Finite-time tracking method, system, device and medium for time-varying conformational formation with unknown leader system matrix

Abstract

This application discloses a finite-time tracking method, system, device, and medium for a time-varying heterogeneous formation with an unknown leader system matrix. The method relates to the field of cluster formation tracking control. The method includes: obtaining the communication topology of the heterogeneous formation; determining a first follower cluster and a second follower cluster based on the communication topology; establishing an Euler-Lagrangian dynamic model of the followers and a dynamic model of the leader; establishing distributed finite-time observers for each of the two follower clusters; establishing a distributed finite-time time-varying formation tracking controller based on the Euler-Lagrangian dynamic model of the followers, the dynamic model of the leader, and the distributed finite-time observer; and controlling the time-varying formation of the followers in the heterogeneous formation using the distributed finite-time time-varying formation tracking controller. This application implements tracking control of a multi-agent formation with an unknown leader system matrix.

Description

Technical Field

[0001] The present application relates to the field of cluster formation tracking control, and in particular to a finite-time tracking method, system, device and medium for a time-varying conformal formation with an unknown leader system matrix. Background Art

[0002] Distributed cooperative control of multi-agent systems is currently a hot topic in the control field and has been widely used in scientific research and engineering. Among them, how to conduct formation control and construct effective controllers are key issues that have been widely studied and discussed in the field of cooperative control of multi-agent systems.

[0003] However, most research on multi-agent formation tracking control assumes that all follower agents know the dynamics of the leader system, such as the system matrix in the case of linear dynamics. While this assumption is also common in studies of leader-follower consensus, it implies direct communication between each follower and the leader, which contradicts the distributed nature of multi-agent systems. In many practical applications, however, no follower agent may fully understand the dynamics of the target being tracked. For example, in non-cooperative scenarios, a UAV tracking an unmanned aerial vehicle cannot directly access the dynamic model of the target UAV. Therefore, the problem of multi-agent formation tracking control with an unknown leader system matrix has become an important and challenging problem that has received increasing attention in recent years. It requires the design of a corresponding parameter observer to estimate the leader's dynamic information. Such heterogeneous multi-agent systems, where the leader system matrix is ​​unknown to all followers, are also referred to as heterogeneous multi-agent systems with uncertain leaders.

[0004] Many observer designs require persistent excitation conditions, which require a sufficiently rich signal from the leader's state. However, ensuring and verifying these conditions in advance can be challenging when dealing with uncertain parameter estimation. Some studies have successfully relaxed the requirements for traditional persistent excitation conditions, but these are primarily used for estimating dynamic information in single adaptive systems or homogeneous multi-agent systems. Extending these techniques to heterogeneous multi-agent systems with uncertain leaders is challenging because leaders and followers often have a non-cooperative relationship in heterogeneous multi-agent systems. For example, in a real-world scenario where a platoon of unmanned vehicles is tracking a drone, it is difficult to guarantee that the follower vehicles can directly obtain the state information of the leader drone. Therefore, designing a formation controller that does not require persistent excitation conditions in heterogeneous swarm systems with uncertain leaders is a challenging problem. Summary of the Invention

[0005] The purpose of this application is to provide a finite-time tracking method, system, device and medium for a time-varying conformal formation with an unknown leader system matrix, which can realize tracking control of a multi-agent formation with an unknown leader system matrix.

[0006] To achieve the above objectives, this application provides the following solutions:

[0007] In a first aspect, the present application provides a finite-time tracking method for a time-varying conformational formation with an unknown leader system matrix, comprising:

[0008] Obtaining a communication topology relationship of a heterogeneous formation; the heterogeneous formation includes multiple followers and a leader; some followers in the heterogeneous formation can directly obtain the state vector of the leader, while the remaining followers cannot directly obtain the state vector of the leader, and the system matrix of the leader is unknown to all followers;

[0009] Determining a first follower cluster and a second follower cluster according to the communication topology relationship; the first follower cluster includes followers that can directly obtain the state vector of the leader; the second follower cluster includes followers that cannot directly obtain the state vector of the leader;

[0010] Establish the Euler-Lagrangian dynamics model of the follower and the dynamics model of the leader;

[0011] By constructing a filter, based on the communication topology, a distributed finite-time observer of the first follower cluster and a distributed finite-time observer of the second follower cluster are respectively established; the distributed finite-time observer of the first follower cluster is used to observe the system matrix of the leader; the distributed finite-time observer of the second follower cluster is used to observe the state vector and system matrix of the leader;

[0012] Establishing a distributed finite-time time-varying formation tracking controller based on the Euler-Lagrangian dynamic model of the followers, the dynamic model of the leader, the distributed finite-time observer of the first follower cluster, and the distributed finite-time observer of the second follower cluster;

[0013] The distributed finite-time time-varying formation tracking controller is used to control the time-varying formation of followers in the heterogeneous formation.

