A fixed time platoon control method and system

Abstract

This invention discloses a fixed-time formation control method and system, belonging to the field of formation control. The method includes: establishing a heterogeneous multi-agent system model corresponding to the system to be controlled, and establishing an ODE-PDE error system model; at any given time, each sparsely distributed agent, according to the calculated control signal, and each densely distributed agent, according to the calculated control signal, transmitting their position errors back to themselves; setting a virtual agent at a location, and having the virtual agent calculate the control signal; where , , and represent the position errors of the sparsely distributed agent, the densely distributed agent, and the virtual agent, respectively; if the ODE-PDE tracking error system converges, the formation control ends; otherwise, the control signal continues to be updated and the entity objects execute corresponding actions. This invention enables fixed-time formation control, improving system formation efficiency.

Description

Technical Field

[0001] This invention belongs to the field of formation control, and more specifically, relates to a fixed-time formation control method and system. Background Technology

[0002] Swarm intelligence is an important development direction of the next generation of artificial intelligence. Multi-agent collaboration is the main way for swarm intelligence to emerge in unmanned systems. Through mutual collaboration, intelligent agents can efficiently complete complex tasks and enhance the robustness of the system. They can exhibit stronger adaptability and responsiveness in the face of uncertainty and dynamic environments, and also provide a new research perspective for understanding and simulating group behavior in nature.

[0003] In recent years, with the rapid development of communication and artificial intelligence technologies, the cooperative control of multi-agent systems has attracted widespread attention due to its promising applications in scenarios such as UAV swarms, intelligent transportation, and microgrid clusters. Formation control, which refers to the movement of entities in a control system from their initial positions to a designated target position or to form a specified formation, is a typical cooperative control problem in multi-agent systems. Due to its superior ability to handle complex tasks and dynamic environments, large-scale development has become an inevitable trend in the development of multi-agent systems. Compared with small-scale multi-agent systems, large-scale multi-agent systems have significant advantages in robustness and flexibility, not only broadening the application areas of multi-agent systems but also improving the overall performance of the system, making it an effective approach to solving modern complex problems.

[0004] Traditional research on multi-agent cooperative control has focused directly on Ordinary Differential Equation (ODE) models, with cooperative objectives achieved through ODE-based control methods (hereinafter referred to as the ODE method). However, as the scale of the multi-agent group increases, the dimensionality and complexity of the ODE model increase accordingly, leading to an exponential increase in the difficulty of system analysis and making it difficult to achieve precise control over each agent, thus weakening the control effectiveness of the ODE method. Furthermore, with the increase in the number of agents, the complexity of communication and computation in the system also increases. Each agent needs to process more communication data and participate in more complex coordination and decision-making processes, resulting in network congestion and increased computational load, thereby affecting overall cooperative efficiency.

[0005] To alleviate the analytical difficulties of high-dimensional ODE models, some scholars have proposed modeling and analysis methods based on Partial Differential Equations (PDEs) in recent years. This method describes the evolution of large-scale spatially discrete individuals as a macroscopic continuous model through a spatial discrete-continuous mapping, thus characterizing collective dynamics in a compact form. Compared with ODE methods, PDE methods show significant advantages in terms of analytical complexity and control performance as the system scale expands. However, existing PDE methods still have obvious limitations: first, they require multiple agents to be spatially approximately uniformly and densely distributed, while in actual operation, multiple agents often exhibit a sparse-dense mixed distribution, thus severely limiting their practical applicability; second, most results focus on formation control problems in ideal environments and infinite time domains, rarely considering non-ideal real-world factors such as nonlinear unknowns at the boundaries and time-sensitive requirements.

[0006] A recent method proposes an ODE-PDE-based formation control approach. It establishes separate ODE error system models for each sparsely distributed agent and a shared PDE error system model for all densely distributed agents. This reduces the analytical complexity while improving applicability. The method also achieves finite-time formation control. However, it still cannot account for the impact of sparsely distributed agents on the stability of densely distributed agents at the boundary, and the system convergence time depends on the initial state. When the initial state deviates significantly from the target state, the convergence time may be excessively long, failing to meet timeliness requirements. Summary of the Invention

[0007] In view of the shortcomings of the existing technology and the need for improvement, the present invention provides a fixed-time formation control method and system, the purpose of which is to realize fixed-time formation control and improve the formation efficiency of the system.

