A method for distributed optimal formation control of unmanned aerial vehicle swarm considering multiplicative noise and a computer readable medium

Abstract

The present application relates to the technical field of unmanned aerial vehicle cluster control, and particularly relates to a kind of unmanned aerial vehicle cluster distributed optimal formation control method considering multiplicative noise and computer readable medium, comprising the following steps: the communication topology graph of unmanned aerial vehicle cluster is built, each node represents an unmanned aerial vehicle, and each edge indicates the communication relationship between adjacent two unmanned aerial vehicles;Laplacian matrix of communication topology graph is built;Unmanned aerial vehicle dynamics equation considering the influence of multiplicative noise is established;Define the objective function to be optimized and constraint condition;Hamilton function of objective function is constructed;Random optimal control theory is used to design distributed optimal control strategy, set running time, system parameters and initial state information of unmanned aerial vehicle cluster, and the formation running track of unmanned aerial vehicle cluster under optimal control and the final formation state are obtained.The present application ensures the global optimality and robustness of unmanned aerial vehicle cluster control algorithm.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) swarm control technology, and in particular to a distributed optimal formation control method for UAV swarms that takes multiplicative noise into account, and a computer-readable medium thereof. Background Technology

[0002] Unmanned aerial vehicle (UAV) swarms are widely used in military, agricultural, and other fields due to their autonomy and coordination. Existing research on swarm control largely focuses on additive noise models, but in real-world scenarios, the state of UAVs is often affected by multiplicative noise (such as sensor noise and communication interference). The noise intensity is related to the system state, making it difficult for traditional methods to guarantee swarm stability and optimality. Furthermore, existing technologies do not fully integrate energy and time constraints, making it difficult to meet the requirements of actual missions. Therefore, there is an urgent need for a swarm control method that adapts to multiplicative noise and balances global optimality with distributed characteristics. Summary of the Invention

[0003] This invention aims to address at least one of the technical problems existing in related technologies. To this end, this invention provides a distributed optimal formation control method for UAV swarms considering multiplicative noise, along with a computer-readable medium. This addresses the problem that existing UAV control methods fail to fully integrate energy and time constraints, making it difficult to meet the requirements of actual missions, thereby ensuring the global optimality and robustness of the control algorithm.

[0004] This invention provides a distributed optimal formation control method for UAV swarms considering multiplicative noise, comprising the following steps:

[0005] Construct a communication topology graph for a drone swarm, where each node represents a drone and each edge represents the communication relationship between two adjacent drones;

[0006] The Laplace matrix for constructing the communication topology graph;

[0007] Establish the dynamic equations of the UAV that take into account the effects of multiplicative noise;

[0008] Define the objective function to be optimized and the constraints;

[0009] Construct the Hamiltonian function of the objective function;

[0010] By applying stochastic optimal control theory, a distributed optimal control strategy is designed. The running time, system parameters, and initial state information of the UAV swarm are set to obtain the formation trajectory and final formation state of the UAV swarm under optimal control.

[0011] A further improvement of the distributed optimal formation control method for UAV swarms considering multiplicative noise in this invention lies in considering a UAV swarm consisting of N UAVs, wherein the communication topology is an undirected connected graph, and the mathematical expression is:

[0012]

[0013] in, Represents an undirected connected graph. Represents the set of nodes in an undirected connected graph. , Represents the set of edges in an undirected connected graph. , Represents the adjacency matrix. ,in Represents a node and nodes Are there any edges connecting them? If node and nodes If there is an edge connecting them, then If node and nodes If there are no edges connecting them, then ;

[0014] The degree matrix of the undirected connected graph is ,in, ,in, Indicates the first The degree of the i-th node is determined by the degree of the i-th node in the adjacency matrix. All rows corresponding to each node The summation is obtained.

[0015] A further improvement of the distributed optimal formation control method for UAV swarms considering multiplicative noise in this invention lies in constructing the Laplace matrix of the communication topology graph, including:

[0016] The Laplace matrix is: The eigenvalues ​​of the Laplace matrix are ,in ,

[0017] The Laplace matrix can be diagonalized as follows: , Representation matrix The transpose of the matrix, Represents a diagonal matrix. Denotes the matrix composed of eigenvectors, where , , express The corresponding feature vector.

