Second-order multi-agent system control method based on dynamic event triggering

Abstract

The invention relates to the technical field of multi-agent control, in particular to a second-order multi-agent system control method based on dynamic event triggering, and the method comprises the steps: building a kinetic model of a leader-follower second-order multi-agent system considering unknown external interference, and designing a distributed fixed time observer on the basis, so as to achieve the control of the leader-follower second-order multi-agent system. State information of the leader is estimated in real time; introducing a fixed time extended state observer to estimate external disturbance; proposing a sliding mode surface based on the observation error; a distributed fixed-time sliding mode consistency tracking control protocol is designed, so that tracking errors are accurately converged within fixed time, an ideal control effect can be achieved even if external interference exists, the communication burden is effectively reduced through introduction of a dynamic event triggering mechanism, and the sesame phenomenon is avoided; tracking consistency control of the multi-agent system can be realized in a fixed time, the robustness and reliability of the system are improved, and communication resources are saved.

Description

Technical Field

[0001] The present invention relates to the field of multi-agent control technology, and in particular to a second-order multi-agent system control method based on dynamic event triggering. Background Art

[0002] In multi-agent systems, leader-follower structures are widely used in fields such as robotics, drone swarms, and network control. With the continuous advancement of technology, achieving fixed-time consistency control of multi-agent systems has become a research focus. This control method aims to make the state of the follower accurately track the state of the leader within a specified time, and has important application potential, including scenarios such as formation control, coordinated motion, and information sharing.

[0003] However, traditional control methods often rely on global information or frequent communication to achieve consistency, which leads to a waste of communication bandwidth and an increase in computational burden. Therefore, dynamic event triggering mechanisms have gradually attracted attention. This mechanism dynamically adjusts the communication timing according to changes in the system state, which can effectively reduce the communication frequency and reduce the network burden while still ensuring the stability and consistency of the system.

[0004] Therefore, developing a fixed-time consistency control method for a second-order leader-follower multi-agent system based on dynamic event triggering can not only improve the robustness and adaptability of the system, but also help overcome the deficiencies in the prior art. This paper proposes a novel control strategy to achieve more efficient coordination and control of multi-agent systems, which has important theoretical significance and practical application value.

[0005] Chinese patent application publication number: CN117348414A, discloses a second-order multi-agent system specified time dynamic event trigger control method, the method first sets the second-order multi-agent system, reconstructs the speed information time as T1, and sets the time used by the agent to reach bounded consistency as T2; secondly, designs a time observer for each agent in the second-order multi-agent system, and reconstructs the agent state value; then, based on the reconstructed agent state value, designs the dynamic variables and trigger conditions triggered by the dynamic event, so that the controller is updated when the trigger condition is met; finally, based on the reconstructed agent state value, sets the second-order multi-agent system specified time consistency control protocol based on dynamic event triggering, so that the agent reaches bounded consistency at time T1+T2. In the present invention, each agent can make decisions based on its own information and environmental conditions, so that the system can adapt to changes and keep running.

[0006] However, there are still the following problems in the prior art:

[0007] Although a variety of control strategies have been proposed to achieve fixed-time consistency control of multi-agent systems, most existing methods rely on fixed trigger conditions and are difficult to adapt to dynamically changing environments and system states. In addition, existing research mainly focuses on the control of first-order systems, while relatively few studies have been conducted on fixed-time consistency control of second-order systems, especially when considering uncertainties and external disturbances. Summary of the invention

[0008] To this end, the present invention provides a second-order multi-agent system control method based on dynamic event triggering to overcome the limitations of the prior art in the field of consistency tracking control of multi-agent systems.

[0009] To achieve the above object, the present invention provides a second-order multi-agent system control method based on dynamic event triggering, which includes:

[0010] Establish a second-order leader-follower multi-agent system dynamics model;

[0011] Determining a communication topology of the multi-agent system based on the dynamic model;

[0012] Designing a distributed fixed-time observer based on the dynamic model to estimate the state information of the leader, wherein the state information includes the position and speed of the leader;

[0013] Designing a fixed-time extended state observer to estimate unknown external disturbances included in the dynamic model;

[0014] Determining an observation error based on the distributed fixed-time observer and the fixed-time extended state observer to design a distributed fixed-time sliding surface;

[0015] According to the fixed-time sliding mode surface, a distributed fixed-time sliding mode consistency tracking control scheme based on a dynamic event triggering strategy is designed.

[0016] Furthermore, the leader is a system with dual integration characteristics of position and speed, and also includes an intelligent agent i as a follower.

[0017] Further, the leader-follower second-order multi-agent system dynamics model includes a dynamics model for the leader and a dynamics model for the follower;

[0018] The dynamic model for the leader and the dynamic model for the follower are established according to formula (1) and formula (2) respectively, including:

[0019] According to formula (1), the leader's dynamic model is established.