[0008] To achieve the above objectives, according to one aspect of the present invention, a fixed-time formation control method is provided, comprising: Establish a heterogeneous multi-agent system model corresponding to the system to be controlled; in the heterogeneous multi-agent system model, each agent corresponds to an entity object in the system to be controlled; Establish an ODE error system model for each sparsely distributed agent and a PDE error system model shared by densely distributed agents, which are used to describe the position error of the actual position of the corresponding sparsely distributed agent relative to the target position, and the position error of the actual position of the densely distributed agent relative to the target position, respectively. In any At any given time, perform formation control as follows: S1: The positional errors of each sparsely distributed agent Feedback is transmitted to itself, enabling each sparsely distributed agent to... Calculate control signals ; S2: The positional errors of each densely distributed agent Feedback is transmitted to itself, enabling each densely distributed agent to... Calculate control signals ; S3: In A virtual agent is set up at the location, and the position error vector of the sparsely distributed agent is used as the basis for the calculation. calculate Afterwards, Position error of virtual intelligent agent Transmitted to the virtual intelligent agent, enabling the virtual intelligent agent to... Calculate control signals ; S4: Determine whether the position errors of all agents converge within a fixed time. If yes, the formation control ends; otherwise, continue to update the control signals to each agent so that the position errors of all agents converge within a fixed time and the entities perform the corresponding actions. in, Represents the agent index, and Represents an index for sparsely distributed agents. This represents an index of densely distributed agents. and These represent the number of sparsely distributed agents and densely distributed agents, respectively. This represents the relative spatial location of densely distributed intelligent agents. Indicates the distribution range of densely distributed intelligent agents; , and All are controller gains; , represents a given constant; Represents a symbolic function; Represents a nonlinear function; This represents the continuous basis function vector of a radial basis function neural network. The weight vector of the neural network, with the superscript "T" indicating transpose; control signals and These are used to control the speed of sparsely distributed agents and densely distributed agents, respectively. Used to control the rate of change of the virtual agent's position error with respect to space.

[0009] Furthermore, in heterogeneous multi-agent system models, sparsely distributed agents... Communication protocol for: ; in, Represents sparsely distributed intelligent agents exist The actual location at that moment Represents sparsely distributed intelligent agents The target location; Represents sparsely distributed intelligent agents The nonlinear function value of the target location; This represents the self-feedback weights of the intelligent agent.

[0010] Furthermore, in heterogeneous multi-agent system models, agents are densely distributed. Communication protocols with other intelligent agents for: ; in, Indicates the distribution interval of densely distributed intelligent agents; Represents densely distributed intelligent agents exist The actual location at that moment Represents densely distributed intelligent agents The target location; Represents densely distributed intelligent agents The nonlinear function value of the target location; α and μ All are given topological weights.

[0011] Furthermore, controller gain The methods for determining include: Construct the following linear matrix inequality that satisfies fixed-time stability: , ; in, Let be a symmetric matrix, where the expressions for each element are as follows: , , , , ; , All are positive definite constants; It is a positive definite constant.

[0012] If an inducted scalar exists , And there exists a positive definite constant. , and , such that for any If the above linear matrix inequality holds, then at this time... and Substitute the value , obtain the controller gain The value of .

[0013] Furthermore, nonlinear functions and nonlinear functions satisfy: ; ; in, , , and Both represent any real number.

[0014] Furthermore, controller gain , and the resting time of position error convergence The following relationship exists between them: ; in, ,and , , It is a positive definite constant.

[0015] Furthermore, sparsely distributed intelligent agents The corresponding expression for the ODE error system model is: ; in, , ; Furthermore, the expression for the PDE error system model shared by densely distributed agents is: ; in, for The result of spatial continuity , .

[0016] Furthermore, the boundary conditions at the boundary of densely distributed agents are as follows: , .