[0014] In a second aspect, the present application provides a finite-time tracking system for a time-varying conformational formation with an unknown leader system matrix, comprising:

[0015] a communication topology acquisition module, configured to acquire the communication topology of a heterogeneous formation comprising a plurality of followers and a leader; wherein some followers in the heterogeneous formation can directly acquire the leader's state vector, while the remaining followers cannot, and the leader's system matrix is ​​unknown to all followers;

[0016] a cluster division module, configured to determine a first follower cluster and a second follower cluster according to the communication topology; the first follower cluster includes followers that can directly obtain the state vector of the leader; and the second follower cluster includes followers that cannot directly obtain the state vector of the leader;

[0017] Modeling module, used to build the Euler-Lagrangian dynamics model of the follower and the dynamics model of the leader;

[0018] an observer construction module, configured to establish, based on the communication topology, a distributed finite-time observer for the first follower cluster and a distributed finite-time observer for the second follower cluster by constructing a filter; the distributed finite-time observer for the first follower cluster is configured to observe the system matrix of the leader; and the distributed finite-time observer for the second follower cluster is configured to observe the state vector and system matrix of the leader;

[0019] a controller building module for building a distributed finite-time time-varying formation tracking controller based on the Euler-Lagrangian dynamics model of the followers, the dynamics model of the leader, the distributed finite-time observer of the first follower cluster, and the distributed finite-time observer of the second follower cluster;

[0020] A control module is used to control the time-varying formation of followers in the heterogeneous formation by using the distributed finite-time time-varying formation tracking controller.

[0021] In a third aspect, the present application provides a computer device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-mentioned method for finite-time tracking of a time-varying conformal formation with an unknown leader system matrix.

[0022] In a fourth aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned method for finite-time tracking of a time-varying conformal formation with an unknown leader system matrix.

[0023] According to the specific embodiments provided in this application, this application has the following technical effects:

[0024] The present application provides a finite-time tracking method, system, device and medium for a time-varying heterogeneous formation with an unknown leader system matrix, allocates finite-time observers to different follower clusters, and further establishes a time-varying formation tracking controller, which solves the observer design problem of finite-time parameter estimation of a heterogeneous multi-agent system when the leader system matrix is ​​unknown, and realizes tracking control of a multi-agent formation with an unknown leader system matrix. Moreover, the finite-time observer and the time-varying formation tracking controller are constructed in a fully distributed manner, ensuring that the heterogeneous formation can achieve the desired time-varying formation within a finite time and track the state trajectory generated by the uncertain leader without knowing the rest of the information of the entire cluster. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0026] Figure 1 A flowchart of a finite-time tracking method for a time-varying conformational formation with an unknown leader system matrix provided by an embodiment of the present application;

[0027] Figure 2 Schematic diagram of the communication topology relationship of heterogeneous formations in one embodiment of the present application

[0028] Figure 3 This is a graph showing a change in the estimation error of the leader state vector in one embodiment of the present application;

[0029] Figure 4 This is a graph showing the estimated error variation of the leader system matrix in one embodiment of the present application;

[0030] Figure 5 This is a curve diagram of formation tracking error changes in one embodiment of the present application;

[0031] Figure 6 This is a schematic diagram of the positions of the heterogeneous formation at 0 seconds in one embodiment of the present application;

[0032] Figure 7 This is a schematic diagram of the positions of the heterogeneous formation at 10 seconds in one embodiment of the present application;

[0033] Figure 8 This is a schematic diagram of the positions of the heterogeneous formation at 20 seconds in one embodiment of the present application;

[0034] Figure 9 This is a schematic diagram of the positions of the heterogeneous formation at 40 seconds in one embodiment of the present application;

[0035] Figure 10 This is a functional module diagram of a finite-time tracking system for a time-varying conformal formation with an unknown leader system matrix provided by an embodiment of the present application. DETAILED DESCRIPTION

[0036] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0037] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0038] In an exemplary embodiment, Figure 1 As shown, a finite-time tracking method for a time-varying conformational formation with an unknown leader system matrix is ​​provided. The method is executed by a computer device, and specifically can be executed by a computer device such as a terminal or a server alone, or can be executed by a terminal and a server together. In an embodiment of the present application, the method includes the following steps 101 to 106.

