Optimal formation control method and device for finite time mobile car based on distributed optimization

Abstract

This invention discloses a finite-time optimal formation control method and apparatus for mobile vehicles based on distributed optimization. The method combines the zero-gradient sum algorithm with second-order Hessian information optimization to propose a two-stage distributed control protocol for achieving optimal formation control of mobile vehicles. This method ensures that the mobile vehicles form a predetermined formation while minimizing the global cost function, which is the sum of the local cost functions of each mobile vehicle. In the first stage, the controller guides each mobile vehicle to converge to the minimum point of its local cost function and drives the system to achieve the goal of zero gradient sum of the local cost functions of all mobile vehicles based on the zero-gradient algorithm. In the second stage, the controller further coordinates the vehicle system to promote the formation of the predetermined formation. Research results show that, with reasonable parameter design, the proposed two-stage control protocol can guarantee the convergence of the vehicle system within a finite time.

Description

Technical Field

[0001] This invention relates to the field of distributed optimization and formation control technology for multi-agent systems, specifically to a method and apparatus for optimal formation control of finite-time mobile vehicles based on distributed optimization. Background Technology

[0002] The research on multi-agent systems was initially inspired by observations of collective intelligent behavior in nature, such as the efficient self-organization phenomena of coordinated flight in flocks of birds and the division of labor and cooperation in ant colonies. With the deepening of related research, multi-agent system theory has shown enormous application potential in the field of engineering technology. Among them, mobile vehicle formation control, as a key research direction, has attracted much attention due to its outstanding mobility and environmental adaptability in scenarios such as logistics handling, flexible manufacturing, and intelligent warehousing.

[0003] In mobile vehicle platooning systems, the core of achieving stable platooning lies in effective local communication and collaborative control among individual vehicles. Traditional centralized control methods concentrate all sensing and computing tasks at a central node, revealing inherent flaws in large-scale platooning applications: on the one hand, the increased system scale leads to a sharp increase in the central computing load, causing performance bottlenecks; on the other hand, system reliability is highly dependent on the central node, posing a single point of failure risk. These problems significantly restrict the application of centralized methods in real-world complex environments.

[0004] To overcome the aforementioned limitations, distributed optimization algorithms have emerged. This method distributes computational tasks among various agents, with each node relying solely on local neighborhood communication to collaboratively achieve the global optimization objective. This architecture effectively reduces the risk of single-point failures and significantly improves the system's scalability and robustness, thus finding widespread application in fields such as multi-robot collaboration and smart grid scheduling.

[0005] However, most existing studies on formation control based on the leader-follower framework set the relative distance between individuals to a fixed preset value. This approach fails to explore how to dynamically determine the optimal formation configuration from the perspective of overall system performance optimization. Summary of the Invention

[0006] The purpose of this invention is to provide a method and apparatus for optimal formation control of mobile vehicles in a finite time based on distributed optimization. This method introduces a distributed optimization algorithm to coordinate the dynamics of the mobile vehicle system, effectively overcoming the limitations of traditional methods that rely on global information interaction, and realizing efficient formation construction based on local communication.

[0007] The technical solution to achieve the objective of this invention is as follows: Firstly, this invention provides a finite-time optimal formation control method for mobile vehicles based on distributed optimization, comprising the following steps:

[0008] Step 1: Establish a model for the optimal formation control problem of mobile vehicles;

[0009] Step 2: Construct a communication topology diagram between the mobile vehicles;

[0010] Step 3: Design the optimal formation first-stage control method based on the information of the mobile vehicle itself;

[0011] Step 4: Design the optimal formation second-stage control method by using the interactive information between adjacent moving vehicles;

[0012] Step 5: Construct a convergence analysis framework for the optimal formation control method of the mobile vehicles, and verify the effectiveness of the first-stage control method and the second-stage control method respectively.

[0013] Secondly, the present invention provides a finite-time optimal formation control device for mobile vehicles based on distributed optimization, used to implement the method described in the first aspect, the device comprising:

[0014] The first module is used to establish a model for the optimal formation control problem of mobile vehicles;

[0015] The second module is used to construct the communication topology diagram between the mobile vehicles;

[0016] The third module is used to design the optimal formation first-stage control method based on the information of the mobile vehicle itself;

[0017] The fourth module is used to design the optimal formation second-stage control method by using the interactive information between adjacent moving vehicles;

[0018] The fifth module is used to construct a convergence analysis framework for the optimal formation control method of the mobile vehicle, and to verify the effectiveness of the first-stage control method and the second-stage control method respectively.