[0018] A further improvement of the distributed optimal formation control method for UAV swarms considering multiplicative noise in this invention lies in establishing the UAV dynamic equations that take into account the influence of multiplicative noise as follows: ,

[0019] in, Representing the state variables of the drone In time The change It controls the input variables. Indicates the increment of time. Represents the increment of noise. Indicates the initial time. When =0, the drone state variable The initial value is .

[0020] A further improvement of the distributed optimal formation control method for UAV swarms considering multiplicative noise in this invention lies in defining the optimization objective function as follows: ,

[0021] in,

[0022] in, This represents the expected value of the energy cost. This represents the expected value of the cumulative formation error. This represents the expected value of the network cost. This indicates the weights of the balanced items. Represents the mathematical expectation. This represents the transpose operator. Indicates the status of all drones. This represents all control inputs for the drone. This indicates the target status of all drones. express The identity matrix, Represents the state dimension of a single node. Let represent a positive semi-definite matrix with the first dimension. Let represent a positive semi-definite matrix with a second dimension. This represents a positive semi-definite matrix with a third dimension. This represents a positive semidefinite matrix with a fourth dimension.

[0023] A further improvement of the distributed optimal formation control method for UAV swarms considering multiplicative noise in this invention lies in defining the constraints to be optimized, including:

[0024] Based on local information interaction, design a drone swarm that minimizes... Distributed control input ,

[0025]

[0026] in, Represents a node and nodes The relative state of the targets between the drones Indicates the end time of the formation mission. Indicates the steady-state error threshold. This indicates the time point at which the drone swarm formation mission meets the steady-state error requirements. Indicates the first Expected energy consumption of the drone corresponding to each node. Indicates the first The initial energy of the drone corresponding to each node;

[0027] When the constraints of the formation mission termination time and the steady-state error threshold are met, the distributed control input can enable the UAV swarm to complete the formation mission.

[0028] A further improvement of the distributed optimal formation control method for UAV swarms considering multiplicative noise in this invention lies in constructing a Hamiltonian function of the objective function. Specifically

[0029]

[0030] in, This indicates items related to distributed control inputs. Representation and state variables The relevant quadratic terms are used to measure the cost associated with the state of the drone swarm; as well as This indicates that the costate vector and control input related terms are combined to construct the complete Hamiltonian function form to meet the solution requirements of system optimization;

[0031] in, express The The elements corresponding to each node Represents the transformed th The state components corresponding to each node. express The The elements corresponding to each node Represents the transformed th The control input components corresponding to each node. It is a first-order vector about the state. It is a second-order vector about the state. yes The The feature values ​​corresponding to each node yes The The feature values ​​corresponding to each node yes The The feature values ​​corresponding to each node.

[0032] A further improvement of the distributed optimal formation control method for UAV swarms considering multiplicative noise in this invention lies in using stochastic optimal control theory to obtain the necessary conditions for the optimality.

[0033]

[0034] in, Indicates the first The optimal control input for the UAV corresponding to each node. Indicates the first The state components of the UAV corresponding to each node under optimal control input. Represents the Lagrange multipliers;

[0035] Define parametric algebraic Licatti equations ,

[0036] The optimal control input is further obtained as follows: ,

[0037] Right now ,

[0038] in, Indicates the first constraint parameter. This represents the second constraint parameter. , The gain matrix represents the minimum cost function.

[0039] A further improvement of the distributed optimal formation control method for UAV swarms considering multiplicative noise in this invention lies in the fact that the design of the distributed optimal control strategy specifically includes: setting the running time, system parameters, and initial state information of the UAV swarm, formation termination time, and initial energy; and setting... After the operation is completed, the formation trajectory under optimal control and the final formation state are obtained.

[0040] A computer-readable medium storing a distributed optimal formation control method for unmanned aerial vehicle (UAV) swarms that takes multiplicative noise into account, as described above.

[0041] The above-described one or more technical solutions in the embodiments of the present invention have at least one of the following technical effects:

[0042] (1) Through distributed communication, this communication mechanism significantly enhances the robustness of the entire network. Through distributed communication with each node, various abnormal situations can be dealt with more effectively, thereby improving the overall stability and reliability of the UAV swarm.

[0043] (2) Only local communication with nearby drones is required. This communication method avoids the need for large-scale information transmission, which not only greatly reduces communication costs, but also significantly improves computing efficiency and reduces the occupation of system resources.

[0044] (3) The impact of environmental noise on the system, especially multiplicative noise, has been fully considered. Through targeted design, the system is ensured to maintain good convergence when subjected to noise interference, and will not deviate from the expected working state due to noise, thus ensuring the stability of system performance.

