Multi-agent distributed formation control method based on mixed event triggering mechanism

Abstract

The invention belongs to the field of cooperative control of a multi-agent system, and the method aims at a fully heterogeneous linear multi-agent system under a directed topological graph, takes event-triggered communication transmission as a background, and aims at realizing stable formation control on the premise of utilizing a fully distributed control structure. And the formation control problem of the fully heterogeneous multi-agent system based on the mixed event triggering mechanism is researched. According to the method, a mixed event trigger communication strategy is used, network transmission bandwidth occupation can be reduced, and data transmission energy consumption is saved; designing a local state observer and a distributed event trigger state observer to estimate the states of the followers and the leader according to the conditions that the states of the followers are unknown and communication links do not exist between the leader and part of the followers; the designed distributed formation control protocol does not depend on global information, can ensure that followers realize ideal time-varying output formation configuration in a dynamic environment, and can accurately track a motion trail formed by a plurality of leaders at the same time.

Description

Technical Field

[0001] The present invention belongs to the field of collaborative control of multi-autonomous agent systems, and specifically relates to a fully heterogeneous multi-autonomous agent distributed formation control method based on a hybrid event trigger mechanism. Background Art

[0002] Multi-agent systems consist of multiple autonomous and intercommunicating agents that collaborate in complex and dynamic environments to achieve common goals. Each agent typically has perception, decision-making, and execution capabilities to complete tasks autonomously. Such systems are characterized by autonomy, distribution, interactivity, dynamics, robustness, and coordination. Their ability to handle complex tasks and dynamic environments makes them of great value in modern technology. The formation control problem of multi-agents refers to ensuring that followers complete and maintain a predefined formation configuration related to the task in a dynamic environment through information communication between agents and effective cooperative control protocols, while being able to accurately track the movement trajectory of the leader. This problem requires the design and implementation of control strategies that adapt to changes in the environment and tasks to achieve and maintain the formation goals. This problem is of great significance in practical applications such as drone reconnaissance, robot swarms, and satellite formations.

[0003] In the military field, formation control has important application value. In the execution of military tasks such as reconnaissance and detection, ground vehicles, infantry units, and aerial drones, fighter jets, etc. are all regarded as different types of autonomous agents. Here, aerial drone formations are particularly suitable for tasks such as wide-area reconnaissance, target surveillance, and intelligence collection. Through formation flight, these drones can cover a large area, monitor enemy dynamics in real time, and perform target identification and positioning. Formation control ensures that drones maintain a stable formation during flight, thereby maximizing regional coverage and improving intelligence collection efficiency. For example, when ground forces perform combat or patrol missions, drones can serve as air command platforms to provide a global perspective and assist ground units in formulating tactics. This is because ground autonomous agents (such as robot fleets and infantry) may find it difficult to obtain panoramic spatial information, while aerial autonomous agents (such as drones) can provide more accurate geographic coordinates and real-time data, thereby enhancing the decision-making ability and combat efficiency of ground forces. In addition, for the distributed control adopted, autonomous agents can process information locally, reducing the latency of the central node and improving the real-time response capability and robustness to environmental changes.

[0004] In the communication network of multi-agent systems, since the network bandwidth and transmission capacity are usually limited by technical and environmental conditions, it is particularly important to ensure efficient bandwidth and energy utilization. This limitation requires us to fully consider the optimization strategy of data transmission when designing and implementing communication protocols to reduce bandwidth occupancy and energy consumption. Summary of the invention

[0005] In view of this, the present invention provides a distributed formation control method for a completely heterogeneous multi-autonomous system based on a hybrid event trigger mechanism, which can be used for UAV formations to perform tasks. For a completely heterogeneous linear multi-autonomous system, a distributed formation control method based on a fully distributed observer is proposed based on a hybrid event trigger mechanism that does not rely on global communication network information. Under the premise of ensuring that the autonomous agent achieves the desired goal, it can not only improve the data transmission efficiency, but also effectively continue the energy supply of the autonomous agent, ensuring its continuous and reliable operation in a complex environment.

[0006] In order to solve the above technical problems, the present invention is implemented as follows.

[0007] A multi-agent distributed formation control method based on a hybrid event trigger mechanism is applicable to a heterogeneous multi-agent system with multiple leader agents; the system has N+M agents, including N followers and M leaders; there is at least one directed path from each leader to the follower, and the leader has no neighbor agents;

[0008] Step 1: Design the follower’s local state observer to estimate the follower’s own state information;

[0009] Step 2: Design a fully distributed event-triggered observer, assign an observer to each follower to estimate the state of some leaders, so that some followers can obtain the state of some leaders, eliminating the restrictions on the topology structure;

[0010] Step 3: Design a hybrid event trigger mechanism with a positive minimum event trigger interval. The hybrid event trigger mechanism consists of a time trigger part and an event trigger part. represents the triggering time of follower j for the lth time, τ i Represents the waiting time. When , the trigger mechanism is time trigger; when When the triggering mechanism is event-triggered, the subject updates and communicates when the triggering conditions are met;

[0011] Step 4: Design a distributed controller using the followers’ desired formation configuration, the followers’ local state observer, and a fully distributed observer based on a hybrid event-triggered mechanism for estimating the leader’s state.

