Multi-agent event triggering fixed time consistency control method

Abstract

The invention relates to the technical field of multi-agent control and motor control, and discloses a multi-agent event-triggered fixed time consistency control method, which comprises the following steps of: establishing a multi-agent system model and a communication network topology, quantifying local interaction strength among agents through an adjacent matrix, and establishing a multi-agent event-triggered fixed time consistency control system; a Laplacian matrix is utilized to globally describe dynamic behaviors of the system; establishing a measurement error and fixed time consistency controller, obtaining a sampling state through a sensor, and estimating an estimation state through a state estimator; and designing an event triggering function and event triggering conditions based on the fixed time consistency controller, and if an event is triggered, inputting the sampling state into the fixed time consistency controller to obtain an output value of the fixed time consistency controller of each agent. According to the method, state estimation is carried out based on event triggering and the real-time state of the system, the triggering frequency is reduced, continuous communication between intelligent agents is avoided, the system efficiency is improved, and the service life of the controller is prolonged.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-agent control and motor control, and in particular relates to a multi-agent event-triggered fixed-time consistency control method. Background Art

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

[0003] In the study of multi-agents, convergence speed is a key indicator for evaluating controller performance, reflecting the time required for the system to reach a consistent state from the initial state. Most of the research on consistency control of traditional multi-agent systems is based on asymptotic consistency. Therefore, scholars have proposed finite-time consistency to improve the convergence speed of the system. However, the finite-time control method depends on the initial state of the system. The greater the difference in the initial state of the system, the longer the convergence time. Moreover, for large real network systems, the initial value of the system is usually difficult to obtain. Fixed-time control can improve the convergence speed of the system while the convergence time is not affected by the initial state of the system, ensuring that the system reaches the set state within a fixed time at any initial state. Fixed-time control is more suitable for application scenarios with strong real-time and strict time requirements, such as autonomous driving and robot collaborative operations.

[0004] However, the above control algorithm needs to continuously update the controller, which requires sufficient computing resources. Obviously, this is impossible in practical applications. In order to avoid this problem, the event-triggered control method provides a positive solution. The salient feature of event-triggered control is that agents communicate only when communication is needed, thereby reducing the communication load and unnecessary use of computing resources. However, traditional event triggering requires continuous communication between agents because it requires real-time judgment on whether to trigger. Therefore, it is necessary to introduce a more flexible event triggering scheme to save communication resources.

[0005] In a multi-agent system, it is difficult to avoid time delays caused by undesirable data transmission and post-data processing problems. The existence of time delays may affect the performance of the closed-loop system and even destroy the stability of the system. For example, the patent number CN118331047A, "A multi-agent dynamic event-triggered fixed-time binary consistency control method", does not consider the time delay and interference that are difficult to avoid in practical applications while achieving binary consistency. Therefore, it is necessary to introduce a controller that can be applied to the time delay and disturbance system 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 is used to avoid continuous communication between agents based on the event trigger mechanism through a state estimator, save the communication resources of the system, and is suitable for time delay and disturbance systems. At the same time, fixed-time control is adopted to improve the convergence speed of the system, thereby realizing consistency control of multi-agents.

[0007] In order to solve the above technical problems, the present invention provides a multi-agent event-triggered fixed-time consistency control method, which includes the following process:

[0008] Step S1, establishing a multi-agent system model and a communication network topology of the multi-agent system, quantifying the local interaction strength between each agent through the adjacency matrix, and using 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 sampling state at the triggering moment of the intelligent agent through the sensor, and obtain the estimated state at other moments through the state estimator;

[0010] Step S3: Design an event trigger function and event trigger conditions based on the fixed time consistency controller. The sampling state and the estimated state are used to determine whether the event is triggered by the event trigger conditions. After the event is triggered, the sampling 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 trigger 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 according to 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 expected trajectory.

[0013] As an improvement of 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 topology graph: ε represents the set of communication paths between agents, represents the set of agent vertices, Representation diagram The adjacency matrix of a is such that if edge (i,j)∈ε then a ij >0, indicating that there is a communication link between agents i and j;

[0015] The local interaction strength is quantified as:

[0016] a ij The size of is quantified by the local interaction strength between agents. If the agents are directly connected, then a ij =1; otherwise, if there is no communication link, then a ij =0;

[0017] The Laplace matrix is:

[0018]

[0019] in, The degree matrix constructed for the degree of the agent vertex, the element is diag[d 1 ,d 2 ,…,d N ],d i =deg in (v i ) or d i =deg out (v i ), is the in-degree of node i, To go out.