[0017] According to another aspect of the present invention, a fixed-time formation control system is provided, comprising: an initialization module, an ODE-PDE error model establishment module, a first controller, a second controller, a neural adaptive controller, and an execution module; The initialization module is used to establish a heterogeneous multi-agent system model corresponding to the system to be controlled; in the heterogeneous multi-agent system model, each agent corresponds to an entity object in the system to be controlled; The ODE-PDE error model building module is used to build the ODE error system model corresponding to each sparsely distributed agent and the PDE error system model shared by the densely distributed agents. These models are used to describe the position error of the actual position of the corresponding sparsely distributed agent relative to the target position, and the position error of the actual position of the densely distributed agent relative to the target position, respectively. The first controller is used to... At any given time, the positional errors of each sparsely distributed agent will be considered. Feedback is transmitted to itself, enabling each sparsely distributed agent to... Calculate control signals ; The second controller is used for... At any given moment, the positional errors of each densely distributed agent will be considered. Feedback is transmitted to itself, enabling each densely distributed agent to... Calculate control signals ; Neural adaptive controller, used in At time 1, based on the position error vector of the sparsely distributed agent calculate Afterwards, Position error of virtual intelligent agent Transmitted to the virtual intelligent agent, enabling the virtual intelligent agent to... Calculate control signals Virtual agents are set at the boundaries of the densely distributed agent distribution area. Place; The execution module is used to determine at each moment whether the position errors of all agents have converged within a fixed time. If so, the formation control ends; otherwise, the control signal is updated to each agent to make the position errors of all agents converge within a fixed time and to make the entities perform the corresponding actions. in, Represents the agent index, and Represents an index for sparsely distributed agents. This represents an index of densely distributed agents. and These represent the number of sparsely distributed agents and densely distributed agents, respectively. This represents the relative spatial location of densely distributed intelligent agents. Indicates the distribution range of densely distributed intelligent agents; , and All are controller gains; , represents a given constant; Represents a symbolic function; Represents a nonlinear function; This represents the continuous basis function vector of a radial basis function neural network. The weight vector of the neural network, with the superscript "T" indicating transpose; control signals and These are used to control the speed of sparsely distributed agents and densely distributed agents, respectively. Used to control the rate of change of the virtual agent's position error with respect to space.

[0018] Furthermore, a computer-readable storage medium includes a stored computer program that, when executed by a processor, implements the fixed-time formation control method provided by the present invention.

[0019] In summary, the above-described technical solutions conceived in this invention can achieve the following beneficial effects: (1) This invention establishes an ODE error system model for each sparsely distributed agent and a shared PDE error system model for all densely distributed agents, enabling multi-agent formation control of arbitrary scale, distribution, and time. Based on this, this invention designs control signal calculation expressions for sparsely and densely distributed agents based on Lyapunov stability, enabling fixed-time formation control. This not only improves control efficiency but also eliminates the dependence of system convergence time on the initial state. Furthermore, the relevant expressions contain only one sign function term, further reducing control costs and improving control smoothness. In addition, this invention establishes ODE error system models for each sparsely distributed agent and a shared PDE error system model for all densely distributed agents at the boundary (…). A virtual intelligent agent was set up, and the corresponding control signal calculation expression of the virtual intelligent agent was designed. Under the condition of fixed-time formation control, the influence of sparsely distributed intelligent agents on the boundary of densely distributed intelligent agents can be fully considered, thereby further improving the system stability.

[0020] (2) This invention proposes the controller gain corresponding to the virtual agent at the boundary. The method for determining the value of can further guarantee fixed-time stability when considering unknown nonlinearities at the boundary. Attached Figure Description

[0021] Figure 1 A control block diagram of a fixed-time formation control method provided in an embodiment of the present invention.

[0022] Figure 2 The present invention provides tracking error trajectories for sparsely distributed and densely distributed intelligent agents in the absence of communication protocols and controllers.

[0023] Figure 3 The RBF neural network provided by this invention provides the fitting error trajectory for an unknown nonlinear function.

[0024] Figure 4 The motion trajectory of an intelligent agent in three-dimensional space provided by this invention.

[0025] Figure 5 The position tracking error trajectory of the sparsely distributed intelligent agent in a single spatial dimension provided by the present invention.

[0026] Figure 6 The present invention provides the position tracking error trajectory of a densely distributed intelligent agent in a single spatial dimension. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0028] In this invention, the terms "first," "second," etc. (if present) in the invention and the accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0029] To address the technical problem that existing formation control methods fail to consider non-ideal real-world factors such as unknown nonlinearities at boundaries and timeliness requirements, thus hindering the achievement of fixed-time stability, this invention provides a fixed-time formation control method and system. It establishes an ODE error system model for each sparsely distributed agent and a shared PDE error system model for all densely distributed agents to improve applicability. Based on this, agent control signals are designed using fixed-time stability theory, and virtual agents are placed at the boundaries of the densely distributed agents. Their control signals reflect the influence of sparsely distributed agents on the boundaries of the densely distributed agents, thereby fully considering unknown nonlinearities, achieving fixed-time formation control, and improving system stability.