[0012] Step 5: Through the intermittent communication between nodes caused by the hybrid event triggering mechanism, the distributed controller is used to control the multi-autonomous system. The followers can achieve the desired formation configuration and track the motion trajectories formed by multiple heterogeneous leaders.

[0013] In step 1, the local state observer of the follower is:

[0014]

[0015] in, represents the local state observer of the ith follower, which is also the follower state estimate; A represents the first-order derivative of the local state observer of the i-th follower at time t, which is used to calculate the estimated state quantity at the next moment; i is the system state matrix of the follower, B i is the input matrix, C i are the output matrices of the followers respectively; y i (t) is the measured output of the ith follower at time t; L i is the local state observer of the ith follower The feedback matrix satisfies A i +L i C i It's Hurwitz's.

[0016] In step 2, the fully distributed event-triggered observer is:

[0017] An observer is designed for each follower to estimate the state of the leader. The observer realizes the global estimation of the leader state through event triggering mechanism and distributed structure, and adjusts the leader state through adaptive gain α ik (t) and β ij (t), a feedback control term that incorporates error information to adjust the estimation process;

[0018]

[0019] The meaning of each symbol is:

[0020] ξ i (t): represents the augmented vector of the i-th follower’s estimated values ​​of all leader states at time t, represents the corresponding first-order derivative, and Its weight ik (t) represents the estimated value of the i-th follower to the k-th leader; k = {N+1, N+2, ..., N+M}; the indexes of the N followers and the M leaders are numbered consecutively from 1 to N+M;

[0021] The diagonal matrix of the system matrix in the dynamic equation of the leader is represented by D k represents the system matrix of the kth leader;

[0022] ω ij and ω ik: represents the coupling weight coefficient between the two autonomous entities. If the coupling weight coefficient is greater than 0, it means that there is a communication link between the two autonomous entities. If the coupling weight coefficient is equal to 0, it means that there is no communication link between the two autonomous entities.

[0023] K: K = diag {K N+1 ,K N+2 ,...,K N+M} is the gain matrix, and K = -P, P>0 is a positive definite matrix that satisfies the Riccati equation in σ 2 >0,α>0,q k is the dimension of leader k;

[0024] s k (t) is the state variable of the kth leader at time t;

[0025] α ik (t), β ij (t): represents the adaptive coupling coefficient of the distributed event-triggered observer; are the adaptive coupling coefficients α ik (t) and β ij The first derivative of (t);

[0026] κ ik and κ ij : and are two positive constants, used to adjust the adaptive coupling coefficient α ik (t) and β ij (t) rate of change;

[0027] They are α ik (t) and β ij The low-pass filter weight estimate of (t) satisfies the initial value

[0028] δ ik and δ ij : and are two positive constants, used to adjust the weight estimates and The rate of change of

[0029] Indicates jk (t) is an open-loop estimate; each follower Required equipment An open-loop estimator estimates the state information of itself and its neighboring followers, where represents the number of neighboring followers of follower i; follower j transmits information to neighbor follower i only when the event of follower j is triggered; specifically, its dynamics are:

[0030]

[0031] The above formula indicates that during the communication interval, the open-loop estimator continuously updates the state estimate according to the system state equation; Follower i predicts the future state of follower j; once communication is restored, follower i uses the latest state information To correct the prediction error;

[0032] η i (t): represents the augmented vector of the open-loop estimates of all leaders by the ith follower at time t, i.e.

[0033] In step 3, the hybrid event triggering mechanism is designed as follows:

[0034] make Indicates the triggering moment of follower j for the lth time, which is used to describe the triggering instant interval. Indicates time The next trigger moment after that;

[0035] Introduce the auxiliary function φ i (t), its expression is:

[0036]

[0037] in, m i (t) is a time-varying coefficient that satisfies: If φ i (t)>0, then m i (t)=1, otherwise, m i (t) = 0; φ i (0) is a positive constant; is the time-varying coefficient:

[0038]

[0039] represents the square of the largest eigenvalue of the matrix P, Is a dynamic variable that satisfies μ 4 , μ 5 is the adjustment factor;

[0040] The hybrid event triggering mechanism is:

[0041]

[0042] Among them, τ i Represents the waiting time, at the triggering moment After i The first time that (t) = 0 holds is recorded as when When , the trigger mechanism is time trigger; when When the trigger mechanism is event trigger, F i is the event triggering condition; i (t) from φ i The time it takes for (0) to decrease to 0 is τ i ; Waiting time τ i By adjusting the size of φ i The coefficient μ of (t) 4 and μ 5 to make adjustments.

