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

Abstract

The application 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; a dynamic model of a leader-following second-order multi-agent system considering unknown external disturbance is established, on the basis of which, a distributed fixed-time observer is designed to estimate the state information of the leader in real time; a fixed-time extended state observer is introduced to estimate the external disturbance; a sliding surface is proposed based on the observation error; and then a distributed fixed-time sliding mode uniformity tracking control protocol is designed, so that the tracking error accurately converges in fixed time, and ideal control effect can be achieved even if external disturbance exists; the introduction of the dynamic event triggering mechanism effectively reduces the communication burden and avoids the Zeno phenomenon; the tracking uniformity control of the multi-agent system can be realized in fixed time, the robustness and reliability of the system are improved, and the communication resources are saved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of multi-agent control, and particularly relates to a second-order multi-agent system control method based on dynamic event triggering. BACKGROUND

[0002] In multi-agent systems, the leader-follower structure is widely used in fields such as robots, UAV swarms, and network control. With the continuous progress of technology, achieving fixed-time consensus 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 formation control, coordinated motion, and information sharing scenarios.

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

[0004] Therefore, developing a second-order leader-follower multi-agent system fixed-time consensus control method based on dynamic event triggering can not only improve the robustness and adaptability of the system, but also help overcome the shortcomings in the prior art. The present application proposes a novel control strategy aimed at achieving more efficient multi-agent system coordination and control, which has important theoretical significance and practical application value.

[0005] Chinese Patent Application Publication No. CN117348414A discloses a second-order multi-agent system specified time dynamic event triggering control method. The method first sets up a second-order multi-agent system, reconstructs the time of speed information as T1, and sets the time for the agent to reach bounded consensus as T2. Second, a time observer is designed for each agent of the second-order multi-agent system, and the agent state value is reconstructed. Then, based on the reconstructed agent state value, a dynamic event triggered dynamic variable and trigger condition are designed, so that the controller is updated when the trigger condition is met. Finally, based on the reconstructed agent state value, a second-order multi-agent system specified time consensus control protocol based on dynamic event triggering is set, so that the agent reaches bounded consensus at time T1+T2. Each agent can make decisions based on its own information and environmental conditions, so that the system can adapt to changes and maintain operation.

[0006] However, the prior art still has the following problems,

[0007] Although various control strategies have been proposed to achieve fixed-time consensus control of multi-agent systems, existing methods mostly rely on fixed triggering conditions, which are difficult to adapt to dynamic changes in the environment and system state. In addition, existing research has mainly focused on the control of first-order systems, while the study of fixed-time consensus control for second-order systems is relatively less, especially in the presence of uncertainty and external disturbances. SUMMARY

[0008] To this end, the present application provides a dynamic event-triggered second-order multi-agent system control method to overcome the limitations of existing technologies in the field of multi-agent system consensus tracking control.

[0009] To achieve the above-mentioned purpose, the present application provides a dynamic event-triggered second-order multi-agent system control method, which comprises:

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

[0011] determining the communication topology of the multi-agent system based on the dynamics model;

[0012] designing a distributed fixed-time observer based on the dynamics model to estimate the state information of the leader, including the position and velocity of the leader;

[0013] designing a fixed-time extended state observer to estimate the unknown external disturbance contained in the dynamics model;

[0014] determining the observation error according to the distributed fixed-time observer and the fixed-time extended state observer to design a distributed fixed-time sliding mode surface;

[0015] designing a distributed fixed-time sliding mode consensus tracking control scheme based on a dynamic event-triggered strategy according to the fixed-time sliding mode surface.

[0016] Further, the leader is a system with position and velocity double integral characteristics, and also includes an 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] wherein the dynamics model for the leader and the dynamics model for the follower are established according to formula (1) and formula (2) respectively, including

[0019] the dynamics model for the leader is established according to formula (1),

[0020]

[0021] In formula (1), x0(t) represents the position of the leader, v0(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;

[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 velocity 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 an 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), denotes the position estimation value of the leader by agent i, denotes the position estimation value of the leader by agent j, denotes the estimation value of the leader speed by agent i, denotes the estimation value of the leader speed by agent j, a1 denotes the first observer gain for adjusting the position error, b1 denotes the second observer gain for adjusting the position error, a2 denotes the first observer gain for adjusting the speed error, b2 denotes the second observer gain for adjusting the speed error, a3 denotes the third observer gain for adjusting the speed error, μ denotes the response parameter, ξ i denotes the error term of the leader position estimation by follower i at time t, denotes the error term of the leader speed estimation by follower i at time t, a ij denotes the connection relationship between followers, d i

[0032] denotes the connection relationship between the follower and the leader, wherein μ>1;

[0033] wherein the distributed fixed-time observer needs to satisfy a first fixed-time condition.