[0039] Step 101: Obtain the communication topology relationship of the heterogeneous formation.

[0040] A heterogeneous formation consists of multiple followers and a leader. The leader is tracked by the followers. Both the followers and the leader in a heterogeneous formation are intelligent agents.

[0041] Some followers in a heterogeneous formation can directly obtain the leader's state vector q0, while the rest of the followers cannot directly obtain the leader's state vector q0, and the leader's system matrix E is unknown to all followers.

[0042] Step 102: Determine a first follower cluster PI1 and a second follower cluster PI2 based on the communication topology. The first follower cluster PI1 includes followers that can directly obtain the state vector of the leader. The second follower cluster PI2 includes followers that cannot directly obtain the state vector of the leader.

[0043] In one optional implementation, the communication topology within a formation cluster is abstracted into a graph, and the corresponding Laplace matrix and other related quantitative variables are derived, providing a foundation for the design of subsequent observers and controllers. For example, in a formation tracking control scenario, it is necessary to determine whether each individual can directly communicate with the others, establish a communication topology based on this, and obtain relevant quantitative values ​​for use in subsequent steps.

[0044] The communication topology relationship of the second follower cluster PI2 is undirected, and there is at least one follower in the first follower cluster PI1, which can directly send information to the second follower cluster PI2.

[0045] The topology of the interactions between N followers in a heterogeneous formation can be described as a graph Where ν={ν1,ν2,…,ν N} represents a node set, is an edge set, is a non-negative element a ij The symmetric adjacency matrix of . For the i-th follower and the j-th follower, You can use the ν in ν i and ν j To refer to. If from ν i to ν j There is an edge between them, that is, there is a communication relationship between the i-th follower and the j-th follower, then a ij =1; otherwise a ij = 0. Let a ii =0,i∈{1,2,…,N}. In order to describe the neighbor relationship in heterogeneous clusters, we define the graph The Laplace matrix of in, is the in-degree matrix.

[0046] In a heterogeneous formation, there is a leader, which is node 0, so the graph Represents the topological structure of the entire heterogeneous formation interaction. If at node 0 (leader) and ν i There is an edge between (i-th follower), then a 0i =1, otherwise, a 0i = 0. Let Representing the adjacency matrix of the leader, define

[0047] For followers in a heterogeneous formation, only a portion of them can directly obtain the leader's state vector q0. Assuming that the number of followers in this portion is m, this portion of followers is denoted as Π1:={1,2,...,m}; the remaining followers in the heterogeneous formation cannot directly obtain the leader's state vector q0. This portion of followers is denoted as Π2:={m+1,m+2,...,N}. Let represents the Laplacian matrix of the corresponding graph of the second follower cluster Π2, definition

[0048] Step 103: Establish an Euler-Lagrangian dynamic model of the follower and a dynamic model of the leader.

[0049] In an exemplary embodiment, based on the physical characteristics of a cluster of intelligent agents (such as drones, unmanned vehicles, etc.), an Euler-Lagrangian dynamic model of the follower and a dynamic model of the leader are established, and the dynamic equation expressions and characteristic equations corresponding to the follower and the leader are obtained, providing a basis for the design of subsequent observers and controllers.

[0050] The Euler-Lagrangian dynamic model of the follower is:

[0051]

[0052] Among them, q i (t) is the position of the i-th follower, is the speed of the ith follower, is the acceleration of the ith follower, u i (t) is the control input vector of the ith follower, M i (q i (t)) is the inertia matrix of the i-th follower, is the Coriolis and centrifugal matrix of the ith follower, G i (q i (t)) is the gravity matrix of the ith follower, and t represents the time.

[0053] The Euler-Lagrangian dynamics model of the follower satisfies the following equation:

[0054]

[0055] in, is the regression matrix of the ith follower, x(t) and y(t) are The two variables in φ i (t) is the parameter vector of the ith follower,

[0056] The dynamic model of leadership is:

[0057]

[0058] Among them, q0(t) is the state vector of the leader, which is a bounded vector, is the first-order differential of q0(t) with respect to time, E is the leader's system matrix, And satisfy the assumption that E is an antisymmetric matrix, t represents the time.

