Multi-UAV cooperative task allocation method, system and medium

Abstract

The present application relates to the field of drone control technology and discloses a method, system and medium for cooperative task allocation among multiple drones. The method comprises: S1, defining the problem of cooperative task allocation among multiple drones; S2, solving the optimal control strategy for the problem of cooperative task allocation among multiple drones; S3, solving the dual optimization problem based on the primal-dual theory; S4, solving the convex dual optimization problem using the Q-function and Schur Complementation theory transforms the convex dual optimization problem into a semidefinite programming problem. S5, based on the properties of matrix congruence, transforms the semidefinite programming problem into a model-free semidefinite programming problem. S6, using a solver, obtains the optimal control strategy. S7, by varying the weight coefficients and repeating S2-S6, obtains the optimal energy loss function bound. This application, based on the Q-learning method, requires only a small amount of data collection, not a precise dynamics model or extensive data, to obtain the optimal strategy for multi-UAV cooperative task allocation.

Description

Technical Field

[0001] The present application belongs to the field of drone control technology, and in particular relates to a method, system, and medium for allocating cooperative tasks among multiple drones. Background Art

[0002] With the development and advancement of science and technology, drones (UAVs), owing to their flexibility, efficiency, and safety, have been widely used to perform a variety of tasks, including search and rescue, cargo transportation, agricultural monitoring, environmental monitoring, geographic mapping and exploration, infrastructure inspection, film and television shooting and photography, and scientific research. However, individual UAVs face limitations such as flight time limitations, insufficient payload capacity, susceptibility to interference, and limited processing power, making them incapable of performing complex, long-duration, or demanding missions. This has led to the emergence of multi-UAV collaborative operations. When multiple UAVs operate in a swarm, they can handle long-range, large-scale, and complex missions, such as target reconnaissance, cargo transportation, rescue operations, and equipment inspections.

[0003] Existing technologies for assigning drone tasks primarily focus on single-drone control, typically focusing solely on minimizing a single drone's energy consumption while maximizing task completion. However, when multiple drones collaborate, algorithms must consider the energy consumption of other drones, minimizing the energy consumption of a single drone without increasing the energy consumption of other drones. Furthermore, existing algorithms for assigning drone tasks typically require precise dynamic models or the collection of large datasets. Summary of the Invention

[0004] The technical problem to be solved by this application is to overcome the shortcomings of the existing technology. This application provides a multi-UAV cooperative task allocation method, system and medium.

[0005] To achieve the above objectives, the present application provides, in a first aspect, a method for multi-UAV cooperative task allocation, comprising the following steps:

[0006] S1. Define the multi-UAV cooperative task allocation problem as ;

[0007] S2. Solve the optimal control strategy for multi-UAV cooperative task allocation problem:

[0008] The optimal control strategy is obtained by weighting the energy loss function, and solving the optimal control strategy is equivalent to solving the problem of minimizing the weighted sum of energy losses of all UAVs;

[0009] The weighted multi-UAV cooperative task allocation problem is: ; Through the stabilization control gain matrix Convert to ; According to the Lyapunov stability theorem Equivalent conversion to ;

[0010] S3. Solution based on primal-dual theory The dual optimization problem is:

[0011] Using the primal-dual method, the non-convex optimization problem Equivalent transformation to convex dual optimization problem Solve;

[0012] S4. Use Q-function to solve the convex dual optimization problem, and based on Schur complement theory, convert the convex dual optimization problem into a semi-definite programming problem:

[0013] The Q-function parameters and The equivalence relationship between Lagrange multipliers in the equation is used to solve the convex dual optimization problem using Q-functions. ;

[0014] Using Schur's complement lemma, the convex dual optimization problem Transformed into a semidefinite programming problem Solve;

[0015] S5. Based on the properties of matrix congruence, the semi-positive definite programming problem is transformed into a model-free semi-positive definite programming problem:

[0016] Semidefinite programming problem Equivalent transformation to model-free semidefinite programming problem Solve;

[0017] S6. Solve the problem using the solver to obtain the optimal control strategy for the multi-UAV cooperative task allocation problem:

[0018] calculate The optimal Q-function parameters , determine the optimal feedback gain matrix , we get the optimal decision for multi-UAV cooperative task allocation problem , computing drones The minimum value of the energy loss function , we obtain the optimal solution to the multi-UAV cooperative task allocation problem, i.e. the minimum energy loss of all UAVs;

[0019] S7. By changing the weight coefficient , repeat S2-S6 to obtain the boundary of the UAV cooperative task allocation problem, that is, the optimal solution of all multi-UAV cooperative task allocation problems.

[0020] Optionally, the multi-UAV cooperative task allocation problem is defined in S1 as , including: The cooperative task allocation problem of multiple UAVs is expressed as:

[0021] ;

[0022] (3);

[0023] (4);

[0024] in, Indicates drone The infinite time domain original problem, represents linear quadratic, Indicates drone of energy loss, represents the control strategy for multi-UAV cooperative task allocation problem before considering the control gain, represents the initial number of tasks, represents the k moment, i represents the number of the drone, represents the number of remaining tasks for all drones at time k, represents transpose, Indicates drone The quadratic state weight matrix of energy loss, Indicates the drone before considering the control gain exist The control strategy at all times, Indicates the drone before considering the control gain exist The control strategy at all times, Indicates drone The energy loss of the quadratic state input weight matrix, Represents the set of numbers of all drones, N represents the number of drones, Represents constraints, Indicates that all drones are The number of remaining tasks at time A and denote the state transfer matrix of the system and the control input matrix of UAV i, respectively. Indicates the number of remaining tasks for all drones at the initial moment, Represents the real number field Euclidean space.

[0025] Optionally, the optimal control strategy for solving the multi-UAV cooperative task allocation problem in S2 includes: the minimum value of the weighted sum of energy losses of all UAVs is expressed as:

[0026] ;

[0027] (5);

[0028] ;

[0029] in, Represents the infinite time domain original problem after all UAVs are weighted, represents linear quadratic, represents the weighted energy loss of all drones, , Represent the weighted quadratic state weight matrix and quadratic input weight matrix of all UAVs, Indicates drone The quadratic state weight matrix of energy loss, Represents each drone The assigned weight coefficient, i represents the number of the drone.