[0019] Thirdly, the present invention provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method described in the first aspect.

[0020] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0021] Fifthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the method described in the first aspect.

[0022] Compared with existing technologies, the significant advantages of this invention are as follows: First, it imposes no specific constraints on the initial state of the mobile vehicle, allowing the system to start from any random initial state. Second, based on a distributed collaborative design framework, it significantly reduces the dependence on a centralized control unit, thereby improving system robustness while effectively saving communication bandwidth and computing resources. This method, while ensuring formation control accuracy, also possesses good system scalability and fault tolerance. Furthermore, the control architecture proposed in this invention is universal and can be extended to collaborative control scenarios of multi-agent systems such as smart grids, multi-robot collaboration, and network resource scheduling. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention or related technologies, the drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0024] Figure 1 A flowchart of a finite-time optimal formation control method for mobile vehicles based on distributed optimization provided in an embodiment of the present invention;

[0025] Figure 2 This is a communication topology diagram between mobile vehicles provided in an embodiment of the present invention;

[0026] Figure 3 The graph shows the change in the trajectory of the mobile car under the control of the designed optimal formation algorithm.

[0027] Figure 4 This shows the changes in the total cost function of the mobile vehicle system. Detailed Implementation

[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] This invention proposes a finite-time optimal formation control method and apparatus for mobile vehicles based on distributed optimization. This method innovatively combines zero-gradient sum algorithms with second-order Hessian matrix information optimization, proposing a two-stage distributed control strategy: in the first stage, it guides each mobile vehicle to converge to a local optimum of the cost function; in the second stage, it further drives the entire vehicle system to converge to the global optimum within a finite time and form a predetermined formation configuration. Compared with existing technologies, this invention has the following significant advantages: it adopts a distributed architecture, achieving globally optimal formation without relying on a leader node; the introduction of second-order Hessian matrix information significantly accelerates the convergence speed; it has no special requirements for the initial state of the mobile vehicles, and parameter adjustment is simple; while ensuring finite-time convergence, it avoids the complex requirements of global information sharing. The technology proposed in this invention is not only applicable to mobile vehicle systems but can also be extended to fields such as drone swarms, autonomous driving fleets, robot collaborative systems, and smart grid scheduling.

[0030] Combination Figure 1 The present invention provides a finite-time optimal formation control method for mobile vehicles based on distributed optimization, applied to a robot cooperative system, comprising the following steps:

[0031] S101. Establish a model for the optimal formation control problem of mobile trolleys;

[0032] S102. Construct a communication topology diagram between mobile vehicles;

[0033] S103. Design the first-stage control method based on the local information of the mobile vehicle;

[0034] S104. Design the second-stage method through information interaction between adjacent mobile vehicles;

[0035] S105. Construct a convergence analysis framework for the control method of the optimal formation problem of mobile cars, and ensure that the state of the mobile cars can converge to the global optimal solution by adjusting the parameters.

[0036] This invention provides a finite-time optimal formation control method for mobile vehicles based on distributed optimization, achieving precise formation control of the mobile vehicle system through a distributed collaborative optimization mechanism. This method uses a distributed optimization algorithm to dynamically and collaboratively control the system, constructing a fully distributed control architecture. Each mobile vehicle interacts with its neighbors based only on local perception information, without requiring global information sharing. This effectively enhances the system's privacy protection capabilities while ensuring control accuracy.

[0037] In terms of algorithm design, this invention innovatively employs the zero gradient sum algorithm, achieving the optimization objective with only a small number of adjustable parameters. Compared to existing technologies, this scheme eliminates the need for auxiliary variables or time-varying gain terms, significantly simplifying the algorithm structure, reducing computational complexity, and thus improving engineering feasibility.

[0038] In terms of control performance, by adopting a two-stage distributed optimization strategy, under the constraint that the local gradient and Hessian matrix information are not exchanged between the mobile vehicles, on the one hand, the sum of the gradients of all mobile vehicles is accurately asymptotically converged to zero, and on the other hand, the global optimal convergence of the formation system state is guaranteed, effectively avoiding local suboptimal solutions.