[0043] In step 3, the triggering condition F of the event triggering i for:

[0044]

[0045] In the above formula, Γ=P 2 , where P>0 is a positive definite matrix; η ij (t) = η i (t)-η j (t), are the follower and leader index sets respectively; μ 4 , μ 5 and α are three positive constants, satisfying and α>0;

[0046] Dynamic variables in event trigger conditions According to the error dynamic adjustment, to ensure that the error dynamic When the error is small, the communication is reduced, while the error dynamics When it is larger, the acceleration trigger is accelerated; by adjusting the coefficient μ 4 and μ 5 To adjust the event triggering frequency.

[0047] Beneficial effects:

[0048] (1) Compared with the traditional time-triggered mechanism, the event-triggered mechanism enables the autonomous agent to update and communicate only when a specific event is met, thus avoiding unnecessary calculations and communications, improving efficiency and saving communication resources. In addition, for complex practical scenarios, the trigger conditions can be adjusted to meet the communication and accuracy requirements, thus improving the adaptability and stability of the system.

[0049] (2) Unlike the existing event trigger mechanism, the event trigger mechanism designed by the present invention has a strict positive minimum event trigger interval. This is because the operating frequency of the actual device is usually limited, and too high an update frequency will accelerate hardware wear, thereby shortening the system life. In fact, requiring the minimum event interval to be a positive value, rather than just greater than zero (to exclude Zeno behavior), is more in line with the strict conditions of actual application scenarios. This is because hardware constraints usually limit the positive minimum event interval between two consecutive trigger moments.

[0050] (3) The application scope of the present invention is wider. For complex engineering tasks, such as air-ground collaborative control tasks, multiple drones and unmanned vehicles with different functions are required to work together to meet the task requirements such as target tracking and interception. At this time, the control method only for homogeneous systems is no longer applicable. The present invention is not only applicable to homogeneous systems, but also to completely heterogeneous systems with wider applications.

[0051] (4) The present invention can improve the robustness and flexibility of the system. By introducing a fully distributed observer to estimate the status of multiple leaders, the restriction on the topological structure is eliminated, that is, it is no longer required that there is at least one follower directly adjacent to all leaders, and the adaptability and stability under different communication conditions are enhanced.

[0052] (5) The present invention can improve the reliability of the system and has the advantages of high efficiency and energy saving. In the application context of modern intelligent transportation systems, if a single central control unit is relied upon to manage all vehicles, once the central control unit fails, the entire transportation system may suffer serious paralysis. However, in a distributed control system, each autonomous subject collaborates through an independent control mechanism. Even if the communication of some autonomous subjects fails, other autonomous subjects can continue to operate normally and maintain the overall functionality of the system. Therefore, the use of a distributed control scheme can significantly enhance the robustness of the system, allowing it to maintain high reliability and stability in the face of local failures.

[0053] (6) The present invention can be directly applied to the formation mission of a multi-autonomous system with multiple heterogeneous leaders, and can effectively deal with the problem of mission failure caused by the failure of a leader in complex environments such as network attacks. In addition, in air-to-ground unmanned systems that perform tasks such as target reconnaissance, multiple different leaders can be used to guide the various follower subgroups in the formation and achieve multiple mission objectives at the same time. The invention improves the flexibility, fault tolerance and efficiency of the system, and has important theoretical significance and broad practical application prospects.

[0054] The method proposed in the present invention has potential value in many application fields, such as intelligent transportation, multi-UAV reconnaissance and detection, satellite formation, smart grid, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 This is a computer flow chart of the multi-autonomous distributed formation control method based on the hybrid event trigger mechanism described in the present invention.

[0056] Figure 2 It is a directed communication topology relationship between completely heterogeneous multi-autonomous agents, where numbers 1-3 represent heterogeneous leader autonomous agents, numbers 4-9 represent heterogeneous follower autonomous agents, connecting arrows represent directed transmission of information flow between autonomous agents, and connecting lines represent undirected transmission of information flow between autonomous agents;

[0057] Figure 3 is the error norm of the observer generated locally for the computer simulation curve The changing trajectory of

[0058] Figure 4 shows the estimated error norm ||e produced by the distributed event-triggered observer ik (t)||, where e ik (t) = ξ ik (t)-s k (t), i=4,5,…,9,k=1,2,3. Figure 4 The first subgraph in is the state ||e i1 (t)||’s trajectory change diagram, the second sub-graph is the state||e i2 (t)||’s trajectory change diagram, the third sub-diagram is the state||e i3 (t)||’s trajectory change diagram.

