for applications with high real-time requirements and strict time constraints, such as autonomous driving and collaborative robot operations.

[0004] However, the aforementioned control algorithm requires continuous updates to the controller, necessitating substantial computational resources. This is clearly impractical in real-world applications. To avoid this problem, event-triggered control offers a proactive solution. A key characteristic of event-triggered control is that agents communicate only when necessary, reducing communication overhead and unnecessary use of computational resources. However, traditional event-triggered control requires continuous communication between agents due to the need for real-time determination of trigger status. Therefore, a more flexible event-triggered scheme is needed to conserve communication resources.

[0005] In multi-agent systems, time delays caused by imperfect data transmission and post-reception processing are difficult to avoid. These delays can negatively impact the performance of the closed-loop system and even compromise its stability. For example, the patent CN118331047A, titled "A Multi-Agent Dynamic Event-Triggered Fixed-Time Binary Consistency Control Method," fails to consider unavoidable time delays and disturbances in practical applications while achieving binary consistency. Therefore, it is necessary to introduce a controller applicable to systems with time delays and disturbances to improve practicality. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a multi-agent event-triggered fixed-time consistency control method, which avoids continuous communication between agents based on the event triggering mechanism and through the state estimator, saves the system's communication resources, is applicable to systems with time delay and disturbance, and improves the system's convergence speed by adopting fixed-time control, thereby realizing multi-agent consistency control.

[0007] To address the aforementioned technical problems, this invention provides a multi-agent event-triggered fixed-time consistency control method, comprising the following steps:

[0008] Step S1: Establish a multi-agent system model and the communication network topology of the multi-agent system. Quantify the local interaction strength between each agent through the adjacency matrix and use the Laplace matrix to globally describe the dynamic behavior of the system.

[0009] Step S2: Establish a measurement error and fixed-time consistency controller based on the state estimator, sample the state at the trigger time of the agent through the sensor, and estimate the estimated state at other times through the state estimator.

[0010] Step S3: Design the event triggering function and event triggering conditions based on the fixed-time consistency controller. The sampled state and estimated state determine whether the event is triggered by the event triggering conditions. After the event is triggered, the sampled state is input into the fixed-time consistency controller to obtain the output value of the fixed-time consistency controller of each agent.

[0011] Step S4: Determine the parameters of the fixed-time consistency controller and the parameters of the event triggering function that meet the event triggering conditions, and verify that the fixed-time consistency controller can avoid Zeno behavior.

[0012] Step S5: Estimate the upper limit of the fixed convergence time based on the fixed-time consistency controller. Under the action of the fixed-time consistency controller, the measurement error of the multi-agent system gradually converges to zero, and the multi-agent system reaches a stable desired trajectory.

[0013] As an improvement to the multi-agent event-triggered fixed-time consistency control method of the present invention:

[0014] The communication network topology of the multi-agent system is an undirected topological graph: ε represents the set of communication paths between agents. Represents the set of vertices of an agent. Representation diagram The adjacency matrix, if edge (i,j)∈ε, then a ij >0 indicates that there is a communication link between agent i and agent j;

[0015] The intensity of the local interaction is quantified as follows:

[0016] a ij The magnitude is quantified by the intensity of local interactions between agents; if agents are directly connected, then a ij =1; conversely, if there is no communication link, then a ij =0;

[0017] The Laplace matrix is:

[0018]

[0019] in, The degree matrix is ​​constructed for the degree of the vertices of the agent, with elements diag[d1,d2,…,d]. N ], d i =deg in (v i ) or d i =deg out (v i ), Let i be the in-degree of node i. This is for the degree of departure.

[0020] As a further improvement to the multi-agent event-triggered fixed-time consistency control method of the present invention:

[0021] The mathematical model for the multi-agent system is as follows:

[0022]

[0023] Where, x i (t) represents the real-time location information of the i-th agent, u i (t) represents the output of the fixed-time consistency controller for the i-th agent, τ i Given the input delay, f i (x i (t),t) represents the dynamic nonlinear term, d i (x i (t),t) represents an unknown perturbation, and N represents the number of agents;

[0024] Assumption 1: f i (x i (t),t) are the dynamic nonlinear terms of agent i, and satisfy the Lipschitz condition:

[0025] for ρ>0 is a constant and satisfies:

[0026] |f i (x i (t),t)-fj (x j (t),t)|≤ρ|x i (t)-x j (t)| (3)

[0027] Assumption 2: The unknown disturbances experienced by agent i are bounded, and are bounded by a known positive constant d: |d| i (x i (t),t)|≤d.