[0030] The fixed-time formation control method and system provided by this invention can be applied to the formation control of any physical system, such as UAV swarms, intelligent transportation systems, and microgrid swarms. It is easy to understand that, in order to apply intelligent agent systems to solve the control problem of actual swarm systems, it is necessary to first establish a multi-agent system model corresponding to the swarm system. In the multi-agent system model, each agent corresponds to an entity object in the swarm system. For example, in the multi-agent system corresponding to a UAV swarm, each agent corresponds to a UAV; in the multi-agent system corresponding to an intelligent transportation system, each agent corresponds to an unmanned vehicle or a traffic light; in the multi-agent system corresponding to a microgrid swarm, each agent corresponds to a microgrid. After establishing the corresponding multi-agent system model, subsequent control can be performed using relevant multi-agent system theories and methods. Without loss of generality, the following embodiments will use the formation control of UAV swarms as an example for illustration.

[0031] To achieve formation control of a drone swarm, a heterogeneous multi-agent system model corresponding to the actual drone swarm to be controlled needs to be established. Each agent corresponds to a drone entity, and the number of sparsely distributed agents and densely distributed agents are respectively... and express.

[0032] by If the agent index is represented, then Represents an index for sparsely distributed agents. Indicates the index of densely distributed agents. Sparsely distributed agents. The initial position is represented as The target location is represented as Densely distributed intelligent agents The initial position is represented as The target location is represented as , This represents the distribution interval of densely distributed agents. This indicates the distribution range of densely distributed intelligent agents.

[0033] Based on the above information, dynamic equations for each agent in the heterogeneous multi-agent system model can be established in each spatial dimension based on the ODE model.

[0034] For sparsely distributed agents Its initial dynamic equations are as follows: ; in, ; express t Time-sparse distribution of intelligent agents Location, express The rate of change, i.e., velocity information; Represents sparsely distributed intelligent agents Communication protocol; Represents sparsely distributed intelligent agents The position is a nonlinear function; This represents the control signals that need to be designed for sparsely distributed agents; among the symbols above, the superscript... Representing spatial dimension, when considering two-dimensional space, When considering three-dimensional space, .

[0035] For densely distributed agents Its initial dynamic equations are as follows: ; in, ; express Densely distributed intelligent agents at all times Location, express The rate of change, i.e., velocity information; Represents densely distributed intelligent agents Communication protocols with other intelligent agents; Represents densely distributed intelligent agents The position is a nonlinear function; This represents the control signals that need to be designed for densely distributed intelligent agents; similarly, in the above symbols, the superscript... Representing spatial dimension, when considering two-dimensional space, When considering three-dimensional space, .

[0036] Since the dynamics are expressed in the same way in each dimension, we can study the dynamics in only one dimension, thus obtaining the overall dynamic equations of the agent as follows: ; in, , .

[0037] The dynamic equations established based on the ODE model describe the relationship between the agent's velocity, the communication protocol between agents, and the nonlinear function values ​​of the agent's position.

[0038] The following is an example.

[0039] Example 1: A fixed-time formation control method, such as Figure 1 As shown, it includes: Establish a heterogeneous multi-agent system model corresponding to the system to be controlled; in the heterogeneous multi-agent system model, each agent corresponds to an entity object in the system to be controlled; Establish an ODE error system model for each sparsely distributed agent and a PDE error system model shared by densely distributed agents, which are used to describe the position error of the actual position of the corresponding sparsely distributed agent relative to the target position, and the position error of the actual position of the densely distributed agent relative to the target position, respectively. In any At any given time, perform formation control as follows: S1: The positional errors of each sparsely distributed agent Feedback is transmitted to itself, enabling each sparsely distributed agent to... Calculate control signals ; S2: The positional errors of each densely distributed agent Feedback is transmitted to itself, enabling each densely distributed agent to... Calculate control signals ; S3: In A virtual agent is set up at the location, and the position error vector of the sparsely distributed agent is used as the basis for the calculation. calculate Afterwards, Position error of virtual intelligent agent Transmitted to the virtual intelligent agent, enabling the virtual intelligent agent to... Calculate control signals ; S4: Determine whether the position errors of all agents converge within a fixed time. If yes, the formation control ends; otherwise, continue to update the control signals to each agent so that the position errors of all agents converge within a fixed time and the entities perform the corresponding actions. in, Represents the agent index, and Represents an index for sparsely distributed agents. This represents an index of densely distributed agents. and These represent the number of sparsely distributed agents and densely distributed agents, respectively. This represents the relative spatial location of densely distributed intelligent agents. Indicates the distribution range of densely distributed intelligent agents; , and All are controller gains; , represents a given constant; Represents a symbolic function; Represents a nonlinear function; This represents the continuous basis function vector of a radial basis function neural network. The weight vector of the neural network, with the superscript "T" indicating transpose; control signals and These are used to control the speed of sparsely distributed agents and densely distributed agents, respectively. Used to control the rate of change of the virtual agent's position error with respect to space.