[0039] In terms of applicability, this method imposes no constraints on the initial state of the mobile vehicle, exhibiting strong engineering universality. Through an optimized algorithm architecture, the system convergence speed is significantly improved, enabling rapid formation and stable maintenance of the optimal formation configuration. While retaining the inherent advantages of distributed control systems, this scheme achieves globally optimal performance through algorithmic innovation, providing an efficient and reliable solution for mobile vehicle formation control.

[0040] Furthermore, in specific implementation, in the above-mentioned finite-time optimal formation control method for mobile vehicles based on distributed optimization provided in the embodiments of the present invention, step S101 establishes a model for the optimal formation control problem of mobile vehicles, specifically including:

[0041] Establish a state-space model for the mobile vehicle and define the set of mobile vehicles. , Indicates a moving car Position information in a two-dimensional plane, The derivative information representing the position of the moving car. Indicates the first The desired position of each moving car in the formation. The system model for the mobile vehicle is as follows: ,in Indicates the first The control input for a mobile vehicle.

[0042] Establish a model for the optimal formation control problem of moving vehicles, where the objective of all moving vehicles is:

[0043]

[0044]

[0045] in, express A vector set of location information for each vehicle. This represents the global cost function of the mobile vehicle system. It is a quadratic differentiable function, representing the moving car. The cost function, assuming there exists a convex set. , , then when When the following conditions are met, It is Strongly convex functions:

[0046]

[0047]

[0048] in, It is a constant and , yes Lipsch's constant, express An identity matrix of order 1; Let $\mathbf{ ... The formation configurations for all implementations of the mobile vehicle are defined;

[0049] The local optimum of the mobile vehicle system is defined as follows:

[0050]

[0051] in, Let represent the local optimum of the mobile vehicle system; then, define the global optimum of the mobile vehicle system as follows:

[0052]

[0053]

[0054] in This represents the global optimal solution of the car system.

[0055] Furthermore, step 2 specifically includes:

[0056] Step 2-1, constructing a structure containing The communication topology of a mobile vehicle is undirected and connected:

[0057]

[0058] in, Represents a set of nodes, corresponding to the system's... A mobile cart, This represents the set of edges used to describe the communication connections of the mobile workshops.

[0059] Step 2-2, utilize the algebraic connectivity of the communication topology graph. Design a distributed control protocol where the eigenvalues ​​of the Laplace matrix of the mobile vehicle system are undirected and connected. ,in It is a communication topology diagram The second smallest eigenvalue of the Laplace matrix, due to the communication topology graph It is undirected and connected, therefore it has Then As a design parameter for controlling the gain, and based on Determine the lower bound of the system's convergence rate.

[0060] Furthermore, step 3 specifically includes:

[0061] Design the first-stage control method:

[0062]

[0063] in, It is the upper bound of the time for the first-stage control method to converge to a local optimum. It is about controlling the gain. , It is a mobile car The gradient vector of the cost function, It is a cost function The Hessian matrix, yes Power sign function.

[0064] Furthermore, step 4 specifically includes:

[0065] Design a second-stage control method:

[0066]

[0067] in It is a gain parameter. , It is a mobile vehicle in the communication topology diagram. and mobile cart The weights of the edges between them (note that the communication topology is undirected and connected, therefore...) By designing the second-stage control method described above, the system can find the global optimal solution within a finite time.

[0068] Furthermore, step 5 specifically includes:

[0069] Step 5-1: Design the Lyapunov function for the first-stage control method. Adjusting parameters allows the system to perform within a limited time. It converges to a local optimum. The first-stage Lyapunov function is given:

[0070]

[0071] Find the time-related information for the Lyapunov function in the first stage. Taking the derivative of the partial derivative function, we get:

[0072]

[0073] This means the status of the moving car In a limited time Reaching the local optimum .

[0074] Step 5-2: If the communication topology between the mobile vehicles is undirected and connected, then... Then we can get:

[0075]

[0076] Combining step 5-1, all the moving cars within a finite time To reach their respective local optima, we have:

[0077]

[0078] Then it is possible to obtain the time limit when the time exceeds the first stage time limit. hour:

[0079]

[0080] This means that for At any time, regardless of the state of the moving car Regardless of the changes, the gradient of the sum of the cost functions of all moving vehicles remains 0. The control objective for the first stage is achieved.

