Unmanned aerial vehicle cluster distributed optimal formation control method considering multiplicative noise and computer readable medium

Abstract

The invention relates to the technical field of unmanned aerial vehicle cluster control, in particular to an unmanned aerial vehicle cluster distributed optimal formation control method considering multiplicative noise and a computer readable medium, and the method comprises the following steps: constructing a communication topological graph of an unmanned aerial vehicle cluster, each edge represents a communication relationship between two adjacent unmanned aerial vehicles; constructing a Laplacian matrix of the communication topological graph; establishing an unmanned aerial vehicle kinetic equation considering the multiplicative noise influence; defining an objective function needing to be optimized and constraint conditions; constructing a Hamilton function of the target function; and designing a distributed optimal control strategy by applying a random optimal control theory, setting operation time, system parameters and initial state information of the unmanned aerial vehicle cluster, and obtaining a formation operation track and a final formation state of the unmanned aerial vehicle cluster under optimal control. According to the invention, the global optimality and robustness of the unmanned aerial vehicle cluster control algorithm are ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of UAV swarm control, and particularly to a distributed optimal formation control method and a computer-readable medium for UAV swarms considering multiplicative noise. Background Art

[0002] Due to their autonomy and cooperation, UAV swarms are widely used in military, agricultural and other fields. Existing formation control research mostly focuses on additive noise models. However, in actual scenarios, the states of UAVs are often affected by multiplicative noise (such as sensor noise and communication interference), and the noise intensity is related to the system state, making it difficult for traditional methods to ensure formation stability and optimality. In addition, existing technologies do not fully combine energy and time constraints, making it difficult to meet the requirements of actual tasks. Therefore, there is an urgent need for a formation control method that can adapt to multiplicative noise and take into account global optimality and distributed characteristics. Summary of the Invention

[0003] The present invention aims to solve at least one of the technical problems existing in the related art. For this purpose, the present invention provides a distributed optimal formation control method and a computer-readable medium for UAV swarms considering multiplicative noise, which solves the problem that the existing UAV control methods fail to fully integrate the constraints of energy and time and are difficult to meet the requirements of actual tasks, thereby ensuring the global optimality and robustness of the control algorithm.

[0004] The present invention provides a distributed optimal formation control method for UAV swarms considering multiplicative noise, including the following steps: Construct a communication topology graph of the UAV swarm, where each node represents a UAV, and each edge represents the communication relationship between two adjacent UAVs; Construct the Laplacian matrix of the communication topology graph; Establish the dynamic equation of the UAV considering the influence of multiplicative noise; Define the objective function and constraints to be optimized; Construct the Hamiltonian function of the objective function; Using the stochastic optimal control theory, design a distributed optimal control strategy, set the running time, system parameters, and the initial state information of the UAV swarm, and obtain the formation operation trajectory and the final formation state of the UAV swarm under optimal control.

[0005] A further improvement of the distributed optimal formation control method for UAV swarms considering multiplicative noise according to the present invention is that it considers a UAV swarm composed of N UAVs, and the communication topology graph is an undirected connected graph, and the mathematical expression is: Where represents an undirected connected graph, represents the set of nodes of an undirected connected graph, , represents the set of edges of an undirected connected graph, , represents the adjacency matrix, , where represents node and node whether there is an edge connection between them, , if there is an edge between node and node , then ; if there is no edge between node and node , then ; The degree matrix of the undirected connected graph is , where, , where, represents the degree of the -th node, obtained by summing all in the row corresponding to the -th node in the adjacency matrix.

[0006] A further improvement of a distributed optimal formation control method for UAV swarms considering multiplicative noise in the present invention lies in constructing the Laplacian matrix of the communication topology graph, including: The Laplacian matrix is , and the eigenvalues of the Laplacian matrix are , where , The Laplacian matrix can be diagonalized as , represents the transpose matrix of matrix , represents a diagonal matrix, represents the matrix composed of eigenvectors, where , , represents -corresponding eigenvector.

[0007] A further improvement of a distributed optimal formation control method for UAV swarms considering multiplicative noise in the present invention lies in establishing the UAV dynamics equation considering the influence of multiplicative noise as , where, represents the small change of the UAV state variable at time , is the control input variable, Represents a tiny increment of time, represents a tiny increment of noise, Indicates that at the initial moment t = 0, the initial value of the UAV state variable is .

