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

Abstract

The invention discloses a finite time tracking method, system and device for a time-varying heterogeneous formation with an unknown leader system matrix, and a medium, and relates to the field of cluster formation tracking control, and the method comprises the steps: obtaining a communication topological relation of the heterogeneous formation; determining a first follower cluster and a second follower cluster according to the communication topological relation; establishing an Euler-Lagrange kinetic model of the follower and a kinetic model of the leader; respectively establishing distributed finite time observers of the two follower clusters; establishing a distributed finite time time-varying formation tracking controller based on an Euler-Lagrange kinetic model of a follower, a kinetic model of a leader and a distributed finite time observer; and a distributed finite time time-varying formation tracking controller is adopted to control the time-varying formation of followers in the heterogeneous formation. According to the invention, tracking control of the multi-agent formation with an unknown leader system matrix is realized.

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 a hot topic in the current 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 studies on multi-agent formation tracking control assume that all follower agents know the dynamic information of the leader system, such as the system matrix in the case of linear dynamics. Although this assumption is also common in the study of leader-follower consistency problems, this requirement means that each follower agent has direct communication with the leader agent, which contradicts the distributed nature of multi-agents. In many practical applications, no follower agent may fully understand the dynamic information of the tracking target. For example, in non-cooperative scenarios, a drone tracking an unmanned aerial vehicle cannot directly obtain the dynamic model of the target drone. Therefore, the multi-agent formation tracking control problem with an unknown leader system matrix has become an important and challenging problem that has received increasing attention in recent years. It is necessary to design a corresponding parameter observer to estimate the dynamic information of the leader. This heterogeneous multi-agent system with a leader system matrix unknown to all followers is also called a heterogeneous multi-agent system with an uncertain leader.

[0004] Many observer designs require persistent excitation conditions, which require that the signal from the leader state is rich enough. However, when dealing with uncertain parameter estimation problems, it may be difficult to ensure and verify persistent excitation conditions in advance. Some studies have successfully relaxed the requirements for traditional persistent excitation conditions, but they are mainly used for dynamic information estimation in single adaptive systems or homogeneous multi-agent systems. It is very difficult to extend these technologies to heterogeneous multi-agent systems with uncertain leaders, because in heterogeneous multi-agent systems, there is a non-cooperative relationship between leaders and followers. For example, in the actual combat scenario of an unmanned vehicle formation tracking a drone, it is difficult to ensure that the follower unmanned vehicle can directly obtain the state information of the leader drone. Therefore, how to design a formation controller that does not require persistent excitation conditions in a heterogeneous cluster system with an uncertain leader is also 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 and 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] Acquire the communication topology relationship of a heterogeneous formation; the heterogeneous formation includes a plurality of 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] Determine 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 adopting the method of constructing filters, based on the communication topology relationship, 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 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;

[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 time-varying conformational formation finite-time tracking system with an unknown leader system matrix, comprising:

[0015] A communication topology acquisition module, used to acquire the communication topology relationship of a heterogeneous formation; the heterogeneous formation includes a plurality of followers and a leader; some followers in the heterogeneous formation can directly acquire the state vector of the leader, while the remaining followers cannot directly acquire the state vector of the leader, and the system matrix of the leader is unknown to all followers;

[0016] A cluster division module, used to determine 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;

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

[0018] An observer construction module is used to respectively establish a distributed finite-time observer of the first follower cluster and a distributed finite-time observer of the second follower cluster based on the communication topology relationship by means of constructing filters; 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;

[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 method, system, device and medium for finite-time tracking of 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 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. 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 drawings required for use in the embodiments will be briefly introduced below. 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 paying 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 in 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 A curve diagram 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 curve diagram of the estimated error change of the leader system matrix in one embodiment of the present application;

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

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

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

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

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

[0035] Fig.10 A schematic diagram of functional modules of a finite-time tracking system for a time-varying conformal formation with an unknown leader system matrix provided in one embodiment of the present application. DETAILED DESCRIPTION

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

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

[0038] In an exemplary embodiment, Figure 1 As shown, a method for finite-time tracking of a time-varying conformal formation with an unknown leader system matrix is ​​provided. The method is executed by a computer device, and can be specifically executed by a computer device such as a terminal or a server alone, or 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, obtaining the communication topology relationship of the heterogeneous formation.