[0028] As a further improvement to the multi-agent event-triggered fixed-time consistency control method of the present invention:

[0029] The fixed-time consistency control objective is:

[0030] There exists a positive value C such that:

[0031] sup t≥T ||x i (t)-x j (t)||≤C (4)

[0032] Furthermore, there exists a constant value T. max The upper limit time T satisfies: T≤T max ;

[0033] Lemma 1: For any nonnegative number y k For k = 1, 2, ..., N, the following inequalities hold:

[0034]

[0035] Lemma 2: Undirected connected graph The Laplace matrix is It is positive semi-definite and its eigenvalues, from smallest to largest, can be represented as 0 < λ² ≤ … ≤ λ. N , It is the eigenvector corresponding to the eigenvalue 0, if and So there are

[0036] in,

[0037] Lemma 3: For the following multi-agent system

[0038]

[0039] in Let y(0) represent the state vector, where y(0) is the initial state of the multi-agent system. It is a nonlinear function. Suppose there exists a function V(y(t)), V(y(t))≥0, and satisfies:

[0040]

[0041] Where a, b > 0, m ∈ (1, +∞), n ∈ (0, 1), then the so agent system can achieve fixed-time consistency within the upper bound time T, and:

[0042]

[0043] As a further improvement to the multi-agent event-triggered fixed-time consistency control method of the present invention:

[0044] The state estimator is:

[0045]

[0046] in, It is the estimated state of the i-th agent. It is the sampled state of the i-th agent, and It is the k-th trigger moment of agent i;

[0047] The fixed-time consistency controller is:

[0048]

[0049] Where b1, b2, b3 are constants, b1>0, b2>0, b3>0, and p is the ratio of two positive odd numbers, where p∈(1,+∞). Used to solve input latency.

[0050] As a further improvement to the multi-agent event-triggered fixed-time consistency control method of the present invention:

[0051] One form of the event triggering condition is:

[0052]

[0053] Among them, g i (t) is the event trigger function;

[0054]

[0055] Where δ is the design parameter of the trigger function, E i (t) represents the measurement error:

[0056]

[0057] As a further improvement to the multi-agent event-triggered fixed-time consistency control method of the present invention:

[0058] Another form of the event triggering condition is:

[0059]

[0060] Among them, G i (t) represents another form of the event triggering function:

[0061]

[0062] in,

[0063]

[0064] As a further improvement to the multi-agent event-triggered fixed-time consistency control method of the present invention:

[0065] The parameters b2 and b3 of the fixed-time consistency controller and the parameter δ of the event triggering function must satisfy the following conditions:

[0066]

[0067] Derivation get This proves that the Zeno phenomenon has been avoided.

[0068] As a further improvement to the multi-agent event-triggered fixed-time consistency control method of the present invention:

[0069] The upper limit of the fixed convergence time is:

[0070]

[0071] Construct the following Lyapunov function:

[0072]

[0073] Differentiating the Lyapunov function yields in According to Lemma 3, the multi-agent system achieves fixed-time consistency and the fixed upper limit of convergence time satisfies equation (22).

[0074] The beneficial effects of this invention are mainly reflected in:

[0075] 1. The control protocol designed in this invention enables multi-agent systems to achieve convergence in any initial state within a fixed time, and the system convergence speed is faster.

[0076] 2. The controller designed in this invention adopts model-based event triggering and estimates the state of the agent based on the real-time state of the system. Compared with traditional event triggering, it further reduces the number of system triggers, avoids continuous communication between agents, improves system efficiency, reduces energy consumption, and extends the life of the controller.

[0077] 3. The controller designed in this invention takes into account the effects of time delay and disturbance on the system. It is applicable not only to situations with input delay but also to situations with external disturbance, thus making the application scenarios of this invention more extensive.