[0008] A further improvement of the distributed optimal formation control method for UAV swarms considering multiplicative noise in the present invention lies in defining the optimization objective function as , wherein, wherein, represents the expected value of the energy cost, represents the expected value of the cumulative formation error, represents the expected value of the network cost, represents the weight for balancing various items, represents the mathematical expectation, represents the transpose operator, represents the states of all UAVs, represents the control inputs of all UAVs, represents the target states of all UAVs, represents the identity matrix of represents the state dimension of a single node, represents a positive semi - definite matrix with the first dimension, represents a positive semi - definite matrix with the second dimension, represents a positive semi - definite matrix with the third dimension, represents a positive semi - definite matrix with the fourth dimension.

[0009] A further improvement of the distributed optimal formation control method for UAV swarms considering multiplicative noise in the present invention lies in defining the constraints to be optimized, including: Based on local information interaction, design a distributed control input for the UAV swarm that can minimize the cost function , wherein, represents the target relative state of the UAVs between node and node , represents the termination time of the formation task, represents the steady - state error threshold, represents the time point when the UAV swarm formation task meets the steady - state error requirement, represents the The expected energy consumption of the UAV corresponding to the initial energy of the UAV corresponding to the When the termination time of the formation mission and the constraint conditions of the steady-state error threshold are both satisfied, the distributed control input can enable the UAV swarm to complete the formation mission.

[0010] A further improvement of the distributed optimal formation control method for UAV swarms considering multiplicative noise according to the present invention lies in constructing the Hamiltonian function of the objective function , specifically where is the relevant term involving the distributed control input, is the quadratic form term related to the state variable , and is used to measure the cost related to the state of the UAV swarm; and combine the co-state vector and the control input related terms, and are used to construct a complete Hamiltonian function form to meet the solution requirements of system optimization; where represents the th element corresponding to the th node, represents the state component corresponding to the transformed th node, represents the control input component corresponding to the transformed th is the first-order vector with respect to the state, is the second-order vector with respect to the state, is the th th eigenvalue corresponding to the th node, is the

[0011] A further improvement of the distributed optimal formation control method for UAV swarms considering multiplicative noise according to the present invention lies in applying the stochastic optimal control theory to obtain the necessary conditions for optimality; where represents the optimal control input of the UAV corresponding to the th node,​ denotes the state component of the UAV corresponding to the th node under the optimal control input, denotes the Lagrange multiplier; Define the parametric algebraic Riccati equation , Furthermore, the optimal control input is obtained as , That is, , wherein, denotes the first constraint parameter, denotes the second constraint parameter, , denotes the gain matrix of the minimum cost function.

[0012] A further improvement of the method for distributed optimal formation control of an unmanned aerial vehicle (UAV) cluster considering multiplicative noise according to the present invention lies in that the design of the distributed optimal control strategy specifically includes: setting the running time, system parameters, and initial state information of the UAV cluster, the formation termination time, and the initial energy, setting , and after the operation ends, the formation operation trajectory under the optimal control and the final formation state are obtained.

[0013] A computer-readable medium stores a method for distributed optimal formation control of an unmanned aerial vehicle (UAV) cluster considering multiplicative noise as described above.

[0014] One or more of the above technical solutions in the embodiments of the present invention have at least one of the following technical effects: (1) Through the distributed communication method, this communication mechanism significantly enhances the robustness of the entire network. Each node can more effectively cope with various abnormal situations through the distributed communication of mutual cooperation, thereby improving the overall stability and reliability of the UAV cluster.

[0015] (2) Only local communication with neighboring UAVs is required. This communication method avoids the need for large-scale information transmission, not only greatly reducing the communication cost, but also significantly improving the computing efficiency and reducing the occupation of system resources in terms of computing.

[0016] (3) The influence of environmental noise on the system is fully considered, especially the case of multiplicative noise. Through targeted design, it is ensured that the system can still maintain good convergence when affected by noise and will not deviate from the expected working state due to noise, ensuring the stability of system performance.

[0017] (4) The control method of the present invention fully considers the energy and time constraints in practical applications, has stronger practicability and operability in actual operation, and avoids the disconnection between theoretical design and practical application.

[0018] (5) The present invention mainly focuses on how to ensure the feasibility of the formation mission in a complex situation considering energy and time constraints and the existence of multiplicative noise in the system. The core method is to design the algorithm based on network cost, and this method has many advantages. On the one hand, it can ensure that the control algorithm reaches global optimality and ensure that the system operates with the best performance. On the other hand, it has low requirements for the network structure. During the formation process, each UAV only relies on the information of neighboring UAVs. This simple and efficient information transmission method greatly improves the computational efficiency and enables the entire formation mission to proceed more smoothly.

