A multi-agent collaborative interception method based on distributed preset time convergence

Abstract

The present invention relates to the field of multi-agent cooperative control, and specifically to a multi-agent cooperative interception method based on distributed preset time convergence, comprising the following steps: considering a two-dimensional multi-agent nonlinear cooperative interception model composed of n agents, establishing a relative motion equation between the multi-agent and the target; defining a residual interception time error estimate, and designing a preset time control law for the leader agent along the line of sight angle; defining a residual interception time consistency cooperative error variable, and designing a preset time cooperative control law for the follower multi-agent along the line of sight angle; and constructing a preset time convergence sliding mode surface s of the multi-agent system. i Design a pre-set time coordinated control law for a multi-agent system along the normal line of sight; optimize and adjust the control law parameters through simulation and data collection and analysis, and repeat the above steps to achieve pre-set time coordinated interception by multi-agent systems. This invention can achieve efficient coordinated interception by multi-agent systems in complex mission environments.

Description

Technical Field

[0001] The present invention relates to the field of multi-agent collaborative control, and in particular to a multi-agent collaborative interception method based on distributed preset time convergence. Background Art

[0002] With the continuous advancement of science and technology, multi-agent collaborative interception technology has demonstrated significant application potential in a variety of fields, including aerospace and civil applications, and has become a hot topic in academic research. Faced with increasingly complex tasks such as protecting the airspace around airports, clearing space debris, and tracking maneuvering targets, the limitations of traditional single-agent interception capabilities and low operational efficiency are becoming increasingly apparent. Multi-agent collaborative interception technology, due to its superior accuracy and significant advantages in interception range, has occupied an indispensable position in a variety of fields, including aerospace safety and civil security protection.

[0003] Multi-agent collaborative control technology has developed rapidly. Early research focused on ensuring the consistency of the states of the agents, and subsequently a variety of control algorithms were developed, such as distributed control protocols. Compared with the traditional "two-layer" architecture, the leader-follower architecture has obvious advantages. On the one hand, the leader-follower architecture can effectively manage communication traffic and reduce unnecessary information transmission. In the face of agent failure or communication interference, it can maintain system stability and robustness through adjustments made by the leader. On the other hand, the leader-follower architecture has a clear division of labor, with the leader making overall plans and the followers executing tasks efficiently. In multi-agent collaborative interception, pursuit strategies can be quickly formulated and tasks assigned, thereby improving interception efficiency. In these studies, scholars have continuously proposed innovative collaborative interception methods to meet the needs of different interception scenarios.

[0004] In the research field of multi-agent systems, controlling convergence time is a core issue. Early research mainly focused on achieving asymptotic stability of the system or convergence in a finite time, but the realization of asymptotic stability requires infinite time, which does not meet the strict timeliness requirements of practical applications. Although finite-time control speeds up convergence, it is limited by the initial state of the system. When the initial value of the system is large or unknown, the convergence time becomes difficult to predict and control, which may have an adverse effect on the overall performance of the system. There are still some shortcomings in existing research, especially most methods are based on finite-time or fixed-time convergence theory, and cooperative interception methods with preset time convergence still need further research.

[0005] The proposed theory of preset time convergence has opened up a new research path for solving a series of problems faced by multi-agent system collaborative tasks. This theory enables researchers to precisely set the upper bound of the system's convergence time based on specific task requirements, thereby ensuring that the entire multi-agent collaborative system converges quickly and stably within the preset time, achieving efficient and accurate collaborative interception. Summary of the Invention

[0006] The purpose of this invention is to propose a multi-agent collaborative interception method based on distributed preset time convergence to overcome the shortcomings of existing multi-agent collaborative control technology in time performance and realize efficient collaborative interception of multi-agent systems in complex mission environments.