[0078] 4. The control protocol designed in this invention can avoid continuous communication with neighboring intelligent agents by designing a second event triggering protocol and event triggering conditions. The first event triggering protocol and conditions are suitable for rapidly changing systems, while the second event triggering protocol and conditions can reduce the real-time computing burden when applied to systems with known models. Attached Figure Description

[0079] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0080] Figure 1 This is a flowchart illustrating a multi-agent event-triggered fixed-time consistency control method according to the present invention.

[0081] Figure 2 The diagram shows four communication topologies of the multi-agent system of the present invention (a) and a schematic diagram of topology switching methods (b).

[0082] Figure 3 This is a diagram showing the triggering function and the multi-agent state trajectory under the triggering conditions in Embodiment 1 of the present invention.

[0083] Figure 4 This is the output trajectory diagram of the fixed-time consistency controller under the triggering function and triggering conditions in Embodiment 1 of the present invention;

[0084] Figure 5 This is a diagram showing the triggering time of multi-agent events under the triggering conditions in Embodiment 1 of the present invention;

[0085] Figure 6 This is a diagram showing the triggering function and the multi-agent state trajectory under the triggering conditions in Embodiment 2 of the present invention.

[0086] Figure 7 This is the output trajectory diagram of the fixed-time consistency controller under the triggering function and triggering conditions in Embodiment 2 of the present invention;

[0087] Figure 8 This is a diagram showing the triggering time of multi-agent events under the triggering conditions in Embodiment 2 of the present invention. Detailed Implementation

[0088] The present invention will be further described below with reference to specific embodiments, but the scope of protection of the present invention is not limited thereto:

[0089] Example 1: A multi-agent event-triggered fixed-time consistency control method. Each agent obtains sampled states through its own sensors, and estimates the estimated states using a state estimator. A signed undirected topological graph and Laplace matrix of the multi-agent system are constructed, and the Laplace matrix is ​​used to globally describe the dynamic behavior of the system. A measurement error and fixed-time consistency controller based on the state estimator are designed for multi-agent systems with time delays and disturbances. The sampled states of the agents at the trigger time are sampled by sensors, and the estimated states at other times are obtained by the state estimator. An event trigger function and event trigger conditions are designed based on the fixed-time consistency controller. The sampled states are calculated by the event trigger function and then input into the event trigger conditions to determine whether an event is triggered. After the event is triggered, the sampled states and estimated states of the agents are input into the fixed-time consistency controller to obtain the output values ​​of each agent's fixed-time consistency controller. Based on the multi-agent stability method and event triggering conditions, the controller parameters and multi-agent system parameters that meet the discrimination conditions are determined, and the designed fixed-time consistency controller is verified to avoid Zeno behavior. Based on the designed fixed-time consistency protocol, the upper limit of the fixed convergence time of the multi-agent event-triggered consistency control is estimated. Under the action of the fixed-time consistency controller, the multi-agent system error gradually converges to zero, and the multi-agent system reaches a stable expected trajectory.

[0090] The process of achieving consensus among multiple agents under the action of a designed fixed-time consensus controller is as follows: Figure 1 As shown, specifically:

[0091] 1. Establish a multi-agent system model with a communication network structure of an undirected topological graph under the influence of time delay and disturbance.

[0092] Define the communication network topology of a multi-agent system as an undirected topological graph. ε represents the set of edges, that is, the set of communication paths between agents. The connectivity between agents i and j is represented by edge (i,j)∈ε, where i is the incoming neighbor of j and j is the outgoing neighbor of i. This represents the set of vertices in a graph, that is, the set of vertices of an agent.

[0093] Called a diagram The adjacency matrix, if edge (i,j)∈ε, then a ij >0 indicates that there is a communication link between agent i and agent j. ijThe size of the adjacency matrix is ​​quantified by the intensity of local interactions between agents. In the system used in this paper, the value of the adjacency matrix can be directly determined by the communication network structure of the system. If agents are directly connected, then a... ij =1; conversely, if there is no communication link, then a ij =0. The neighbor set of agent i is N. i This means that the in-degree of node i is defined as... Out-degree is defined as An undirected topological graph can be constructed from the degrees of the vertices of the agents. The degree matrix, whose elements are defined as diag[d1,d2,…,d] N ], d i =deg in (v i ) or d i =deg out (v i From the definitions of the degree matrix and adjacency matrix mentioned above, we can obtain the undirected topological graph. The Laplace matrix is:

[0094]

[0095] in, The degree matrix is ​​constructed for the degree of the vertices of the agent.