[0059] Step 104 : constructing filters based on the communication topology to establish a distributed finite-time observer for the first follower cluster and a distributed finite-time observer for the second follower cluster.

[0060] The distributed finite-time observer of the first follower cluster is used to observe the system matrix of the leader. The distributed finite-time observer of the second follower cluster is used to observe the state vector and system matrix of the leader.

[0061] In one exemplary embodiment, a distributed finite-time observer of the leader's system matrix is ​​designed for a cluster of followers that can directly access the leader's state vector by constructing a filter. This allows the observations of the leader's system matrix by these follower clusters to converge to the true value within a finite time. In practical applications, if some followers (e.g., unmanned vehicles) do not know the system matrix of their leader (e.g., a drone) but can measure the leader's position, velocity, and other state information, this observer can be constructed to accurately measure the leader's system matrix.

[0062] By constructing a filter, a distributed finite-time observer of the leader's state vector and its system matrix is ​​designed for follower clusters that cannot directly access the leader's state vector. This allows the observations of the leader's state vector and its system matrix by these follower clusters to converge to their true values ​​within a finite time. In practical applications, if some followers (such as unmanned vehicles) do not know the leader's system matrix (such as a drone) and lack access to the leader's position, velocity, and other state information, this observer can be constructed to accurately measure the leader's system matrix.

[0063] Step 104 includes the following steps 201 to 204 .

[0064] Step 201: Construct a first set of filters using the following formula:

[0065]

[0066] in, is the first-order differential of N(t) with respect to time, is the first-order differential of g(t) with respect to time, k is the scalar gain used to ensure filter stability, k>0, N(t) is the state variable of a filter in the first group of filters, g(t) is the state variable of another filter in the first group of filters, Since the derivative information of the leader state vector is unknown, g(t) is obtained by calculate, q0(t) is the state vector of the leader, is the first-order differential of q0(t) with respect to time, is the first-order derivative of f(t) with respect to time, f(t) is the state variable in g(t), is the variable obtained by performing a tensor product operation on q0(t) and the identity matrix, Represents the tensor product operation, I n is the identity matrix.

[0067] Step 202: Based on the first set of filters, construct a second set of filters using the following formula:

[0068]

[0069] in, is the state variable of one filter in the second set of filters, G(t) is the state variable of another filter in the second set of filters, is the first-order differential of G(t) with respect to time, for First-order differential with respect to time.

[0070] Step 203: Based on the second set of filters, a distributed finite-time observer of the first follower cluster is established:

[0071]

[0072] Among them, Π1 is the first follower cluster, ξ i (t) is the estimated value of the leader’s state vector by the i-th follower at time t, θ i (t) is the vector form of the system matrix of the i-th follower to the leader at time t The estimated value of is θ i (t) is the first-order differential of time, and β is a constant greater than 0 and less than 1.

[0073] vec(·) is defined as: for any matrix col(·) is defined as: for any matrix sig β (·) is defined as: for any vector sig β (e i )=col(sig β (e i1 ),sig β (e i2 ),…,sigβ (e is ))(0<β<1),sig β (e ik )=sign(e ik )|e ik | β (k=1,2,…,s), sign(·) is the sign function.

[0074] Step 204: Based on the second set of filters and the communication topology, establish a distributed finite-time observer for the second follower cluster:

[0075]

[0076] Among them, Π2 is the second follower cluster, for ξ i (t) is the variable obtained by performing a tensor product operation with the identity matrix, for ξ i (t) is the first-order differential with respect to time, μ1 is a constant greater than 0, η i (t) is the intermediate value of the i-th follower to the leader’s state vector, is the intermediate quantity of the i-th follower to leader system matrix,

[0077]

[0078] Where m is the number of followers in the first follower cluster, N is the total number of followers in the heterogeneous formation, and a ij Indicates whether there is a communication relationship between the ith follower and the jth follower. If there is a communication relationship between the ith follower and the jth follower, then a ij =1, otherwise a ij =0.

[0079] Step 105 : Establish a distributed finite-time time-varying formation tracking controller based on the Euler-Lagrangian dynamic model of the followers, the dynamic model of the leader, the distributed finite-time observer of the first follower cluster, and the distributed finite-time observer of the second follower cluster.

