Multi-agent collaborative interception method based on distributed preset time convergence

Abstract

The invention relates to the field of multi-agent cooperative control, in particular to a multi-agent cooperative interception method based on distributed preset time convergence, which comprises the following steps of: considering a two-dimensional planar multi-agent nonlinear cooperative interception model consisting of n agents, and establishing a multi-agent and target relative motion equation; defining a residual interception time error estimation value, and designing a preset time control law of the leader agent along the sight angle direction; defining a residual interception time consistency collaborative error variable, and designing a preset time collaborative control law of the follower multi-agent along the sight angle direction; constructing a preset time convergence sliding mode surface si of the multi-agent system; designing a preset time cooperative control law of the multi-agent system in the normal direction of the sight line; and through simulation operation and data acquisition and analysis, control law parameters are optimized and adjusted, the previous steps are repeated, and multi-agent preset time collaborative interception is realized. According to the invention, efficient collaborative interception of the multi-agent system in a complex task environment can be realized.

Description

Technical Field

[0001] The present invention relates to the field of multi-agent collaborative control, and specifically 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 shown significant application potential in aerospace and civil fields, and has become one of the hot topics in current academic research. Faced with increasingly complex tasks, such as airspace protection around airports, cleaning up space debris, and tracking mobile targets, the limitations of traditional single-agent interception capabilities and low operational efficiency have gradually emerged. Multi-agent collaborative interception technology has an indispensable and important position in aerospace safety and civil safety protection due to its excellent performance in accuracy and significant advantages in interception range.

[0003] Multi-agent collaborative control technology has developed rapidly. Early research focused on ensuring the consistency of the state of the agents, and then 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 by the leader. On the other hand, the leader-follower architecture has a clear division of labor, the leader makes overall plans, and the followers perform tasks efficiently. In multi-agent collaborative interception, pursuit strategies can be quickly formulated and tasks can be assigned to improve 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 studies 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 requirements of timeliness in 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 the collaborative interception method with preset time convergence still needs further research.

[0005] The introduction of the preset time convergence theory 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 accurately set the upper limit of the system's convergence time in advance according to 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 the present 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 to achieve efficient collaborative interception of multi-agent systems in complex mission environments.

[0007] In order to achieve the above object, the technical solution specifically adopted by the present invention is 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 composed 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;

[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 of the multi-agent system along the normal direction of the line of sight;

[0014] Step 6: Repeat step 25 to optimize and adjust the control law parameters through simulation operation and data collection and analysis to achieve the optimization of the multi-agent collaborative interception method. Specifically, the MATLAB simulation software platform is used to build a multi-agent collaborative interception simulation environment, set the initial parameters of the agent and the target, and set the directed graph communication topology structure according to the actual communication network conditions. According to the collected data, the coefficients of p1, p2, p3, μ, α and other non-physical meanings in the controller 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 ith 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 orthogonal 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 Define the remaining interception time variable of the i-th agent as t goi , It is expressed as:

[0020]

[0021] S2.2 Assuming that agent 1 is the leader, the estimated error value 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 get:

[0025]

[0026] S2.4 Assume that the target's acceleration A along the line of sight 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 ith agent and the target along the line of sight, V λirepresents the relative speed between the ith 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 defines the remaining interception time consistency coordination error variable ξ of follower agent i (i = 2, 3,, n) i :

[0031]

[0032] S3.2 Design the preset time control law A of the 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 also can be widely applied to various task scenarios that require multi-agent collaboration, such as logistics transportation, disaster relief, etc., showing a wide range of application prospects and having the following characteristics and beneficial effects:

[0043] 1) Accurate interception time coordinated control

[0044] In the multi-agent system proposed by the present invention, the preset time convergence collaborative control strategy based on the line of sight angle direction achieves the remarkable effect of making the remaining interception time between each agent tend to be consistent within the predetermined time frame. Compared with the traditional method, there is no need to consider complex relationships, which simplifies the design process. By accurately 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 limit, ensuring that the leader intercepts the target according to the preset time, and the followers cooperate to achieve simultaneous interception of multiple agents, improve the suddenness and effectiveness of interception, and enhance the ability to intercept targets.