[0030] Optionally, in S2, the stabilization control gain matrix is ​​used to Convert to ; According to the Lyapunov stability theorem Equivalent conversion to ;include:

[0031] Assumption 1: Formula (4) is stabilizable;

[0032] definition ,make Express formula (4) from The initial solution, then Expressed as:

[0033] ;

[0034] (6);

[0035] Formula (6) Formula (4);

[0036] in, Represents the infinite time domain original problem after all UAVs are weighted, represents the linear quadratic after considering the control gain, Indicates The weighted energy loss of all drones under the action, represents the control gain matrix, represents the diagonal matrix combination of the weighted quadratic weight matrix, represents the weighted quadratic state weight matrix of all UAVs, represents the weighted secondary input weight matrix of all UAVs, represents the control strategy for multi-UAV cooperative task allocation, Represents constraints, Represents the real number field dimensional Euclidean space;

[0037] According to the Lyapunov stability theorem, the Lyapunov equation is There is a unique solution for every choice Sometimes, there are , that is, formula (4) in the control feedback gain matrix The lower is calm, therefore, Equivalent to ,Will Equivalently converted to:

[0038] ;

[0039] ;

[0040] ;

[0041] (8);

[0042] in, Represents the infinite time domain original problem after all UAVs are weighted, Indicates that new variables are considered The linear quadratic, It means The minimum value of the cumulative sum of the weighted UAV energy consumption under different conditions, represents the set of stabilizing feedback control gain matrices, represents the spectral radius of the matrix, The function represents the additional variable of energy loss, represents the additional variable of the UAV’s energy consumption, It represents the combination matrix of the remaining task state and the coefficient matrix of the joint control strategy and the control gain matrix. express dimensional identity matrix, represents the transpose of the matrix, represents the trace of the matrix.

[0043] Optionally, S3 uses the primal-dual method to transform non-convex optimization problems into Equivalent transformation to convex dual optimization problem Solve, including:

[0044] make and express The constrained Lagrange multiplier of , then the Lagrange equation is expressed as ;

[0045] The corresponding dual optimization problem is expressed as:

[0046] (10);

[0047] in, represents the infimum;

[0048] The energy loss of the UAV in the dual optimization problem is expressed as:

[0049] (15);

[0050] in, and for The sub-matrix of represents the outer product matrix of the initial task, represents the trace of the matrix, represents the inverse of a matrix; Represents the transpose of a matrix;

[0051] definition Make

[0052] (16);

[0053] in, represents the slack extra variables of the drone, Indicates all A collection of dimensional symmetric matrices;

[0054] The energy loss of the drone is expressed as:

[0055] (17);

[0056] make and They represent the optimal solutions of formula (15) and formula (17), namely The optimal Lagrange multiplier of the constraint and the optimal relaxation additional variable of the UAV are derived by formula (16) and formula (17) satisfy:

[0057] (18);

[0058] in, 、 、 Denote the optimal Lagrange multiplier The upper left block matrix, the upper right block matrix and the lower right block matrix of ;

[0059] The convex dual optimization problem is expressed as:

[0060] ;

[0061] ;

[0062] ;

[0063] ;

[0064] (19);

[0065] in, represents the dual problem of infinite time domain after all UAVs are weighted, represents the slack extra variables of the drone, and for The sub-matrix of , Represents the energy consumption of the drone.

[0066] Optionally, S4 uses Q-function to solve the convex dual optimization problem, and based on Schur complement theory, the convex dual optimization problem is equivalently transformed into a semi-positive programming problem; including the derivation of KKT conditions The explicit structure of Substitute into the Q-function definition and make the association explicit With Lagrange multipliers, using The convexity of , transforms the dual problem into an optimization problem of the Q-function parameters; specifically including:

[0067] Obtained through KKT conditions Optimality;

[0068] set up and for The Lagrange multiplier, the corresponding Lagrange function is expressed as ;

[0069] According to the Lyapunov stability theorem, the Lagrange multiplier Designed to be with stabilizing control gain The associated matrix is ​​expressed as:

[0070] ;

[0071] ;

[0072] (31);

[0073] in, represents the optimal stabilizing control gain, 、 Indicates another possible Lagrange multiplier The upper left block matrix of represents the identity matrix, express submatrix of ;

[0074] pass represents the optimal parameters of the optimal Q-function, and the optimal Q-function is defined as:

[0075] (32);

[0076] in, represents the initial joint control strategy of the UAV, represents the optimal Q-function, represents the solution of the optimal algebraic Riccati equation, represents the minimum value of energy loss after weighting of all UAVs;

[0077] (33);

[0078] in, represents the quadratic input weight matrix after weighting of the UAV;

[0079] By using Schur complement theory, The equivalent conversion is:

[0080] ;

[0081] ;

[0082] ;

[0083] (34);

[0084] in, represents the dual problem of infinite time domain after all UAVs are weighted, represents a semi-positive programming, express energy consumption of drones.

[0085] Optionally, in S5, the semidefinite programming problem Equivalent transformation to model-free semidefinite programming problem Perform a solution; including:

[0086] definition , expressed as:

[0087] (38);

[0088] in, Indicates the time of first collection. Indicates the status of the first collection. Indicates the status of the second collection. Represents the input of the first collection, Represents the input of the second collection, Indicates the The status of the collection, Indicates the The input of the acquisition, represents the matrix of collected data, Represents the real number field Violet's space;

[0089] Based on formula (38) , expressed as:

[0090] (39);

[0091] in, represents the matrix of collected data, represents the number of samples collected, Represents the real number field dimensional Euclidean space, Indicates the status of the third collection. Indicates the The status of the acquisition;

[0092] Based on the matrix congruence property, if the matrix have The column rank of can be multiplied by and , and using Schur complement theory we get:

[0093] (40);

[0094] in, 、 Respectively and The dimension of the matrix;

[0095] Semi-positive programming Equivalently transformed into a model-free semidefinite programming problem:

[0096] ;

[0097] ;

[0098] ;

[0099] (41);

[0100] in, Indicates no model.

[0101] Optionally, S6 uses a solver to obtain the optimal control strategy for the multi-UAV cooperative task allocation problem, including:

[0102] Assumption 2: For all It is entirely appreciable;

[0103] Under the condition of assumption 2, use the solver CVX to solve The optimal Q-function parameters defined in , and obtain the optimal control gain matrix for:

[0104] (42);

[0105] Finally, we get the optimal strategy for UAV cooperative task allocation problem for:

[0106] (43);

[0107] in, Indicates that each drone The optimal control gain matrix is 、 、 Indicates 1st, 2nd, The optimal control gain matrix of a UAV, n represents finding the independent variable that makes the function achieve the minimum value, represents the joint control strategy space of all UAVs;

[0108] For a given weight coefficient , when the PE condition is met, through formula (38) and in formula (39) collect Sample, get each drone The minimum energy loss is:

[0109] (44);

[0110] in, Represents the set of conditions that the weight coefficient must meet, Respectively represent the 1st, 2nd, The weight coefficient of the drone allocation;

[0111] The optimal solution of the optimal control strategy is further obtained as:

[0112] (45);

[0113] Among them, the optimal solution of the optimal control strategy represents the minimum energy loss of all drones. 、 、 Indicates 1st, 2nd, The energy loss of the drone is minimized.