[0096] The Laplace matrix contains topological information about the graph, thus describing the interactions between agents in a multi-agent system. Through differential equations, the Laplace matrix can describe how the system state evolves over time. Furthermore, the eigenvalues ​​of the Laplace matrix provide information about the system's stability and convergence rate. Therefore, the Laplace matrix is ​​used to globally describe the dynamic behavior of a system.

[0097] N is the number of agents in the multi-agent system, where the nonlinear system model of the i-th agent can be represented as follows:

[0098]

[0099] Where, x i (t) represents the real-time location information of the i-th agent, u i (t) represents the output of the fixed-time consistency controller for the i-th agent, τ i Given the input delay, f i (x i (t),t) represents the dynamic nonlinear term, d i (x i (t),t) represents an unknown perturbation, and N represents the number of agents.

[0100] Assumption 1: f i (xi (t),t) are the dynamic nonlinear terms of agent i, and satisfy the Lipschitz condition, that is, for ρ>0 is a constant and satisfies:

[0101] |f i (x i (t),t)-f j (x j (t),t)|≤ρ|x i (t)-x j (t)| (3)

[0102] Assumption 2: The unknown disturbances experienced by agent i are bounded, and are bounded by a known positive constant d, i.e., |d| i (x i (t),t)|≤d.

[0103] The goal is for multiple agents to achieve consensus within a fixed time frame, given any initial state. The states of the agents must satisfy the following conditions:

[0104] There exists a positive value C such that:

[0105] sup t≥T ||x i (t)-x j (t)||≤C (4)

[0106] And there exists a constant value T. max The upper limit time T satisfies: T≤T max .

[0107] Lemma 1: For any nonnegative number y k For k = 1, 2, ..., N, the following inequalities hold:

[0108]

[0109] Lemma 2: Undirected connected graph The Laplace matrix is It is positive semidefinite and its eigenvalues, from smallest to largest, can be expressed as 0 < λ² ≤ … ≤ λ. N , It is the eigenvector corresponding to the eigenvalue 0, if and So there are

[0110] in,

[0111] x is an arbitrary N-dimensional vector, and L is the Laplace matrix;

[0112] Lemma 3: For the following multi-agent system

[0113]

[0114] in, Let y(0) represent the state vector, where y(0) is the initial state of the multi-agent system (i.e., Equation (7)). It is a nonlinear function.

[0115] Suppose there exists a function V(y(x)), V(y(t))≥0 and satisfies:

[0116]

[0117] Where a, b, m, n are all constants, a, b > 0, m ∈ (1, +∞), n ∈ (0, 1), then the so agent system can achieve fixed-time consistency within the upper bound time T, and:

[0118]

[0119] 2. Establish a state estimator and a fixed-time consistency controller triggered by multi-agent events.

[0120] The state estimator is:

[0121]

[0122] in, It is the estimated state of the i-th agent. It is the sampled state of the i-th agent, and It is the kth trigger moment of agent i.

[0123] The fixed-time consistency controller designed for multi-agent systems with time delays and disturbances is as follows:

[0124]

[0125] Where b1, b2, b3 are constants, b1>0, b2>0, b3>0, and p is the ratio of two positive odd numbers, where p∈(1,+∞). Designed to address input latency.

[0126] 3. Design event triggering functions and event triggering conditions based on a fixed-time consistency controller.

[0127] 3.1 Definition of measurement error:

[0128]

[0129] 3.2 Determine the event triggering function:

[0130]

[0131] Where δ is the design parameter of the trigger function.

[0132] 3.3 Determine the event trigger time (i.e., the event trigger condition):

[0133]

[0134] When the condition of equation (14) is met, the sampled state of each agent (i.e., the state of the agent at the trigger time obtained by the sensor sampling) is input into the fixed time consistency controller (i.e., equation (11)). The fixed time consistency controller is updated to obtain the fixed time consistency controller output value of each agent. Otherwise, the fixed time consistency controller (i.e., equation (11)) is not updated.