[0034] Further, the fixed-time extended state observer is designed according to formula (5), comprising,

[0035]

[0036] In formula (5), x i denotes the position of follower i at time t, denotes the estimation value of the position of follower i at time t, v i denotes the speed of follower i, denotes the estimation value of the speed of follower i, denotes the estimation value of the bounded external disturbance ω i of follower i at time t, a1 denotes the first exponential parameter for adjusting the position error, b1 denotes the second exponential parameter for adjusting the position error, a2 denotes the first exponential parameter for adjusting the speed error, b2 denotes the second exponential parameter for adjusting the speed error, a3 denotes the first exponential parameter for adjusting the external disturbance error, b3 denotes the second exponential parameter for adjusting the external disturbance error, μ1 denotes the first gain coefficient for adjusting the position error, the second gain coefficient for adjusting the position error, μ2 the first gain coefficient for adjusting the speed error, the second gain coefficient for adjusting the speed error, μ3 denotes the first gain coefficient for adjusting the external disturbance error, the second gain coefficient for adjusting the external disturbance error, δi to extend the dynamic gain coefficient of the state observer;

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

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

[0039] determining the observation error of the distributed fixed-time observer according to formula (6) comprises,

[0040]

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

[0042] determining the observation error of the fixed-time extended state observer according to formula (7) comprises,

[0043]

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

[0045] Further, the process of designing the distributed fixed-time sliding mode surface comprises,

[0046] determining the tracking error of the position and speed of the follower i according to the observation error;

[0047] designing the distributed fixed-time sliding mode surface according to formula (8) based on the tracking error, comprising,

[0048]

[0049] In formula (8), s i (t) represents the sliding mode surface, e 1i (τ) represents the position tracking error, e 2i (τ) represents the speed tracking error, e 1i (t) represents the position tracking error at time t, e 2i(t) represents the velocity 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 velocity error, l2 represents the second sliding mode gain of the velocity error; w1 represents the first exponential parameter of the nonlinear function related to the position error in the adjustment sliding surface; w2 represents the first exponential parameter of the nonlinear function related to the velocity error in the sliding surface; It represents the second exponential parameter of the nonlinear function related to the velocity error in the adjustment 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 a dynamic event triggering mechanism;

[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, c1 represents the first control gain, o1 represents the second control gain, o2 represents the third control gain, and satisfies represents the kth triggering moment of agent i, Indicates the next event triggering time of agent i.

[0056] Compared with the existing technology, the present invention establishes a dynamic model of a second-order leader-follower multi-agent system that takes into account unknown external interference; 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 observation 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 in the presence of external interference, the ideal control effect can be achieved. In addition, the introduction of a dynamic event triggering mechanism effectively reduces the communication burden and avoids the Zeno phenomenon. This method can achieve tracking consistency control of the 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] Especially, the application estimates the leader information by designing a distributed fixed-time observer, effectively deals with the problem that the leader information cannot be fully acquired, and significantly improves the adaptability and cooperation efficiency of the system, considering the reality that the leader information cannot be acquired by all followers.

[0058] Especially, the application designs a fixed-time extended state observer to accurately estimate unknown disturbances, improves the anti-interference ability of the system, and ensures the adaptability and effectiveness of the control strategy.

[0059] Especially, the application designs a distributed fixed-time sliding surface according to the observation error of the distributed fixed-time observer and the fixed-time extended state observer, so that the system can maintain stability in the presence of unknown disturbances.