[0114] To achieve the above objectives, the second aspect of the present application provides a system for multi-UAV cooperative task allocation, the system comprising:

[0115] Setting unit, used to define the multi-UAV cooperative task allocation problem as ;

[0116] The first calculation unit is used to solve the optimal control strategy for the multi-UAV cooperative task allocation problem: the optimal control strategy is obtained by weighting the energy loss function, and solving the optimal control strategy is equivalent to solving the minimum value problem of the weighted sum of energy losses of all UAVs; the weighted multi-UAV cooperative task allocation problem is ; Through the stabilization control gain matrix Convert to ; According to the Lyapunov stability theorem Equivalent conversion to ;

[0117] The second calculation unit is based on the original dual theory to solve Dual optimization problem: Using the original dual method to transform the non-convex optimization problem Equivalent transformation to convex dual optimization problem Solve;

[0118] The third computing unit uses Q-function to solve the convex dual optimization problem, and based on Schur complement theory, the convex dual optimization problem is equivalently transformed into a semi-positive programming problem: the KKT condition is used to derive the Q-function parameters and The equivalence relationship between Lagrange multipliers in the equation is used to solve the convex dual optimization problem using Q-functions. ; Using Schur's complement lemma, the convex dual optimization problem Transformed into a semidefinite programming problem Solve;

[0119] The fourth computational unit, based on the properties of matrix congruence, transforms the semi-positive definite programming problem into a model-free semi-positive definite programming problem: Equivalent transformation to model-free semidefinite programming problem Solve;

[0120] The fifth calculation unit uses the solver to solve the problem and obtain the optimal control strategy for the multi-UAV cooperative task allocation problem: The optimal Q-function parameters , determine the optimal feedback gain matrix , we get the optimal decision for multi-UAV cooperative task allocation problem , computing drones The minimum value of the energy loss function , we obtain the optimal solution to the multi-UAV cooperative task allocation problem, i.e. the minimum energy loss of all UAVs;

[0121] Control unit, by changing the weight coefficient , repeatedly execute the first to fifth calculation units to obtain the optimal energy loss function boundary, that is, the optimal solution to all multi-UAV cooperative task allocation problems.

[0122] To achieve the above-mentioned purpose, the third aspect of the present application provides a computer-readable storage medium storing a computer program, characterized in that when the computer program is executed by a processor, it is used to implement the method as described above.

[0123] After adopting the above technical solution, this application has the following beneficial effects compared with the prior art:

[0124] This application fully combines the advantages of the primal-dual method and semi-definite programming, and uses the superior learning ability of Q-learning to effectively solve the UAV task allocation problem; this application only needs to collect a small amount of data, and does not require an accurate dynamic model and a large amount of data to obtain the optimal strategy for multi-UAV cooperative task allocation; this application minimizes the energy loss of UAVs without increasing the energy loss of other UAVs, improves the efficiency of multi-UAV collaborative operations, and reduces the energy loss of multiple UAVs.

[0125] The specific implementation methods of the present application are further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0126] The accompanying drawings are part of this application and are used to provide a further understanding of this application. The illustrative embodiments of this application and their descriptions are used to explain this application but do not constitute an undue limitation of this application. Obviously, the drawings described below are only some embodiments. For those of ordinary skill in the art, other drawings can be derived from these drawings without inventive effort.

[0127] In the attached figure:

[0128] Figure 1 Schematic diagram of the process of multi-UAV cooperative task allocation method in this specific implementation method;

[0129] Figure 2 This is a schematic diagram of multi-UAV cooperative task allocation in this specific implementation method;

[0130] Figure 3 is a graph showing the number of remaining tasks for the UAV at time k in this specific implementation;

[0131] Figure 4 This is the control strategy diagram made by the UAV at time k in this specific implementation method;

[0132] Figure 5 This is the optimal control strategy boundary diagram for the multi-UAV cooperative task allocation problem in this specific implementation method;

[0133] Figure 6 Schematic diagram of the structure of the multi-UAV cooperative task allocation system in this specific implementation method. DETAILED DESCRIPTION

[0134] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. The following embodiments are used to illustrate the present application but are not used to limit the scope of the present application.

[0135] See Figure 1-Figure 5 , the present application provides a method for multi-UAV cooperative task allocation, comprising the following steps:

[0136] S1. Define the multi-UAV cooperative task allocation problem as ;

[0137] S2. Solve the optimal control strategy for multi-UAV cooperative task allocation problem:

[0138] The optimal control strategy is obtained by weighting the energy loss function, and solving the optimal control strategy is equivalent to solving the problem of minimizing the weighted sum of energy losses of all UAVs;

[0139] By stabilizing the control gain matrix Convert to ; According to the Lyapunov stability theorem Equivalent conversion to ;

[0140] S3. Solution based on primal-dual theory The dual optimization problem is:

[0141] Using the primal-dual method, the non-convex optimization problem Equivalent transformation to convex dual optimization problem Solve;

[0142] S4. Based on Schur complement theory, the convex dual optimization problem is equivalently transformed into a semi-positive programming problem:

[0143] Using Schur's complement lemma, the convex dual optimization problem Transformed into a semidefinite programming problem Solve;

[0144] S5. Based on the properties of matrix congruence, the semi-positive definite programming problem is transformed into a model-free semi-positive definite programming problem:

[0145] Semidefinite programming problem Equivalent transformation to model-free semidefinite programming problem Solve;

[0146] S6. Solve the problem using the solver to obtain the optimal control strategy for the multi-UAV cooperative task allocation problem:

[0147] calculate The optimal Q-function parameters , determine the optimal feedback gain matrix , we get the optimal decision for multi-UAV cooperative task allocation problem , computing drones The minimum value of the energy loss function , we obtain the optimal solution to the multi-UAV cooperative task allocation problem, i.e. the minimum energy loss of all UAVs;

[0148] S7. By changing the weight coefficient , repeat S2-S6 to obtain the boundary of the UAV cooperative task allocation problem, that is, the optimal solution of all multi-UAV cooperative task allocation problems.

[0149] It is worth noting that this application expands the task allocation control of a single drone to the cooperative task allocation control of multiple drones. When multiple drones work together, the energy loss of other drones is taken into consideration while ensuring the completion of the task. The energy loss of a single drone is minimized as much as possible without increasing the energy loss of other drones.

[0150] It should be noted that the multi-UAV cooperative task allocation method in this embodiment is executed by a multi-UAV cooperative task allocation device, which can be an electronic device, a component of an electronic device, an integrated circuit, or a chip. The electronic device can be a mobile electronic device or a non-mobile electronic device. Exemplary mobile electronic devices include mobile phones, tablet computers, laptop computers, PDAs, in-vehicle electronic devices, wearable devices, etc., while non-mobile electronic devices include servers and personal computers, etc., although this application does not specifically limit these. The following describes the multi-UAV cooperative task allocation method in this embodiment, using a server as an example.

[0151] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the embodiments of this application, the meaning of "plurality" is two or more, unless otherwise clearly specified.