[0045] (4) The control method of the present invention fully considers the energy and time constraints in practical applications, and has stronger practicality and operability in actual operation, avoiding the disconnect between theoretical design and practical application.

[0046] (5) This invention mainly focuses on how to ensure the feasibility of formation tasks under complex conditions that consider energy and time constraints and the presence of multiplicative noise in the system. Its core method is to design algorithms based on network cost. This method has many advantages. On the one hand, it can ensure that the control algorithm reaches global optimality and ensure that the system runs with the best performance. On the other hand, it has low requirements for network structure. During the formation process, each UAV only relies on the information of its neighboring UAVs. This simple and efficient information transmission method greatly improves the computational efficiency and enables the entire formation task to proceed more smoothly.

[0047] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0049] Figure 1 This is a block diagram illustrating a distributed optimal formation control method for UAV swarms that considers multiplicative noise, provided by the present invention.

[0050] Figure 2This is a schematic diagram of the communication topology in a distributed optimal formation control method for UAV swarms that considers multiplicative noise, provided in an embodiment of the present invention.

[0051] Figure 3 This is a schematic diagram of the drone swarm operation trajectory and final formation provided in an embodiment of the present invention.

[0052] Figure 4 This is a schematic diagram of the energy consumption and initial energy of each UAV provided in the embodiments of the present invention. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention. The following embodiments are used to illustrate this invention but should not be used to limit the scope of this invention.

[0054] The following is combined Figure 1 The present invention describes a distributed optimal formation control method for UAV swarms considering multiplicative noise, comprising the following steps:

[0055] Construct a communication topology graph for a drone swarm, where each node represents a drone and each edge represents the communication relationship between two adjacent drones;

[0056] The Laplace matrix for constructing the communication topology graph;

[0057] Establish the dynamic equations of the UAV that take into account the effects of multiplicative noise;

[0058] Define the objective function to be optimized and the constraints;

[0059] Construct the Hamiltonian function of the objective function;

[0060] By applying stochastic optimal control theory, a distributed optimal control strategy is designed. The running time, system parameters, and initial state information of the UAV swarm are set to obtain the formation trajectory and final formation state of the UAV swarm under optimal control.

[0061] The UAV dynamics equations fully consider the impact of multiplicative noise on the UAV's motion state, making the control strategy more closely reflect reality. The objective function is defined according to mission requirements, such as minimizing the energy consumption of the UAV swarm or achieving optimal formation. Constraints include physical limitations and communication range limitations of the UAVs. When constructing the Hamiltonian function, the objective function is combined with the system's state and control variables to form a function containing Lagrange multipliers. By solving for the optimal value of the Hamiltonian function, the optimal control strategy can be obtained. Finally, using stochastic optimal control theory, combined with the set running time, system parameters, and initial state information of the UAV swarm, the formation trajectory and final formation state of the UAV swarm under optimal control can be obtained through numerical calculation or simulation methods. This method realizes distributed optimal formation control of UAV swarms under multiplicative noise environment, exhibiting high robustness and practicality.

[0062] In a preferred embodiment of the distributed optimal formation control method for UAV swarms considering multiplicative noise of the present invention, a UAV swarm consisting of N UAVs is considered, and the communication topology is an undirected connected graph, the mathematical expression of which is:

[0063]

[0064] in, Represents an undirected connected graph. Represents the set of nodes in an undirected connected graph. , Represents the set of edges in an undirected connected graph. , Represents the adjacency matrix. ,in Represents a node and nodes Are there any edges connecting them? If node and nodes If there is an edge connecting them, then If node and nodes If there are no edges connecting them, then ;

[0065] The degree matrix of the undirected connected graph is ,in, ,in, Indicates the first The degree of the i-th node is determined by the degree of the i-th node in the adjacency matrix. All rows corresponding to each node The summation is obtained.

[0066] The distributed optimal formation control problem of UAV swarms can be solved by constructing an objective function. The objective function can be defined as the relative positional relationships between the individual UAVs in the swarm, and the deviation between the overall shape of the swarm and the desired shape. To achieve this objective, a Laplace matrix is ​​further introduced, reflecting the connection and relative positional relationships between the individual UAVs in the swarm.

[0067] Specifically, constructing the Laplace matrix of the communication topology graph includes:

[0068] The Laplace matrix is: The eigenvalues ​​of the Laplace matrix are ,in ,

[0069] The Laplace matrix can be diagonalized as follows: , Representation matrix The transpose of the matrix, Represents a diagonal matrix. Denotes the matrix composed of eigenvectors, where , , express The corresponding feature vector.