[0020]

[0021] In formula (1), x 0 (t) represents the position of the leader, v 0 (t) represents the speed of the leader, Represents x 0 The derivative of (t), Indicates v 0 The derivative of (t), u 0 (t) represents the control input of the leader, where u 0 (t)∈R n , R n represents an n-dimensional real vector space;

[0022] According to formula (2), the dynamic model of the follower is established.

[0023]

[0024] In formula (2), i = 1, 2, ..., N, x i (t) represents the position of follower i, v i (t) represents the speed of follower i, Represents x i The derivative of (t), Indicates v i The derivative of (t), u i (t) represents the control input, ω i (t) represents the unknown bounded external disturbance of the follower, where N represents the number of followers, u i (t)∈R n .

[0025] Furthermore, it is characterized in that the communication topology is determined as follows, including:

[0026] G=(V,E,A)

[0027] In the formula, G represents the topological graph, V represents the node set, and E represents the edge set connecting two nodes. A represents the adjacency matrix, where A = [a ij ]∈R N×N , a ij Represents the connection relationship between followers, R N×N Represents the N×N dimensional real matrix space.

[0028] Furthermore, it is characterized in that the distributed fixed-time observer is designed according to formula (3) and formula (4), including:

[0029]

[0030] in,

[0031] In formula (3) and formula (4), represents the position estimate of the leader by agent i, represents agent j’s estimate of the leader’s position, represents agent i’s estimate of the leader’s speed, represents agent j’s estimated speed of the leader, α 1 represents the first observer gain for adjusting the position error, β 1 represents the gain of the second observer for adjusting the position error, α 2 represents the first observer gain for adjusting the speed error, β 2 represents the gain of the second observer for adjusting the speed error, α 3 represents the third observer gain for adjusting the speed error, μ represents the response parameter, ξ i (t) represents the error term of follower i’s estimate of the leader’s position, represents the error term of follower i’s estimate of the leader’s speed, a ij Represents the connection relationship between followers, d i

[0032] represents the connection relationship between the follower and the leader, where μ>1;

[0033] The distributed fixed-time observer needs to meet a first fixed-time condition.

[0034] Furthermore, the fixed-time extended state observer is designed according to formula (5), including:

[0035]

[0036] In formula (5), x i (t) represents the position of follower i at time t, represents the estimated value of the position of follower i at time t, v i (t) represents the speed of follower i, represents the estimated value of the velocity of follower i, Denotes the bounded external disturbance ω on follower i i The estimated value of (t), a 1 represents the first exponential parameter used to adjust the position error, b 1 represents the second exponential parameter used to adjust the position error, a 2 represents the first exponential parameter used to adjust the speed error, b 2 represents the second exponential parameter used to adjust the speed error, a 3represents the first exponential parameter used to adjust the external disturbance error, b 3 represents the second exponential parameter used to adjust the external disturbance error, μ 1 represents the first gain coefficient for adjusting the position error, The second gain coefficient, μ, used to adjust the position error 2 A first gain coefficient for adjusting the speed error, The second gain coefficient, μ, used to adjust the speed error 3 represents the first gain coefficient used to adjust the external disturbance error, The second gain coefficient, δ i is the dynamic gain coefficient of the extended state observer;

[0037] The fixed-time extended state observer needs to satisfy a second fixed-time condition.

[0038] Furthermore, the process of determining the observation error according to the distributed fixed-time observer and the fixed-time extended state observer includes:

[0039] The observation error of the distributed fixed-time observer is determined according to formula (6), including:

[0040]

[0041] In formula (6), represents the observation error of the leader's position, represents the observation error of the leader's velocity;

[0042] The observation error of the fixed-time extended state observer is determined according to formula (7), including:

[0043]

[0044] In formula (7), represents the observation error of the position of follower i, represents the observation error of the velocity of follower i, represents the observation error of external disturbance for follower i.

[0045] Furthermore, it is characterized in that the process of designing the distributed fixed-time sliding surface includes:

[0046] Determining the tracking error of the position and velocity of follower i based on the observation error;

[0047] Based on the tracking error, the distributed fixed-time sliding surface is designed according to formula (8), including:

[0048]

[0049] In formula (8), s i (t) represents the sliding surface, e 1i (τ) represents the position tracking error, e 2i (τ) represents the velocity tracking error, e 1i (t) represents the position tracking error at time t, e 2i (t) represents the speed tracking error at time t, k 1 The first sliding mode gain of the position error, k 2 The second sliding mode gain representing the position error, l 1 Represents the first sliding mode gain of the velocity error, l 2 The second sliding mode gain representing the speed error; w 1 A first exponential parameter representing a nonlinear function related to the position error in the regulated sliding surface; The second exponential parameter representing the nonlinear function related to the position error in the regulated sliding surface; 2 The first exponential parameter of the nonlinear function related to the speed error in the regulated sliding surface; It represents the second exponential parameter of the nonlinear function related to the velocity error in the adjusted sliding surface, and t represents the time variable.