[0060] Especially, the application proposes a distributed fixed-time sliding mode consensus tracking control strategy based on dynamic event triggering, ensures that the system tends to be consistent within a fixed time without being affected by the initial conditions, and adopts a dynamic event triggered control strategy to update the controller only when a specific event occurs, thereby reducing the communication frequency of the system, reducing the communication burden, and improving the overall efficiency of the system. BRIEF DESCRIPTION OF DRAWINGS

[0061] Figure 1 The figure is a step schematic diagram of the second-order multi-agent system control method based on dynamic event triggering of the application embodiment;

[0062] Figure 2 The figure is a communication topology structure diagram of the leader-following second-order multi-agent system of the application embodiment;

[0063] Figure 3 The figure is an error curve diagram of the observer estimating the information of the position and speed of the leader of the application embodiment;

[0064] Figure 4 The figure is an error curve diagram of the observer estimating the information of the position, speed and disturbance of the follower of the application embodiment;

[0065] Figure 5 The figure is a position tracking error curve diagram of the application embodiment;

[0066] Figure 6 The figure is a speed tracking error curve diagram of the application embodiment;

[0067] Figure 7 The figure is a control input curve diagram of the application embodiment;

[0068] Figure 8 The figure is an event triggering sequence diagram of the application embodiment. DETAILED DESCRIPTION

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

[0070] The preferred embodiments of the present application will be described below with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are only used to explain the technical principles of the present application and not used to limit the protection scope of the present application.

[0071] Please refer to Figure 1 Fig. 1 is a schematic diagram of steps of a second-order multi-agent system control method based on dynamic event triggering according to an embodiment of the present application, and the second-order multi-agent system control method based on dynamic event triggering according to the embodiment of the present application comprises:

[0072] establishing a leader-following second-order multi-agent system dynamics model;

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

[0074] designing a distributed fixed-time observer based on the dynamics model, to estimate state information of the leader, the state information comprising a position and a speed of the leader;

[0075] designing a fixed-time extended state observer, to estimate unknown external disturbances contained in the dynamics model;

[0076] determining an observation error according to the distributed fixed-time observer and the fixed-time extended state observer, to design a distributed fixed-time sliding mode surface;

[0077] designing a distributed fixed-time sliding mode consensus tracking control scheme based on a dynamic event triggering strategy according to the fixed-time sliding mode surface.

[0078] The present application proposes a second-order multi-agent system control method based on dynamic event triggering, to realize a fixed-time consensus tracking control method, according to Figure 1It can be known that the application firstly establishes a model, converts the dynamic characteristics of the multi-agent system and environmental factors into a mathematical model, so as to carry out control design and simulation analysis. Then, the communication topology structure of the whole system is determined. Next, a distributed fixed-time observer is proposed to be designed for estimating leader information, and a fixed-time extended state observer is introduced to estimate unknown external disturbance. Meanwhile, for the second-order multi-agent system with external disturbance, an integral sliding surface with faster convergence speed in fixed time is proposed, which guarantees the stability of the system. Finally, in order to reduce the loss of resources, a dynamic event triggering mechanism is applied to the sliding mode control, a dynamic event triggering condition is designed, and the controller is updated only when the condition is met, so as to ensure that the system completes the consistent tracking control task in fixed time.

[0079] Specifically, the leader is a system with position and speed double integral characteristics, 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 dynamics model for the leader and the dynamics model for the follower are established according to formula (1) and formula (2) respectively, including

[0082] The dynamics model for the leader is established according to formula (1),

[0083]

[0084] In formula (1), x0(t) represents the position of the leader, v0(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, wherein u0(t)∈R n , R n represents an n-dimensional real vector space;

[0085] It is assumed that is the maximum control input of the leader;

[0086] The dynamics model for the follower is established according to formula (2),

[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, denotes x i derivative of (t), denotes v i derivative of (t), u i(t) denotes control input, ω i (t) denotes unknown bounded external disturbance of the follower, where N denotes the number of followers, u i (t)∈R n ;

[0089] Assume is a known constant.

[0090] In particular, it is characterized in that the communication topology is determined as follows, comprising,

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

[0092] wherein G denotes a topology graph, V denotes a node set, wherein V={v1,v2,…,vi,…,v N} denotes the i-th node, E denotes an edge set connecting two nodes, wherein, A denotes an adjacency matrix, wherein A=[a ij ]∈R N×N , a ij denotes the connection relationship between followers, R N×N denotes an N×N-dimensional real matrix space.