[0019] Additional aspects and advantages of the present invention will be given in part in the following description, will become apparent in part from the following description, or will be learned through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0021] Figure 1 It is a block diagram of a distributed optimal formation control method for a UAV swarm considering multiplicative noise provided by the present invention.

[0022] Figure 2 It is a schematic diagram of the communication topology in a distributed optimal formation control method for a UAV swarm considering multiplicative noise provided by an embodiment of the present invention.

[0023] Figure 3 It is a schematic diagram of the operation trajectory and the final formation shape of a UAV swarm provided by an embodiment of the present invention.

[0024] Figure 4 It is a schematic diagram of the energy consumption and initial energy of each UAV provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0025] To make the objectives, technical solutions, and advantages of the present invention clearer, the following will clearly and completely describe the technical solutions in the present invention in conjunction with the drawings in the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention. The following embodiments are used to illustrate the present invention but cannot be used to limit the scope of the present invention.

[0026] The following is combined with Figure 1 to describe a distributed optimal formation control method for UAV swarms considering multiplicative noise, including the following steps: Construct a communication topology graph for the UAV swarm, where each node represents a UAV, and each edge represents the communication relationship between two adjacent UAVs; Construct the Laplacian matrix of the communication topology graph; Establish the UAV dynamics equation considering the influence of multiplicative noise; Define the objective function to be optimized and the constraints; Construct the Hamiltonian function of the objective function; Apply the stochastic optimal control theory, design a distributed optimal control strategy, set the running time, system parameters, and the initial state information of the UAV swarm, and obtain the formation operation trajectory and the final formation state of the UAV swarm under optimal control.

[0027] The UAV dynamics equation fully considers the influence of multiplicative noise on the UAV motion state, making the control strategy closer to the actual situation. The objective function is defined according to the task requirements. For example, it can be the lowest energy consumption of the UAV swarm, the optimal formation shape, etc. The constraints include the physical limitations of the UAVs, the communication range limitations, etc. When constructing the Hamiltonian function, the objective function is combined with the state variables and control variables of the system to form a function form containing Lagrange multipliers. By solving the optimal value of the Hamiltonian function, the optimal control strategy can be obtained. Finally, applying the stochastic optimal control theory, combined with the set running time, system parameters, and the initial state information of the UAV swarm, through numerical calculation or simulation methods, the formation operation trajectory and the final formation state of the UAV swarm under optimal control can be obtained. This method realizes the distributed optimal formation control of UAV swarms in a multiplicative noise environment and has high robustness and practicality.

[0028] In a preferred embodiment of the distributed optimal formation control method for UAV swarms considering multiplicative noise of the present invention, a UAV swarm composed of N UAVs is considered, and the communication topology graph is an undirected connected graph, and the mathematical expression is: where represents the undirected connected graph, represents the node set of the undirected connected graph, , represents the edge set of the undirected connected graph, , represents the adjacency matrix, , where represents node and node Whether there is an edge connection between , if node and node are connected by an edge, then ; if node and node are not connected by an edge, then ; The degree matrix of the undirected connected graph is , where , where represents the degree of the -th node, which is obtained by summing all in the row corresponding to the in the adjacency matrix.

[0029] The distributed optimal formation control problem of the UAV swarm can be solved by constructing an objective function. The objective function can be defined as the relative position relationship between the UAVs in the UAV swarm and the deviation between the overall shape of the UAV swarm and the desired shape. To achieve this goal, the Laplacian matrix is further introduced, which reflects the connection relationship and relative position relationship between the UAVs in the UAV swarm.

[0030] Specifically, constructing the Laplacian matrix of the communication topology graph includes: The Laplacian matrix is , and the eigenvalues of the Laplacian matrix are , where , The Laplacian matrix can be diagonalized as , represents the transpose matrix of matrix , represents the diagonal matrix, represents the matrix composed of eigenvectors, where , , represents -corresponding eigenvector.