[0040] The following provides a further explanation of the specific implementation methods for each step.

[0041] In this embodiment, an ODE error system model corresponding to each sparsely distributed agent and a PDE error system model shared by densely distributed agents are established, including: Based on the ODE model, dynamic equations for each agent in the heterogeneous multi-agent system model are established to describe the relationship between the agent's velocity, communication protocol between agents, and the nonlinear function values ​​of agent position. The communication protocol is related to the distribution characteristics of the agents. In the heterogeneous multi-agent system model, the nonlinear functions corresponding to sparsely distributed agents and densely distributed agents are different, and the corresponding control schemes are also different.

[0042] Optionally, in this embodiment, in the heterogeneous multi-agent system model, sparsely distributed agents... Communication protocol for: ; in, Represents sparsely distributed intelligent agents exist The actual location at that moment Represents sparsely distributed intelligent agents The target location; Represents sparsely distributed intelligent agents The nonlinear function value of the target location; This represents the self-feedback weights of the intelligent agent.

[0043] Furthermore, in heterogeneous multi-agent system models, agents are densely distributed. Communication protocols with other intelligent agents for: ; in, Indicates the distribution interval of densely distributed intelligent agents; Represents densely distributed intelligent agents exist The actual location at that moment Represents densely distributed intelligent agents The target location; Represents densely distributed intelligent agents The nonlinear function value of the target location; α and μ All are given topological weights.

[0044] In this embodiment, the nonlinear functions in the motion equations of sparsely distributed and densely distributed agents can be set according to specific control requirements. As a preferred implementation, in this embodiment, the nonlinear functions are based on the Lipschitz condition. and The rate of change of the function is limited to prevent system crashes due to excessively rapid changes. Specifically, in this embodiment, the nonlinear function... and satisfy: ; ; in, and It is a positive definite constant and is related to the nonlinearity of the system; , , and Both represent any real number.

[0045] Based on the dynamic equations of each intelligent agent, any... At any given time, the position error of each agent relative to the target position is used to obtain the ODE tracking error system model. The ODE representation of the tracking error model of sparsely distributed agents is maintained, and the ODE tracking error model of densely distributed agents is processed into a continuous model to obtain the ODE error system model corresponding to each sparsely distributed agent and the PDE error system model shared by the densely distributed agents.

[0046] In this embodiment, sparsely distributed intelligent agents The corresponding expression for the ODE error system model is: ; in, , ; Furthermore, the expression for the PDE error system model shared by densely distributed agents is: ; in, for The result of spatial continuity , .

[0047] Furthermore, virtual agents are designed at the boundary of densely distributed agents, and their spatiotemporal distribution states are mapped to the boundary conditions of the PDE as follows: , ; in, This represents an unknown nonlinear function. In this embodiment, the boundary ( Setting up virtual agents at the boundary and setting corresponding boundary conditions can fully consider the impact of sparsely distributed agents on the stability at the boundary of densely distributed agents, so that the entire heterogeneous multi-agent system model can more accurately depict the actual situation; with the help of communication protocols between agents, the influence at the boundary can spread to other densely distributed agents, thereby indirectly considering the influence of sparsely distributed agents on other densely distributed agents.

[0048] This embodiment further addresses the controller gain in the control signals of virtual intelligent agents. The design included: Construct the following linear matrix inequality that satisfies fixed-time stability: , ; in, Let be a symmetric matrix, where the expressions for each element are as follows: , , , , ; , All are positive definite constants related to the nonlinearity of the system; It is a positive definite constant and is related to the controller; If an inducted scalar exists , And there exists a positive definite constant. , and , such that for any If the above linear matrix inequality holds, then at this time... and Substitute the value , obtain the controller gain The value of .

[0049] In this embodiment, the controller gain , and the resting time of position error convergence The following relationship exists between them: ; in, ,and , ; It is a positive definite constant and is related to the controller.