[0080] In an exemplary embodiment, the distributed finite-time time-varying formation tracking controller is:

[0081]

[0082] in, That is, the regression matrix in the characteristic equation of the Euler-Lagrangian dynamics model of the follower in k s and k d are all positive quantities, σ is a constant greater than 0 and less than 1, s i (t) is the sliding vector, for The first derivative with respect to time, E i (t) is the estimate of the system matrix of the leader by the i-th follower, ξ i (t) is the estimated value of the leader’s state vector by the i-th follower at time t, h i (t) first-order differential with respect to time, h i (t) is the state offset between the i-th follower and the leader, which is only used to describe a time-varying formation. α1 and α2 are both constants greater than 0. pi (t) is the tracking error of the first formation, e νi (t) is the tracking error of the second formation, N is the total number of followers in the heterogeneous formation, a ij Indicates whether there is a communication relationship between the ith follower and the jth follower in the heterogeneous formation. If there is a communication relationship between the ith follower and the jth follower, then a ij =1, otherwise a ij =0, β and θ are both constants greater than 0 and less than 1, h ij (t) is the difference in state offset between the i-th follower and the j-th follower and the leader, h ij (t) = h i (t)-h j (t), h0(t)=0,

[0083] In the above operation, Sig β (·) is defined as: for any vector have

[0084] Sig β (e i )=0 s (if e i =0 s ).

[0085] h(t)=col(h1(t),h2(t),…,h N (t)) is the time-varying formation vector, which is used to represent the expected time-varying formation. i (t) and h j (t) are the i-th and j-th variables in h(t), and h i (t) and h j (t) The first-order differential with respect to time.

[0086] Step 106 : Using the distributed finite-time time-varying formation tracking controller, control the time-varying formation of followers in the heterogeneous formation.

[0087] A distributed finite-time time-varying formation tracking controller enables a cluster of followers to achieve finite-time formation tracking, meaning the formation tracking error converges to zero within a finite time. Under the control of the control variables output by this distributed finite-time time-varying formation tracking controller, the followers can achieve the desired time-varying formation around the leader. For example, in the case of an unmanned vehicle, the included control module can directly respond to the controller output to achieve the desired control of the vehicle.

[0088] The effectiveness of the proposed method is verified by a specific example of time-varying formation control in a heterogeneous cluster system. The specific implementation steps of this example are as follows:

[0089] (1) Heterogeneous cluster communication topology setting.

[0090] like Figure 2 As shown, consider a cluster consisting of 6 agents, where number 0 represents the leader and the rest are followers, that is, the follower set Among the five followers, followers numbered 1 and 2 can directly obtain the leader's state vector q0(t), which is Π1; followers numbered 3, 4, and 5 cannot directly obtain the leader's state vector q0(t), which is Π2.

[0091] (2) Establish the Euler-Lagrangian dynamic model of the follower and the dynamic model of the leader.

[0092] In two dimensions, the Euler-Lagrangian dynamics model of the follower is set as follows:

[0093]

[0094] Where, qi=col(q1i(t),q2i(t)), M i (q i (t))=m i I2, G i (q i (t))=[m i ;m i ],q 1i (t) and q 2i (t) are q i The two components of (t), mi represents the mass of the i-th follower, and I2 represents the 2×2 identity matrix.

[0095] for For the 5 followers in , let their masses be: m1 = 0.5, m2 = 0.6, m3 = 1.0, m4 = 1.5, m5 = 2.0.

[0096] In the two-dimensional dimension, the dynamic model of the leader is as follows:

[0097]

[0098] Where, E = [0 2; -2 0].

[0099] (3) Set the expected time-varying formation.

[0100] Here, the desired time-varying formation is set as a circular rotation formation. For the i-th follower (i=1,2,...,5), the state offset h is set to i (t) is set to:

[0101]

[0102] (4) Construct a distributed finite-time observer of the leader system matrix for the follower cluster Π1 that can directly obtain the leader state vector, so that the observation value of Π1 on the leader system matrix can converge to the true value in a finite time.

[0103] Construct the first set of filters:

[0104]

[0105] Wherein, the constant k=0.5.

[0106] Construct the second set of filters:

[0107]

[0108] The distributed finite-time observer is constructed as follows:

[0109]

[0110] Wherein, the constant β=0.5.

[0111] (5) For the follower cluster Π2 that cannot directly obtain the leader state vector, a distributed finite-time observer of the leader state vector and its system matrix is ​​constructed, so that the observation values ​​of Π2 on the leader state vector and its system matrix can converge to the true values ​​within a finite time.

[0112] The distributed finite-time observer is constructed as follows:

[0113]

[0114] Where μ1 is any positive constant.

[0115] (6) Set up a distributed finite-time time-varying formation tracking controller.