[0050] Furthermore, it is characterized in that the process of the dynamic event triggering strategy includes:

[0051] Define measurement errors and introduce dynamic variables to build dynamic event triggering mechanisms;

[0052] The dynamic event triggering mechanism needs to meet the convergence time condition.

[0053] Furthermore, it is characterized in that the distributed fixed-time sliding mode consistency tracking control scheme based on dynamic event triggering strategy includes:

[0054]

[0055] In formula (9), u i (t) represents the designed controller, c 1 represents the first control gain, o 1 represents the second control gain, o 2 represents the third control gain and satisfies represents the kth triggering time of agent i, Indicates the next event triggering time of agent i.

[0056] Compared with the prior art, the present invention establishes a dynamic model of a second-order multi-agent system of leader-follower considering unknown external disturbances; on this basis, a distributed fixed-time observer is designed to estimate the state information of the leader in real time, and a fixed-time extended state observer is introduced to estimate external disturbances; based on the observed data, a sliding mode control surface is proposed; and then a distributed fixed-time sliding mode consistency tracking control protocol is designed, so that the tracking error converges accurately within a fixed time, and even if there is external interference, the ideal control effect can be achieved. In addition, the introduction of a dynamic event trigger mechanism effectively reduces the communication burden and avoids the Zeno phenomenon. This method can achieve tracking consistency control of a multi-agent system within a fixed time, improve the robustness and reliability of the system, and save communication resources. The invention is suitable for multi-agent scenarios such as drone clusters, autonomous driving fleets, and robot formations, and has a wide range of application value.

[0057] In particular, the present invention estimates the leader information by designing a distributed fixed-time observer. Taking into account the reality that the leader's information cannot be obtained by all followers, it effectively addresses the problem that the leader's information cannot be fully obtained, and significantly improves the system's adaptability and collaboration efficiency.

[0058] In particular, the present invention simultaneously designs a fixed-time extended state observer to accurately estimate unknown disturbances, thereby improving the anti-interference capability of the system and ensuring the adaptability and effectiveness of the control strategy.

[0059] In particular, the present invention designs a distributed fixed-time sliding surface, and based on the observation errors of the distributed fixed-time observer and the fixed-time extended state observer, the system can maintain stability in the presence of unknown disturbances.

[0060] In particular, the present invention proposes a distributed fixed-time sliding mode consistency tracking control strategy based on dynamic event triggering, which ensures that the system converges to consistency within a fixed time without being affected by initial conditions. At the same time, a dynamic event triggering control strategy is adopted to update the controller only when a specific event occurs, thereby reducing the system communication frequency, reducing the communication burden, and improving the overall efficiency of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 A schematic diagram of the steps of a second-order multi-agent system control method based on dynamic event triggering according to an embodiment of the invention;

[0062] Figure 2 A communication topology diagram of a second-order multi-agent system of leader-follower according to an embodiment of the invention;

[0063] Figure 3 It is a graph showing the error in the information estimation of the position and speed of the leader by the observer of the embodiment of the invention;

[0064] Figure 4 It is a graph showing the error in the information estimation of the position, velocity and disturbance of the follower by the observer of the embodiment of the invention;

[0065] Figure 5 It is a position tracking error curve diagram of an embodiment of the invention;

[0066] Figure 6 It is a speed tracking error curve diagram of an embodiment of the invention;

[0067] Figure 7 A graph of control input for an embodiment of the invention;

[0068] Figure 8 This is an event-triggered sequence diagram of an embodiment of the invention. DETAILED DESCRIPTION

[0069] In order to make the objects and advantages of the present invention more clearly understood, the present invention is further described below in conjunction with embodiments; it should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0070] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood by those skilled in the art that these embodiments are only used to explain the technical principles of the present invention and are not intended to limit the protection scope of the present invention.

[0071] See also Figure 1 As shown, it is a schematic diagram of the steps of a second-order multi-agent system control method based on dynamic event triggering according to an embodiment of the present invention. The second-order multi-agent system control method based on dynamic event triggering according to an embodiment of the present invention includes:

[0072] Establish a second-order leader-follower multi-agent system dynamics model;

[0073] Determining a communication topology of the multi-agent system based on the dynamic model;

[0074] Designing a distributed fixed-time observer based on the dynamic model to estimate the state information of the leader, wherein the state information includes the position and speed of the leader;

[0075] Designing a fixed-time extended state observer to estimate unknown external disturbances included in the dynamic model;

[0076] Determining an observation error based on the distributed fixed-time observer and the fixed-time extended state observer to design a distributed fixed-time sliding surface;

[0077] According to the fixed-time sliding mode surface, a distributed fixed-time sliding mode consistency tracking control scheme based on a dynamic event triggering strategy is designed.