[0070] First, by defining the communication topology of the UAV swarm as an undirected connected graph and elaborating it mathematically, a solid theoretical foundation is laid for subsequent formation control. This step not only ensures information flow between UAVs but also clarifies their connections, providing the necessary conditions for constructing the objective function and introducing the Laplace matrix. Second, constructing the objective function is key to solving the problem. The objective function defines the relative positional relationships between the UAVs in the swarm and the deviation between the overall shape of the swarm and the desired shape. This setting provides a clear direction for the optimization process: minimizing the objective function value to achieve optimal formation. Furthermore, the Laplace matrix is ​​introduced. The Laplace matrix reflects the connections and relative positional relationships between the UAVs in the swarm, providing an important basis for the design of distributed control protocols. Through in-depth analysis of the eigenvalues ​​and diagonalization properties of the Laplace matrix, the position and speed of the UAVs can be controlled more precisely, enabling collaborative operation of the UAV swarm.

[0071] Furthermore, the dynamic equations of the UAV considering the effects of multiplicative noise are established as follows: ,

[0072] in, Representing the state variables of the drone In time The change It controls the input variables. Indicates the increment of time. Represents the increment of noise. Indicates the initial time. When =0, the drone state variable The initial value is .

[0073] First, the proposed UAV dynamics equations more accurately describe the dynamic behavior of UAVs in real-world environments. By introducing multiplicative noise, we consider the impact of external disturbances and uncertainties on the UAV's state, making the UAV dynamics equations closer to reality and improving the model's prediction accuracy. Second, the control strategy designed based on these UAV dynamics equations exhibits stronger robustness. Because the equations include noise terms, we can consider the impact of noise when designing the control algorithm and take corresponding compensation measures to weaken the influence of noise on the UAV's state, ensuring that the UAV can stably perform formation tasks.

[0074] Furthermore, the optimization objective function is defined as follows: ,

[0075] in,

[0076] in, This represents the expected value of the energy cost. This represents the expected value of the cumulative formation error. This represents the expected value of the network cost. This indicates the weights of the balanced items. Represents the mathematical expectation. This represents the transpose operator. Indicates the status of all drones. This represents all control inputs for the drone. This indicates the target status of all drones. express The identity matrix, Represents the state dimension of a single node. Let represent a positive semi-definite matrix with the first dimension. Let represent a positive semi-definite matrix with a second dimension. This represents a positive semi-definite matrix with a third dimension. This represents a positive semidefinite matrix with a fourth dimension.

[0077] Specifically, define the constraints that need to be optimized, including:

[0078] Based on local information interaction, design a drone swarm that minimizes... Distributed control input ,

[0079]

[0080] in, Represents a node and nodes The relative state of the targets between the drones Indicates the end time of the formation mission. Indicates the steady-state error threshold. This indicates the time point at which the drone swarm formation mission meets the steady-state error requirements. Indicates the first Expected energy consumption of the drone corresponding to each node. Indicates the first The initial energy of the drone corresponding to each node;

[0081] When the constraints of the formation mission termination time and the steady-state error threshold are met, the distributed control input can enable the UAV swarm to complete the formation mission.

[0082] The objective function comprehensively considers the expected values ​​of energy cost, cumulative formation error, and network cost, and balances the relationship between these three factors through weighting coefficients. This optimization objective function design brings significant benefits: First, by minimizing the expected value of energy cost, the energy consumption of the UAV swarm during formation tasks can be significantly reduced, extending the UAVs' endurance and improving overall mission efficiency. This is particularly important for UAV swarms that need to perform tasks for extended periods. Second, incorporating the expected value of cumulative formation error into the optimization objective function ensures that the UAV swarm maintains high coordination and accuracy during formation. This helps improve the stability and reliability of the UAV swarm when performing complex tasks, avoiding mission failures or performance degradation due to formation errors. Furthermore, the expected value of network cost is also considered, which helps optimize the communication and collaboration efficiency between UAV swarms. By reducing unnecessary communication overhead and redundant information transmission, the response speed and overall performance of the UAV swarm can be improved, further reducing mission execution costs.