[0059] Figure 5 It is the changing curve value of the output formation error of all followers within 0-15 seconds. Figure 5 The first subgraph in is state e yi1 (t) state change diagram, the second sub-diagram is state e yi2 (t) state change diagram, the third sub-diagram is state e yi3 (t) state change diagram.

[0060] Figure 6 This is a screenshot of the multi-agent output state at different times of the computer simulation curve. Figure 6 Figures (a)-(d) represent state snapshots at 0 seconds, 3 seconds, 10 seconds, and 15 seconds respectively; the dotted line represents the formation configuration formed by the followers, the five-pointed star represents the output information of the leader, and the remaining shapes represent the output information of the followers. DETAILED DESCRIPTION

[0061] The technical solution of the present invention is further described in detail below through drawings and examples.

[0062] The block diagram of the multi-agent distributed formation control method based on the hybrid event trigger mechanism in the embodiment of the present invention is as follows: Figure 1 As shown, it includes the following steps:

[0063] Step 1: Here we consider a more practical fully heterogeneous multi-agent system, which refers to a system composed of multiple agents with different functions, physical characteristics or task objectives. These agents can exhibit a variety of heterogeneity. The number of follower agents (followers) is N, and the number of leader agents (leaders) is M; represents the index set of followers, Represents the index set of the leader. Here, the follower and leader indexes need to be arranged consecutively, and their dynamic equations are:

[0064]

[0065] Among them, x i (t) is the state variable of the ith follower at time t, is the first-order derivative of the state of the ith follower at time t, u i (t) is the control input of the ith follower at time t, y i (t) is the measured output of the ith follower at time t, s k (t) is the state variable of the kth leader at time t, is the first-order derivative of the kth leader state, z k (t) is the measured output of the kth leader.

[0066] The initial state of the follower is The initial state of the leader is They are n i ×n i The system state matrix of dimension n i ×m i dimensional input matrix, p×n i dimensional output matrix, and the matrix B i The rank is m i ; are the system state matrix and output matrix of the leader respectively. i , m i , p, q k All are normal numbers.

[0067] Step 2: Examine the Leader’s System Matrix The eigenvalues ​​of are on the imaginary axis; the topological diagram between the followers of the design is connected and undirected; the communication topology of the system It is necessary to satisfy that there is at least one directed path from each leader to the follower; since the leader does not have any neighboring agents, the Laplace matrix of the topological graph It can be expressed as:

[0068]

[0069] in

[0070] Step 3: Since the state of the follower is unmeasurable, it is necessary to design a local state observer for each follower agent to estimate its own state. For the i-th agent, design the corresponding local state observer and use the output and input information to estimate the state information of the follower itself:

[0071]

[0072] in, represents the local observation state of the ith agent, represents the first-order derivative of the local state observer of the i-th autonomous body at time t, which is used to calculate its estimated state at the next moment; is the local state observer of the ith agent The feedback matrix satisfies A i +L i C i It was Hurwitz's;

[0073] Step 4: Considering the limited communication in actual projects, it is assumed that only some followers can obtain the status of some leaders. Therefore, it is necessary to design a fully distributed event-triggered observer for each follower to estimate the status of the leader:

[0074]

[0075] The core design idea of ​​the observer is to achieve global estimation of the leader state through event triggering mechanism and distributed structure, and to achieve global estimation of the leader state through adaptive gain α ik (t) and β ij (t), combined with the error information feedback control term (such as K(η i (t)-η j (t))) is used to adjust the estimation process to ensure accuracy and robustness under discontinuous communication.

[0076] The setting values ​​of relevant parameters and the requirements that need to be met are as follows:

[0077] ξ i (t): represents the augmented vector of the i-th follower’s estimated values ​​of all leader states at time t, represents the corresponding first-order derivative, and Its weight ik (t) represents the estimate of the kth leader by the ith follower;

[0078] The diagonal matrix of the system matrix representing the leader is

[0079] ω ij (ω ik ): represents the coupling weight coefficient between agent j (agent k) and agent i, satisfying ω ij ≥0; if ω ij > 0 means that there is a communication link between agent j (agent k) and agent i; if ω ij =0, indicating that there is no communication link between agent j (agent k) and agent i;

[0080] K: K = diag {K N+1 ,K N+2 ,…,K N+M} is a gain matrix, and K = -P, P>0 is a positive definite matrix that satisfies the Riccati equation in σ 2 >0,α>0,q k is the dimension of the state variable of leader k.