[0050] After a period of rest Subsequently, the position errors of each agent will converge to a relatively small interval, thus achieving fixed-time formation control. In other words, this embodiment determines the controller gain using the above method. This can achieve the actual fixed-time stability of the error system, better meet the timeliness requirements of the actual system, and further improve the practicality of formation control.

[0051] In this embodiment, a suitable controller gain can be preset and the corresponding rest time can be determined. Alternatively, the rest time can be preset according to actual timeliness requirements, and the corresponding controller gain can be designed in reverse.

[0052] It is easy to understand that when each intelligent agent receives the corresponding control signal, the corresponding entity performs actions including adjustments to acceleration, speed, etc.

[0053] In summary, this embodiment proposes a cooperative control framework based on ODE-PDE for large-scale multi-agent systems with sparse-dense mixed spatial distribution and unknown nonlinearity, which has wider applicability. Through the design of control signals, this invention achieves fixed-time formation control, which not only improves control efficiency but also eliminates the dependence of system convergence time on the initial state. By setting virtual agents at the boundary and designing corresponding control signals, the influence of sparsely distributed agents on the stability of densely distributed agents at the boundary can be fully considered, further improving the stability of the final formation control result.

[0054] Furthermore, in existing research on fixed-time cooperative control of multi-agent systems, controller design typically requires the introduction of at least two symbolic function terms to meet performance requirements. This not only increases control costs but also inevitably introduces severe control chattering. To address this issue, this embodiment designs a simplified fixed-time controller, in which the corresponding control signal expression contains only one symbolic function term, thereby reducing control costs and improving control smoothness.

[0055] Example 2: A fixed-time formation control system includes: an initialization module, an ODE-PDE error model establishment module, a first controller, a second controller, a neural adaptive controller, and an execution module; The initialization module is used to establish a heterogeneous multi-agent system model corresponding to the system to be controlled; in the heterogeneous multi-agent system model, each agent corresponds to an entity object in the system to be controlled; The ODE-PDE error model building module is used to build the ODE error system model corresponding to each sparsely distributed agent and the PDE error system model shared by the densely distributed agents. These models are used to describe the position error of the actual position of the corresponding sparsely distributed agent relative to the target position, and the position error of the actual position of the densely distributed agent relative to the target position, respectively. The first controller is used to... At any given time, the positional errors of each sparsely distributed agent will be considered. Feedback is transmitted to itself, enabling each sparsely distributed agent to... Calculate control signals ; The second controller is used for... At any given moment, the positional errors of each densely distributed agent will be considered. Feedback is transmitted to itself, enabling each densely distributed agent to... Calculate control signals ; Neural adaptive controller, used in At time 1, based on the position error vector of the sparsely distributed agent calculate Afterwards, Position error of virtual intelligent agent Transmitted to the virtual intelligent agent, enabling the virtual intelligent agent to... Calculate control signals Virtual agents are set at the boundaries of the densely distributed agent distribution area. Place; The execution module is used to determine at each moment whether the position errors of all agents have converged within a fixed time. If so, the formation control ends; otherwise, the control signal is updated to each agent to make the position errors of all agents converge within a fixed time and to make the entities perform the corresponding actions. in, Represents the agent index, and Represents an index for sparsely distributed agents. This represents an index of densely distributed agents. and These represent the number of sparsely distributed agents and densely distributed agents, respectively. This represents the relative spatial location of densely distributed intelligent agents. Indicates the distribution range of densely distributed intelligent agents; , and All are controller gains; , represents a given constant; Represents a symbolic function; Represents a nonlinear function; This represents the continuous basis function vector of a radial basis function neural network. The weight vector of the neural network, with the superscript "T" indicating transpose; control signals and These are used to control the speed of sparsely distributed agents and densely distributed agents, respectively. Used to control the rate of change of the virtual agent's position error with respect to space.

[0056] In this embodiment, the specific implementation of each module can be referred to the description in Embodiment 1 above, and will not be repeated here.

[0057] Example 3: A computer-readable storage medium includes a stored computer program that, when executed by a processor, implements the fixed-time formation control method provided in Embodiment 1 above.

[0058] The following example of the cooperative control of a drone swarm in three-dimensional space further illustrates the beneficial effects of this invention. The drone swarm comprises 64 drones. A global XYZ Cartesian coordinate system is established within the space where the 64 drones operate. Each drone is considered a point mass, and its kinematic model is established according to the system model considered in this invention. Five agents are sparsely distributed, while the other 59 agents are densely distributed.