[0093] If a ij >0, otherwise a ij =0, diagonal elements a ii =0, the set of all neighbors of agent i is described as The Laplacian matrix is L=l ij ∈R N×N , wherein l ij =-a ij when i≠j, and l N =0 when i=j. The degree matrix is D=diag{d1,d2,…,di,…,d i}, which indicates the communication information between leaders and followers, if agent i can directly obtain the information of the leader, d i >0, otherwise d i =0, then the matrix H=L+D is defined, the H matrix combines the relative topological relationship between followers and the connection degree of followers to leaders, and can be used to describe how each agent is affected by other agents (including leaders).

[0094] Specifically, the distributed fixed-time observer is designed according to formula (3) and formula (4), comprising,

[0095]

[0096] wherein,

[0097] In formula (3) and formula (4), represents the position estimation value of the leader by the agent i, represents the position estimation value of the leader by the agent j, represents the estimation value of the leader speed by the agent i, represents the estimation value of the leader speed by the agent 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 a response parameter, and ξ i represents the error term of the leader position estimation by the follower i, represents the error term of the leader speed estimation by the follower i, a ij represents the connection relationship between the followers, d i represents the connection relationship between the follower and the leader, wherein μ>1 is an important parameter for adjusting how quickly the control system responds to the error and reaches the target state;

[0098] The embodiment can prove that the position and speed information of the leader can be accurately estimated within a fixed time for any initial condition by selecting appropriate gain coefficients, parameters and Lyapunov functions;

[0099] wherein the distributed fixed-time observer needs to satisfy a first fixed-time condition, comprising,

[0100]

[0101] In the formula, T1 is the time of observation error convergence, 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, so a distributed fixed-time observer is introduced to estimate the position and speed of the leader, and a fixed-time extended state observer is further proposed to estimate the unknown external disturbance of the system and apply the estimated value to the controller.

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

[0104]

[0105] In formula (5), x i (t) represents the position of the follower i at time t, represents the estimated value of the position of the follower i at time t, v i (t) represents the speed of the follower i, represents the estimated value of the speed of the follower i, represents the estimated value of the bounded external disturbance ω i of the follower i at time t, a1 represents a first exponential parameter for adjusting a position error, b1 represents a second exponential parameter for adjusting the position error, a2 represents a first exponential parameter for adjusting a speed error, b2 represents a second exponential parameter for adjusting the speed error, a3 represents a first exponential parameter for adjusting an external disturbance error, b3 represents a second exponential parameter for adjusting the external disturbance error, μ1 represents a first gain coefficient for adjusting the position error, a second gain coefficient for adjusting the position error, μ2 represents a first gain coefficient for adjusting the speed error, a second gain coefficient for adjusting the speed error, μ3 represents a first gain coefficient for adjusting the external disturbance error, a second gain coefficient for adjusting the external disturbance error, δ i is a dynamic gain coefficient of the extended state observer;

[0106] In the embodiment, by reasonably setting the above-mentioned exponential parameters, it is possible to determine that the system converges quickly, and δ i is used to enhance the suppression ability of the external disturbance, wherein the gain δ i satisfies and assuming that is a known constant, by selecting appropriate gain coefficients, parameters and Lyapunov functions, it can be proved that the information of the position, speed and disturbance of the follower i can be accurately estimated within a fixed time for any initial condition;

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

[0108]

[0109] In formula (7), T2 represents a convergence time of the observation error, wherein P1 represents a first parameter of the fixed-time extended state observer, P2 represents a second parameter of the fixed-time extended state observer, represents a first auxiliary variable, denotes a second auxiliary variable, denotes a first constant, denotes a second constant, λ min denotes the minimum eigenvalue of the matrix Λ1, λ min denotes the minimum eigenvalue of the matrix Λ2, λ max denotes the maximum eigenvalue of the matrix Q1, λ min denotes the maximum eigenvalue of the matrix Q2, ξ denotes a constant, the constant ξ ≤ λ min (Q2), Λ1, Λ2, Q1 and Q2 are all non-singular, symmetric and positive definite matrices;

[0110] wherein Λ1, Λ2, Q1 and Q2 are constructed to satisfy the following conditions:

[0111]

[0112] wherein A T denotes the transpose of the matrix A, B T denotes the transpose of the matrix B, the matrices A, 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] According to formula (8), the observation error of the distributed fixed-time observer is determined, including,

[0116]

[0117] In formula (8), denotes the observation error of the position of the leader, denotes the observation error of the speed of the leader;

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

[0119]

[0120] In formula (9), denotes the observation error of the position of the follower i, denotes the observation error of the speed of the follower i, denotes the observation error of the external disturbance of the follower i.