[0081] Step 5-3: Design the Lyapunov function for the second-stage control method. Adjusting parameters allows the system to perform within a limited time. It converges to a local optimum. The second-stage Lyapunov function is given:

[0082]

[0083] in Combining with step 3, we can obtain:

[0084]

[0085] If and only if When the state of the moving car reaches the global optimum, that is, when the state of the moving car reaches the global optimum.

[0086] Step 5-4: Calculate the Lyapunov function for the second stage with respect to time. The partial derivatives of the function yield:

[0087]

[0088] in This indicates that all moving cars are in The state vector at any given time; A vector representing the desired position of all moving cars in the formation;

[0089] Step 5-5: Construct a set :

[0090]

[0091] Combination And from step 3, we get:

[0092]

[0093] Therefore, the set It is a compact set. To utilize the properties of strongly convex functions, we need to find a convex and compact set; we take the set... ,in Describe the convex hull of a set. express The union of convex hulls and sets. Based on the operational properties of convex hulls and sets, sets... It is a set that is both tight and convex.

[0094] Steps 5-6, Define Then we can get:

[0095]

[0096] in , It is a communication topology diagram The Laplace matrix, It is a communication topology diagram. A complete graph is a communication topology where any two nodes are connected by a unique edge. It is a complete graph The Laplace matrix, express An identity matrix of order 1. From this, we can obtain:

[0097]

[0098] Therefore, it can be concluded that the second-stage control method is capable of... The system can find the global optimum within a short time. Therefore, the system is able to... Complete optimal formation control of the mobile vehicles within the specified time.

[0099] Based on the same inventive concept, the present invention also provides a distributed optimization-based finite-time mobile vehicle optimal formation control device for implementing the above method, the device comprising:

[0100] The first module is used to establish a model for the optimal formation control problem of mobile vehicles;

[0101] The second module is used to construct the communication topology diagram between the mobile vehicles;

[0102] The third module is used to design the optimal formation first-stage control method based on the information of the mobile vehicle itself;

[0103] The fourth module is used to design the optimal formation second-stage control method by using the interactive information between adjacent moving vehicles;

[0104] The fifth module is used to construct a convergence analysis framework for the optimal formation control method of the mobile vehicle and to verify the effectiveness of the first-stage control method and the second-stage control method.

[0105] The specific implementation methods of the first to fifth modules mentioned above are the same as the specific steps of the aforementioned finite-time moving car optimal formation control method, and will not be repeated here.

[0106] In summary, this invention utilizes a distributed optimization algorithm for collaborative control of the dynamics of a mobile vehicle system. This allows each vehicle to achieve globally optimal formation without sharing global state information or relying on a centralized controller, significantly enhancing the system's distributed autonomy. Based on an undirected connected communication topology, each vehicle makes distributed decisions based solely on its own state information and local interactions with neighboring vehicles. Notably, the gradient vectors and Hessian matrices of each vehicle do not need to be broadcast and shared among agents, greatly reducing the system's communication load. Furthermore, the invention involves a relatively small number of adjustable parameters, effectively reducing the complexity and computational cost of the algorithm. In terms of system performance, this invention ensures that the formation converges to the globally optimal configuration within a finite time, enabling the mobile vehicle group system to form a predetermined formation with high precision. The resulting formation is not only stable and reliable but also exhibits excellent control accuracy.

[0107] The technical effects achieved by the present invention will be described in detail below with reference to embodiments. Figure 2 The mobile vehicle system with the communication method shown in the invention may include the following:

[0108] According to step S101, the cost function for the six mobile carts is as follows:

[0109]

[0110]

[0111]

[0112]

[0113]

[0114]

[0115] in Representing the The x-coordinate of the position of the moving car. Representing the The ordinate of the position of each mobile car is randomly selected in the initial state of the system.

[0116] According to step S102, the communication topology between the mobile vehicles is undirected and connected;

[0117] Based on step S103, construct the local optimal solution search function for the optimal formation control problem of the mobile vehicles:

[0118]

[0119] From the cost function of each mobile vehicle, we can see that the local optimal solutions for each mobile vehicle are as follows: , , , , , .

[0120] Based on step S104, construct the global optimal solution search function for the optimal formation control problem of the mobile vehicles:

[0121]

[0122] And the global total cost function:

[0123]

[0124] This allows us to obtain the global optimum of the system. .