[0078] The present invention proposes a second-order multi-agent system control method based on dynamic event triggering to realize a control method for fixed-time consistency tracking. Figure 1 It can be seen that the present invention first establishes a model to convert the dynamic characteristics and environmental factors of the multi-agent system into a mathematical model for control design and simulation analysis. Then, the communication topology of the entire system is determined. Next, a distributed fixed-time observer is proposed to estimate the leader information, and a fixed-time extended state observer is introduced to estimate unknown external disturbances. At the same time, for the second-order multi-agent system with external interference, an integral sliding surface with a faster convergence speed within a fixed time is proposed to ensure the stability of the system. Finally, in order to reduce the loss of resources, the dynamic event trigger mechanism is applied to the sliding mode control, and a dynamic event trigger condition is designed. The controller is updated only when the condition is met to ensure that the system completes the consistency tracking control task within a fixed time.

[0079] Specifically, the leader is a system with dual integration characteristics of position and speed, and also includes an intelligent agent i as a follower.

[0080] Specifically, the leader-follower second-order multi-agent system dynamics model includes a dynamics model for the leader and a dynamics model for the follower;

[0081] The dynamic model for the leader and the dynamic model for the follower are established according to formula (1) and formula (2) respectively, including:

[0082] According to formula (1), the leader's dynamic model is established.

[0083]

[0084] In formula (1), x 0 (t) represents the position of the leader, v 0 (t) represents the speed of the leader, Represents x 0 The derivative of (t), Indicates v 0 The derivative of (t), u 0 (t) represents the control input of the leader, where u 0 (t)∈R n , R n represents an n-dimensional real vector space;

[0085] Assumptions The biggest control input for leaders;

[0086] According to formula (2), the dynamic model of the follower is established.

[0087]

[0088] In formula (2), i = 1, 2, ..., N, x i (t) represents the position of the follower, v i (t) represents the speed of the follower, Represents x i The derivative of (t), Indicates v i The derivative of (t), u i(t) represents the control input, ω i (t) represents the unknown bounded external disturbance of the follower, where N represents the number of followers, u i (t)∈R n ;

[0089] Assumptions is a known constant.

[0090] Specifically, it is characterized in that the communication topology is determined as follows, including:

[0091] G=(V,E,A)

[0092] In the formula, G represents the topological graph, V represents the node set, and V = {v 1 ,v 2 ,…,v N},v i represents the i-th node, and E represents the edge set connecting two nodes, where A represents the adjacency matrix, where A = [a ij ]∈R N×N , a ij Represents the connection relationship between followers, R N×N Represents the N×N dimensional real matrix space.

[0093] like Then a ij >0, otherwise a ij =0, diagonal element a ii = 0, the set of all neighbors of agent i is described as The Laplace matrix is ​​L = l ij ∈R N×N , where, when i≠j, l ij =-a ij , when i=j, The degree matrix is ​​D = diag{d 1 ,d 2 ,…,dN}, which represents the communication information between the leader and the follower. If agent i can directly obtain the leader's information, then d i >0, otherwise d i =0, then define the matrix H=L+D. The H matrix combines the relative topological relationship between followers and the degree of connection between followers and leaders, and can be used to describe how each agent is affected by other agents (including leaders).

[0094] Specifically, it is characterized in that the distributed fixed-time observer is designed according to formula (3) and formula (4), including:

[0095]

[0096] in,

[0097] In formula (3) and formula (4), represents the position estimate of the leader by agent i, represents agent j’s estimate of the leader’s position, represents agent i’s estimate of the leader’s speed, represents agent j’s estimated speed of the leader, α 1 represents the first observer gain for adjusting the position error, β 1 represents the gain of the second observer for adjusting the position error, α 2 represents the first observer gain for adjusting the speed error, β 2 represents the gain of the second observer for adjusting the speed error, α 3 represents the third observer gain for adjusting the speed error, μ represents the response parameter, ξ i (t) represents the error term of follower i’s estimate of the leader’s position, represents the error term of follower i’s estimate of the leader’s speed, a ij Represents the connection relationship between followers, d i represents the connection relationship between the follower and the leader, where μ>1, and is an important parameter for regulating how the control system responds to errors quickly and reaches the target state;

[0098] By selecting appropriate gain coefficients, parameters, and Lyapunov functions, this implementation can prove that the position and velocity information of the leader can be accurately estimated in a fixed time for arbitrary initial conditions;

[0099] The distributed fixed-time observer needs to satisfy a first fixed-time condition, including:

[0100]

[0101] Where, T 1 is the time for the observation error to converge, λ min (H) is the minimum eigenvalue of the matrix H.