[0152] In a feasible implementation, the multi-UAV cooperative task allocation problem is defined in S1 as , including: the number of drones is ,definition A collection of numbers for all drones, a single drone , exist The control strategy made at each moment is expressed as , control the drone to complete or assist in completing certain tasks; all drones in The number of remaining tasks at time is expressed as , the initial number of tasks is expressed as ; Represents a single drone The energy loss is related to the control decision of the UAV and the number of remaining tasks; then the cooperative task allocation problem of multiple UAVs can be expressed as:

[0153] ;

[0154] (3);

[0155] (4);

[0156] in, Indicates drone The infinite time domain original problem, represents linear quadratic, Indicates drone of energy loss, represents the control strategy for multi-UAV cooperative task allocation problem before considering the control gain, represents the initial number of tasks, represents the k moment, i represents the number of the drone, represents the number of remaining tasks for all drones at time k, represents transpose, Indicates drone The quadratic state weight matrix of energy loss, Indicates the drone before considering the control gain exist The control strategy at all times, Indicates the drone before considering the control gain exist The control strategy at all times, Indicates drone The energy loss of the quadratic state input weight matrix, Represents the set of numbers of all drones, N represents the number of drones, Represents constraints, Indicates that all drones are The number of remaining tasks at time A and denote the state transfer matrix of the system and the control input matrix of UAV i, respectively. Indicates the number of remaining tasks for all drones at the initial moment, Represents the real number field dimensional Euclidean space. and Distributed by blocks, it can be expressed as and ,in 、 、 Respectively 1st, 2nd, and 3rd blocks distributed by block Block matrix, 、 、 Respectively 1st, 2nd, and 3rd blocks distributed by block Block matrix, express For the convenience of representation, let , , ,in, 、 、 They represent the 1st, 2nd, and A drone in The control strategy at all times, Represents the secondary input weight matrix The diagonal matrix of Respectively represent the 1st, 2nd, The quadratic state input weight matrix of the energy consumption of the UAV, represents a diagonal matrix, represents the control input matrix of the system, Respectively represent the 1st, 2nd, The control input matrix of the UAV.

[0157] The multi-UAV cooperative task allocation problem can be rewritten as:

[0158] ;

[0159] (3);

[0160] (4);

[0161] in, Indicates the rewritten drone of energy loss.

[0162] For each drone , The feasible control strategy is expressed as ,in Indicates drone The feasible control strategy space of represents the feasible control strategy space. Then the joint feasible control strategy of all UAVs can be expressed as ,in represents the joint control strategy space of all UAVs, Variables representing the space of feasible control strategies.

[0163] When there is no other joint control strategy Make holds, and at least one inequality holds strictly, then It is called Pareto optimal strategy, which is the optimal control strategy for multi-UAV cooperative task allocation problem. It is called the Pareto optimal solution, that is, the minimum energy loss of all drones without increasing the energy loss of other drones. All Pareto optimal solutions constitute the Pareto frontier.

[0164] As a specific implementation method, the optimal control strategy for solving the multi-UAV cooperative task allocation problem in S2 includes: represents the weight coefficient, because , , through derivation and proof, we can get the feasible joint control strategy space and drone energy consumption It is convex, which shows that the minimum value of the weighted sum of energy consumption of all UAVs is equivalent to the Pareto optimal strategy, that is, the optimal control strategy for the multi-UAV cooperative task allocation problem. Consider the minimum value problem of the weighted sum of energy consumption of all UAVs, which can be expressed as:

[0165] ;

[0166] (5);

[0167] ;

[0168] in, Represents the infinite time domain original problem after all UAVs are weighted, represents the weighted energy loss of all drones, , Represent the weighted secondary state weight matrix and secondary state input matrix of all UAVs, Represents each drone The weight coefficient of the assignment.

[0169] In this application, when the objective function and control strategy space are convex, the weighted method can equivalently obtain the optimal control strategy for the multi-UAV cooperative task allocation problem, namely the Pareto optimal strategy, and can further obtain the minimum energy loss of all UAVs, namely the Pareto optimal solution.

[0170] In one feasible implementation, the stabilization control gain matrix is ​​used in S2 to Convert to ; According to the Lyapunov stability theorem Equivalent conversion to ;include:

[0171] Assumption 1: Formula (4) is stabilizable;

[0172] Assumption 2: For all It is entirely appreciable;

[0173] consider in ,in represents the control strategy for multi-UAV cooperative task allocation, represents the control gain matrix;

[0174] Under the condition of assumption 1, we define , that is, in The number of remaining tasks of the drone can eventually be 0

[0175] make Express formula (4) from The initial solution, then Expressed as:

[0176] ;

[0177] (6);

[0178] Formula (6) Formula (4);

[0179] in, Represents the infinite time domain original problem after all UAVs are weighted, represents the linear quadratic after considering the control gain, Indicates The weighted energy loss of all drones under the action, represents the control gain matrix, represents the diagonal matrix combination of the weighted quadratic weight matrix, represents the weighted quadratic state weight matrix of all UAVs, represents the weighted secondary input weight matrix of all UAVs, represents the control strategy for multi-UAV cooperative task allocation, Represents constraints, Represents the real number field dimensional Euclidean space;

[0180] Because the stabilizing feedback control gain matrix is is an open set and non-convex, so is a non-convex problem. For formula (4), assuming that satisfy ,in Indicates The initial number of remaining tasks under different circumstances, Represents the outer product matrix of the initial task. Note that for different initial remaining tasks Different energy loss minima can be generated ,but and is irrelevant, so for any , Expressed as:

[0181] (7);

[0182] in, represents the optimal control gain matrix, express The cumulative sum of the weighted UAV energy consumption under different situations; n represents finding the independent variable that makes the function achieve the minimum value;

[0183] For any control gain matrix , Expressed as ,here represents the additional variable of the UAV’s energy consumption, It represents the combination matrix of the remaining task state and the coefficient matrix of the joint control strategy and the control gain matrix. Satisfies the Lyapunov equation , according to the Lyapunov stability theorem, if and only if the Lyapunov equation for every There is a unique solution for every choice Sometimes, there are , that is, formula (4) in the control feedback gain matrix The lower is calm, therefore, Equivalent to , then Equivalently converted to:

[0184] ;

[0185] ;

[0186] ;

[0187] (8);

[0188] in, Represents the infinite time domain original problem after all UAVs are weighted, Indicates that new variables are considered The linear quadratic, It means The minimum value of the cumulative sum of the weighted UAV energy consumption under different conditions, represents the set of stabilizing feedback control gain matrices, represents the spectral radius of the matrix, The function represents the additional variable of energy loss, represents the additional variable of the UAV’s energy consumption, It represents the combination matrix of the remaining task state and the coefficient matrix of the joint control strategy and the control gain matrix. express dimensional identity matrix, represents the transpose of the matrix, represents the trace of the matrix.

[0189] It should be noted that formula (8) is nonlinear, so This is still a non-convex optimization problem. In the UAV cooperative task allocation problem, non-convexity can lead to unstable control strategies, unpredictable paths, and even system safety risks. Therefore, while non-convexity is closer to reality, it still requires extreme caution in engineering practice. The next step is to convert the non-convex problem into a convex one. This means that the UAV energy consumption is smooth, controllable, and predictable, making the system easier to optimize, coordinate, and control in real time.