[0083] Furthermore, the Hamiltonian function of the objective function is constructed. Specifically

[0084]

[0085] in, This indicates items related to distributed control inputs. Representation and state variables The relevant quadratic terms are used to measure the cost associated with the state of the drone swarm; as well as This indicates that the costate vector and control input related terms are combined to construct the complete Hamiltonian function form to meet the solution requirements of system optimization;

[0086] in, express The The elements corresponding to each node Represents the transformed th The state components corresponding to each node. express The The elements corresponding to each node Represents the transformed th The control input components corresponding to each node. It is a first-order vector about the state. It is a second-order vector about the state. yes The The feature values ​​corresponding to each node yes The The feature values ​​corresponding to each node yes The The feature values ​​corresponding to each node.

[0087] Furthermore, by applying stochastic optimal control theory, the necessary conditions for optimality are obtained;

[0088]

[0089] in, Indicates the first The optimal control input for the UAV corresponding to each node. Indicates the first The state components of the UAV corresponding to each node under optimal control input. Represents the Lagrange multipliers;

[0090] Define parametric algebraic Licatti equations ,

[0091] The optimal control input is further obtained as follows: ,

[0092] Right now ,

[0093] in, Indicates the first constraint parameter. This represents the second constraint parameter. , The gain matrix represents the minimum cost function.

[0094] The Hamiltonian function of this invention not only integrates basic information about the system state and control input, but also incorporates the statistical characteristics of noise, thus more accurately describing the behavior of UAV swarms in uncertain environments. Numerical iteration techniques are employed to obtain an approximate optimal control strategy under multiplicative noise disturbances.

[0095] Specifically, designing a distributed optimal control strategy includes: setting the running time, system parameters, and initial state information of the UAV swarm, formation termination time, and initial energy; and setting... , as well as After the operation is completed, the formation trajectory under optimal control and the final formation state are obtained.

[0096] A computer-readable medium storing a distributed optimal formation control method for unmanned aerial vehicle (UAV) swarms that takes multiplicative noise into account, as described above.

[0097] In one specific implementation example, the drone has 10 units, and the communication topology is as follows: Figure 2 As shown, according to the control method of this application, the running time is set to 40 seconds, the initial energy is randomized, the given formation time is set, and the parameters are set. , as well as The application's control method was simulated in an experiment: the communication mode of the UAV was set, and its communication topology diagram is as follows. Figure 2 As shown, settings =0.6, =1.2, =6.3, =43s, initial state and initial energy are random, formation target is a pentagram with an outer circle radius of 25, simulation results are as follows. Figure 3 and Figure 4 As shown, where Figure 3 This indicates the trajectory and final formation of the drone swarm, where "△" represents the initial position of the drone (UAV) and "*" represents the final position of the drone. Figure 4 The values ​​represent the energy consumed (A) and initial energy (B) during the formation process of each UAV. Experimental results show that the UAV swarm can complete the formation task under given formation time and energy constraints.

[0098] Through the above process, the drone swarm can converge to the target formation state in a distributed manner. The advantages of this invention are mainly twofold. Firstly, it ensures that the control algorithm achieves global optimality, guaranteeing that the system operates at its best performance. Secondly, it has lower requirements for the network structure; during formation, each drone only relies on information from its neighbors. This simple and efficient information utilization method greatly improves computational efficiency, enabling the entire formation task to proceed more smoothly.

[0099] Preferably, the distributed communication method enhances the robustness of the entire network. Nodes within the network collaborate through distributed communication, better responding to various anomalies and thus improving the overall stability and reliability of the network. Communicating only with local neighboring drones significantly reduces communication costs and computational resource consumption. The system maintains good convergence even under noise interference, preventing deviation from its expected operating state and ensuring stable performance. Furthermore, the controller designed in this invention fully considers energy and time constraints in practical applications, making it more practical and avoiding a disconnect between theoretical design and real-world application.

[0100] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate 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 swarms considering multiplicative noise, characterized in that, Includes the following steps: Construct a communication topology graph for a drone swarm, where each node represents a drone and each edge represents the communication relationship between two adjacent drones; The Laplace matrix for constructing the communication topology graph; Establish the UAV dynamic equations considering the effects of multiplicative noise. The UAV dynamic equations are as follows: , in, Representing the state variables of the drone In time The change It controls the input variables. Indicates the increment of time. Represents the increment of noise. Indicates the initial time. When =0, the drone state variable The initial value is ; Define the objective function to be optimized and the constraints; Construct the Hamiltonian function of the objective function; By applying stochastic optimal control theory, a distributed optimal control strategy is designed. The running time, system parameters, and initial state information of the UAV swarm are set to obtain the formation trajectory and final formation state of the UAV swarm under optimal control.