[0125] The simulation results of this embodiment are as follows: Figure 3 , Figure 4 As shown. Figure 2The communication topology of a mobile vehicle system is demonstrated. Vehicles connected by an edge are neighbors and can communicate with each other to exchange information. Specifically, vehicle 1 can communicate with vehicles 2 and 6; vehicle 2 can communicate with vehicles 1 and 3; vehicle 3 can communicate with vehicles 2 and 4; vehicle 4 can communicate with vehicles 3 and 5; and vehicle 5 can communicate with vehicles 4 and 6. This verifies that the distributed optimization algorithm can achieve globally optimal formation with only local neighborhood communication. Figure 3 The motion trajectories of the six moving cars are shown. All the moving cars eventually converge precisely to the global optimum, forming the desired formation configuration, which is consistent with the theoretical analysis results. Figure 4 The global cost function of the mobile vehicle system is given. The curve shows the change in total system cost over time. The simulation results demonstrate that the proposed method can effectively converge to the global optimum, achieving stability at the target location. These simulation results fully demonstrate the superiority of the proposed method in terms of formation control accuracy, optimization performance, and communication efficiency.

[0126] The optimal formation control method for mobile vehicles based on distributed optimization proposed in this invention has the following significant features: First, through an innovative distributed cooperative optimization architecture, each mobile vehicle only needs its own information and exchanges necessary state information with neighboring vehicles, without sharing global information, reducing the system's communication load and improving system privacy protection. Second, compared to other algorithms that require specifying the initial state information of the studied agents, the algorithm proposed in this invention allows for arbitrary selection of the initial state of the mobile vehicles, requiring fewer adjustable parameters, auxiliary parameters, and time-varying gains, thus reducing the computational complexity of the system. Third, a two-stage distributed control strategy is adopted. The first-stage controller uses a zero-gradient sum algorithm to ensure that after a certain time, regardless of changes in the state of the mobile vehicles, the sum of the gradients of the cost functions of all mobile vehicles remains zero. The second-stage controller uses a distributed optimization algorithm that incorporates Hessian matrix information to ensure that the formation state converges to a predetermined formation shape. Finally, simulation experiments show that the formation can accurately converge to the globally optimal configuration, rather than a suboptimal solution. Actual tests show that this method performs excellently in large-scale agent clusters, providing an innovative solution to large-scale distributed cooperative control problems.

[0127] In summary, this invention provides a finite-time optimal formation control method for mobile vehicles based on distributed optimization, applicable to multi-agent cooperative control systems. The core of this method lies in: achieving autonomous decision-making and cooperative control for each mobile vehicle based on a distributed optimization algorithm, completing the formation task without relying on global information sharing; achieving globally optimal formation through local neighborhood information interaction, significantly reducing the consumption of communication and computing resources; and in terms of control performance, this method ensures that the system state accurately converges to the globally optimal formation configuration, effectively avoiding local suboptimal solutions, and the resulting formation possesses both stability and high precision.

Claims

1. A finite-time optimal formation control method for mobile vehicles based on distributed optimization, characterized in that, Includes the following steps: Step 1: Establish a model for the optimal formation control problem of the mobile vehicles, specifically including: Step 1-1: Establish the state space model of the mobile vehicle and define the set of mobile vehicles. , Indicates a moving car Position information in a two-dimensional plane, The derivative information representing the position of the moving car. Indicates the first The desired position of each moving car in the formation; The system model for the mobile vehicle is as follows: ,in Indicates the first The control input for a mobile cart; Steps 1-2 establish a model for the optimal formation control problem of the moving cars. The objective function for all moving cars is: ； （1） in, express A vector set of location information for each vehicle. This represents the global cost function of the mobile vehicle system. It is a quadratic differentiable function, representing the moving car. The cost function, assuming there exists a convex set. , , then when When the following conditions are met, It is Strongly convex functions: （2） （3） in, It is a constant and , yes Lipsch's constant, express An identity matrix of order 1; The formation configurations for all implementations of the mobile vehicle are defined; Steps 1-3 define the local optimal solution of the mobile vehicle system as follows: （4） in, Let represent the local optimum of the mobile vehicle system; then, define the global optimum of the mobile vehicle system as follows: ； （5） in This represents the global optimal solution of the car system; Step 2: Construct a communication topology diagram between the mobile vehicles; Step 3: Design the optimal formation control method for the first stage based on the information of the mobile vehicles themselves, specifically including: Design the first-stage control method: （7） in, It is the upper bound of the time for the first-stage control method to converge to a local optimum. It is about controlling the gain. , It is a mobile car The gradient vector of the cost function, It is a cost function The Hessian matrix, yes Power sign function; Step 4: Design the optimal formation second-stage control method by utilizing the interaction information between adjacent moving vehicles; employ the zero gradient sum algorithm to search for the global optimal solution of the system, specifically including: Design a second-stage control method: （8） in It is a gain parameter. , It is a moving car in the communication topology diagram and mobile cart The weight values ​​of the edges between them. By designing the second-stage control method described above, the system can find the global optimal solution within a finite time. Step 5: Construct a convergence analysis framework for the optimal formation control method of the mobile vehicles, and verify the effectiveness of the first-stage control method and the second-stage control method respectively.