[0040] A heterogeneous formation includes multiple followers and a leader. The leader is followed 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 state vector q0 of the leader, while the remaining followers cannot directly obtain the state vector q0 of the leader, and the system matrix E of the leader is unknown to all followers.

[0042] Step 102: Determine a first follower cluster PI1 and a second follower cluster PI2 according to the communication topology relationship. 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 an optional implementation, the communication topology relationship in the formation cluster is abstracted into a graph, and the corresponding Laplace matrix and other related quantitative variables are obtained to provide a basis for the design of subsequent observers and controllers. For example, in a formation tracking control scenario, it is necessary to obtain whether each individual can communicate directly with the other individuals, and establish a communication topology relationship 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 topological structure 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 For the ith follower and the jth follower, You can use the ν in ν i and ν j To refer to. If from ν i to 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 (the 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 part of them can directly obtain the state vector q0 of the leader. Assuming that the number of followers in this part is m, this part of followers is recorded as Π1:={1,2,...,m}; the rest of the followers in the heterogeneous formation cannot directly obtain the state vector q0 of the leader, and this part of followers is recorded 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, establishing the Euler-Lagrangian dynamics model of the follower and the dynamics 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 dynamics model of the follower and a dynamics model of the leader are established, and the dynamics equation expressions and characteristic equations corresponding to the followers and leaders are obtained, providing a basis for the design of subsequent observers and controllers.

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

[0051]

[0052] Among them, q i (t) is the position of the ith 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 ith 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 leaders 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 the assumption that E is an antisymmetric matrix is ​​satisfied, and t represents the time.

[0059] Step 104 : constructing filters to establish 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 relationship.

[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 the system matrix of the leader.

[0061] In an exemplary embodiment, a distributed finite-time observer of the leader's system matrix is ​​designed for the follower cluster that can directly obtain the leader's state vector by constructing a filter, so that the observation value of the leader's system matrix by this part of the follower cluster can converge to the true value within a finite time. In practical applications, if some followers (such as unmanned vehicles) do not know the system matrix of the leader (such as a drone), but can measure the position, speed and other state information of the leader, the observer can be constructed through this step to accurately measure the system matrix information of the leader.

[0062] By constructing a filter, a distributed finite-time observer of the leader's state vector and its system matrix is ​​designed for the follower cluster that cannot directly obtain the leader's state vector, so that the observation value of the leader's state vector and its system matrix by this part of the follower cluster can converge to the true value within a finite time. In practical applications, if some followers (such as unmanned vehicles) do not know the system matrix of the leader (such as a drone) and cannot obtain the leader's position, speed and other state information, the observer can be constructed through this step to accurately measure the leader's system matrix information.

[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 the stability of the filter, 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 set of filters, Since the derivative information of the leader’s 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 group of filters, a second group of filters is constructed 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 ith 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, 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: Establish a distributed finite-time observer of a second follower cluster based on the second set of filters and the communication topology relationship:

[0075]

[0076] Among them, Π2 is the second follower cluster, For i (t) is the variable obtained by performing a tensor product operation with the identity matrix, For i (t) is the first-order differential of 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 the 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, 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.

[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 ith follower, ξ i (t) is the estimated value of the leader’s state vector by the ith follower at time t, h i (t) is the first-order differential with respect to time, h i (t) is the state offset between the ith 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 ith follower and the jth 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), respectively. and h i (t) and h j (t) The first-order differential with respect to time.

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

[0087] The follower cluster can realize finite-time formation tracking under the action of the distributed finite-time time-varying formation tracking controller, that is, the formation tracking error converges to zero within a finite time. The followers can realize the desired time-varying formation around the leader under the control of the control quantity output by the distributed finite-time time-varying formation tracking controller. For example, for an unmanned vehicle, the control module it contains can directly respond to the controller output to realize the desired control of the unmanned vehicle.

[0088] The effectiveness of the method proposed in this application is verified by a specific example of time-varying formation control of 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 No. 1 and No. 2 can directly obtain the state vector q0(t) of the leader, which is Π1; followers No. 3, No. 4, and No. 5 cannot directly obtain the state vector q0(t) of the leader, 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 (t) two components, mi represents the mass of the i-th follower, and I2 represents the 2×2 identity matrix.