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

[0021] The mathematical model of the multi-agent is:

[0022]

[0023] Among them, x i (t) is the real-time location information of the ith agent, u i (t) is the fixed-time consistency controller output of the ith agent, τ i is the known input delay, f i (x i (t),t) is the dynamic nonlinear term, d i (x i (t), t) is the unknown disturbance, N is the number of agents;

[0024] Assumption 1: f i (x i (t),t) is the nonlinear term of the dynamics of agent i and satisfies the Lipschitz condition:

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

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

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

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

[0029] The fixed time consistency control target is:

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

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

[0032] And, there exists a constant value T max , the upper limit time T satisfies: T≤T max ;

[0033] Lemma 1: For any non-negative number y k , and k=1,2,…,N, the following inequality holds:

[0034]

[0035] Lemma 2: Undirected connected graph The Laplacian matrix of is positive semidefinite and its eigenvalues ​​can be expressed from small to large as 0<λ 2 ≤…≤λ N , is the eigenvector corresponding to the eigenvalue 0, if and Then there is

[0036] in,

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

[0038]

[0039] in represents the state vector, y(0) is the initial state of the multi-agent system, 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), the multi-agent system can achieve fixed-time consistency within an upper limit time T, and:

[0042]

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

[0044] The state estimator is:

[0045]

[0046] in, is the estimated state of the ith agent, is the sampled state of the ith agent, and is the kth triggering moment of agent i;

[0047] The fixed time consistency controller is:

[0048]

[0049] Among them, b 1 ,b 2 ,b 3 is a constant, b 1 >0,b 2 >0,b 3 >0, p is the ratio of two positive odd numbers and p∈(1,+∞), Used to solve input delay.

[0050] As a further improvement of 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] Among them, δ is the design parameter of the trigger function, E i (t) is the measurement error:

[0056]

[0057] As a further improvement of 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) is another form of event trigger function:

[0061]

[0062] in,

[0063]

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

[0065] The parameter b of the fixed time consistency controller 2 ,b 3 , the parameter δ of the event trigger function must meet the following conditions:

[0066]

[0067] Derivation get Prove that the Zeno phenomenon is avoided.

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

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

[0070]

[0071] Construct the following Lyapunov function:

[0072]

[0073] After taking the derivative of the Lyapunov function, we get in According to Lemma 3, it can be concluded that the multi-agent achieves fixed-time consistency, and the fixed convergence time upper limit satisfies equation (22).

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

[0075] 1. The control protocol designed by the present invention can enable the multi-agent system to achieve convergence in any initial state within a fixed time, and the system converges faster.

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

[0077] 3. The controller designed by the present invention takes into account the influence of time delay and disturbance on the system, and is not only applicable to the occasions with input time delay, but also applicable to the occasions with external disturbance. Therefore, the present invention has a wider range of application scenarios.

[0078] 4. The control protocol designed by the present invention can avoid continuous communication with neighboring intelligent agents by designing the second event triggering protocol and event triggering conditions. The first event triggering protocol and conditions are suitable for rapidly changing systems, and the second event triggering protocol and conditions can reduce the real-time computing burden when applied to systems with known models. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] The specific implementation modes of the present invention are further described in detail below with reference to the accompanying drawings.

[0080] Figure 1 A flowchart of a multi-agent event-triggered fixed-time consistency control method of the present invention;

[0081] Figure 2 Four communication topology diagrams of multi-agents of the present invention (a) and a schematic diagram of topology switching methods (b);

[0082] Figure 3 The trigger function and multi-agent state trajectory diagram under the triggering condition of Example 1 of the present invention;

[0083] Figure 4 The fixed time consistency controller output trajectory diagram under the trigger function and trigger conditions of embodiment 1 of the present invention;

[0084] Figure 5 A multi-agent event triggering time diagram under the triggering function and triggering conditions of Example 1 of the present invention;

[0085] Figure 6 The trigger function and multi-agent state trajectory diagram under the triggering condition of Example 2 of the present invention;

[0086] Figure 7 The fixed time consistency controller output trajectory diagram under the trigger function and trigger conditions of embodiment 2 of the present invention;

[0087] Figure 8 This is a diagram of the triggering time of a multi-agent event under the triggering function and triggering conditions of Example 2 of the present invention. DETAILED DESCRIPTION

[0088] The present invention is further described below in conjunction with specific embodiments, but the protection scope of the present invention is not limited thereto:

[0089] Embodiment 1, a multi-agent event-triggered fixed-time consistency control method, each agent obtains the sampling state through its own sensor, and the estimated state is estimated by the state estimator, to construct the signed undirected topological graph and Laplace matrix of the multi-agent, and use the Laplace matrix to globally describe the dynamic behavior of the system. Designing the measurement error and fixed-time consistency controller based on the state estimator is suitable for multi-agent systems with time lag and disturbance, sampling the sampling state of the agent at the triggering moment through the sensor, and obtaining the estimated state at the remaining moments through the state estimator; designing the event trigger function and event trigger condition based on the fixed-time consistency controller, the sampling state is calculated by the event trigger function and then input into the event trigger condition to determine whether the event is triggered, and after the event is triggered, the sampling state and estimated state of the agent are input into the fixed-time consistency controller to obtain the output value of the fixed-time consistency controller of each agent. According to the multi-agent stability method and event triggering conditions, the controller parameters and multi-agent system parameters that meet the judgment conditions are determined, and it is verified that the designed fixed-time consistency controller can avoid the occurrence of Zeno behavior. The upper limit of the fixed convergence time of the multi-agent event-triggered consistency control is estimated based on the designed fixed-time consistency protocol. 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 consistency among multiple agents under the action of the designed fixed-time consistency controller is as follows: Figure 1 As shown, specifically:

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

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

[0093] It is called graph The adjacency matrix of a is such that if edge (i,j)∈ε then aij >0, indicating that there is a communication link between agents i and j, a ij The size of is quantified by the local interaction strength between agents. In the system adopted in this paper, the value of the adjacency matrix can be directly determined by the communication network structure of the system. If the agents are directly connected, then a ij =1; otherwise, if there is no communication link, then a ij = 0. The neighbor set of agent i is represented by N i Indicates that the in-degree of node i is defined as The out-degree is defined as An undirected topological graph can be constructed from the degrees of the agent vertices The degree matrix of 1 ,d 2 ,…,d N ],d i =deg in (v i ) or d i =deg out (v i ). Based on the above definitions of degree matrix and adjacency matrix, we can get the undirected topological graph The Laplace matrix of is:

[0094]

[0095] in, The degree matrix constructed for the degrees of the agent's vertices.

[0096] The Laplace matrix contains the topological information of the graph, so it can describe the interaction between the agents in the multi-agent system. Through differential equations, the Laplace matrix can describe how the system state evolves over time. Moreover, the eigenvalues ​​of the Laplace matrix provide information about the stability and convergence speed of the system. Therefore, the Laplace matrix is ​​used to globally describe the dynamic behavior of the 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 expressed as:

[0098]

[0099] Among them, x i (t) is the real-time location information of the ith agent, u i (t) is the fixed-time consistency controller output of the ith agent, τ i is the known input delay, f i (x i (t),t) is the dynamic nonlinear term, d i (x i(t), t) is the unknown disturbance, and N is the number of agents.

[0100] Assumption 1: f i (x i (t),t) is the nonlinear term of the dynamics of agent i and satisfies 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 interference to agent i is bounded and bounded by a known positive constant d, that is, |d i (x i (t),t)|≤d.

[0103] It is expected that multiple agents can achieve consistency within a fixed time under any initial state. The state of the multi-agent must satisfy:

[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 non-negative number y k , and k=1,2,…,N, the following inequality holds:

[0108]

[0109] Lemma 2: Undirected connected graph The Laplacian matrix of is semi-positive definite and its eigenvalues ​​can be expressed as 0<λ from small to large 2 ≤…≤λ N , is the eigenvector corresponding to the eigenvalue 0, if and Then there is

[0110] in,

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

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

[0113]

[0114] in, represents the state vector, y(0) is the initial state of the multi-agent system (i.e., formula (7)), is a nonlinear function.

[0115] Assume 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), the multi-agent system can achieve fixed-time consistency within the upper limit time T, and:

[0118]

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

[0120] The state estimator is:

[0121]

[0122] in, is the estimated state of the ith agent, is the sampled state of the ith agent, and is the kth triggering moment of agent i.

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

[0124]

[0125] Among them, b 1 ,b 2 ,b 3 is a constant, b 1 >0,b 2 >0,b 3 >0, p is the ratio of two positive odd numbers and p∈(1,+∞), Designed to address input latency.