[0081] α ik (t), β ij (t): represents the adaptive coupling coefficient of the distributed event-triggered observer. The introduction of this adaptive mechanism can free the observer and controller from dependence on global information (such as the Laplace matrix) during the design process to achieve a fully distributed structure. are the adaptive coupling coefficients α ik (t) and β ij The first derivative of (t);

[0082] κ ik and κ ij : and are two positive constants used to adjust the adaptive coupling coefficient α ik (t) and β ij (t) rate of change;

[0083] They are α ik (t) and β ij The low-pass filter weight estimate of (t) satisfies the initial value

[0084] δ ik and δij : and are two positive constants used to adjust the weight estimates and The rate of change of

[0085] Indicates jk (t) is an open-loop estimate of each follower. Required equipment An open-loop estimator estimates the state information of itself and its neighboring followers, where represents the number of neighboring followers of follower i. Follower j transmits information to neighbor follower i only when the event of follower j is triggered. Specifically, its dynamics are:

[0086]

[0087] The above formula indicates that during the communication interval, the open-loop estimator continuously updates the state estimate based on the system state equation. Follower i can predict the future state of follower j. Once communication is restored, follower i can use the latest state information To correct the prediction error. This mechanism ensures that the performance of the system will not be greatly affected when communication is temporarily lost. It can be seen that the design of an open-loop estimator for the follower realizes intermittent communication between followers.

[0088] η i (t): represents the augmented vector of the open-loop estimates of all leaders by the ith follower at time t, i.e.

[0089] Step 5: In order to further reduce the number of communications, a hybrid event trigger mechanism is designed. This trigger mechanism consists of a time trigger part and an event trigger part. represents the triggering moment of follower j, l represents the sequence number of its lth event triggering, which is used to describe the triggering instant interval. Indicates time The next triggering moment after. is the set of natural numbers;

[0090] In order to design the subsequent mixed event triggering mechanism, we first introduce an auxiliary function φ i (t), its expression is:

[0091]

[0092] in, m i(t) is a time-varying coefficient that satisfies: If φ i (t)>0, then m i (t)=1, otherwise, m i (t) = 0; as well as is the time-varying coefficient; is a dynamic variable that satisfies in φ i (0) is a positive constant, Denotes the square of the largest eigenvalue of the matrix P.

[0093] Specifically, the designed hybrid event trigger mechanism is as follows:

[0094]

[0095] where τ i represents the waiting time, whose size is determined by the auxiliary function φ introduced above i (t)(φ i (0)) to characterize. At the triggering moment After i The first time that (t) = 0 holds is recorded as when When , the trigger mechanism is time trigger; when , the trigger mechanism is event triggering. That is, φ i (t) from φ i The time it takes for (0) to decrease to 0 is τ i . It can be seen that the waiting time τ designed here i The size of φ can be adjusted by i (t) coefficients (e.g. μ 4 and μ 5 ) to adjust, which also improves the flexibility and practicality of the design;

[0096] Accordingly, the designed trigger condition is

[0097]

[0098] The event trigger condition combines the error dynamic information η ij (t), and the adaptive adjustment method, which not only reduces the communication frequency but also ensures the control performance of the multi-agent system. Some dynamic variables in the event triggering conditions It will also adjust dynamically according to the error to ensure that When the error is small, the communication is reduced, while the error dynamics When μ is large, the acceleration triggering is performed to ensure the robustness and energy saving of the control system. 4 and μ 5 Equal coefficients to adjust the event trigger frequency.

[0099] The above variables are η ij (t) = η i (t)-η j (t), μ 4 , μ 5 and α are three positive constants, satisfying and α>0; Γ=diag{Γ N+1 ,Γ N+2 ,…,Γ N+M} is a gain matrix, and Γ=P 2 , where P>0 is a positive definite matrix that satisfies the Riccati equation in σ 2 >0,α>0,q k is the dimension of the state variable of leader k.

[0100] Step 6: Design three appropriate control gain matrices Q 1i , and Q ik . Where Q 1i Make A i +B i Q 1i The real part of all eigenvalues ​​is less than or equal to 0, Q ik Satisfy Q ik =U ik -Q 1i X ik , satisfy Choose ρ k Make

[0101] For Followers The expected time-varying output formation configuration h yi The dynamics of (t) is:

[0102]

[0103] in is the state of the local external system, is the corresponding output. System state matrix Output Matrix are two constant matrices. p is the dimension of the follower’s output variable, is a normal number.