[0031] First, by clarifying that the communication topology graph of the UAV swarm is an undirected connected graph and elaborating it with mathematical expressions, a solid theoretical foundation is laid for subsequent formation control. This step not only ensures the information flow among UAVs but also clarifies the connection relationships among UAVs, providing necessary conditions for constructing the objective function and introducing the Laplacian matrix. Secondly, constructing the objective function is the key to solving the problem. The objective function defines the relative position relationships among UAVs in the UAV swarm and the deviation between the overall shape of the UAV swarm and the desired shape. This setting gives a clear direction to the optimization process, that is, minimizing the objective function value to achieve the optimal formation. Further, the Laplacian matrix is introduced. The Laplacian matrix reflects the connection relationships and relative position relationships among UAVs in the UAV swarm, providing an important basis for the design of distributed control protocols. Through in-depth analysis of properties such as the eigenvalues and diagonalization of the Laplacian matrix, the positions and velocities of UAVs can be controlled more precisely to achieve the collaborative operation of the UAV swarm.

[0032] Furthermore, the dynamic equation of the UAV considering the influence of multiplicative noise is established as , where, represents the UAV state variable at time with a small change, is the control input variable, represents a small increment of time, represents a small increment of noise, represents that at the initial time = 0, the initial value of the UAV state variable is .

[0033] First of all, this UAV dynamic equation can more accurately describe the dynamic behavior of UAVs in the real environment. By introducing multiplicative noise, we take into account the influence of external disturbances and uncertainties on the UAV state, which makes the UAV dynamic equation closer to the actual situation and improves the prediction accuracy of the model. Secondly, the control strategy designed based on this UAV dynamic equation has stronger robustness. Since the equation contains a noise term, we can consider the influence of noise when designing the control algorithm and take corresponding compensation measures to weaken the influence of noise on the UAV state and ensure that the UAV can stably perform the formation task.

[0034] Furthermore, the optimization objective function is defined as , where, where, represents the expected value of the energy cost, represents the expected value of the cumulative formation error, represents the expected value of the network cost, represents the weight for balancing various terms, represents the mathematical expectation, represents the transpose operator, represents the states of all unmanned aerial vehicles (UAVs), represents the control inputs of all UAVs, represents the target states of all UAVs, represents the identity matrix of represents the state dimension of a single node, represents a positive semi - definite matrix with the first dimension, represents a positive semi - definite matrix with the second dimension, represents a positive semi - definite matrix with the third dimension, represents a positive semi - definite matrix with the fourth dimension.

[0035] Specifically, define the constraints to be optimized, including: Based on local information interaction, design a distributed control input for the UAV swarm that can minimize the cost function , where, represents the target relative state of the UAVs between node and node , represents the termination time of the formation mission, represents the steady - state error threshold, represents the time point when the UAV swarm formation mission meets the steady - state error requirement, represents the expected value of the energy consumption of the UAV corresponding to the th node, the initial energy of the UAV corresponding to the th node; When the constraints of the termination time of the formation mission and the steady - state error threshold are both met, the distributed control input can enable the UAV swarm to complete the formation mission.

[0036] ​The objective function comprehensively considers the expected values of energy cost, cumulative formation error, and network cost, and balances the relationship among the three through weight coefficients. The design of this optimized objective function brings significant benefits: First, by minimizing the expected value of energy cost, the energy consumption of the UAV swarm during the formation mission can be significantly reduced, the endurance of the UAVs can be extended, and the overall mission efficiency can be improved. This is particularly important for UAV swarms that need to perform tasks for a long time. Second, the expected value of the cumulative formation error is incorporated into the optimized objective function, which can ensure a high degree of coordination and accuracy of the UAV swarm during the formation process. This helps to enhance the stability and reliability of the UAV swarm when performing complex tasks and avoid mission failures or performance degradation caused by formation errors. In addition, the expected value of the network cost is also considered, which helps to optimize the communication and collaboration efficiency among the UAVs. By reducing unnecessary communication overhead and redundant information transmission, the response speed and overall performance of the UAV swarm can be improved, and the mission execution cost can be further reduced.

[0037] Furthermore, the Hamiltonian function of the objective function is constructed , specifically where is the relevant term involving the distributed control input, is the quadratic form term related to the state variable , which is used to measure the cost related to the state of the UAV swarm; and combine the co-state vector and the control input related terms to construct a complete Hamiltonian function form to meet the solution requirements of system optimization; where represents the element corresponding to the th node of represents the state component corresponding to the th transformed node, represents the element corresponding to the th node of represents the control input component corresponding to the th transformed node, is the first-order vector with respect to the state, is the second-order vector with respect to the state, is the eigenvalue corresponding to the th node of is the eigenvalue corresponding to the th node of is the The eigenvalue corresponding to a node.