[0007] In order to achieve the above object, the technical solutions specifically adopted by the present invention are as follows:

[0008] A multi-agent collaborative interception method based on distributed preset time convergence includes the following steps:

[0009] Step 1: Consider a two-dimensional multi-agent nonlinear cooperative interception model consisting of n agents, and establish the relative motion equation between the multi-agent and the target;

[0010] Step 2: Define the estimated value of the remaining interception time error and design the preset time control law of the leader agent along the line of sight angle;

[0011] Step 3: Define the remaining interception time consistency cooperative error variable and design the preset time cooperative control law of the follower multi-agent along the line of sight angle direction;

[0012] Step 4: Construct the preset time convergence sliding surface s of the multi-agent system i :

[0013] Step 5: Design a preset time cooperative control law for the multi-agent system along the normal direction of the line of sight;

[0014] Step 6: Repeat step 25 through simulation and data collection and analysis to optimize the control law parameters and achieve the optimization of the multi-agent collaborative interception method. Specifically, using the MATLAB simulation software platform, a multi-agent collaborative interception simulation environment is constructed. The initial parameters of the agents and targets are set, and a directed graph communication topology is established based on the actual communication network conditions. Based on the collected data, the non-physically meaningful coefficients in the controller, such as p1, p2, p3, μ, and α, are adjusted and optimized to make the entire control process smooth, reduce errors, and improve accuracy.

[0015] Furthermore, in step 1, the relative motion equation between the multi-agent and the target is established as follows:

[0016]

[0017] Among them, r i is the relative distance between the ith agent and the target, Represents r i The derivative with respect to time; λ iis the sight angle of the ith agent to the target, Represents λ i The derivative with respect to time; V ri represents the relative speed between the i-th agent and the target along the line of sight, V λi A represents the relative speed between the i-th agent and the target orthogonal to the line of sight; Mri 、A Mλi Denote the acceleration of the ith agent along and perpendicular to the line of sight respectively; A Tr 、A Tλ They represent the acceleration of the target along and perpendicular to the line of sight, respectively.

[0018] Furthermore, the step 2 specifically includes the following steps:

[0019] S2.1 defines the remaining interception time variable of the i-th agent as t goi , Expressed as:

[0020]

[0021] S2.2 Assume that agent 1 is the leader, then the estimated error of the leader's interception target time is:

[0022]

[0023] Among them, t is the current time, T c1 The leader is given a preset interception time; therefore, at the preset time T c1 Intercepting the target is equivalent to intercepting the time error Converges to zero;

[0024] S2.3 Estimated time error for interception target Taking the derivative, we can get:

[0025]

[0026] S2.4 Assume that the target's acceleration A along the line of sight is Tr <A MrMAX , A MrMAX represents the maximum acceleration of the agent along the line of sight angle, and designs the preset time control law A of the leader agent 1 along the line of sight direction. Mr1 as follows:

[0027]

[0028] Among them, r i is the relative distance between the ith agent and the target, V ri represents the relative speed between the i-th agent and the target along the line of sight, V λirepresents the relative velocity between the i-th agent and the target orthogonal to the line of sight, 0<p1<1, T c1 Set the interception time for the leader, T c1 >0.

[0029] Furthermore, the step 3 specifically includes the following steps:

[0030] S3.1 Define the remaining interception time consistency collaborative error variable ξ of follower agent i (i = 2, 3,, n) i :

[0031]

[0032] S3.2 Design the preset time control law A of follower agent i (i=2,3,,n) along the line of sight Mri as follows:

[0033]

[0034] Furthermore, the preset time convergence sliding surface s of the multi-agent system constructed in step 4 is i as follows:

[0035]

[0036] in, 0<μ<1, 0<p2<1, α>0, T c2 >0;

[0037] When the sliding surface s i = 0, there is Among them, p1, p2, p3, and μ are coefficients without physical meaning. They are the power of a certain item in the controller, which affects the convergence rate of the controller and can be optimized according to different systems.

[0038] Furthermore, in step S5, it is assumed that the acceleration of the target along the normal direction of the line of sight |A Tλ |<A MλMAX , where A MλMAX represents the maximum acceleration of the agent along the normal direction of the line of sight; the sliding surface s that converges at the preset time constructed in step 4 i Based on this, the sight line normal control law A is designed Mλi :

[0039]

[0040] in,

[0041] 0<p3<1,T c3 >0.