[0116] First define the sliding vector s i (t) are as follows:

[0117]

[0118] in, α1=0.5, α2=1.5.

[0119] The distributed finite-time time-varying formation tracking controller is constructed as follows:

[0120]

[0121] Among them, k s =1.5, k d =0.8.

[0122] (7) Simulation condition settings and results.

[0123] For all agents in a heterogeneous cluster, their state vector q i =col(q 1i (t),q 2i The initial value of (t)) is set to: ij (0) = (θ - 0.5), Here, θ is a random number in the range [0,1].

[0124] Figure 3 and Figure 4 Represents the estimation error curves of the leader state vector q0(t) and the system matrix E of the five followers, Figure 5 is the tracking error variation curve of the formation of 5 followers, Figures 6 to 9 The positions of the five followers and the leader at different times are shown. Figure 3 and Figure 4 It can be seen that the distributed finite-time observer provided by this application can effectively converge to the true value of the leader state information and the system matrix; Figures 5 to 9 It can be seen that, based on the observer converging to the true value, the distributed finite-time formation controller provided by this application can also make the formation error converge to 0, effectively controlling the followers to achieve the desired circular rotation formation. This example verifies the effectiveness of the method proposed in this application.

[0125] In summary, this application designs a distributed finite-time observer and a distributed finite-time time-varying formation tracking controller to achieve tracking control of a multi-agent formation with an unknown leader system matrix. The main advantages are as follows:

[0126] 1) It solves the problem of observer design for finite-time parameter estimation of heterogeneous multi-agent systems when the leader system matrix is ​​unknown, and ensures that the relevant adaptive parameters converge to their true values ​​within a finite time under the initial excitation (IE) condition, rather than being restricted by the traditional persistence of excitation (PE) condition.

[0127] 2) The finite-time observer and time-varying formation tracking controller proposed in this application for each follower do not need to know the leader's system matrix or the leader's state derivative information.

[0128] 3) The finite-time observer and time-varying formation tracking controller proposed in this application are constructed in a fully distributed manner, ensuring that the heterogeneous formation system can achieve the desired time-varying formation and track the state trajectory generated by the uncertain leader within a finite time without knowing the rest of the information of the entire cluster.

[0129] Based on the same inventive concept, embodiments of the present application also provide a system for finite-time tracking of a time-varying, time-varying, and time-varying formation with an unknown leader system matrix, which is used to implement the aforementioned method for finite-time tracking of a time-varying, time-varying, and time-varying formation with an unknown leader system matrix. The solution provided by this system is similar to the solution described in the aforementioned method. Therefore, the specific limitations of the embodiments of the system for finite-time tracking of one or more time-varying, time-varying, and time-varying formations with an unknown leader system matrix provided below can be found in the aforementioned limitations of the method for finite-time tracking of a time-varying, time-varying, and time-varying formation with an unknown leader system matrix, and will not be further elaborated here.

[0130] In an exemplary embodiment, Figure 10 As shown, a finite-time tracking system for a time-varying conformal formation with an unknown leader system matrix is ​​provided, comprising: a communication topology acquisition module 301, a cluster division module 302, a modeling module 303, an observer construction module 304, a controller construction module 305 and a control module 306.

[0131] The communication topology acquisition module 301 is used to obtain the communication topology of a heterogeneous formation. The heterogeneous formation includes multiple followers and a leader. Some followers in the heterogeneous formation can directly obtain the leader's state vector, while the remaining followers cannot. The leader's system matrix is ​​unknown to all followers.

[0132] The cluster division module 302 is configured to determine a first follower cluster and a second follower cluster based on the communication topology. The first follower cluster includes followers that can directly obtain the leader's state vector. The second follower cluster includes followers that cannot directly obtain the leader's state vector.

[0133] The modeling module 303 is used to establish the Euler-Lagrangian dynamic model of the follower and the dynamic model of the leader.

[0134] The observer construction module 304 is configured to construct a distributed finite-time observer for the first follower cluster and a distributed finite-time observer for the second follower cluster based on the communication topology using a filter construction method. The distributed finite-time observer for the first follower cluster is configured to observe the system matrix of the leader. The distributed finite-time observer for the second follower cluster is configured to observe the state vector and system matrix of the leader.

[0135] The controller construction module 305 is used to establish a distributed finite-time time-varying formation tracking controller based on the Euler-Lagrangian dynamic model of the follower, the dynamic model of the leader, the distributed finite-time observer of the first follower cluster and the distributed finite-time observer of the second follower cluster.