[0102] Due to the limitation of communication capability, not all agents can directly obtain the information of the leader. Therefore, a distributed fixed-time observer is introduced to estimate the position and velocity of the leader. Then, a fixed-time extended state observer is proposed to estimate the unknown external disturbances of the system and apply the estimated values ​​to the controller.

[0103] Specifically, the fixed-time extended state observer is designed according to formula (5), including:

[0104]

[0105] In formula (5), x i (t) represents the position of follower i at time t, represents the estimated value of the position of follower i at time t, v i (t) represents the speed of follower i, represents the estimated value of the speed of follower i, Denotes the bounded external disturbance ω on follower i i The estimated value of (t), a 1 represents the first exponential parameter used to adjust the position error, b 1 represents the second exponential parameter used to adjust the position error, a 2 represents the first exponential parameter used to adjust the speed error, b 2 represents the second exponential parameter used to adjust the speed error, a 3 represents the first exponential parameter used to adjust the external disturbance error, b 3 represents the second exponential parameter used to adjust the external disturbance error, μ 1 represents the first gain coefficient for adjusting the position error, The second gain coefficient, μ, used to adjust the position error 2 A first gain coefficient for adjusting the speed error, The second gain coefficient, μ, used to adjust the speed error 3 represents the first gain coefficient used to adjust the external disturbance error, The second gain coefficient, δ i is the dynamic gain coefficient of the extended state observer;

[0106] In this embodiment, by reasonably setting the above-mentioned exponential parameters, it is possible to ensure that the system converges quickly. iUsed to enhance the ability to suppress external disturbances, where the gain δ i satisfy And assume is a known constant. By choosing appropriate gain coefficients, parameters and Lyapunov functions, it can be proved that for any initial conditions, the position, velocity and disturbance information of follower i can be accurately estimated within a fixed time.

[0107] Wherein, the fixed-time extended state observer needs to satisfy a second fixed-time condition, including:

[0108]

[0109] In formula (7), T 2 represents the convergence time of the observation error, where P 1 represents the first parameter of the fixed-time extended state observer, P 2 represents the second parameter of the fixed-time extended state observer, represents the first auxiliary variable, represents the second auxiliary variable, represents the first positive constant, represents the second normal number, λ min (Λ 1 ) represents the matrix Λ 1 The minimum eigenvalue of min (Λ 2 ) represents the matrix Λ 2 The minimum eigenvalue of max (Q 1 ) represents the matrix Q 1 The maximum eigenvalue of min (Q 2 ) represents the matrix Q 2 The maximum eigenvalue of , ξ represents a normal number, normal number ξ≤λ min (Q 2 ), Λ 1 ,Λ 2 , Q 1 and Q 2 are all non-singular, symmetric and positive definite matrices;

[0110] Among them, Λ 1 ,Λ 2 , Q 1 and Q 2 The following conditions must be met for the build:

[0111]

[0112] Among them, AT represents the transpose of matrix A, B T Represents the transpose of matrix B. Matrices A and B are Hurwitz matrices, and the expressions are as follows:

[0113]

[0114] Specifically, the process of determining the observation error according to the distributed fixed-time observer and the fixed-time extended state observer includes:

[0115] The observation error of the distributed fixed-time observer is determined according to formula (8), including:

[0116]

[0117] In formula (8), represents the observation error of the leader's position, represents the observation error of the leader's velocity;

[0118] The observation error of the fixed-time extended state observer is determined according to formula (9), including:

[0119]

[0120] In formula (9), represents the observation error of the position of follower i, represents the observation error of the velocity of follower i, represents the observation error of external disturbance for follower i.

[0121] Specifically, it is characterized in that the process of designing the distributed fixed-time sliding surface includes:

[0122] Determining the tracking error of the position and velocity of follower i based on the observation error;

[0123] Based on the tracking error, the distributed fixed-time sliding surface is designed according to formula (10), including:

[0124]

[0125] In formula (10), s i (t) represents the sliding surface, e 1i (τ) represents the position tracking error, e 2i (τ) represents the velocity tracking error, e 1i (t) represents the position tracking error at time t, e 2i (t) represents the speed tracking error at time t, k 1 The first sliding mode gain of the position error, k 2The second sliding mode gain representing the position error, l 1 Represents the first sliding mode gain of the velocity error, l 2 The second sliding mode gain representing the speed error; w 1 A first exponential parameter representing a nonlinear function related to the position error in the regulated sliding surface; The second exponential parameter representing the nonlinear function related to the position error in the regulated sliding surface; 2 The first exponential parameter of the nonlinear function related to the speed error in the regulated sliding surface; represents the second exponential parameter of the nonlinear function related to the speed error in the regulated sliding surface, and t represents the time variable;

[0126] Among them, the tracking error of the position and velocity of the system is:

[0127]

[0128] A distributed fixed-time sliding surface is further designed for the leader-follower second-order multi-agent system with unknown external disturbances. The sliding surface is used to define the tracking error between the follower and the leader. The sliding mode control can make the error converge to zero within a fixed time, thereby ensuring that the follower of the second-order multi-agent system can reach a consensus with the leader within a fixed time. The sliding mode controller is designed based on the sliding surface. It adjusts the control signal to offset the uncertainty and disturbance in the system, thereby enhancing the robustness and anti-interference ability of the system.