[0038] Furthermore, by applying the stochastic optimal control theory, the necessary conditions for optimality are obtained; Among them, denotes the optimal control input of the unmanned aerial vehicle corresponding to the -th node, denotes the state component of the unmanned aerial vehicle corresponding to the -th node under the optimal control input, denotes the Lagrange multiplier; Define the parametric algebraic Riccati equation , Furthermore, the optimal control input is obtained as , That is, , Among them, denotes the first constraint parameter, denotes the second constraint parameter, , denotes the gain matrix of the minimum cost function.

[0039] The Hamiltonian function of this application not only integrates the basic information of the system state and control input, but also incorporates the statistical characteristics of the noise, thus more accurately describing the behavior pattern of the unmanned aerial vehicle cluster in an uncertain environment. Numerical iteration techniques are used to obtain an approximate optimal control strategy under multiplicative noise interference.

[0040] Specifically, designing the distributed optimal control strategy specifically includes: setting the running time, system parameters, and the initial state information, formation termination time, and initial energy of the unmanned aerial vehicle cluster, setting , and , and after the operation ends, the formation operation trajectory under optimal control and the final formation state are obtained.

[0041] A computer-readable medium stores a distributed optimal formation control method for an unmanned aerial vehicle cluster considering multiplicative noise as described above.

[0042] In a specific implementation case, there are 10 unmanned aerial vehicles, and the communication topology diagram formed is as Figure 2 shown. According to the control method of this application, set the running time of 40 s, the initial energy is random, the given formation time is set, and set , and , and conduct a simulation experiment using the control method of this application: set the communication method of the unmanned aerial vehicle, and its communication topology diagram is as Figure 2As shown, set =0.6, =1.2, =6.3, = 43s, the initial state and initial energy are random, the formation target is a five-pointed star with an outer circle radius of 25, the simulation results are as follows Figure 3 and Figure 4 As shown, Figure 3 Indicates the trajectory and final formation of the drone cluster, where “△” indicates the initial position of the drone and “*” indicates the final position of the drone. Figure 4 Represents the energy consumed by each UAV formation process (red) and the initial energy (blue). The experimental results show that the UAV cluster can complete the formation task under the given formation time and energy constraints.

[0043] Through the above process, the drone cluster can converge to the target formation state in a distributed manner. The advantages of the present invention are mainly two-fold. On the one hand, it can ensure that the control algorithm reaches global optimality and ensure that the system runs at optimal performance; on the other hand, it has low requirements on the network structure. During the formation process, each drone only relies on the information of neighboring drones. This concise and efficient way of using information greatly improves the computing efficiency and enables the entire formation task to proceed more smoothly.

[0044] Preferably, a distributed communication method is adopted so that the entire network exhibits higher robustness. Each node in the network cooperates with each other through distributed communication, and can better cope with various abnormal situations, thereby improving the overall stability and reliability of the network; only need to communicate with local neighboring drones, not only greatly reducing the communication cost, but also reducing the occupation of system resources in terms of calculation; ensuring that the system can still maintain good convergence when disturbed by noise, and will not deviate from the expected working state due to noise, ensuring the stability of system performance; the controller designed by the present invention fully considers the energy and time constraints in practical applications, so that the controller has stronger practicality in actual operation, avoiding the disconnection between theoretical design and practical application.

[0045] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A distributed optimal formation control method for UAV swarm considering multiplicative noise, characterized in that: The steps include: Construct a communication topology graph of the drone cluster, where each node represents a drone and each edge represents the communication relationship between two adjacent drones; Construct the Laplace matrix of the communication topology graph; Establish the UAV dynamic equation considering the influence of multiplicative noise; Define the objective function and constraints to be optimized; Construct Hamiltonian function of objective function; Using stochastic optimal control theory, a distributed optimal control strategy is designed. The running time, system parameters and the initial state information of the UAV cluster are set to obtain the formation operation trajectory and final formation state of the UAV cluster under optimal control.

2. The distributed optimal formation control method of a UAV swarm considering multiplicative noise according to claim 1 is characterized in that: Consider a drone cluster consisting of N drones. The communication topology graph is an undirected connected graph, and the mathematical expression is: in, represents an undirected connected graph, represents a set of nodes in an undirected connected graph, , represents the edge set of an undirected connected graph, , represents the adjacency matrix, ,in Representation Node and nodes Is there an edge connection between them? , if the node and nodes There are edges connecting them, then ; If the node and nodes There is no edge connecting them, then ; The degree matrix of the undirected connected graph is ,in, ,in, Indicates The degree of a node is calculated by All rows corresponding to the nodes Summing is performed to obtain .