[0190] In one feasible implementation, S3 uses the primal-dual method to transform the non-convex optimization problem into Equivalent transformation to convex dual optimization problem Solve, including:

[0191] Consider the original problem based on the original dual theory The dual optimization problem of and express The constrained Lagrange operator is then expressed as:

[0192] (9);

[0193] in, represents the Lagrange equation;

[0194] The corresponding dual optimization problem is expressed as

[0195] (10);

[0196] in, represents the infimum;

[0197] The first term of formula (9) is used to ensure boundedness and , you must have:

[0198] (11);

[0199] definition ,in , and for The second term of formula (9) is written as:

[0200] (12);

[0201] if , for formula (12) Taking the partial derivative, we get , substituting into formula (11) and formula (12) we get:

[0202] (13);

[0203] (14);

[0204] Therefore, the energy consumption of the UAV in the dual optimization problem is expressed as:

[0205] (15);

[0206] in, and for The sub-matrix of represents the outer product matrix of the initial task, represents the trace of the matrix, represents the inverse of a matrix; Represents the transpose of a matrix;

[0207] definition Make

[0208] (16);

[0209] in, represents the slack extra variables of the drone, Indicates all The energy loss of the UAV is expressed as a set of dimensional symmetric matrices:

[0210] (17);

[0211] make and They represent the optimal solutions of formula (15) and formula (17), namely The optimal Lagrange operator of the constraint and the optimal relaxation additional variable of the UAV are derived by formula (16) and formula (17) satisfy:

[0212] (18);

[0213] in, 、 、 Denote the optimal Lagrange multiplier The upper left block matrix, the upper right block matrix and the lower right block matrix;

[0214] Then, the dual optimization problem (10) is expressed as:

[0215] ;

[0216] ;

[0217] ;

[0218] ;

[0219] (19);

[0220] in, represents the dual problem of infinite time domain after all UAVs are weighted, represents the slack extra variables of the drone, , and for The sub-matrix of , Represents the energy consumption of the drone.

[0221] As a specific implementation method, S4 uses Q-function to solve the convex dual optimization problem, and based on Schur complement theory, the convex dual optimization problem is equivalently transformed into a semi-positive programming problem; including deriving The explicit structure of Substitute into the Q-function definition and make the association explicit With the Lagrange operator, using The convexity of , transforms the dual problem into an optimization problem of the Q-function parameters; specifically including:

[0222] because is convex, so the KKT condition gives The optimality of and for The Lagrange multiplier of , the corresponding Lagrange function is expressed as:

[0223] (20);

[0224] Use well-posedness conditions, complementary slackness, and dual feasibility to ensure Optimality:

[0225] Among them, the dual feasibility is expressed as:

[0226] (twenty one);

[0227] Complementary slackness is expressed as:

[0228] ;

[0229] (twenty two);

[0230] ;

[0231] The well-posedness condition is expressed as:

[0232] (twenty three);

[0233] in, 、 Respectively represent the Lagrange function about and The partial derivative of .

[0234] set up and Indicates that there may be other The optimal Lagrange operator of the constraints and the optimal relaxation additional variables of the UAV;

[0235] Bundle Substituting into the left side of formula (16), we can get:

[0236] (twenty four);

[0237] in, 、 、 Indicates another possible Lagrange multiplier The upper left block matrix, the upper right block matrix and the lower right block matrix, and is the algebraic Riccati equation The solution;

[0238] Bundle Substituting into the left side of formula (13), we can get:

[0239] (25);

[0240] This shows that formula (22) does not require the Lagrange multiplier and It can be established under any requirements;

[0241] In addition, if , then the Lagrange multiplier is zero;

[0242] Let matrix ,So It can be expressed as:

[0243] (26);

[0244] in, and represents the UAV auxiliary matrix, express -dimensional identity matrix;

[0245] Therefore, formula (23) is expressed as:

[0246] ;

[0247] ;

[0248] ;

[0249] (27);

[0250] in, Respectively represent the Lagrange function about , and The partial derivative of

[0251] Based on formula (27), it can be deduced that satisfy:

[0252] ;

[0253] (28);

[0254] set up , , and express The sub-matrix of , then formula (28) can be expressed as:

[0255] ;

[0256] (29);

[0257] Substituting formula (29) into the second equation of formula (27), we can obtain:

[0258] (30);

[0259] According to the Lyapunov stability theorem, It can be seen that formula (4) has the possible optimal stabilization control gain , if and only if there exists a unique and So that formula (30) holds true;

[0260] This can be done by setting:

[0261] ;

[0262] ;

[0263] (31);

[0264] therefore, and Not related, and It can be expressed as the optimal parameters of the optimal Q-function, and the optimal Q-function is defined as:

[0265] (32);

[0266] in, represents the initial joint control strategy of the UAV, represents the optimal Q-function, represents the optimal algebraic Riccati solution, represents the minimum value of energy loss after weighting of all UAVs;

[0267] (33);

[0268] in, represents the quadratic input weight matrix after weighting of the UAV;

[0269] Then the dual optimization problem The energy loss of the UAV can be expressed as:

[0270] (34);

[0271] Furthermore, by using Schur complement theory, formula (13) and formula (16) can be expressed as:

[0272] (35);

[0273] (36);

[0274] So can be equivalently converted to:

[0275] ;

[0276] ;

[0277] ;

[0278] (37);

[0279] It should be noted that It can be solved efficiently by multiple solvers, such as CVX. In addition, SDP can efficiently solve large-scale problems and is known for its robustness in the face of uncertainty and noise. It can be combined with other optimization techniques to solve more complex tasks.

[0280] In one feasible implementation, the optimal control strategy for the multi-UAV cooperative task allocation problem is obtained by solving the problem through a solver in S6, including:

[0281] Assumption 2: For all It is entirely appreciable;

[0282] definition for:

[0283] (38);

[0284] in, Indicates the time of first collection. Indicates the status of the first collection. Indicates the status of the second collection. Represents the input of the first collection, Represents the input of the second collection, Indicates the The status of the collection, Indicates the The input of the acquisition, represents the matrix of collected data, Represents the real number field Violet's space;

[0285] Based on formula (38) for:

[0286] (39);

[0287] in, represents the matrix of collected data, represents the number of samples collected, Represents the real number field dimensional Euclidean space, Indicates the status of the third collection. Indicates the The status of the acquisition;

[0288] Based on the matrix congruence property, if the matrix have The column rank of can be multiplied by and , and using Schur complement theory we get:

[0289] (40);

[0290] in, 、 Respectively and The dimension of the matrix;

[0291] Then the semidefinite programming It can be equivalently transformed into a model-free semidefinite programming problem:

[0292] ;

[0293] ;

[0294] ;

[0295] (41);

[0296] exist The number of samples collected Must be no less than the sum of the number of control inputs and states To ensure that the matrix The column rank of Therefore, it is necessary to collect samples, of which In addition, due to the linear relationship between the state and input between the current moment and the previous moment, the definition of The input samples on must be The continuous excitation (PE) of the order and satisfy Therefore, to ensure the PE condition, a small Gaussian white noise is added to the collected control input.