[0129] Specifically, it is characterized in that the process of the dynamic event triggering strategy includes:

[0130] Define measurement errors and introduce dynamic variables to build dynamic event triggering mechanisms;

[0131] The dynamic event triggering mechanism needs to meet the convergence time condition.

[0132] This implementation defines the measurement error by the following formula, including,

[0133]

[0134] In the formula, i (t) represents the measurement error, c 1 represents the first control gain, o 1 represents the second control gain, o 2 represents the third control gain, represents the time when agent i is triggered for the kth time;

[0135] In the implementation, dynamic variables are introduced according to the following formula, including:

[0136]

[0137] In the formula, Г i (t) represents the introduced dynamic variable, Represents Γ i The derivative of (t), The first parameter representing the dynamic variable, η i The second parameter representing the dynamic variable, γ 1 represents the first gain coefficient, γ 2 represents the second gain coefficient, ε i represents the third gain of the dynamic variable, where η i are all positive numbers greater than 0, 0<ε i <1,γ 1 >0,γ 2 >0;

[0138] By using the measurement error and the dynamic variable determined above, the event triggering condition is designed according to the following formula, including:

[0139]

[0140] In the formula, inf represents the lower bound, f i (t) is an event trigger function, wherein the event trigger event f i The expression of (t) is: i (t) = |Ξ i (t)|-∈ i η i ,By choosing a suitable Lyapunov function, for arbitrary initial conditions, it can be proved that the system can achieve consistent tracking control in a fixed time;

[0141] Among them, the convergence time conditions include,

[0142]

[0143] In the formula, min(..,.) represents the minimum function, which means that the two take the minimum value.

[0144] Specifically, it is characterized in that the distributed fixed-time sliding mode consistency tracking control scheme based on dynamic event triggering strategy includes:

[0145]

[0146] In formula (16), u i (t) represents the designed controller, c 1 represents the first control gain, o 1 represents the second control gain, o 2represents the third control gain and satisfies represents the kth triggering time of agent i, Indicates the next event triggering time of agent i.

[0147] Due to energy constraints, adding an event-triggered strategy allows the system to trigger controller updates only when specific events occur, and can achieve the consistency tracking problem of the system within a fixed time. Compared with the periodic update strategy, it significantly reduces the number of communications, saves communication resources, reduces unnecessary control updates and communications, and optimizes the use of system resources, allowing the system to run more efficiently under resource-constrained conditions, reducing the communication frequency and computational burden between intelligent agents, thereby reducing the energy consumption of the system.

[0148] This embodiment illustrates the effectiveness of the implementation method through the following simulation examples:

[0149] Suppose there is a second-order integrated multi-agent system with 6 agents, including 5 followers and 1 leader. Figure 2 As shown in FIG. 1 , it is a communication topology diagram of a second-order multi-agent system of leader-follower according to an embodiment of the present invention, where 0 represents a leader, and 1, 2, 3, 4, and 5 represent five followers, respectively. The dynamic model of the system is shown in formula (1) and formula (2), respectively. The initial conditions of the leader and the follower are selected as follows: 0 =1,x 1 =-3,x 2 =-1.5, x 3 =2,x 4 =4,x 5 =8,v 0 =1,v 1 =0.5, v 2 =1.5, v 3 =3, v 4 =1,v 5 =2.5, the leader’s control input is u 0 =0.01, the perturbation equation is ω i (t) = 0.1sin(t). The parameters of the distributed fixed-time observer are: α 1 =2,α 2 =1,α 3 =0.5,β 1 =2,β 2 =0.5, μ=1.7, the initial state of the distributed fixed-time observer is 0. The parameters of the fixed-time extended state observer are: μ 1 =8,μ 2 =18,μ 3 =20, δ i =0.1, a 1 =0.8, a 2 =0.6, a 3 =0.4, b 1 =1.3, b 2 =1.6, b 3 = 1.9, the initial state of the fixed time extended state observer is 0. The parameters of the sliding surface are: k 1 =5, k 2 =5,l 1 =3,l 2 =3,w 1 =2 / 3, w 2 =4 / 5, The parameters of the controller are: 1 =4,o 1 =0.7,o 2 =0.3. The parameters of the dynamic variables are: ∈ 1 =∈ 2 =∈ 3 =ε 4 =ε 5 =0.7, l 1 = l 2 = l 3 = l 4 = l 5 =4,η 1 =1.5,η 2 =0.4,η 3 =1,η 4 =2,η 5 =1.5,γ 1 =2,γ 2 =8.