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

[0127] 3.1 Definition of measurement error:

[0128]

[0129] 3.2 Determine the event trigger function:

[0130]

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

[0132] 3.3 Determine the event triggering time (i.e. event triggering conditions):

[0133]

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

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

[0136] The parameters in the fixed-time consistency controller (i.e., equation (11)) and the parameters in the event trigger function (i.e., equation (13)) need to satisfy the following conditions:

[0137]

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

[0139]

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

[0141]

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

[0143]

[0144] Assumptions:

[0145]

[0146] When the event trigger condition is met and the event is triggered, the event trigger function g i becomes 0, which means therefore:

[0147]

[0148] According to the event trigger functions (13) and (20), we can get:

[0149]

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

[0151] To sum up, under the action of the fixed-time consistency controller of the present invention, under the premise 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, avoiding the occurrence of the Zeno phenomenon.

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

[0153]

[0154] The fixed time upper limit of multi-agent is formula (22), which is a fixed time value and has nothing to do with the initial state of the system.

[0155] Consider the Lyapunov function:

[0156]

[0157] Derivative of the Lyapunov function:

[0158]

[0159] According to Lemma 1, we can get:

[0160]

[0161] From Lemma 2, we can get:

[0162]

[0163] therefore:

[0164]

[0165] in,

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

[0167]

[0168] And T(χ) satisfies:

[0169]

[0170] The above results show that when t = T(χ), the control input u i (t) will become 0, and It will also be in T max +τ i Therefore, when time t=T(x)≤T max +max(τ i ), we can get Therefore, the multi-agent system can achieve fixed-time consistency, and the fixed convergence time upper limit satisfies equation (22).

[0171] Therefore, under the action of the proposed fixed-time consistency controller, the error of the multi-agent system gradually converges to zero, the multi-agent system reaches a stable expected trajectory, and the fixed-time state consistency of the multi-agent system can be achieved.

[0172] Note: The above reasoning is based on a fixed topology. For a switching topology that is more in line with actual application scenarios, the reasoning process is the same as that of a fixed topology. It is only necessary to replace λ in condition (15) with 2 Replace with the smallest λ in the Laplace matrix corresponding to all topologies 2 That's it.

[0173] Embodiment 2: A method for controlling the consistency of fixed time triggered by multi-agent events, the specific process is as follows:

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

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

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

[0177] By designing the second event triggering condition and event triggering function, the next triggering time can be calculated to avoid continuous communication with neighboring agents and reduce the real-time computing burden;

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

[0179] 3.2 Define event trigger function

[0180]

[0181] in,

[0182]

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

[0184] 3.3 Event triggering conditions are:

[0185]

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

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

[0188]

[0189] Substituting it into formula (30), we can get

[0190]

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

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

[0193] Using the same Lyapunov function as in step 5 in Example 1 and taking the derivative with respect to t, we can obtain:

[0194]

[0195] Based on formula (18), we can get

[0196]

[0197] By integrating formula (36), we can get

[0198]

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

[0200] Gi (t)≤0 (38)

[0201] From this we can get

[0202]

[0203] Substituting it into equation (33) we get

[0204]

[0205] where b 1 >0,b 3 >0,δ∈(0,1),λ 2 ,V(t),N>0, so under the event trigger function (Equation (31)) and event trigger condition (Equation (32)), the system can achieve fixed time consistency, and the fixed convergence time upper limit satisfies Equation (22).

[0206] experiment:

[0207] The effectiveness of the multi-agent event-triggered fixed-time consistency control method of the present invention is verified by numerical simulation. Determine the topological structure and switching mode of the multi-agent as follows Figure 2 shown.

[0208] The initial position of the multi-intelligence is obtained by the sensor The dynamic equation of the intelligent agent is f(x i (t),t)=0.2x i (t)+0.6cos(t), the disturbance to the agent is d i (x i (t),t)=0.1cos(x i (t)). The remaining parameters take the values ​​of b 1 =0.5,b 2 =15,b 3 =0.45,p=1.2,δ=0.1,a=-0.02,τ 1 =τ 2 =τ 3 =τ 4 =τ 5 =τ 6 =0.05. Figure 3 and Figure 4 The position simulation diagram of the multi-agent and the fixed-time consistency controller output simulation diagram show that the multi-agent can achieve fixed-time consistency. The convergence time is less than the upper limit of the calculated convergence time of 49.527s, and is much shorter than the 2.1s of the conventional controller triggered by the same type of consistency event. Figure 5This is a diagram of multi-agent event triggering time obtained by the method of Example 1. The present invention adopts model-based event triggering, which further reduces the number of system triggering times compared to traditional event triggering. Because multi-agents only exchange information with each other at the triggering moment, the present invention can save communication resources and extend the service life of the controller.