[0095] for There are 5 followers in , and their masses are: m1=0.5, m2=0.6, m3=1.0, m4=1.5, m5=2.0.

[0096] In two dimensions, the dynamic model of setting leaders is as follows:

[0097]

[0098] Among them, 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 rotating formation. For the i-th follower (i=1, 2, ..., 5), the state offset h is 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] Among them, 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] Among them, the constant β=0.5.

[0111] (5) For the follower cluster Π2 that cannot directly obtain the leader's state vector, a distributed finite-time observer of the leader's state vector and its system matrix is ​​constructed, so that the observation values ​​of the leader's state vector and its system matrix by Π2 can converge to the true value 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 They represent the estimated error curves of the five followers for the leader’s state vector q0(t) and the system matrix E. 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 in 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 the present 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 the present application.

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

[0126] 1) It solves the observer design problem of finite-time parameter estimation for heterogeneous multi-agent systems when the leader system matrix is ​​unknown, and can ensure 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 system matrix of the leader or the state derivative information of the leader.

[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, the embodiment of the present application also provides a finite time tracking system for a time-varying configuration formation with an unknown leader system matrix for implementing the finite time tracking method for a time-varying configuration formation with an unknown leader system matrix. The implementation scheme for solving the problem provided by the system is similar to the implementation scheme recorded in the above method, so the specific limitations in the embodiments of the finite time tracking system for a time-varying configuration formation with an unknown leader system matrix provided below can be referred to the limitations of the finite time tracking method for a time-varying configuration formation with an unknown leader system matrix above, and will not be repeated here.

[0130] In an exemplary embodiment, Fig.10 As shown, a finite time tracking system for a time-varying conformational 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 acquire the 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.

[0132] The cluster division module 302 is used to determine 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.

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

[0134] The observer construction module 304 is used to construct a distributed finite time observer of the first follower cluster and a distributed finite time observer of the second follower cluster based on the communication topology relationship by means of constructing filters. 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.

[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 used 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, wherein a computer program is stored in the memory, and the processor implements the steps in the above-mentioned method embodiments when executing the computer program.

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

[0139] In an exemplary embodiment, a computer program product is provided, including a computer program, and 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 of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed 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 the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can 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 can 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 database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.

[0144] The technical features of the above embodiments may 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 article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will 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 of a time-varying conformational formation with an unknown leader system matrix comprises: Acquire the communication topology relationship of a heterogeneous formation; the heterogeneous formation includes a plurality of 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; Determine 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 adopting the method of constructing filters, based on the communication topology relationship, 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 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; 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 dynamics model of the follower is: Among them, q i (t) is the position of the ith 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 ith 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 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: 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, 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 estimated value of the leader’s state vector by the ith follower at time t, θ i (t) is the vector estimate of the system matrix of the leader by the ith follower at time t, is θ i (t) is the first-order differential with respect to time, 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 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 i (t) is the first-order differential of 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 the 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 ith follower, ξ i (t) is the estimated value of the leader’s state vector by the ith follower at time t, h i (t) is the 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 ith follower and the jth 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 a finite time tracking method for a time-varying configuration formation with an unknown leader system matrix as claimed in any one of claims 1 to 7, characterized in that: The leader system matrix unknown time-varying conformational formation finite time tracking system includes: A communication topology acquisition module, used to acquire the communication topology relationship of a heterogeneous formation; the heterogeneous formation includes a plurality of followers and a leader; some followers in the heterogeneous formation can directly acquire the state vector of the leader, while the remaining followers cannot directly acquire the state vector of the leader, and the system matrix of the leader is unknown to all followers; A cluster division module, used to determine 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; Modeling module, used to build the Euler-Lagrangian dynamics model of the followers and the dynamics model of the leader; An observer construction module is used to respectively establish a distributed finite-time observer of the first follower cluster and a distributed finite-time observer of the second follower cluster based on the communication topology relationship by means of constructing filters; 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; 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 as described in 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 method for finite-time tracking of 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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