[0059] First, for sparsely distributed agents, the nonlinear functions of each dimension are set as follows: For densely distributed agents, the nonlinear functions of each dimension are set as follows: .

[0060] When no network communication protocol and controller are designed, i.e. and The original multi-agent system cannot autonomously form a target formation from its initial position. In this case, the tracking error trajectories of the multi-agent system along the three spatial directions are as follows: Figure 2 As shown, it is clear that the tracking errors of each agent are divergent, which underscores the necessity of communication protocols and controller design.

[0061] In the designed communication protocol, the relevant parameters are set as follows: , , , , , , , Furthermore, the obtained linear matrix inequalities are set as control-related tuning constants. , , , , , Therefore, using the LMI toolbox in MATLAB, a set of feasible controller gain and parameter solutions can be obtained as follows: , , , , , , .

[0062] The continuous basis vectors of the RBF neural network are designed as follows: ; in, .definition Let be the fitting error of the RBF neural network for the unknown nonlinear function, then The state trajectory is as follows Figure 3 As shown in the figure, it can be seen that the neural network designed in this invention can quickly and accurately fit unknown nonlinearities.

[0063] Furthermore, the target positions for each dimension of the sparsely distributed agent are set as follows: , , The target positions for each dimension of the densely distributed agent are set as follows: , , The initial positions of each dimension of the sparsely distributed agent are set as follows: , , The initial positions of the densely distributed agents in each dimension are set as follows: , , .

[0064] Under the above parameters and initial conditions, the operational trajectories of multiple agents in 3D space can be obtained through MATLAB simulation, such as... Figure 4 As shown, the lines connecting the initial and target positions of each agent represent the agent's trajectory. Furthermore, to better demonstrate the control effect, Figure 5 The state trajectory of a sparsely distributed agent tracking errors in a single spatial dimension is presented. Figure 6 The state trajectories of the tracking errors of densely distributed agents in each spatial dimension are given respectively.

[0065] according to Figures 4-6 As can be seen from the state trajectory shown, the communication protocol and control strategy designed in this invention are effective and can both be implemented in [the following contexts]. The convergence to near 0 means that the present invention can realize fixed-time collaborative tasks of large-scale heterogeneous multi-agent systems under time delay conditions.

[0066] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A fixed-time formation control method, characterized in that, include: Establish a heterogeneous multi-agent system model corresponding to the system to be controlled; in the heterogeneous multi-agent system model, each agent corresponds to an entity object in the system to be controlled; Establish an ODE error system model for each sparsely distributed agent and a PDE error system model shared by densely distributed agents, which are used to describe the position error of the actual position of the corresponding sparsely distributed agent relative to the target position, and the position error of the actual position of the densely distributed agent relative to the target position, respectively. In any At any given time, perform formation control as follows: S1: The positional errors of each sparsely distributed agent Feedback is transmitted to itself, enabling each sparsely distributed agent to... Calculate control signals ; S2: The positional errors of each densely distributed agent Feedback is transmitted to itself, enabling each densely distributed agent to... Calculate control signals ; S3: In A virtual agent is set up at the location, and the position error vector of the sparsely distributed agent is used as the basis for the calculation. calculate Afterwards, Position error of virtual intelligent agent Transmitted to the virtual intelligent agent, enabling the virtual intelligent agent to... Calculate control signals ; S4: Determine whether the position errors of all agents converge within a fixed time. If yes, the formation control ends; otherwise, continue to update the control signals to each agent so that the position errors of all agents converge within a fixed time and the entities perform the corresponding actions. in, Represents the agent index, and Represents an index for sparsely distributed agents. This represents an index of densely distributed agents. and These represent the number of sparsely distributed agents and densely distributed agents, respectively. This represents the relative spatial location of densely distributed intelligent agents. Indicates the distribution range of densely distributed intelligent agents; , and All are controller gains; , represents a given constant; Represents a symbolic function; Represents a nonlinear function; This represents the continuous basis function vector of a radial basis function neural network. The weight vector of the neural network, with the superscript "T" indicating transpose; control signals. and These are used to control the speed of sparsely distributed agents and densely distributed agents, respectively. Used to control the rate of change of the virtual agent's position error with respect to space.