[0042] The multi-agent collaborative interception method based on distributed preset time convergence of the present invention can not only be applied to the tracking and interception of targets by agents, but can also be widely applied to various task scenarios that require the collaboration of multiple agents, such as logistics and transportation, disaster relief, etc., showing a broad application prospect and having the following characteristics and beneficial effects:

[0043] 1) Accurate interception time coordinated control

[0044] In the multi-agent system proposed by this invention, a preset time convergence collaborative control strategy based on the line of sight angle direction achieves the remarkable effect of achieving consistency in the remaining interception time among each agent within a predetermined time frame. Compared with traditional methods, there is no need to consider complex relationships, which simplifies the design process. By precisely adjusting the acceleration in the line of sight angle direction, the remaining interception time error can converge to zero within the preset convergence time upper bound, ensuring that the leader intercepts the target according to the preset time, and the followers cooperate to achieve simultaneous interception by multiple agents, improving the suddenness and effectiveness of the interception, and enhancing the target interception capability.

[0045] 2) Distributed features enhance system robustness and adaptability

[0046] This invention utilizes a distributed architecture, enabling coordinated control among multiple agents through information exchange. This distributed nature ensures that the system maintains a certain level of interception effectiveness even in the face of partial agent failures or communication interruptions, resulting in high robustness. Furthermore, each agent can adjust its control strategy in real time based on its own and neighboring agent status information, enhancing the multi-agent system's adaptability to complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is the communication topology diagram of the leader-slave structure.

[0048] Figure 2 Flowchart of an embodiment of the present invention.

[0049] Figure 3 This is a two-dimensional multi-agent collaborative interception model diagram in an embodiment of the present invention.

[0050] Figure 4 Graph showing the motion trajectories of the agent and the target in an embodiment of the present invention.

[0051] Figure 5 is a distance diagram between the agent and the target in an embodiment of the present invention. DETAILED DESCRIPTION

[0052] The present invention is described in detail below in conjunction with specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

[0053] In order to enable multiple agents to achieve collaborative consistency control within a preset time, ultimately achieve effective interception and control of the target, and improve the efficiency and accuracy of multi-agent collaborative interception, the present invention proposes a multi-agent collaborative interception method based on distributed preset time convergence. This method carries out collaborative control law design work based on the leader-follower control architecture under the directed graph framework. Specifically, it sets a preset interception time for the leader agent and ensures that some followers can receive the leader's remaining interception time information, thereby carrying out the design of a collaborative control strategy. Figure 2 The specific steps are as follows:

[0054] Step 1: Consider a two-dimensional multi-agent nonlinear cooperative interception model consisting of n agents (e.g. Figure 3 As shown), establish the relative motion equation between the multi-agent and the target:

[0055]

[0056] Among them, r i is the relative distance between the ith agent and the target, Represents r i The derivative with respect to time; λ i is the sight angle of the ith agent to the target, Represents λ i The derivative with respect to time; V ri represents the relative speed between the i-th agent and the target along the line of sight, V λi A represents the relative speed between the i-th agent and the target orthogonal to the line of sight; Mri 、A Mλi Denote the acceleration of the ith agent along and perpendicular to the line of sight respectively; A Tr 、A Tλ They represent the acceleration of the target along and perpendicular to the line of sight, respectively.

[0057] When constructing a two-dimensional multi-agent nonlinear cooperative interception model, we first need to identify the target T to be intercepted. Its movement in the two-dimensional plane can be represented by the position vector (x T (t),y T (t)), the velocity vector is Assume there are N agents, and the position of each agent i is (x i (t),y i (t)), the speed is r i is the relative distance between the ith intelligence and the target, that is, (x T (t),y T (t))-(x i (t),y i (t)). Along r i The direction is the sight angle direction of each agent. The target T velocity vector (x T (t),y T (t)) and the velocity vector of agent i can be decomposed into i direction and perpendicular to r i The velocity component in the direction of r i direction and perpendicular to r i The relative motion velocity components in the direction are V ri and V λi .

[0058] Then, the number of agents n in the network multi-agent system is determined, and a communication topology is constructed. The multi-agents exchange information with each other according to the communication topology, and some agents can perceive the time-varying target position; the communication topology is denoted by the symbol G(V,E), where V = {v1,v2,...,v N} represents the point set, Represents the edge set. i ,v j > indicates that node v i Points to node v j A directed edge of node v j Can receive node v i The information transmitted. If there is a node v in the communication topology graph G l , so that there is no other node in the communication topology graph G to v l The communication topology graph G is called a leader-slave graph, and the node v l is the leader and all other nodes are followers.