[0121] Specifically, the process of designing the distributed fixed-time sliding mode surface includes,

[0122] determining a tracking error of the position and velocity of the follower i according to the observation error;

[0123] designing the distributed fixed-time sliding mode surface according to formula (10) based on the tracking error, including,

[0124]

[0125] In formula (10), s i (t) represents a sliding mode surface, e 1i (τ) represents a position tracking error, e 2i (τ) represents a velocity tracking error, e 1i (t) represents a position tracking error at time t, e 2i (t) represents a velocity tracking error at time t, k1 represents a first sliding mode gain of the position error, k2 represents a second sliding mode gain of the position error, l1 represents a first sliding mode gain of the velocity error, l2 represents a second sliding mode gain of the velocity error; w1 represents a first exponential parameter of a nonlinear function related to the position error in the adjusted sliding mode surface; w2 represents a second exponential parameter of the nonlinear function related to the position error in the adjusted sliding mode surface; w2 represents a first exponential parameter of a nonlinear function related to the velocity error in the adjusted sliding mode surface; w2 represents a second exponential parameter of the nonlinear function related to the velocity error in the adjusted sliding mode surface, and t represents a time variable;

[0126] wherein the tracking error of the position and velocity of the system is:

[0127]

[0128] For a leader-follower second-order multi-agent system with unknown external disturbance, a distributed fixed-time sliding mode surface is further designed. The sliding mode surface is used to define the tracking error between the follower and the leader, and through the sliding mode control, the error can be converged to zero in a fixed time, so as to ensure that the follower of the second-order multi-agent system can reach consistency with the leader in a fixed time. The sliding mode controller is designed based on the sliding mode surface, and the control signal is adjusted to offset the uncertainty and disturbance in the system, thereby enhancing the robustness and anti-interference ability of the system.

[0129] Specifically, the process of the dynamic event triggering strategy includes,

[0130] defining a measurement error, and introducing a dynamic variable to construct a dynamic event triggering mechanism;

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

[0132] The embodiment defines the measurement error by the following formula, including,

[0133]

[0134] In the formula, Ξ i (t) represents the measurement error, c1 represents the first control gain, o1 represents the second control gain, o2 represents the third control gain, represents the time of the kth triggering of the intelligent agent i;

[0135] The embodiment introduces the dynamic variable according to the following formula, including,

[0136]

[0137] In the formula, Г i (t) represents the introduced dynamic variable, represents the derivative of Γ i (t), represents the first parameter of the dynamic variable, η i represents the second parameter of the dynamic variable, γ1 represents the first gain coefficient, γ2 represents the second gain coefficient, and ε i represents the third gain of the dynamic variable, wherein, η i are positive numbers greater than 0, 0<ε i <1, γ1>0, and γ2>0;

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

[0139]

[0140] In the formula, inf represents the lower limit, f i (t) is an event triggering function, wherein the expression of the event triggering function f i (t) is: f i (t) = |Ξ i (t) |-∈ i η i By selecting a suitable Lyapunov function, it can be proved that the system can achieve consistent tracking control in a fixed time for any initial condition.

[0141] The convergence time condition includes,

[0142]

[0143] Wherein, min(..,) represents a minimum value function, and min(a,b) represents taking the minimum value of a and b.

[0144] Specifically, the distributed fixed-time sliding mode consensus tracking control scheme based on the dynamic event-triggered strategy comprises,

[0145]

[0146] In formula (16), u i (t) represents a designed controller, c1 represents a first control gain, o1 represents a second control gain, o2 represents a third control gain, and c1, o1 and o2 satisfy represents the kth triggering time of the intelligent agent i, represents the next event-triggering time of the intelligent agent i.