[0136] The control module 306 is configured to control the time-varying formation of followers in the heterogeneous formation by using the distributed finite-time time-varying formation tracking controller.

[0137] In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor implements the steps in the above method embodiments when executing the computer program.

[0138] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0139] In an exemplary embodiment, a computer program product is provided, including a computer program. When the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0140] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0141] In this application, all actions to obtain signals, information or data are carried out in compliance with the relevant data protection laws and policies of the country where they are located and with the authorization given by the owner of the corresponding device.

[0142] Those skilled in the art will understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, database or other media used in the embodiments provided in this application may include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory may include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0143] The databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided herein may include, but are not limited to, general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic units, data processing logic units based on quantum computing, and the like.

[0144] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0145] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A finite-time tracking method for a time-varying conformational formation with an unknown leader system matrix, characterized in that: The finite-time tracking method for a time-varying conformational formation with an unknown leader system matrix includes: Obtaining a communication topology relationship of a heterogeneous formation; the heterogeneous formation includes multiple followers and a leader; some followers in the heterogeneous formation can directly obtain the state vector of the leader, while the remaining followers cannot directly obtain the state vector of the leader, and the system matrix of the leader is unknown to all followers; Determining a first follower cluster and a second follower cluster according to the communication topology relationship; the first follower cluster includes followers that can directly obtain the state vector of the leader; the second follower cluster includes followers that cannot directly obtain the state vector of the leader; Establish the Euler-Lagrangian dynamics model of the follower and the dynamics model of the leader; By constructing a filter, based on the communication topology, a distributed finite-time observer of the first follower cluster and a distributed finite-time observer of the second follower cluster are respectively established; the distributed finite-time observer of the first follower cluster is used to observe the system matrix of the leader; the distributed finite-time observer of the second follower cluster is used to observe the state vector and system matrix of the leader; Establishing a distributed finite-time time-varying formation tracking controller based on the Euler-Lagrangian dynamic model of the followers, the dynamic model of the leader, the distributed finite-time observer of the first follower cluster, and the distributed finite-time observer of the second follower cluster; The distributed finite-time time-varying formation tracking controller is used to control the time-varying formation of followers in the heterogeneous formation.

2. The finite time tracking method for a time-varying conformational formation with an unknown leader system matrix according to claim 1, characterized in that: Both the followers and the leaders in the heterogeneous formation are intelligent agents.

3. The finite time tracking method for a time-varying conformational formation with an unknown leader system matrix according to claim 1, characterized in that: The Euler-Lagrangian dynamic model of the follower is: Among them, q i (t) is the position of the i-th follower, is the speed of the ith follower, is the acceleration of the ith follower, u i (t) is the control input vector of the ith follower, M i (q i (t)) is the inertia matrix of the i-th follower, is the Coriolis and centrifugal matrix of the ith follower, G i (q i (t)) is the gravity matrix of the ith follower, and t represents the time.

4. The finite time tracking method for a time-varying conformational formation with an unknown leader system matrix according to claim 3, characterized in that: The Euler-Lagrangian dynamics model of the follower satisfies the following equation: in, is the regression matrix of the ith follower, x(t) and y(t) are The two variables in φ i (t) is the parameter vector of the i-th follower.

5. The finite time tracking method for a time-varying conformational formation with an unknown leader system matrix according to claim 1, characterized in that: The dynamic model of the leader is: Among them, q0(t) is the state vector of the leader, is the first-order differential of q0(t) with respect to time, E is the system matrix of the leader, and t represents the moment.