[0104] Control gain matrix Q ik =U ik -Q 1i X ik X in ik and U ik is the solution matrix of the following regulation equation:

[0105]

[0106] Among them A i , B i , C i are the system state matrix, input matrix and output matrix of the ith follower, respectively, D k and F k is the system state matrix and output matrix of the kth leader.

[0107] Control Gain Matrix In and is the solution matrix of the following local regulation equation:

[0108]

[0109] Among them, H i represents the state matrix of the local external system of the ith follower, Y i is the corresponding output matrix; based on the above preparation, the distributed controller is designed as follows:

[0110]

[0111] The setting values ​​of relevant parameters and the requirements that need to be met are as follows:

[0112] u i (t): control input of the ith autonomous agent,

[0113] Q 1i : The control gain matrix of the ith autonomous agent,

[0114] Q ik : The control gain matrix of the ith autonomous agent,

[0115] The control gain matrix of the ith agent,

[0116] ρ k : Used to construct the convex hull composed of multiple leader outputs;

[0117] The local state observer of the i-th agent uses the output and input information to estimate the state information of follower i itself;

[0118] ξ ik (t): The fully distributed event-triggered observer designed by the i-th follower for the k-th leader to estimate the state of the k-th leader.

[0119] Step 7: Through the intermittent communication between nodes caused by the hybrid event trigger mechanism, the distributed formation control law is used to control the multi-autonomous system. The followers can achieve the desired formation configuration and accurately track the motion trajectories formed by multiple heterogeneous leaders.

[0120] The effectiveness of the method of the present invention will be tested through simulation experiments below.

[0121] Consider a completely heterogeneous multi-agent system, which consists of 6 heterogeneous followers (numbered 4, 5, ..., 9) and 3 heterogeneous leaders (numbered 1, 2, 3). The system matrix of their kinematic model is set as:

[0122]

[0123] The ideal formation configuration is The system matrix of the external system is designed as and

[0124] The initial values ​​of the states of all follower agents and observers are any value between [-2, 2], and the initial value of the leader state is s 1 (0) = s 2 (0) = s 3 (0) = [0.2, 0.3, 0.3, 0.5, 0.2, 0.3] T The initial value of the adaptive coupling coefficient and its weight estimation is set as: α 41 (0), α 42 (0), α 63 (0) is any value in [0.6,1], β 48 (0) = 0.4, β 84 (0) = 0.4, β 56 (0) = β 65 (0) = 0.5, β 58 (0) = β 85 (0) = 0.6, β 68 (0) = β 86 (0) = 0.7, β 78 (0) = 0.8, β 87 (0) = 0.8, β69 (0) = β 96 (0) = 0.9, i,j=4,5,...,9. Set the parameter value in the event trigger condition to μ 4 =4,μ 5 =6,α=0.7,σ 2 =19,l i =0.9,δ ij =δ ik =2,κ ij =κ ik =3, i,j=4,5,...,9, k=1,2,3. Coefficient ρ k (k=1,2,3) is selected as The initial value of the auxiliary system is φ i (0)=5.

[0125] To satisfy the conditions in step 2, set

[0126]

[0127] Consider the ideal formation configuration h yi (t), in order to satisfy the conditions in step 6, we can deduce

[0128]

[0129] Choose the appropriate control gain matrix Q 1i (i=4,5,…,9) is:

[0130]

[0131] Then, the control gain matrix of each follower can be solved as follows:

[0132]

[0133] The gain matrix of each local state observer is

[0134]

[0135] The present invention discretizes the linear continuous system under study, and the discretization interval is 10 -4 seconds, and observe the effectiveness of the proposed algorithm. The simulation results are shown in Figure 3-6 And as shown in Table 1.

[0136] Figure 2 Represents the communication topology between the leader and followers. Figure 2It can be seen that numbers 4-9 are followers, and numbers 1, 2, and 3 are leaders. In addition, it can be seen that there is at least one directed path from each leader to a follower, while the communication between followers is undirected.

[0137] Figure 3 represents the error norm of the local state observer The change trajectory diagram of . It can be seen from the figure that under the designed local state observer, the observation error It is asymptotically convergent, that is, the designed local state observer can estimate the state of the self-agent i.

[0138] Figure 4 represents the changing trajectory of the observed error norm under the designed distributed event-triggered observer, Figure 4 The first subgraph in is the state ||e i1 (t)|| state change diagram, the second sub-graph is state||e i2 (t)|| state change diagram, the third sub-graph is state||e i3 (t)|| state change diagram. It can be seen from the figure that under the designed distributed event-triggered observer, the observation error of agent i on the leader is asymptotically convergent, which means that the designed event-triggered observer can effectively estimate the states of leaders 1, 2, and 3 under intermittent communication.