[0209] Figure 6 and Figure 7 This is a position simulation diagram of multiple agents under event triggering conditions and a simulation diagram of fixed time consistency controller output using the event triggering function of Example 2. It can be seen from the figure that multiple agents can also achieve fixed time consistency. Figure 8 The event triggering timing diagram of the multi-agent of Example 2 is adopted. Compared with the event triggering conditions of Example 1, the number of event triggering is increased while reducing the real-time computing burden.

[0210] Finally, it should be noted that the above examples are only some specific embodiments of the present invention. Obviously, the present invention is not limited to the above embodiments, and there are many variations. All variations that can be directly derived or associated with the content disclosed by a person skilled in the art should be considered as the protection scope of the present invention.

Claims

1. A multi-agent event-triggered fixed-time consistency control method, characterized by: Step S1, establishing a multi-agent system model and a communication network topology of the multi-agent system, quantifying the local interaction strength between each agent through the adjacency matrix, and using 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 sampling state at the triggering moment of the intelligent agent through the sensor, and obtain the estimated state at other moments through the state estimator; Step S3: Design an event trigger function and event trigger conditions based on the fixed time consistency controller. The sampling state and the estimated state are used to determine whether the event is triggered by the event trigger conditions. After the event is triggered, the sampling 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 trigger 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 according to 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 expected trajectory.

2. A 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 topology graph: ε represents the set of communication paths between agents, represents the set of agent vertices, Representation diagram The adjacency matrix of a is such that if edge (i,j)∈ε then a ij >0, indicating that there is a communication link between agents i and j; The local interaction strength is quantified as: a ij The size of is quantified by the local interaction strength between agents. If the agents are directly connected, then a ij =1; otherwise, if there is no communication link, then a ij =0; The Laplace matrix is: in, The degree matrix constructed for the degree of the agent vertex is diag[d1,d2,…,d N ],d i =deg in (v i ) or d i =deg out (v i ), is the in-degree of node i, To go out.

3. A multi-agent event-triggered fixed-time consistency control method according to claim 2, characterized in that: The mathematical model of the multi-agent is: Among them, x i (t) is the real-time location information of the ith agent, u i (t) is the fixed-time consistency controller output of the ith agent, τ i is the known input delay, f i (x i (t),t) is the dynamic nonlinear term, d i (x i (t), t) is the unknown disturbance, N is the number of agents; Assumption 1: f i (x i (t),t) is the nonlinear term of the dynamics of agent i and satisfies the Lipschitz condition: for 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 disturbance to agent i is bounded and bounded by a known positive constant d: |d i (x i (t),t)|≤d。 4. A multi-agent event-triggered fixed-time consistency control method according to claim 3, characterized in that: The fixed time consistency control target is: There exists a positive value C such that: sup t≥T ||x i (t)-x j (t)||≤C (4) And, there exists a constant value T max , the upper limit time T satisfies: T≤T max ; Lemma 1: For any non-negative number y k , and k=1,2,…,N, the following inequality holds: Lemma 2: Undirected connected graph The Laplacian matrix of is semi-positive definite and its eigenvalues ​​can be expressed from small to large as 0<λ2≤…≤λ N , is the eigenvector corresponding to the eigenvalue 0, if and Then there is in, Lemma 3: For the following multi-agent system in represents the state vector, y(0) is the initial state of the multi-agent system, 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), the multi-agent system can achieve fixed-time consistency within an upper limit time T, and:

5. A multi-agent event-triggered fixed-time consistency control method according to claim 4, characterized in that: The state estimator is: in, is the estimated state of the ith agent, is the sampled state of the ith agent, and is the kth triggering moment of agent i; The fixed time consistency controller is: Where b1, b2, b3 are constants, b1>0, b2>0, b3>0, p is the ratio of two positive odd numbers and p∈(1,+∞), Used to solve input delay.

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

7. A multi-agent event-triggered fixed-time consistency control method according to claim 5, characterized in that: Another form of the event triggering condition is: Among them, G i (t) is another form of event trigger function: in, 8. A multi-agent event-triggered fixed-time consistency control method according to any one of claims 6 or 7, characterized in that: The parameters b2 and b3 of the fixed time consistency controller and the parameter δ of the event trigger function must meet the following conditions: Derivation get Prove that the Zeno phenomenon is avoided.

9. A multi-agent event-triggered fixed-time consistency control method according to claim 8, characterized in that: The fixed upper limit of convergence time is: Construct the following Lyapunov function: After taking the derivative of the Lyapunov function, we get in According to Lemma 3, it can be concluded that the multi-agent achieves fixed-time consistency, and the fixed convergence time upper limit satisfies equation (22).

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