[0297] Under the condition of Assumption 2, by collecting enough state and control input samples, we construct the and in formula (39) , and needs to meet the PE condition, use the solver CVX to solve The optimal Q-function parameters defined in , and obtain the optimal control gain matrix for:

[0298] (42);

[0299] Finally, we get the optimal strategy for UAV cooperative task allocation problem (Pareto optimal strategy) is: (43);

[0300] in, Indicates that each drone The optimal control gain matrix is 、 、 Indicates 1st, 2nd, The optimal control gain matrix of a UAV;

[0301] For a given weight coefficient , when the PE condition is met, through formula (38) and in formula (39) collect Sample, get each drone The minimum energy loss is:

[0302] (44);

[0303] in, Represents the set of conditions that the weight coefficient must meet, Respectively represent the 1st, 2nd, The weight coefficient of the drone allocation;

[0304] The optimal solution of the optimal control strategy is further obtained as:

[0305] (45);

[0306] Among them, the optimal solution of the optimal control strategy represents the minimum energy loss of all drones. 、 、 Indicates 1st, 2nd, The energy loss of the drone is minimized.

[0307] The above embodiment combines the advantages of the primal-dual method and semidefinite programming, and takes advantage of the superior learning ability of Q-learning. First, the primal-dual method is used to equivalently transform the non-convex optimization problem into a convex dual optimization problem. Then, the Karush-Kuhn-Tucker (KKT) condition is used to derive the equivalence relationship between the Q-function parameters and the Lagrange multipliers in the dual problem, which shows that the Q-function can be used to solve the convex dual optimization problem. In addition, with the help of Schur complement theory, the dual problem is equivalently transformed into a semidefinite programming problem. Then, with the help of the properties of matrix congruence, the semidefinite programming problem can be transformed into a model-free semidefinite programming problem, which can be efficiently solved using the CVX solver. Finally, the optimal control strategy for the multi-UAV cooperative task allocation problem is obtained.

[0308] As a specific implementation, S7, by changing The Pareto frontier is obtained by taking the value of , which further proves that the energy loss of the UAV can be minimized without increasing the energy loss of other UAVs.

[0309] Figure 2 This is a schematic diagram of the UAV cooperative task allocation. Figure 2 The figure shows the task allocation of the first and second drones, that is, N=2, where Task 1, Task 2, Task 3 and Task 4 represent target reconnaissance mission, cargo transportation mission, rescue operation mission and equipment inspection mission respectively, that is, the initial number of tasks z=4.

[0310] Figure 3 This is the simulation verification of the proposed solution based on this application. The horizontal axis represents the time , the vertical axis represents the number of drones in The number of remaining tasks at the moment is Let n=2 be expressed as block distribution It can be seen that as time increases, the number of remaining tasks of the drone eventually converges to 0.

[0311] Figure 4 This is a simulation verification based on the proposed solution. The horizontal axis represents the time k, and the vertical axis represents the time when the first and second drones are in the The control strategy at this moment is and Let n=2 and m=4 represent the block distribution ,and It can be seen that due to the influence of detection noise, the control strategy of the UAV is fluctuating at the beginning, but as the number of remaining tasks of the UAV converges to 0, the control strategy of the UAV also converges to 0 in the end.

[0312] Figure 5This is a simulation verification based on the solution proposed in this application. The horizontal axis represents the energy loss of drone 1, and the vertical axis represents the energy loss of drone 2. and That is and It can be seen that the energy consumption of the UAV can be minimized without increasing the energy consumption of other UAVs.

[0313] See Figure 6 Based on the same inventive concept, the present application also provides a system for multi-UAV cooperative task allocation, the system comprising:

[0314] Setting unit, used to define the multi-UAV cooperative task allocation problem as ;

[0315] The first calculation unit is used to solve the optimal control strategy for the multi-UAV cooperative task allocation problem: the optimal control strategy is obtained by weighting the energy loss function, and solving the optimal control strategy is equivalent to solving the minimum value problem of the weighted sum of energy losses of all UAVs; the weighted multi-UAV cooperative task allocation problem is ; Through the stabilization control gain matrix Convert to ; According to the Lyapunov stability theorem Equivalent conversion to ;

[0316] The second calculation unit is based on the original dual theory to solve Dual optimization problem: Using the original dual method to transform the non-convex optimization problem Equivalent transformation to convex dual optimization problem Solve;

[0317] The third computing unit uses Q-function to solve the convex dual optimization problem, and based on Schur complement theory, the convex dual optimization problem is equivalently transformed into a semi-positive programming problem: the KKT condition is used to derive the Q-function parameters and The equivalence relationship between Lagrange multipliers in the equation is used to solve the convex dual optimization problem using Q-functions. ; Using Schur's complement lemma, the convex dual optimization problem Transformed into a semidefinite programming problem Solve;

[0318] The fourth computational unit, based on the properties of matrix congruence, transforms the semi-positive definite programming problem into a model-free semi-positive definite programming problem: Equivalent transformation to model-free semidefinite programming problem Solve;

[0319] The fifth calculation unit uses the solver to solve the problem and obtain the optimal control strategy for the multi-UAV cooperative task allocation problem: The optimal Q-function parameters , determine the optimal feedback gain matrix , we get the optimal decision for multi-UAV cooperative task allocation problem , computing drones The minimum value of the energy loss function , we obtain the optimal solution to the multi-UAV cooperative task allocation problem, i.e. the minimum energy loss of all UAVs;

[0320] Control unit, by changing the weight coefficient , repeatedly execute the first to fifth calculation units to obtain the optimal energy loss function boundary, that is, the optimal solution to all multi-UAV cooperative task allocation problems.

[0321] Based on the same inventive concept, the present application also provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the method described above is implemented.

[0322] The program product of the present application for implementing the above-mentioned method may be a portable compact disk read-only memory and include program code, and may be run on a terminal device, such as a personal computer. However, the program product of the present application is not limited thereto. In the present application, a readable storage medium may be any tangible medium containing or storing a program, which may be used by or in conjunction with an instruction execution system, apparatus, or device.

[0323] It should be noted that a computer-readable storage medium may include a data signal propagated in baseband or as part of a carrier wave, which carries readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable storage medium may also be any readable medium other than a readable storage medium, which may send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium may be transmitted using any appropriate medium, including but not limited to wireless, wired, optical cable, RF, etc., or any suitable combination thereof.

[0324] The above is only a preferred embodiment of the present application and does not constitute any form of limitation to the present application. Although the present application has been disclosed as above with preferred embodiments, it is not intended to limit the present application. Any technician familiar with the present application can make some changes or modifications to equivalent embodiments with equivalent changes using the technical content suggested above without departing from the scope of the technical solution of the present application. The implementation schemes in the above embodiments can also be further combined or replaced. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present application that do not depart from the content of the technical solution of the present application still fall within the scope of the solution of the present application.