6. The finite time tracking method for a time-varying conformational formation with an unknown leader system matrix according to claim 1, characterized in that: A distributed finite-time observer for the first follower cluster and a distributed finite-time observer for the second follower cluster are respectively established based on the communication topology relationship by constructing a filter, specifically including: The first set of filters is constructed using the following formula: in, is the first-order differential of N(t) with respect to time, is the first-order differential of g(t) with respect to time, k is the scalar gain, k>0, N(t) is the state variable of one filter in the first set of filters, g(t) is the state variable of another filter in the first set of filters, g(t)=q0(t)-e -kt q0(0)-kf(t), q0(t) is the state vector of the leader, is the first-order differential of q0(t) with respect to time, is the first-order derivative of f(t) with respect to time, f(t) is the state variable in g(t), is the variable obtained by performing a tensor product operation on q0(t) and the identity matrix, I n is the identity matrix, represents the tensor product operation, t represents the time; Based on the first set of filters, the second set of filters is constructed using the following formula: in, is the state variable of one filter in the second set of filters, G(t) is the state variable of another filter in the second set of filters, is the first-order differential of G(t) with respect to time, for First-order differential with respect to time; Based on the second set of filters, a distributed finite-time observer of the first follower cluster is established: Among them, Π1 is the first follower cluster, ξ i (t) is the estimate of the leader’s state vector by the i-th follower at time t, θ i (t) is the vectorial estimate of the system matrix of the leader by the i-th follower at time t, is θ i (t) is the first-order differential with respect to time, where β is a constant greater than 0 and less than 1; Based on the second set of filters and the communication topology, a distributed finite-time observer of the second follower cluster is established: Among them, Π2 is the second follower cluster, for ξ i (t) is the variable obtained by performing a tensor product operation with the identity matrix, I n is the identity matrix, represents the tensor product operation, for ξ i (t) is the first-order differential with respect to time, μ1 is a constant greater than 0, η i (t) is the intermediate value of the i-th follower to the leader’s state vector, is the intermediate quantity of the i-th follower to leader system matrix, m is the number of followers in the first follower cluster, N is the total number of followers in the heterogeneous formation, a ij Indicates whether there is a communication relationship between the ith follower and the jth follower. If there is a communication relationship between the ith follower and the jth follower, then a ij =1, otherwise a ij =0.

7. The finite time tracking method for a time-varying conformational formation with an unknown leader system matrix according to claim 4, characterized in that: The distributed finite-time time-varying formation tracking controller is: Among them, k s and k d are all positive quantities, σ is a constant greater than 0 and less than 1, s i (t) is the sliding vector, for The first derivative with respect to time, E i (t) is the estimate of the system matrix of the leader by the i-th follower, ξ i (t) is the estimated value of the leader’s state vector by the i-th follower at time t, h i (t) first-order differential with respect to time, h i (t) is the state offset between the ith follower and the leader, α1 and α2 are both constants greater than 0, e pi (t) is the tracking error of the first formation, e νi (t) is the tracking error of the second formation, N is the total number of followers in the heterogeneous formation, a ij Indicates whether there is a communication relationship between the ith follower and the jth follower in the heterogeneous formation. If there is a communication relationship between the ith follower and the jth follower, then a ij =1, otherwise a ij =0, β and θ are both constants greater than 0 and less than 1, h ij (t) is the difference in state offset between the i-th follower and the j-th follower and the leader, h ij (t) = h i (t)-h j (t), 8. A finite-time tracking system for a time-varying configuration formation with an unknown leader system matrix, applied to the finite-time tracking method for a time-varying configuration formation with an unknown leader system matrix according to any one of claims 1 to 7, characterized in that: The time-varying conformational formation finite-time tracking system with an unknown leader system matrix includes: a communication topology acquisition module, configured to acquire the communication topology of a heterogeneous formation comprising a plurality of followers and a leader; wherein some followers in the heterogeneous formation can directly acquire the leader's state vector, while the remaining followers cannot, and the leader's system matrix is ​​unknown to all followers; a cluster division module, configured to determine a first follower cluster and a second follower cluster according to the communication topology; the first follower cluster includes followers that can directly obtain the state vector of the leader; and the second follower cluster includes followers that cannot directly obtain the state vector of the leader; Modeling module, used to build the Euler-Lagrangian dynamics model of the follower and the dynamics model of the leader; an observer construction module, configured to establish, based on the communication topology, a distributed finite-time observer for the first follower cluster and a distributed finite-time observer for the second follower cluster by constructing a filter; the distributed finite-time observer for the first follower cluster is configured to observe the system matrix of the leader; and the distributed finite-time observer for the second follower cluster is configured to observe the state vector and system matrix of the leader; a controller building module for building a distributed finite-time time-varying formation tracking controller based on the Euler-Lagrangian dynamics model of the followers, the dynamics model of the leader, the distributed finite-time observer of the first follower cluster, and the distributed finite-time observer of the second follower cluster; A control module is used to control the time-varying formation of followers in the heterogeneous formation by using the distributed finite-time time-varying formation tracking controller.

9. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the finite-time tracking method for a time-varying conformal formation with an unknown leader system matrix according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the finite-time tracking method for a time-varying conformal formation with an unknown leader system matrix according to any one of claims 1 to 7 is implemented.

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