[0059] For a directed graph, the adjacency matrix of its communication topology is generally expressed as To express it, the Laplace matrix is ​​expressed as To indicate that, in addition to this, there is another way to connect The matrix of L is called the degree matrix, which is commonly used For the adjacency matrix, if there is an interaction edge between agent i and agent j, that is, <v i ,v j >∈E, then a ij =1, otherwise, a ij = 0. For any node v i, the degree of the vertex is the sum of the in-degree and out-degree of the vertex. The in-degree is the number of directed edges ending at the vertex, and the out-degree is the number of directed edges starting at the vertex. Therefore, the degree matrix of a directed graph can be subdivided into the in-degree matrix and out-degree matrix Degree Matrix Is a diagonal matrix, the elements on the diagonal are the sum of the in-degree and out-degree of each vertex, that is So the relationship between the above three matrices is And the elements in L are defined as follows: when i≠j, l ij =-a ij , when i=j, then l ii =d i .

[0060] Step 2: Define the estimated value of the remaining interception time error and design the preset time control law of the leader agent along the line of sight angle; specifically:

[0061] Define the remaining interception time variable as t goi , its estimated value It can be expressed as:

[0062]

[0063] Assuming that agent 1 is the leader, the estimated error value of the leader's interception target time is:

[0064]

[0065] Among them, t is the current time, T c1 The interception time is preset for the leader. Therefore, at the preset time T c1 Intercepting the target is equivalent to intercepting the time error Converges to zero.

[0066] Estimated time error for intercepting target Taking the derivative, we can get:

[0067]

[0068] Assume that the acceleration of the target along the line of sight |A Tr |<A MrMAX , A MrMAX represents the maximum acceleration of the agent along the line of sight angle, and designs the preset time control law A of the leader agent 1 along the line of sight direction. Mr1 as follows:

[0069]

[0070] Among them, r iis the relative distance between the ith agent and the target, V ri represents the relative speed between the i-th agent and the target along the line of sight, V λi represents the relative velocity between the i-th agent and the target orthogonal to the line of sight, 0<p1<1, T c1 Set the interception time for the leader, T c1 >0;

[0071] Constructing Lyapunov function but

[0072]

[0073] therefore, Therefore, the system is stable within a predetermined time, and its predetermined convergence time is T c .

[0074]

[0075] It can be seen that the interception time error of leader agent 1 is within the leader's preset interception time T c1 It converges to zero internally, achieving the requirement of preset time interception.

[0076] Step 3: Define the remaining interception time consistency coordination error variable and design the preset time coordination control law of the follower multi-agent along the line of sight angle direction; specifically:

[0077] Define the remaining interception time consistency cooperative error variable ξ of follower agent i (i=2,3,,n) i :

[0078]

[0079] Design the preset time control law A of follower agent i (i=2,3,,n) along the line of sight Mri as follows:

[0080]

[0081] Constructing Lyapunov function but

[0082]

[0083] It can be seen that the remaining interception time consistency coordination error of each follower agent is within the leader's preset interception time T c1 When the inner tendency approaches zero, the requirement of multiple agents intercepting the target simultaneously can be achieved.

[0084] Step 4: Construct the preset time convergence sliding surface s of the multi-agent system i :

[0085]

[0086] in, 0<μ<1, 0<p2<1, α>0, T c2 >0.

[0087] When the sliding surface s i = 0, there is

[0088] Step 5: Design the preset time cooperative control law of the multi-agent system along the normal direction of the line of sight; Specifically: Assume that the acceleration of the target along the normal direction of the line of sight |A Tλ |<A MλMAX , A MλMAX Represents the maximum acceleration of the agent along the normal direction of the line of sight; Based on the preset time convergence sliding surface constructed in step 4, the normal control law A of the line of sight is designed. Mλi :

[0089]

[0090] in,

[0091] 0<p3<1,T c3 >0.