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

[0046] The present invention adopts a distributed architecture, and multiple agents achieve collaborative control through information exchange. This distributed feature enables the system to maintain a certain interception efficiency when facing partial agent failures or communication interruptions, and has strong robustness. At the same time, each agent can adjust the control strategy in real time according to the status information of itself and adjacent agents, which enhances the adaptability of the multi-agent system 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 is a flow chart 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 It is a distance diagram between the agent and the target in the embodiment of the present invention. DETAILED DESCRIPTION

[0052] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments 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 a leader-follower control architecture under a 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 As shown, 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 multi-agent and 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 ith 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 orthogonal 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)). i The direction is the line of sight 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 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 represent it, the Laplace matrix is ​​expressed as To indicate that, in addition to this, there is another way to contact 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 refers to the sum of the in-degree and out-degree of the vertex. The in-degree refers to the number of directed edges with the vertex as the end point, and the out-degree refers to the number of directed edges with the vertex as the starting point. 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, and 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 we have 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 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.

[0066] Estimated time error for intercepting target Taking the derivative, we 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 ith agent and the target along the line of sight, V λi represents the relative speed between the ith 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 functions 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. 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 functions 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 line of sight normal; based on the preset time convergence sliding surface constructed in step 4, the line of sight normal control law A 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, repeat steps 2 to 5, and realize multi-agent collaborative interception at preset time; specifically, use the MATLAB simulation software platform to build a multi-agent collaborative interception simulation environment, set the initial parameters of the agent and the target, and set the directed graph communication topology structure according to 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 shown in 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 intercepted the target at the same time at 50.2s, and 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 by the above embodiments. The above embodiments and descriptions are only preferred examples of the present invention and are not intended to limit the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A multi-agent collaborative interception method based on distributed preset time convergence, characterized in that: The steps include: Step 1: Consider a two-dimensional multi-agent nonlinear cooperative interception model composed of n agents, and 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; 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; Step 4: Construct the preset time convergence sliding surface s of the multi-agent system i : Step 5, design a preset time cooperative control law of the multi-agent system along the normal direction of the line of sight; Step 6: Repeat steps 2 to 5 through simulation operation and data collection and analysis to optimize and adjust the control law parameters to achieve the optimization of the multi-agent collaborative interception method.

2. A multi-agent collaborative interception method based on distributed preset time convergence as claimed in claim 1, characterized in that: In step 1, the relative motion equation between the multi-agent and the target is established as follows: 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 ith 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 orthogonal 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.

3. A multi-agent collaborative interception method based on distributed preset time convergence as claimed in claim 1, characterized in that: The step 2 specifically includes the following steps: S2.1 defines the remaining interception time variable of the i-th agent as t goi , It is expressed as: S2.2 Assuming that agent 1 is the leader, the estimated error value of the leader's interception target time is: Among them, t is the current time, T c1 Preset interception times for leaders; S2.3 Estimated time error for interception target Taking the derivative, we get: S2.4 Assume that the target's acceleration 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: Among them, r i is the relative distance between the ith agent and the target, V ri represents the relative speed between the ith agent and the target along the line of sight, V λi represents the relative speed between the ith 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.

4. A multi-agent collaborative interception method based on distributed preset time convergence as claimed in claim 1, characterized in that: The step 3 specifically includes the following steps: S3.1 Define the remaining interception time consistency cooperative error variable ξ of follower agent i (i = 2, 3, ..., n) i : S3.2 Design the preset time control law A of the follower agent i (i = 2, 3, ..., n) along the line of sight Mri as follows:

5. The multi-agent collaborative interception method based on distributed preset time convergence as claimed in claim 1, characterized in that: The preset time convergence sliding surface s of the multi-agent system constructed in step 4 is i as follows: Among them, 0<μ<1,0<p2<1,α>0,T c2 >0.

6. A multi-agent collaborative interception method based on distributed preset time convergence as claimed in claim 1, characterized in that: 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 : in, 0<p3<1,T c3 >0.

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