2. The distributed optimal formation control method for UAV swarms considering multiplicative noise according to claim 1, characterized in that, Consider a drone swarm consisting of N drones, where the communication topology is an undirected connected graph, and the mathematical expression is: in, Represents an undirected connected graph. Represents the set of nodes in an undirected connected graph. , Represents the set of edges in an undirected connected graph. , Represents the adjacency matrix. ,in Represents a node and nodes Are there any edges connecting them? If node and nodes If there is an edge connecting them, then If the node and nodes If there are no edges connecting them, then ; The degree matrix of the undirected connected graph is ,in, ,in, Indicates the first The degree of the i-th node is determined by the degree of the i-th node in the adjacency matrix. All rows corresponding to each node The summation is obtained.

3. The distributed optimal formation control method for UAV swarms considering multiplicative noise according to claim 2, 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 Laplace matrix can be diagonalized as follows: , Representation matrix The transpose of the matrix, Represents a diagonal matrix. Denotes the matrix composed of eigenvectors, where , , express The corresponding feature vector.

4. The distributed optimal formation control method for UAV swarms considering multiplicative noise according to claim 3, characterized in that, Define the optimization objective function as follows: , in, in, This represents the expected value of the energy cost. This represents the expected value of the cumulative formation error. This represents the expected value of the network cost. This indicates the weights of the balanced items. Represents the mathematical expectation. This represents the transpose operator. Indicates the status of all drones. This represents all control inputs for the drone. This indicates the target status of all drones. express The identity matrix, Represents the state dimension of a single node. Let this be a positive semi-definite matrix with the first dimension. Let represent a positive semi-definite matrix with a second dimension. This represents a positive semi-definite matrix with a third dimension. This represents a positive semidefinite matrix with a fourth dimension.

5. The distributed optimal formation control method for UAV swarms considering multiplicative noise according to claim 4, characterized in that, Define the constraints that need to be optimized, including: Based on local information interaction, design a drone swarm that minimizes... Distributed control input , in, Represents a node and nodes The relative state of the targets between the drones Indicates the end time of the formation mission. Indicates the steady-state error threshold. This indicates the time point at which the drone swarm formation mission meets the steady-state error requirements. Indicates the first Expected energy consumption of the drone corresponding to each node. Indicates the first The initial energy of the drone corresponding to each node; When the constraints of the formation mission termination time and the steady-state error threshold are met, the distributed control input can enable the UAV swarm to complete the formation mission.

6. The distributed optimal formation control method for UAV swarms considering multiplicative noise according to claim 5, characterized in that, Constructing the Hamiltonian function of the objective function Specifically in, This indicates items related to distributed control inputs. Representation and state variables The relevant quadratic terms are used to measure the cost associated with the state of the drone swarm; as well as This indicates that the costate vector and control input related terms are combined to construct the complete Hamiltonian function form to meet the solution requirements of system optimization; in, express The The elements corresponding to each node Represents the transformed th The state components corresponding to each node. express The The elements corresponding to each node Represents the transformed th The control input components corresponding to each node. It is a first-order vector about the state. It is a second-order vector about the state. yes The The feature values ​​corresponding to each node yes The The feature values ​​corresponding to each node yes The The feature values ​​corresponding to each node.

7. The distributed optimal formation control method for UAV swarms considering multiplicative noise according to claim 6, characterized in that, Using stochastic optimal control theory, the necessary conditions for optimality are obtained; in, Indicates the first The optimal control input for the UAV corresponding to each node. Indicates the first The state components of the UAV corresponding to each node under optimal control input. Represents the Lagrange multipliers; Define parametric algebraic Licatti equations , The optimal control input is further obtained as follows: , Right now , in, Indicates the first constraint parameter. This represents the second constraint parameter. , The gain matrix represents the minimum cost function.

8. The distributed optimal formation control method for UAV swarms considering multiplicative noise according to claim 7, characterized in that, Designing a distributed optimal control strategy specifically includes: setting the running time, system parameters, and initial state information of the UAV swarm, formation termination time, and initial energy; and setting... After the operation is completed, the formation trajectory under optimal control and the final formation state are obtained.

9. A computer-readable medium, characterized in that, The computer-readable medium stores a distributed optimal formation control method for unmanned aerial vehicle (UAV) swarms that takes multiplicative noise into account, as described in any one of claims 1 to 8.

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