3. The distributed optimal formation control method of a UAV swarm considering multiplicative noise according to claim 2 is characterized in that: Constructing the Laplace matrix of the communication topology graph includes: The Laplace matrix is , the eigenvalues ​​of the Laplace matrix are ,in , The Laplacian matrix can be diagonalized as , Representation Matrix The transposed matrix of represents a diagonal matrix, represents a matrix of eigenvectors, where , , express The corresponding feature vector.

4. The distributed optimal formation control method for UAV swarm considering multiplicative noise according to claim 3 is characterized in that: The UAV dynamic equation considering the influence of multiplicative noise is established as follows: , in, Represents the drone state variable In time A small change in is the control input variable, Represents small increments of time, represents a small increase in noise, Indicates that at the initial moment =0, the drone state variable The initial value is .

5. The method for controlling a distributed optimal formation of a UAV cluster considering multiplicative noise according to claim 4 is characterized in that: The optimization objective function is defined as , in, in, represents the expected value of energy cost, represents the expected value of the cumulative formation error, represents the expected value of the network cost, represents the weight of each balance, represents the mathematical expectation, represents the transpose operator, Indicates the status of all drones. represents the control input of all drones, Indicates the target status of all drones, express The identity matrix of Represents the state dimension of a single node, represents a positive semidefinite matrix with the first dimension, represents a positive semidefinite matrix with the second dimension, represents a positive semidefinite matrix with the third dimension, represents a positive semidefinite matrix with a fourth dimension.

6. The method for controlling a distributed optimal formation of a UAV cluster considering multiplicative noise according to claim 5 is characterized in that: Define the constraints to be optimized, including: Designing a cost-minimizing function for drone swarms based on local information interaction Distributed control input , in, Representation Node and nodes The relative state of the target of the UAV between them, Indicates the termination time of the formation mission. represents the steady-state error threshold, It indicates the time point when the UAV cluster formation task meets the steady-state error requirement, Indicates The expected energy consumption of the drone corresponding to each node is: No. The initial energy of the drone corresponding to each node; When the constraints of the termination time and steady-state error threshold of the formation mission are met, the distributed control input can enable the UAV cluster to complete the formation mission.

7. The method for controlling a distributed optimal formation of a UAV cluster considering multiplicative noise according to claim 6 is characterized in that: Construct Hamiltonian function of objective function , specifically in, Related terms involving distributed control inputs, is related to the state variable The related quadratic term is used to measure the cost associated with the state of the drone cluster; as well as The co-state vector and control input related terms are combined to construct a complete Hamiltonian function form to meet the solution requirements of system optimization; in, express No. The element corresponding to the node, Represents the transformed The state component corresponding to each node, express No. The element corresponding to the node, Represents the transformed The control input component corresponding to each node is is a first-order vector about the state, is a second-order vector about the state, yes No. The eigenvalues ​​corresponding to the nodes are yes No. The eigenvalues ​​corresponding to the nodes are yes No. The eigenvalues ​​corresponding to the nodes.

8. The method for controlling a distributed optimal formation of a swarm of unmanned aerial vehicles considering multiplicative noise according to claim 7, characterized in that: Use stochastic optimal control theory to find the optimal necessary conditions; in, Indicates The optimal control input of the UAV corresponding to each node is Indicates The state component of the UAV corresponding to each node under the optimal control input, represents the Lagrange multiplier; Defining the parametric algebraic Licatti equation , The optimal control input is further obtained as , Right now , in, represents the first constraint parameter, represents the second constraint parameter, , The gain matrix representing the minimum cost function.

9. The method for controlling a distributed optimal formation of a UAV cluster considering multiplicative noise according to claim 8, characterized in that: Designing a distributed optimal control strategy specifically includes: setting the running time, system parameters, initial state information of the drone cluster, formation termination time and initial energy, setting After the operation is completed, the formation operation trajectory and the final formation state under optimal control are obtained.

10. A computer-readable medium, characterized in that The computer-readable medium stores a distributed optimal formation control method for a drone cluster taking into account multiplicative noise as described in any one of claims 1 to 9.

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