[0147] Due to energy constraints, the event-triggered strategy is added to make the system trigger the controller update only when a specific event occurs, and the consensus tracking problem of the system can be solved in a fixed time, compared with the periodic update strategy, the communication frequency is significantly reduced, the communication resources are saved, unnecessary control update and communication are reduced, the use of system resources is optimized, the system can operate more efficiently under the condition of resource constraints, the communication frequency and the calculation burden between intelligent agents are reduced, and thus the energy consumption of the system is reduced.

[0148] The effectiveness of the embodiments is illustrated by the following example simulation:

[0149] An integral second-order multi-agent system containing 6 intelligent agents is provided, wherein 5 are followers and 1 is a leader, please refer to Figure 2 The communication topology structure diagram of the second-order multi-agent system of the leader-follower of the embodiment is shown in the figure, wherein 0 represents the leader, and 1, 2, 3, 4 and 5 represent the five followers. The dynamic model of the system is shown in formula (1) and formula (2), respectively, and the initial conditions of the leader and the follower are selected as: x0=1, x1=-3, x2=-1.5, x3=2, x4=4, x5=8, v0=1, v1=0.5, v2=1.5, v3=3, v4=1, v5=2.5, the control input of the leader is u0=0.01, and the disturbance equation is ω i (t)=0.1sin(t). The parameters of the distributed fixed-time observer are: α1=2, α2=1, α3=0.5, β1=2, β2=0.5, μ=1.7, and the initial state of the distributed fixed-time observer is 0. The parameters of the fixed-time extended state observer are: μ1=8, μ2=18, μ3=20, δ i= 0.1, a1 = 0.8, a2 = 0.6, a3 = 0.4, b1 = 1.3, b2 = 1.6, b3 = 1.9, the initial state of the fixed time extended state observer is 0. The parameters of the sliding surface are: k1 = 5, k2 = 5, l1 = 3, l2 = 3, w1 = 2 / 3, w2 = 4 / 5, The parameters of the controller are: c1 = 4, o1 = 0.7, o2 = 0.3. The parameters of the dynamic variable are: ∈1 = ∈2 = ∈3 = ∈4 = ∈5 = 0.7, l1 = l2 = l3 = l4 = l5 = 4, η1 = 1.5, η2 = 0.4, η3 = 1, η4 = 2, η5 = 1.5, γ1 = 2, γ2 = 8.

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

[0151] Please refer to Figure 3 and Figure 4 , Figure 3 is the information estimation error curve diagram of the observer of the embodiment of the application for the position and velocity of the leader, Figure 4 is the information estimation error curve diagram of the observer of the embodiment of the application for the position, velocity and disturbance of the follower, in order to realize accurate estimation and control of the state of the leader, the system designs a distributed fixed time observer, which can accurately estimate the state information of the leader within a fixed time. In order to further cope with unknown disturbances in the system, a fixed time extended state observer is added to the system, which can effectively estimate the position, velocity and unknown disturbance of the follower within a fixed time. Through the cooperative action of the distributed fixed time observer and the extended state observer, the system can obtain the necessary state information within a fixed time.

[0152] Please refer to Figures 5 to 7 , Figure 5 is the position tracking error curve diagram of the embodiment of the application, Figure 6 is the velocity tracking error curve diagram of the embodiment of the application, Figure 7 is the curve diagram of the control input of the embodiment of the application, the parameters of the observer and the controller are reasonably configured in this embodiment 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 and set, thereby improving the tracking accuracy and robustness of the system. After the above parameter configuration, the system can realize efficient tracking control of the state of the leader within a fixed time, thereby ensuring the stability and consistency of the multi-agent system.

[0153] Referring to Figure 8 As shown in the figure, it is an event trigger sequence diagram of the embodiment of the application to show the distribution of the trigger time. In order to reduce the consumption of communication resources, the system introduces a dynamic event trigger mechanism. The mechanism triggers the controller only when certain conditions are met, thereby effectively reducing unnecessary communication frequency. The mechanism significantly reduces the communication burden while ensuring the control performance of the system, providing strong support for the efficient operation of the multi-agent system.

[0154] So far, the technical solutions of the application have been described in combination with the preferred embodiments shown in the drawings, but those skilled in the art can easily understand that the protection scope of the application is obviously not limited to these specific embodiments. Those skilled in the art can make equivalent changes or replacements to the related technical features without departing from the principles of the application, and the technical solutions after the changes or replacements will fall within the protection scope of the application.