Claims

1. A multi-UAV cooperative task allocation method, characterized in that: The following steps are involved: S1. Define the multi-UAV cooperative task allocation problem as ; in, Denotes the infinite time domain original problem of UAV i, represents linear quadratic; S2. Optimal control strategy for solving multi-UAV cooperative task allocation problem: The optimal control strategy is obtained by weighting the energy loss function, and solving the optimal control strategy is equivalent to solving the problem of minimizing the weighted sum of energy losses of all drones; The weighted multi-UAV cooperative task allocation problem is: ; Through the stabilization control gain matrix Convert to ; According to the Lyapunov stability theorem Equivalent conversion to ; in, Represents the infinite time domain original problem after all UAVs are weighted, represents the linear quadratic after considering the control gain, Indicates that new variables are considered Linear quadratic of S3. Solution based on primal-dual theory The dual optimization problem is: Using the primal-dual method, the non-convex optimization problem Equivalent transformation to convex dual optimization problem Solve; in, Represent the dual problem in infinite time domain after all UAVs are weighted; S4. Use Q-function to solve the convex dual optimization problem, and based on Schur complement theory, convert the convex dual optimization problem into a semi-definite programming problem: The Q-function parameters and The equivalence relationship between Lagrange multipliers in the equation is used to solve the convex dual optimization problem using Q-functions. ; Using Schur's complement lemma, the convex dual optimization problem Transformed into a semidefinite programming problem Solve; in, represents a semi-positive definite program; S5. Based on the properties of matrix congruence, the semi-positive definite programming problem is transformed into a model-free semi-positive definite programming problem: Semidefinite programming problem Equivalent transformation to model-free semidefinite programming problem Solve; in, Indicates no model; S6. Solve the problem using the solver to obtain the optimal control strategy for the multi-UAV cooperative task allocation problem: Specifically include: Assumption 2: For all It is entirely appreciable; Where A represents the state transition matrix of the system, The quadratic state weight matrix represents the energy loss of UAV i, where i represents the number of the UAV. Represents the set of numbers of all drones; Under the condition of assumption 2, use the solver CVX to solve The optimal Q-function parameters defined in , and obtain the optimal control gain matrix for: ； in, 、 represent the optimal Q-function parameters respectively The lower right block matrix and the upper right block matrix of ; Finally, we get the optimal strategy for UAV cooperative task allocation problem for: ； in, It means finding the independent variable that makes the function achieve the minimum value. represents the energy consumption of UAV i, represents the control strategy for multi-UAV cooperative task allocation problem before considering the control gain, represents the joint control strategy space of all UAVs, N represents the number of UAVs, represents the weight coefficient assigned to each UAV i, z represents the number of initial tasks, 、 、 Indicates 1st, 2nd, The optimal control gain matrix of a UAV, represents the number of remaining tasks for all drones at time k, i represents the number of drones, represents transpose; For a given weight coefficient , when the PE condition is met, the matrix of collected data And collect the matrix of the next moment state Collect the number of remaining tasks for all drones at time k , the minimum energy loss of each UAV i is obtained as: ； in, Represents the set of conditions that the weight coefficient must meet, Respectively represent the 1st, 2nd, The weight coefficient of the drone allocation, represents the quadratic input weight matrix of the energy loss of UAV i, k represents the kth moment; The optimal solution of the optimal control strategy is further obtained as: ； Among them, the optimal solution of the optimal control strategy represents the minimum energy loss of all drones. 、 、 Indicates 1st, 2nd, Minimum energy consumption of a UAV; S7. By changing the weight coefficient , repeat S2-S6 to obtain the boundary of the UAV cooperative task allocation problem, that is, the optimal solution of all multi-UAV cooperative task allocation problems.

2. The method according to claim 1, characterized in that The multi-UAV cooperative task allocation problem is defined in S1 as , including: The cooperative task allocation problem of multiple UAVs is expressed as: ； ； ； in, represents the energy consumption of UAV i, It represents the control strategy of multi-UAV cooperative task allocation problem before considering the control gain, i and j represent the UAV numbers, represents the number of remaining tasks for all drones at time k, represents transpose, The quadratic state weight matrix representing the energy consumption of UAV i, represents the control strategy of UAV i at time k before considering the control gain, represents the control strategy of UAV j at time k before considering the control gain, The quadratic state input weight matrix representing the energy loss of UAV i, Represents the set of numbers of all drones, N represents the number of drones, Represents constraints, Indicates that all drones are The number of remaining tasks at the moment, A and denote the state transfer matrix of the system and the control input matrix of UAV i, respectively. Indicates the number of remaining tasks for all drones at the initial moment, Represents the n-dimensional Euclidean space over the real number field.

3. The method according to claim 2, characterized in that The optimal control strategy for solving the multi-UAV cooperative task allocation problem in S2 includes: solving the minimum value of the weighted sum of energy losses of all UAVs expressed as: ； ； in, represents the minimum value of the weighted sum of energy consumption of all UAVs, , Represent the weighted quadratic state weight matrix and quadratic input weight matrix of all UAVs, The quadratic state weight matrix representing the energy consumption of UAV i, The quadratic input weight matrix representing the energy consumption of UAV i, represents the weight coefficient assigned to each UAV i, and B represents the control input matrix of the UAV.

4. The method according to claim 3, characterized in that In S2, the stabilization control gain matrix is ​​used to Convert to ; According to the Lyapunov stability theorem Equivalent conversion to ;include: Assumption 1: Formula (4) is stabilizable; definition ,make Express formula (4) from The initial solution, then Expressed as: ； （6）； Formula (6) Formula (4); in, Indicates The weighted energy loss of all drones under the action, represents the control gain matrix, represents the set of stabilizing feedback control gain matrices, represents the spectral radius of the matrix, represents the diagonal matrix combination of the weighted quadratic weight matrix, represents the weighted quadratic state weight matrix of all UAVs, represents the weighted secondary input weight matrix of all UAVs, represents the control strategy for multi-UAV cooperative task allocation, Represents constraints; According to the Lyapunov stability theorem, the Lyapunov equation is There is a unique solution for every choice Sometimes, there are , that is, formula (4) in the control feedback gain matrix The lower is calm, therefore, Equivalent to ,Will Equivalently converted to: ； ； ； ； in, It represents the minimum value of the cumulative sum of the weighted UAV energy consumption under r different situations, and Z represents the outer product matrix of the initial task. The function represents the additional variable of energy loss, represents the additional variable of the UAV’s energy consumption, It represents the combination matrix of the remaining task state and the coefficient matrix of the joint control strategy and the control gain matrix. express -dimensional identity matrix, represents the transpose of the matrix, represents the trace of the matrix.