[0135] 4. Under the action of a fixed-time consistency controller, the measurement error of a multi-agent system gradually converges to zero and can avoid Zeno behavior.

[0136] In the fixed-time consistency controller (i.e., Equation (11)), the parameters in the event triggering function (i.e., Equation (13)) need to satisfy the following conditions:

[0137]

[0138] According to the measurement error formula (12), we can obtain:

[0139]

[0140] According to Lemma 1 and Lemma 2, we can obtain:

[0141]

[0142] Therefore, based on formula (16), we can obtain:

[0143]

[0144] Assumption:

[0145]

[0146] When the event triggering condition is met and the event is triggered, the event triggering function g... i Becoming 0 means therefore:

[0147]

[0148] Based on the event triggering functions (13) and (20), we can obtain:

[0149]

[0150] Where η>0, δ>0 and therefore This means that the Zeno phenomenon can be avoided.

[0151] In summary, under the action of the fixed-time consistency controller of this invention, and provided that the fixed-time consistency controller parameters meet the event triggering conditions, the measurement error of the multi-agent system gradually converges to zero, and consistency control can be achieved within a fixed time, thus avoiding the occurrence of the Zeno phenomenon.

[0152] 5. Calculate the upper limit of the fixed convergence time for fixed-time consistency control triggered by multi-agent events.

[0153]

[0154] The fixed time limit for multi-agent systems is given by equation (22), which is a fixed time value and is independent of the initial state of the system.

[0155] Consider the Lyapunov function:

[0156]

[0157] Differentiating the Lyapunov function:

[0158]

[0159] From Lemma 1, we can derive:

[0160]

[0161] By Lemma 2, we can obtain:

[0162]

[0163] therefore:

[0164]

[0165] in,

[0166] According to Lemma 3, we can obtain:

[0167]

[0168] And T(χ) satisfies:

[0169]

[0170] The above results indicate that when t = T(χ), the control input u i (t) will become 0, and Also in T max +τ i The value becomes 0. Therefore, when time t = T(x) ≤ T max +max(τ i We can get Therefore, multi-agent systems can achieve fixed-time consistency, and the fixed upper limit of convergence time satisfies equation (22).

[0171] Therefore, under the proposed fixed-time consistency controller, the error of the multi-agent system gradually converges to zero, and the multi-agent system reaches a stable desired trajectory, thus achieving fixed-time state consistency of the multi-agent system.

[0172] Note: The above reasoning is based on a fixed topology. For a switching topology that is more in line with the actual application, the reasoning process is the same as that of a fixed topology. You only need to replace λ2 in condition (15) with the smallest λ2 in the Laplace matrix of all topologies.

[0173] Example 2: A multi-agent event-triggered fixed-time consistency control method, the specific process of which is as follows:

[0174] 1. Establish a multi-agent system model with time delay and disturbance effects, whose topology is an undirected topological graph, consistent with step 1 of Example 1.

[0175] 2. Establish a state estimator and a fixed-time consistency controller triggered by multi-agent events, consistent with step 2 of Example 1.

[0176] 3. Design event triggering functions and event triggering conditions based on a fixed-time consistency controller.

[0177] By designing a second type of event triggering condition and event triggering function, the next triggering time can be calculated, avoiding continuous communication with neighboring intelligent agents and reducing the real-time computing burden.

[0178] 3.1 The measurement error is consistent with equation (12) of Example 1.

[0179] 3.2 Define the event triggering function

[0180]

[0181] in,

[0182]

[0183] The specific definition of η is given in formula (19).

[0184] 3.3 The event triggering condition is:

[0185]

[0186] 4. Under the action of a fixed-time consistency controller, the measurement error of a multi-agent system gradually converges to zero and can avoid Zeno behavior.

[0187] From equations (18), (19), and (30), we can obtain

[0188]

[0189] Substituting it into equation (30) yields

[0190]

[0191] It can be seen that the last term is the event triggering function (Equation (13)) in Example 1. Therefore, the event triggering condition (Equation (32)) of this embodiment is a sufficient condition for the event triggering condition (Equation (14)) of Example 1. The subsequent proof is the same as that of Example 1. It can be proved that the measurement error of the multi-agent system gradually converges to zero and can avoid Zeno behavior.