[0150] This embodiment provides a second-order integral multi-agent system including 6 agents, including 1 leader and 5 followers. The system adopts a specific network communication topology (such as Figure 2 The initial positions and velocities of the leader and follower are set. The control input of the leader is constant, and a sinusoidal disturbance torque is applied to simulate external disturbance.

[0151] See also Figure 3 as well as Figure 4 As shown, Figure 3 is a curve diagram of the information estimation error of the position and speed of the leader by the observer in the embodiment of the present invention, Figure 4This is a graph of the error in the information estimation of the position, speed and disturbance of the follower by the observer in the embodiment of the present invention. In order to achieve accurate estimation and control of the leader's state, this system designs a distributed fixed-time observer, which can accurately estimate the leader's state information within a fixed time. In order to further deal with unknown disturbances in the system, a fixed-time extended state observer is added to the system, which can effectively estimate the position, speed and unknown disturbance of the follower within a fixed time. Through the synergy of the distributed fixed-time observer and the extended state observer, the system can obtain the necessary state information within a fixed time.

[0152] See also Figures 5 to 7 As shown, Figure 5 is a position tracking error curve diagram of an embodiment of the present invention, Figure 6 This is a speed tracking error curve diagram of an embodiment of the present invention. Figure 7 This is a graph of the control input of the embodiment of the present invention. This embodiment reasonably configures the parameters of the observer and the controller to ensure that the system achieves the expected control effect within a fixed time. In addition, the parameters of the sliding surface and the dynamic adjustment parameters of the controller are optimized to improve the tracking accuracy and robustness of the system. After the above parameter configuration, the system can achieve efficient tracking control of the leader state within a fixed time, thereby ensuring the stability and consistency of the multi-agent system.

[0153] See also Figure 8 As shown in the figure, it is an event trigger sequence diagram of an embodiment of the present invention, which shows the distribution of triggering time. In order to reduce the consumption of communication resources, this system introduces a dynamic event trigger mechanism. This mechanism triggers the controller only when specific conditions are met, thereby effectively reducing unnecessary communication frequency. While ensuring the control performance of the system, this mechanism significantly reduces the communication burden and provides strong support for the efficient operation of the multi-agent system.

[0154] So far, the technical solutions of the present invention have been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it is easy for those skilled in the art to understand that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present invention.

Claims

1. A second-order multi-agent system control method based on dynamic event triggering, characterized in that: include: Establish a second-order leader-follower multi-agent system dynamics model; Determining a communication topology of the multi-agent system based on the dynamic model; Designing a distributed fixed-time observer based on the dynamic model to estimate the state information of the leader, wherein the state information includes the position and speed of the leader; Designing a fixed-time extended state observer to estimate unknown external disturbances included in the dynamic model; Determining an observation error based on the distributed fixed-time observer and the fixed-time extended state observer to design a distributed fixed-time sliding surface; According to the fixed-time sliding mode surface, a distributed fixed-time sliding mode consistency tracking control scheme based on a dynamic event triggering strategy is designed.

2. The second-order multi-agent system control method based on dynamic event triggering according to claim 1 is characterized in that: The leader is a system with dual integration characteristics of position and speed, and also includes an intelligent agent i as a follower.

3. The second-order multi-agent system control method based on dynamic event triggering according to claim 2 is characterized in that: The leader-follower second-order multi-agent system dynamics model includes a dynamics model for the leader and a dynamics model for the follower; Among them, the leader's dynamic model is established according to formula (1): In formula (1), x0(t) represents the position of the leader, u0(t) represents the speed of the leader, represents the derivative of x0(t), represents the derivative of v0(t), and u0(t) represents the control input of the leader, where u0(t)∈R n , R n represents an n-dimensional real vector space; According to formula (2), the dynamic model of the follower is established. In formula (2), i = 1, 2, ..., N, x i (t) represents the position of the follower, v i (t) represents the speed of the follower, Represents x i The derivative of (t), Indicates v i The derivative of (t), u i (t) represents the control input, ω i (t) represents the unknown bounded external disturbance of follower i, where N represents the number of followers and u i (t)∈R n .

4. The second-order multi-agent system control method based on dynamic event triggering according to claim 3 is characterized in that: The communication topology is determined as follows, including: G=(V,E,A) In the formula, G represents the topological graph, V represents the node set, and E represents the edge set connecting two nodes. A represents the adjacency matrix, where A = [a ij ]∈R N×N , a ij Represents the connection relationship between followers, R N×N Represents the N×N dimensional real matrix space.