[0139] Figure 5 It shows the changing trend of each output state of the multi-agent formation control algorithm proposed by the present invention within 0-15 seconds. It can be seen that under the designed fully distributed formation control algorithm, the formation error of the system gradually tends to zero with time t.

[0140] Figure 6 The output status of the follower and the leader at time 0 seconds, 3 seconds, 10 seconds, and 15 seconds. Figure 5 and Figure 6 It can be seen that the multi-autonomous formation control algorithm proposed in the present invention can enable all followers to achieve an ideal formation configuration and track the motion trajectory formed by the output convex hulls of the three leaders, which shows that the proposed control algorithm can achieve the desired formation control.

[0141] The hybrid event trigger mechanism is called event trigger mechanism 1, and the event trigger mechanism without the time trigger part is called It is called event trigger mechanism 2. Table 1 records some comparisons of the number of triggers and the minimum trigger time interval between event trigger mechanism 1 and event trigger mechanism 2. It can be seen from Table 1 that the proposed algorithm can avoid the occurrence of Zeno behavior, that is, it will not produce an infinite number of triggers in a finite time. The comparison results also show that the proposed hybrid event trigger control method has fewer trigger times and larger intervals between events, which means that the proposed hybrid event trigger mechanism is superior to the traditional event trigger mechanism.

[0142] In summary, it can be seen from the simulation of this section that the formation control algorithm based on the hybrid event trigger mechanism proposed in the present invention has a good simulation effect both in terms of the number of triggers and the convergence performance, reflecting the superiority of the overall algorithm.

[0143] Table 1

[0144]

[0145] The above specific embodiments only describe the design principle of the present invention. The shapes and names of the components in the description may be different and are not limited. Therefore, those skilled in the art in the field of the present invention may modify or replace the technical solutions recorded in the above embodiments; and these modifications and replacements do not deviate from the creative purpose and technical solutions of the present invention and should all fall within the protection scope of the present invention.

Claims

1. A multi-agent distributed formation control method based on a hybrid event trigger mechanism, characterized in that: Applicable to heterogeneous multi-agent systems with multiple leader autonomous entities; the system has N+M autonomous entities, including N followers and M leaders; there is at least one directed path from each leader to the follower, and the leader does not have any neighbor autonomous entities; Step 1: Design the follower’s local state observer to estimate the follower’s own state information; Step 2: Design a fully distributed event-triggered observer, assign an observer to each follower to estimate the state of some leaders, so that some followers can obtain the state of some leaders, eliminating the restrictions on the topology structure; Step 3: Design a hybrid event trigger mechanism with a positive minimum event trigger interval. The hybrid event trigger mechanism consists of a time trigger part and an event trigger part. represents the triggering time of follower j for the lth time, τ i Represents the waiting time. When , the trigger mechanism is time trigger; when When the triggering mechanism is event-triggered, the subject updates and communicates when the triggering conditions are met; Step 4: Design a distributed controller using the followers’ desired formation configuration, the followers’ local state observer, and a fully distributed observer based on a hybrid event-triggered mechanism for estimating the leader’s state. Step 5: Through the intermittent communication between nodes caused by the hybrid event triggering mechanism, the distributed controller is used to control the multi-autonomous system. The followers can achieve the desired formation configuration and track the motion trajectories formed by multiple heterogeneous leaders.

2. The method according to claim 1, characterized in that In step 1, the local state observer of the follower is: in, represents the local state observer of the i-th follower, which is also the follower state estimate; A represents the first-order derivative of the local state observer of the i-th follower at time t, which is used to calculate the estimated state quantity at the next moment; i is the system state matrix of the follower, B i is the input matrix, C i are the output matrices of the followers respectively; y i (t) is the measured output of the ith follower at time t; L i is the local state observer of the ith follower The feedback matrix satisfies A i +L i C i It's Hurwitz's.