[0192] 5. Calculate the upper limit of the fixed convergence time for fixed-time consistency control triggered by multi-agent events.

[0193] By using the same Lyapunov function as in step 5 of Example 1 and differentiating it with respect to t, we can obtain:

[0194]

[0195] Based on equation (18), we can obtain

[0196]

[0197] Integrating equation (36) yields

[0198]

[0199] According to the event triggering condition (Equation (32)), we can obtain

[0200] G i (t)≤0 (38)

[0201] From this we can obtain

[0202]

[0203] Substituting it into equation (33) yields

[0204]

[0205] Where b1>0, b3>0, δ∈(0,1), λ2, V(t), N>0, therefore, under the event triggering function (Equation (31)) and the event triggering condition (Equation (32)), the system can achieve fixed-time consistency and the fixed upper limit of convergence time satisfies Equation (22).

[0206] experiment:

[0207] The effectiveness of the multi-agent event-triggered fixed-time consistency control method of this invention was verified through numerical simulation. The topology and switching method of the multi-agent system were determined as follows: Figure 2 As shown.

[0208] The initial position of the multi-intelligent sensor is obtained. The dynamic equation of the agent is f(x) i (t),t)=0.2x i (t)+0.6cos(t), the disturbance experienced by the agent is d i (x i (t),t)=0.1cos(x i (t)). The remaining parameters are b1 = 0.5, b2 = 15, b3 = 0.45, p = 1.2, δ = 0.1, a = -0.02, τ1 = τ2 = τ3 = τ4 = τ5 = τ6 = 0.05. Figure 3 and Figure 4 The simulation diagrams for the multi-agent positions and the output of the fixed-time consistency controller are shown. The diagrams demonstrate that the multi-agent system can achieve fixed-time consistency. The convergence time is less than the calculated upper limit of 49.527 s, and significantly less than the 2.1 s of a conventional consistency event-triggered controller of the same type. Figure 5 To obtain the event triggering time map of multiple agents using the method of Example 1, this invention employs model-based event triggering, which further reduces the number of system triggers compared to traditional event triggering. Because multiple agents only exchange information at the triggering moment, this invention can save communication resources and extend the lifespan of the controller.

[0209] Figure 6 and Figure 7 The figures show the simulation diagrams of the positions of multiple agents and the output of the fixed-time consistency controller under the event-triggered function and event-triggered conditions in Example 2. It can be seen from the figures that multiple agents can also achieve fixed-time consistency. Figure 8 The event triggering timeline of the multi-agent system in Embodiment 2, compared to the event triggering conditions in Embodiment 1, increases the number of event triggers while reducing the real-time computing burden.

[0210] Finally, it should be noted that the above examples are merely some specific embodiments of the present invention. Obviously, the present invention is not limited to the above embodiments and many variations are possible. All variations that can be directly derived or conceived by those skilled in the art from the disclosure of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A multi-agent event-triggered fixed-time consistency control method, characterized in that: Step S1: Establish a multi-agent system model and the communication network topology of the multi-agent system. Quantify the local interaction strength between each agent through the adjacency matrix and use the Laplace matrix to globally describe the dynamic behavior of the system. Step S2: Establish a measurement error and fixed-time consistency controller based on the state estimator, sample the state at the trigger time of the agent through the sensor, and estimate the estimated state at other times through the state estimator. Step S3: Design the event triggering function and event triggering conditions based on the fixed-time consistency controller. The sampled state and estimated state determine whether the event is triggered by the event triggering conditions. After the event is triggered, the sampled state is input into the fixed-time consistency controller to obtain the output value of the fixed-time consistency controller of each agent. Step S4: Determine the parameters of the fixed-time consistency controller and the parameters of the event triggering function that meet the event triggering conditions, and verify that the fixed-time consistency controller can avoid Zeno behavior. Step S5: Estimate the upper limit of the fixed convergence time based on the fixed-time consistency controller. Under the action of the fixed-time consistency controller, the measurement error of the multi-agent system gradually converges to zero, and the multi-agent system reaches a stable desired trajectory. The state estimator is: in, It is the estimated state of the i-th agent. It is the sampled state of the i-th agent, and It is the k-th trigger moment of agent i; The fixed-time consistency controller is: Where b1, b2, b3 are constants, b1>0, b2>0, b3>0, and p is the ratio of two positive odd numbers, where p∈(1,+∞). Used to solve input delay; Representation diagram The adjacency matrix, if edge (i,j)∈ε, then a ij >0 indicates that there is a communication link between agent i and agent j.