5. The second-order multi-agent system control method based on dynamic event triggering according to claim 4 is characterized in that: The distributed fixed-time observer is designed according to formula (3) and formula (4), including: in, In formula (3) and formula (4), represents the position estimate of the leader by follower i, represents the position estimate of the leader by follower j, represents the follower i’s estimate of the leader’s speed, represents the speed estimate of the leader by follower j, α1 represents the first observer gain for adjusting the position error, β1 represents the second observer gain for adjusting the position error, α2 represents the first observer gain for adjusting the speed error, β2 represents the second observer gain for adjusting the speed error, α3 represents the third observer gain for adjusting the speed error, μ represents the response parameter, ξ i (t) represents the error term of follower i’s estimate of the leader’s position, represents the error term of follower i’s estimate of the leader’s speed, a ij Represents the connection relationship between followers, d i represents the connection relationship between the follower and the leader, where μ>1; The distributed fixed-time observer needs to meet a first fixed-time condition.

6. The second-order multi-agent system control method based on dynamic event triggering according to claim 5 is characterized in that: The fixed-time extended state observer is designed according to formula (5), including: In formula (5), x i (t) represents the position of follower i at time t, represents the estimated value of the position of follower i at time t, v i (t) represents the speed of follower i, represents the estimated value of the speed of follower i, represents the bounded external disturbance ω on follower i i (t), a1 represents the first exponential parameter for adjusting the position error, b1 represents the second exponential parameter for adjusting the position error, a2 represents the first exponential parameter for adjusting the speed error, b2 represents the second exponential parameter for adjusting the speed error, a3 represents the first exponential parameter for adjusting the external disturbance error, b3 represents the second exponential parameter for adjusting the external disturbance error, μ1 represents the first gain coefficient for adjusting the position error, The second gain coefficient for adjusting the position error, μ2 is used to adjust the first gain coefficient for the speed error, The second gain coefficient for adjusting the speed error, μ3 represents the first gain coefficient for adjusting the external disturbance error, denoting the second gain coefficient for adjusting the external disturbance error, δ, being the dynamic gain coefficient of the extended state observer; The fixed-time extended state observer needs to satisfy a second fixed-time condition.

7. The second-order multi-agent system control method based on dynamic event triggering according to claim 6 is characterized in that: The process of determining the observation error based on the distributed fixed-time observer and the fixed-time extended state observer includes: The observation error of the distributed fixed-time observer is determined according to formula (6), including: In formula (6), represents the observation error of the leader's position, represents the observation error of the leader's velocity; The observation error of the fixed-time extended state observer is determined according to formula (7), including: In formula (7), represents the observation error of the position of follower i, represents the observation error of the velocity of follower i, represents the observation error of external disturbance for follower i.

8. The second-order multi-agent system control method based on dynamic event triggering according to claim 7 is characterized in that: The process of designing the distributed fixed-time sliding surface includes: Determining the tracking error of the position and velocity of follower i based on the observation error; Based on the tracking error, the distributed fixed-time sliding surface is designed according to formula (8), including: In formula (8), s i (t) represents the sliding surface, e 1i (τ) represents the position tracking error, e 2i (τ) represents the velocity tracking error, e 1i (t) represents the position tracking error at time t, e 2i (t) represents the speed tracking error at time t, k1 represents the first sliding mode gain of the position error, k2 represents the second sliding mode gain of the position error, l1 represents the first sliding mode gain of the speed error, l2 represents the second sliding mode gain of the speed error; w1 represents the first exponential parameter of the nonlinear function related to the position error in the adjustment sliding surface; w2 represents the second exponential parameter of the nonlinear function related to the position error in the adjustment sliding surface; w3 represents the first exponential parameter of the nonlinear function related to the speed error in the adjustment sliding surface; It represents the second exponential parameter of the nonlinear function related to the velocity error in the adjusted sliding surface, and t represents the time variable.

9. The second-order multi-agent system control method based on dynamic event triggering according to claim 8 is characterized in that: The process of the dynamic event triggering strategy includes: Define measurement errors and introduce dynamic variables to build dynamic event triggering mechanisms; The dynamic event triggering mechanism needs to meet the convergence time condition.

10. The second-order multi-agent system control method based on dynamic event triggering according to claim 9 is characterized in that: The distributed fixed-time sliding mode consistency tracking control scheme based on dynamic event triggering strategy includes: In formula (9), u i (t) represents the designed controller, c1 represents the first control gain, o1 represents the second control gain, o2 represents the third control gain, and satisfies represents the kth triggering time of agent i, Indicates the next event triggering time of agent i.

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