[0092] Step 6: Optimize and adjust the control law parameters through simulation operation and data collection and analysis, and repeat steps 2 to 5 to achieve multi-agent coordinated interception at a preset time. Specifically, use the MATLAB simulation software platform to build a multi-agent coordinated interception simulation environment, set the initial parameters of the agents and targets, and set the directed graph communication topology structure based on the actual communication network conditions to ensure the authenticity and reliability of the simulation environment. The specific simulation example is as follows:

[0093] The initial parameters of the agents and targets are shown in Table 1. The multi-agent communication topology is as follows Figure 1 .

[0094] Table 1 Initial parameters of the agent and target

[0095]

[0096] Set the control law parameters as follows: p1 = 0.6, p2 = 0.8, p3 = 0.8, μ = 0.6, α = 5, T c1 =50s, T c2 =15s, T c3 =30s.

[0097] Depend on Figure 4 and Figure 5 It can be seen that the present invention realizes efficient collaborative interception of multiple agents. Specifically, Figure 4 It shows that starting from different initial states, the coordinated interception target is finally achieved at (35667,5335). Figure 5 It shows that agents 1-5 finally intercept the target at the same time at 50.2s, the preset time T c1 =50s, the error is 0.4%.

[0098] The above shows and describes the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely preferred examples of the present invention and are not intended to limit the present invention. Various changes and improvements may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and improvements fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A multi-agent collaborative interception method based on distributed preset time convergence, characterized by: The steps include: Step 1: Consider A two-dimensional multi-agent nonlinear cooperative interception model composed of agents is established to establish the relative motion equation between the multi-agent and the target; Step 2: Define the estimated value of the remaining interception time error and design the preset time control law of the leader agent along the line of sight angle; Among them, the leader agent Preset time control law along the line of sight as follows: ； in, For the The relative distance between the agent and the target, Indicates the The relative speed of the agent-target along the line of sight, Indicates the The relative velocity between the agent and the target perpendicular to the line of sight, , Set the interception time for the leader. ; Step 3: Define the remaining interception time consistency cooperative error variable and design the preset time cooperative control law of the follower multi-agent along the line of sight angle direction; Among them, the design follower agent Preset time control law along the line of sight as follows: ； Step 4: Construct the preset time convergence sliding surface of the multi-agent system : Step 5: Design a preset time cooperative control law for the multi-agent system along the normal direction of the line of sight; In step 5, it is assumed that the acceleration of the target along the normal direction of the line of sight is ,in, Represents the maximum acceleration of the agent orthogonal to the line of sight; the sliding surface converges at the preset time constructed in step 4 Based on this, the sight line normal control law is designed : ； in, , , ; Step 6: Repeat step 2 through simulation operation and data collection and analysis 5. Optimize and adjust the control law parameters to optimize the multi-agent collaborative interception method.

2. The multi-agent collaborative interception method based on distributed preset time convergence according to claim 1, characterized in that: In step 1, the relative motion equation between the multi-agent and the target is established as follows: ； in, For the The relative distance between the agent and the target, express derivative with respect to time; For the The sight angle of each agent to the target, express derivative with respect to time; Indicates the The relative speed of the agent-target along the line of sight, Indicates the The relative velocity between the agent and the target perpendicular to the line of sight; 、 Respectively represent The acceleration of each agent along the line of sight and perpendicular to the line of sight; 、 They represent the acceleration of the target along the line of sight and the acceleration perpendicular to the line of sight, respectively.

3. The multi-agent collaborative interception method based on distributed preset time convergence according to claim 1, characterized in that: The step 2 specifically includes the following steps: S2.1 Definition The remaining interception time variable of an agent is , Expressed as: ； S2.2 Hypothetical Agent If is the leader, then the estimated error of the leader intercepting the target time is: ； in, For the current moment, Preset interception time for leaders; S2.3 Estimated time error for interception target Taking the derivative, we can get: ； S2.4 Assume that the target's acceleration along the line of sight is , Indicates the maximum acceleration of the agent along the line of sight.

4. The multi-agent collaborative interception method based on distributed preset time convergence according to claim 1, characterized in that: In step 3, define the follower agent The residual intercept time consistency collaborative error variable : 。 5. The multi-agent collaborative interception method based on distributed preset time convergence according to claim 1, characterized in that: The preset time convergence sliding surface of the multi-agent system constructed in step 4 is as follows: ； in, , , , , .

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