2. The multi-agent event-triggered fixed-time consistency control method according to claim 1, characterized in that: The communication network topology of the multi-agent system is an undirected topological graph: ε represents the set of communication paths between agents. Represents the set of vertices of an intelligent agent; The intensity of the local interaction is quantified as follows: a ij The magnitude is quantified by the intensity of local interactions between agents; if agents are directly connected, then a ij =1; conversely, if there is no communication link, then a ij =0; The Laplace matrix is: in, The degree matrix is ​​constructed for the degree of the vertices of the agent, with elements diag[d1,d2,...,d]. N ], d i =deg in (v i ) or d i =deg out (v i ), Let i be the in-degree of node i. This is for the degree of departure.

3. The multi-agent event-triggered fixed-time consistency control method according to claim 2, characterized in that: The mathematical model for the multi-agent system is as follows: Where, x i (t) represents the real-time location information of the i-th agent, u i (t) represents the output of the fixed-time consistency controller for the i-th agent, τ i Given the input delay, f i (x i (t),t) represents the dynamic nonlinear term, d i (x i (t),t) represents an unknown perturbation, and N represents the number of agents; Assumption 1: f i (x i (t),t) are the dynamic nonlinear terms of agent i, and satisfy the Lipschitz condition: for ρ>0 is a constant and satisfies: |f i (x i (t),t)-f j (x j (t),t)|≤ρ|x i (t)-x j (t)| (3) Assumption 2: The unknown disturbances experienced by agent i are bounded, and are bounded by a known positive constant d: |d| i (x i (t),t)|≤d.

4. The multi-agent event-triggered fixed-time consistency control method according to claim 3, characterized in that: The fixed-time consistency control objective is: There exists a positive value C such that: sup t≥T ||x i (t)-x j (t)||≤C (4) Furthermore, there exists a constant value T. max The upper limit time T satisfies: T≤T max ; Lemma 1: For any nonnegative number y k For k = 1, 2, ..., N, the following inequalities hold: Lemma 2: Undirected Connected Graph The Laplace matrix is It is positive semidefinite and its eigenvalues, from smallest to largest, can be expressed as 0 < λ² ≤ … ≤ λ. N , It is the eigenvector corresponding to the eigenvalue 0, if and So there is in, Lemma 3: For the following multi-agent system in Let y(0) represent the state vector, where y(0) is the initial state of the multi-agent system. It is a nonlinear function. Suppose there exists a function V(y(t)), V(y(t))≥0, and satisfies: Where a, b > 0, m ∈ (1, +∞), n ∈ (0, 1), then the so agent system can achieve fixed-time consistency within the upper bound time T, and:

5. The multi-agent event-triggered fixed-time consistency control method according to claim 4, characterized in that: One form of the event triggering condition is: Among them, g i (t) is the event trigger function; Where δ is the design parameter of the trigger function, E i (t) represents the measurement error:

6. The multi-agent event-triggered fixed-time consistency control method according to claim 4, characterized in that: Another form of the event triggering condition is: Among them, G i (t) represents another form of the event triggering function: in, 7. A multi-agent event-triggered fixed-time consistency control method according to any one of claims 5 or 6, characterized in that: The parameters b2 and b3 of the fixed-time consistency controller and the parameter δ of the event triggering function must satisfy the following conditions: Derivation get This proves that the Zeno phenomenon has been avoided.

8. The multi-agent event-triggered fixed-time consistency control method according to claim 7, characterized in that: The upper limit of the fixed convergence time is: Construct the following Lyapunov function: Differentiating the Lyapunov function yields in According to Lemma 3, the multi-agent system achieves fixed-time consistency and the fixed upper limit of convergence time satisfies equation (22).

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