2. The fixed-time formation control method as described in claim 1, characterized in that, In the heterogeneous multi-agent system model, agents are sparsely distributed. Communication protocol for: ； in, Represents sparsely distributed intelligent agents exist The actual location at that moment Represents sparsely distributed intelligent agents The target location; Represents sparsely distributed intelligent agents The nonlinear function value of the target location; This represents the self-feedback weights of the intelligent agent.

3. The fixed-time formation control method as described in claim 2, characterized in that, In the heterogeneous multi-agent system model, agents are densely distributed. Communication protocols with other intelligent agents for: ； in, Indicates the distribution interval of densely distributed intelligent agents; Represents densely distributed intelligent agents exist The actual location at that moment Represents densely distributed intelligent agents The target location; Represents densely distributed intelligent agents The nonlinear function value of the target location; α and μ All are given topological weights.

4. The fixed-time formation control method as described in claim 3, characterized in that, Controller gain The methods for determining include: Construct the following linear matrix inequality that satisfies fixed-time stability: ， ； in, Let be a symmetric matrix, where the expressions for each element are as follows: , , , , ; , All are positive definite constants; It is a positive definite constant; If an inducted scalar exists , And there exists a positive definite constant. , and , such that for any If the above linear matrix inequality holds, then at this time... and Substitute the value , obtain the controller gain The value of .

5. The fixed-time formation control method as described in claim 4, characterized in that, nonlinear functions and nonlinear functions satisfy: ； ； in, , , and Both represent any real number.

6. The fixed-time formation control method as described in claim 1, characterized in that, Controller gain , and the resting time of position error convergence The following relationship exists between them: ； in, ,and , , It is a positive definite constant.

7. The fixed-time formation control method as described in claim 1, characterized in that, Sparsely distributed intelligent agents The corresponding expression for the ODE error system model is: ； in, , ; Furthermore, the expression for the PDE error system model shared by densely distributed agents is: ； in, for The result of spatial continuity , .

8. The fixed-time formation control method as described in claim 7, characterized in that, The boundary conditions at the boundary of densely distributed agents are: ， 。 9. A fixed-time formation control system, characterized in that, include: The system includes an initialization module, an ODE-PDE error model establishment module, a first controller, a second controller, a neural adaptive controller, and an execution module. The initialization module is used to establish a heterogeneous multi-agent system model corresponding to the system to be controlled; in the heterogeneous multi-agent system model, each agent corresponds to an entity object in the system to be controlled; The ODE-PDE error model establishment module is used to establish the ODE error system model corresponding to each sparsely distributed agent and the PDE error system model shared by the densely distributed agents, which are used to describe the position error of the actual position of the corresponding sparsely distributed agent relative to the target position and the position error of the actual position of the densely distributed agent relative to the target position, respectively. The first controller is used for in At any given time, the positional errors of each sparsely distributed agent will be considered. Feedback is transmitted to itself, enabling each sparsely distributed agent to... Calculate control signals ; The second controller is used for... At any given moment, the positional errors of each densely distributed agent will be considered. Feedback is transmitted to itself, enabling each densely distributed agent to... Calculate control signals ; The neural adaptive controller is used to... At time 1, based on the position error vector of the sparsely distributed agent calculate Afterwards, Position error of virtual intelligent agent Transmitted to the virtual intelligent agent, enabling the virtual intelligent agent to... Calculate control signals The virtual agent is positioned at the boundary of the densely distributed agent distribution area. Place; The execution module is used to determine at each moment whether the position errors of all agents converge within a fixed time. If yes, the formation control ends; otherwise, the control signal is updated to each agent to make the position errors of all agents converge within a fixed time and to make the entity objects perform the corresponding actions. in, Represents the agent index, and Represents an index for sparsely distributed agents. This represents an index of densely distributed agents. and These represent the number of sparsely distributed agents and densely distributed agents, respectively. This represents the relative spatial location of densely distributed intelligent agents. Indicates the distribution range of densely distributed intelligent agents; , and All are controller gains; , represents a given constant; Represents a symbolic function; Represents a nonlinear function; This represents the continuous basis function vector of a radial basis function neural network. The weight vector of the neural network, with the superscript "T" indicating transpose; control signals. and These are used to control the speed of sparsely distributed agents and densely distributed agents, respectively. Used to control the rate of change of the virtual agent's position error with respect to space.

10. A computer-readable storage medium, characterized in that, The system includes a stored computer program, which, when executed by a processor, implements the fixed-time formation control method according to any one of claims 1 to 8.

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