5. The method according to claim 4, characterized in that In S3, the primal-dual method is used to transform the non-convex optimization problem Equivalent transformation to convex dual optimization problem Solve, including: make and express The constrained Lagrange multiplier of , then the Lagrange equation is expressed as ; The corresponding dual optimization problem is expressed as: ； in, represents the infimum; The energy loss of the UAV in the dual optimization problem is expressed as: ； in, and for The sub-matrix of represents the trace of the matrix, represents the inverse of a matrix; Represents the transpose of a matrix; definition Make ； in, represents the slack extra variables of the drone, represents the set of all n-dimensional symmetric matrices; The energy loss of the drone is expressed as: ； make and They represent the optimal solutions of formula (15) and formula (17), namely The optimal Q-function parameters of the constraints and the optimal relaxation additional variables of the UAV are derived through formulas (16) and (17) satisfy: ； in, 、 、 Denote the optimal Q-function parameters The upper left block matrix, the upper right block matrix and the lower right block matrix, and denote the optimal Q-function parameters and the optimal relaxation extra variables of the UAV, respectively; The convex dual optimization problem is expressed as: ； ； ； ； ； in, represents the slack extra variables of the drone, and for The sub-matrix of , Represents the energy consumption of the drone.

6. The method according to claim 5, characterized in that In S4, Q-function is used to solve the convex dual optimization problem, and the convex dual optimization problem is equivalently transformed into a semi-positive programming problem based on Schur complement theory; including the derivation of KKT conditions The explicit structure of Substitute into the Q-function definition and make the association explicit With Lagrange multipliers, using The convexity of , transforms the dual problem into an optimization problem of the Q-function parameters; specifically including: Obtained through KKT conditions Optimality; set up and for The Lagrange multiplier, the corresponding Lagrange function is expressed as ; According to the Lyapunov stability theorem, the Lagrange multiplier Designed to be with stabilizing control gain The associated matrix is ​​expressed as: ； ； ； in, represents the optimal stabilizing control gain, 、 Indicates another possible Lagrange multiplier The upper left block matrix of represents the identity matrix, express submatrix of ; pass represents the optimal Q-function parameter, and the optimal Q-function is defined as: ； in, represents the initial joint control strategy of UAVs, z represents the number of initial tasks, and x represents the number of remaining tasks for all UAVs at a certain moment. represents the optimal Q-function, represents the solution of the optimal algebraic Riccati equation, represents the minimum value of energy loss after weighting of all UAVs; ； in, represents the quadratic input weight matrix after weighting of the UAV; By using Schur complement theory, The equivalent conversion is: ； ； ； ； in, express energy consumption of drones.

7. The method according to claim 6, characterized in that S5 Semi-positive programming problem Equivalent transformation to model-free semidefinite programming problem Solve; include: definition , expressed as: ； in, Indicates the time of first collection. Indicates the status of the first collection. Indicates the status of the second collection. Represents the input of the first collection, Represents the input of the second collection, Indicates the The status of the collection, Indicates the The input of the acquisition, A matrix representing the collected data; Based on formula (38) , expressed as: ； in, Represents the matrix that collects the state of the next moment, Indicates the status of the third collection. Indicates the The state of the acquisition, B represents the control input matrix of the UAV; Based on the matrix congruence property, if the matrix have The column rank of can be multiplied by and , and using Schur complement theory we get: ； Among them, n and m represent and The dimension of the matrix; Semi-positive programming Equivalently transformed into a model-free semidefinite programming problem: ； ； ； 。 8.Multi-UAV cooperative task allocation system, characterized by: The system comprises: Setting unit, used to define the multi-UAV cooperative task allocation problem as ; in, Denotes the infinite time domain original problem of UAV i, represents linear quadratic; The first calculation unit is used to solve the optimal control strategy for the multi-UAV cooperative task allocation problem: the optimal control strategy is obtained by weighting the energy loss function, and solving the optimal control strategy is equivalent to solving the minimum value problem of the weighted sum of energy losses of all UAVs; the weighted multi-UAV cooperative task allocation problem is ; Through the stabilization control gain matrix Convert to ; According to the Lyapunov stability theorem Equivalent conversion to ; in, Represents the infinite time domain original problem after all UAVs are weighted, represents the linear quadratic after considering the control gain, Indicates that new variables are considered Linear quadratic of The second calculation unit is based on the original dual theory to solve Dual optimization problem: Using the original dual method to transform the non-convex optimization problem Equivalent transformation to convex dual optimization problem Solve; in, Represent the dual problem in infinite time domain after all UAVs are weighted; The third computing unit uses Q-function to solve the convex dual optimization problem, and based on Schur complement theory, the convex dual optimization problem is equivalently transformed into a semi-positive programming problem: the KKT condition is used to derive the Q-function parameters and The equivalence relationship between Lagrange multipliers in the equation is used to solve the convex dual optimization problem using Q-functions. ; Using Schur's complement lemma, the convex dual optimization problem Transformed into a semidefinite programming problem Solve; in, represents a semi-positive definite program; The fourth computational unit, based on the properties of matrix congruence, transforms the semi-positive definite programming problem into a model-free semi-positive definite programming problem: Equivalent transformation to model-free semidefinite programming problem Solve; in, Indicates no model; The fifth computing unit uses the solver to solve the problem and obtain the optimal control strategy for the multi-UAV cooperative task allocation problem: Specifically include: Assumption 2: For all It is entirely appreciable; Where A represents the state transition matrix of the system, The quadratic state weight matrix represents the energy loss of UAV i, where i represents the number of the UAV. Represents the set of numbers of all drones; Under the condition of assumption 2, use the solver CVX to solve The optimal Q-function parameters defined in , and obtain the optimal control gain matrix for: ； in, 、 represent the optimal Q-function parameters respectively The lower right block matrix and the upper right block matrix of ; Finally, we get the optimal strategy for UAV cooperative task allocation problem for: ； in, It means finding the independent variable that makes the function achieve the minimum value. represents the control strategy for multi-UAV cooperative task allocation problem before considering the control gain, represents the joint control strategy space of all UAVs, N represents the number of UAVs, represents the weight coefficient assigned to each UAV i, z represents the number of initial tasks, 、 、 Indicates 1st, 2nd, The optimal control gain matrix of a UAV, represents the number of remaining tasks for all drones at time k, i represents the number of drones, represents transpose; For a given weight coefficient , when the PE condition is met, the matrix of collected data And collect the matrix of the next moment state Collect the number of remaining tasks for all drones at time k , the minimum energy loss of each UAV i is obtained as: ； in, Represents the set of conditions that the weight coefficient must meet, Respectively represent the 1st, 2nd, The weight coefficient of the drone allocation, represents the quadratic input weight matrix of the energy loss of UAV i, k represents the kth moment; The optimal solution of the optimal control strategy is further obtained as: ； Among them, the optimal solution of the optimal control strategy represents the minimum energy loss of all drones. 、 、 Indicates 1st, 2nd, Minimum energy consumption of a UAV; Control unit, by changing the weight coefficient , repeatedly execute the first to fifth calculation units to obtain the optimal energy loss function boundary, that is, the optimal solution to all multi-UAV cooperative task allocation problems.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, it is used to implement the method according to any one of claims 1 to 7.

Images