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 velocity of the leader; Designing a fixed-time extended state observer to estimate the 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; According to formula (3) and formula (4), the distributed fixed-time observer is designed, including: ； in, ; In formula (3) and formula (4), Indicates followers An estimate of the leader's position, Indicates followers An estimate of the leader's position, Indicates followers An estimate of the leader's velocity, Indicates followers The velocity estimate for the leader, represents the first observer gain for adjusting the position error, represents the second observer gain for adjusting the position error, represents the first observer gain for regulating speed error, represents the second observer gain for adjusting the speed error, represents the third observer gain for adjusting the speed error, Indicates the response parameters, Indicates followers The error term in estimating the leader's position, Indicates followers The error term in the estimate of the leader's velocity, Indicates the connection relationship between followers. Represents the connection relationship between the follower and the leader, where ; Wherein, the distributed fixed-time observer needs to meet a first fixed-time condition; The fixed-time extended state observer is designed according to formula (5), including: ； In formula (5), Indicates followers At the moment location, To followers exist The estimated value of the position at the moment, Indicates followers speed, To followers The estimated value of the speed, To followers Bounded external disturbance The estimated value of represents the first exponential parameter used to adjust the position error, represents the second exponential parameter used to adjust the position error, represents the first exponential parameter used to adjust the speed error, represents the second exponential parameter used to adjust the speed error, represents the first exponential parameter used to adjust the external disturbance error, represents the second exponential parameter used to adjust the external disturbance error, represents the first gain coefficient for adjusting the position error, A second gain coefficient for adjusting the position error, A first gain coefficient for adjusting the speed error, A second gain coefficient for adjusting the speed error, represents the first gain coefficient for adjusting the external disturbance error, shows the second gain coefficient for adjusting the external disturbance error, is the dynamic gain coefficient of the extended state observer; The fixed-time extended state observer needs to meet a second fixed-time condition.

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 features of position and velocity, and also includes an intelligent agent 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), Indicates the position of the leader, represents the speed of the leader, express The derivative of express The derivative of Indicates the leader's control output , Indicates a dimensional real vector space; According to formula (2), the dynamic model of the follower is established. ； In formula (2), , Indicates the position of the follower, represents the speed of the follower, express The derivative of express The derivative of represents the control input, Indicates followers An unknown bounded external disturbance of Indicates the number of followers, .

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: ； Where, Represents a topological graph, Represents a node set, represents the set of edges connecting two nodes, where , represents the adjacency matrix, where , Indicates the connection relationship between followers. express dimensional real matrix space.

5. The second-order multi-agent system control method based on dynamic event triggering according to claim 1 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), For followers The observation error of the position, For followers The observation error of the velocity, For followers The observation error of external interference.

6. The second-order multi-agent system control method based on dynamic event triggering according to claim 5 is characterized in that: The process of designing the distributed fixed-time sliding surface includes: Determine the follower based on the observation error Position and velocity tracking errors; Based on the tracking error, the distributed fixed-time sliding mode surface is designed according to formula (8), including: ； In formula (8), represents the sliding surface, represents the position tracking error, represents the speed tracking error, express Time position tracking error, express The momentary velocity tracking error, Represents the first sliding mode gain of the position error, The second sliding mode gain representing the position error, Represents the first sliding mode gain of the velocity error, The second sliding mode gain representing the speed error; The first exponential parameter of the nonlinear function related to the position error in the adjustment sliding surface; A second exponential parameter representing a nonlinear function related to the position error in the regulated sliding surface; The first exponential parameter of the nonlinear function related to the velocity error in the regulated sliding surface; The second exponential parameter of the nonlinear function related to the velocity error in the adjustment sliding surface is represented by Represents a time variable.

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 dynamic event triggering strategy includes: Define measurement errors and introduce dynamic variables to build a dynamic event triggering mechanism; The dynamic event triggering mechanism needs to meet the convergence time condition.

8. The second-order multi-agent system control method based on dynamic event triggering according to claim 7 is characterized in that: The distributed fixed-time sliding mode consistency tracking control scheme based on dynamic event triggering strategy includes: ； In formula (9), represents the designed controller, represents the first control gain, represents the second control gain, represents the third control gain and satisfies , , Representing an agent No. The triggering moment, Representing an agent The next event triggering time.

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