3. The method according to claim 1, characterized in that In step 2, the fully distributed event-triggered observer is: An observer is designed for each follower to estimate the state of the leader. The observer realizes the global estimation of the leader state through event triggering mechanism and distributed structure, and adjusts the leader state through adaptive gain α ik (t) and β ij (t), a feedback control term that incorporates error information to adjust the estimation process; The meaning of each symbol is: ξ i (t): represents the augmented vector of the i-th follower’s estimated values ​​of all leader states at time t, represents the corresponding first-order derivative, and Its weight ik (t) represents the estimated value of the i-th follower to the k-th leader; k = {N+1, N+2, ..., N+M}; the indexes of the N followers and the M leaders are numbered consecutively from 1 to N+M; The diagonal matrix of the system matrix in the dynamic equation of the leader is represented by D k represents the system matrix of the kth leader; ω ij and ω ik : represents the coupling weight coefficient between the two autonomous entities. If the coupling weight coefficient is greater than 0, it means that there is a communication link between the two autonomous entities. If the coupling weight coefficient is equal to 0, it means that there is no communication link between the two autonomous entities. K: K = diag {K N+1 ,K N+2 ,...,K N+M } is the gain matrix, and K = -P, P>0 is a positive definite matrix, satisfying the Riccati equation in σ2>0,α>0,q k is the dimension of leader k; s k (t) is the state variable of the kth leader at time t; α ik (t), β ij (t): represents the adaptive coupling coefficient of the distributed event-triggered observer; are the adaptive coupling coefficients α ik (t) and β ij The first derivative of (t); κ ik and κ ij : and are two positive constants, used to adjust the adaptive coupling coefficient α ik (t) and β ij (t) rate of change; They are α ik (t) and β ij The low-pass filter weight estimate of (t) satisfies the initial value δ ik and δ ij : and are two positive constants, used to adjust the weight estimates and The rate of change of Indicates jk (t) is an open-loop estimate; each follower Required equipment An open-loop estimator estimates the state information of itself and its neighboring followers, where represents the number of neighboring followers of follower i; follower j transmits information to neighbor follower i only when the event of follower j is triggered; specifically, its dynamics are: The above formula indicates that during the communication interval, the open-loop estimator continuously updates the state estimate according to the system state equation; Follower i predicts the future state of follower j; once communication is restored, follower i uses the latest state information To correct the prediction error; η i (t): represents the augmented vector of the open-loop estimates of all leaders by the ith follower at time t, i.e.

4. The method according to claim 3, characterized in that In step 3, the hybrid event triggering mechanism is designed as follows: make Indicates the triggering moment of follower j for the lth time, which is used to describe the triggering instant interval. Indicates time The next trigger moment after that; Introduce the auxiliary function φ i (t), its expression is: in, m i (t) is a time-varying coefficient that satisfies: If φ i (t)>0, then m i (t)=1, otherwise, m i (t) = 0; φ i (0) is a normal number; is the time-varying coefficient: represents the square of the largest eigenvalue of the matrix P, Is a dynamic variable that satisfies μ4 and μ5 are adjustment coefficients; The hybrid event triggering mechanism is: Among them, τ i Represents the waiting time, at the triggering moment After i The first time that (t) = 0 holds is recorded as when When , the trigger mechanism is time trigger; when When the trigger mechanism is event trigger, F i is the event triggering condition; i (t) from φ i The time it takes for (0) to decrease to 0 is τ i ; Waiting time τ i By adjusting the size of φ i (t) is adjusted by using the coefficients μ4 and μ5.

5. The method according to claim 4, characterized in that In step 3, Event triggering condition F i for: In the above formula, Γ=P 2 , where P>0 is a positive definite matrix; η ij (t) = η i (t)-η j (t), are the follower and leader index sets respectively; μ4, μ5 and α are three positive constants satisfying and α>0; Dynamic variables in event trigger conditions According to the error dynamic adjustment, to ensure that the error dynamic When the error is small, the communication is reduced, while the error dynamics The larger the value, the faster the triggering. The event triggering frequency can be adjusted by adjusting the coefficients μ4 and μ5.

6. The method according to claim 4, characterized in that The distributed controller constructed in step 4 is: in, u i (t): control input of the ith follower; The local state observer of the i-th agent uses the output and input information to estimate the state information of follower i itself; h i (t): The expected time-varying formation vector of the ith follower, whose dynamics is described as: where h i (t) is the state of the local external system shown in equation (1), h yi (t) is the corresponding output, H i is the system state matrix of the local external system, Y i is the output matrix of the local external system; Q 1i , Q ik , The three control gain matrices of the i-th follower; Q 1i Make A i +B i Q 1i The real part of all eigenvalues ​​is less than or equal to 0, Q ik Satisfy Q ik =U ik -Q 1i X ik , satisfy A i and B i are the system state matrix and input matrix of the ith follower respectively; U ik and X ik is the solution matrix of the following adjustment equation (2): Among them A i , B i , C i Denote the system state matrix, input matrix and output matrix of the ith follower, respectively. k and F k denote the system state matrix and output matrix of the kth leader respectively; and is the solution matrix of the following local regulation equation (3): Among them, H i represents the state matrix of the local external system of the ith follower, Y i is the corresponding output matrix; Q ik : The control gain matrix of the i-th follower; The control gain matrix of the i-th follower; ρ k :0≤ρ k ≤1, Used to construct the convex hull composed of multiple leader outputs; select ρ k Make ξ ik (t): The fully distributed event-triggered observer designed by the i-th follower for the k-th leader to estimate the state of the k-th leader.

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