2. The optimal formation control method for finite-time mobile vehicles based on distributed optimization according to claim 1, characterized in that, Step 2 includes: Step 2-1, constructing a structure containing The communication topology of a mobile vehicle is undirected and connected: （6） in, Represents a set of nodes, corresponding to the system's... A mobile cart, This represents the set of edges used to describe the communication connections within the mobile workshops; Step 2-2, utilize the algebraic connectivity of the communication topology graph. Design a distributed control protocol where the eigenvalues ​​of the Laplace matrix of the mobile vehicle system are undirected and connected. ,in It is a communication topology diagram The second smallest eigenvalue of the Laplace matrix, due to the communication topology graph It is undirected and connected, therefore it has Then As a design parameter for controlling the gain, and based on Determine the lower bound of the system's convergence rate.

3. The optimal formation control method for finite-time mobile vehicles based on distributed optimization according to claim 1, characterized in that, Step 5 specifically includes: Step 5-1: Design the Lyapunov function for the first-stage control method. Adjusting parameters allows the system to perform within a limited time. Converging to a local optimum; the first-stage Lyapunov function is given: （9） Find the time-related information for the Lyapunov function in the first stage. Taking the partial derivative of the function, we get: （10） Status of the moving car In a limited time Reaching the local optimum ; Step 5-2: If the communication topology between the mobile vehicles is undirected and connected, then... Then we can get: （11） Combining step 5-1, all the moving cars within a finite time To reach their respective local optima, we have: （12） Then it is possible to obtain the time limit when the time exceeds the first stage time limit. hour: （13） for At any time, regardless of the state of the moving car Regardless of the changes, the gradient of the sum of the cost functions of all moving vehicles is always 0; the control objective of the first stage is achieved. Step 5-3: Design the Lyapunov function for the second-stage control method. Adjusting parameters allows the system to perform within a limited time. Converging to a local optimum; the second-stage Lyapunov function is given: （14） in Combining with step 3, we can obtain: （15） If and only if When the state of the moving car reaches the global optimum; Step 5-4: Calculate the Lyapunov function for the second stage with respect to time. The partial derivatives of the function yield: （16） in This indicates that all moving cars are in The state vector at any given time; A vector representing the desired position of all moving cars in the formation; Step 5-5: Construct a set : （17） Combination And from step 3, we get: （18） Therefore, the set It is a compact set; take the set ,in Describe the convex hull of a set. express The union of convex hulls and sets; based on the operational properties of convex hulls and sets, sets... It is a set that is both tight and convex; Steps 5-6, Define Then we can get: （19） in , It is a communication topology diagram The Laplace matrix, It is a communication topology diagram A complete graph is a communication topology where every two nodes are connected by a unique edge. It is a complete graph The Laplace matrix, express An identity matrix of order 1; from this, we can obtain: （20） The second-stage control method can be derived to achieve The system can find the global optimum within a short time; therefore, it is able to... Complete the optimal formation control of the mobile vehicles within the specified time.

4. A finite-time optimal formation control device for mobile vehicles based on distributed optimization, characterized in that, The apparatus for implementing the method according to any one of claims 1 to 3 comprises: The first module is used to establish a model for the optimal formation control problem of mobile vehicles; The second module is used to construct the communication topology diagram between the mobile vehicles; The third module is used to design the optimal formation first-stage control method based on the information of the mobile vehicle itself; The fourth module is used to design the optimal formation second-stage control method by using the interactive information between adjacent moving vehicles; The fifth module is used to construct a convergence analysis framework for the optimal formation control method of the mobile vehicle, and to verify the effectiveness of the first-stage control method and the second-stage control method respectively.

5. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1-3.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method as described in any one of claims 1-3.

7. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the method described in any one of claims 1-3.

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