Multi-aircraft energy optimal cooperative guidance method under communication topology shear condition

Abstract

The invention discloses a multi-aircraft energy optimal cooperative guidance method under a communication topology shear condition. The method comprises the following steps: establishing a multi-aircraft cooperative guidance problem model; establishing a global optimal consistency protocol without considering communication constraints; by minimizing the Euclidean distance between a feasible set constrained by communication and a global optimal solution, an analytic near-optimal consistency protocol under the condition of uncertain communication topology is obtained; obtaining a multi-aircraft energy optimal cooperative guidance law under communication topology shear based on a near optimal distributed consistency protocol; and the aircraft flies based on the multi-aircraft energy optimal cooperative guidance law under communication topology shear. The method disclosed by the invention is less in energy consumption and higher in stability.

Description

Technical Field

[0001] This invention relates to a method for optimal energy cooperative guidance of multiple aircraft under communication topology shearing conditions, belonging to the field of aircraft control technology. Background Technology

[0002] Existing multi-vehicle cooperative guidance methods only focus on the convergence of flight time and do not consider optimality. This can lead to unnecessary maneuvers by multiple vehicles in the process of achieving flight time consistency, resulting in additional energy loss.

[0003] Furthermore, in the practical application of multi-aircraft systems, due to the limited communication distance between aircraft and the possibility of malfunctions, the continuous information exchange between aircraft in complex environments is easily interfered with. In other words, the communication topology between multiple aircraft may be switched, while most existing collaborative methods adopt fixed communication methods, which leads to a decrease in the stability of existing collaborative methods.

[0004] Therefore, it is necessary to conduct more in-depth research on existing aircraft cooperative guidance methods in order to solve the above problems. Summary of the Invention

[0005] To overcome the above problems, in-depth research was conducted, and a multi-vehicle energy-optimal cooperative guidance method under communication topology shear conditions was proposed, including the following steps:

[0006] S1. Establish a model for the cooperative guidance problem of multiple aircraft;

[0007] S2. Establish a globally optimal consensus protocol without considering communication constraints;

[0008] S3. By minimizing the Euclidean distance between the feasible set constrained by communication and the global optimal solution, an analytical near-optimal consensus protocol under communication topology uncertainty is obtained.

[0009] S4. Obtain the energy-optimal cooperative guidance law for multiple aircraft under communication topology shear based on a near-optimal distributed consensus protocol.

[0010] S5. The aircraft flies based on the multi-aircraft energy-optimal cooperative guidance law under communication topology shear.

[0011] In a preferred embodiment, in S1, the aircraft cooperative guidance problem model is established through the following sub-steps:

[0012] S11. Establish the equations of relative motion of multiple aircraft with respect to a single target;

[0013] S12. Set constraints to enable simultaneous interception of targets by multiple aircraft;

[0014] S13. Based on the constraints and relative motion equations, construct a model for the cooperative guidance problem of aircraft.

[0015] In a preferred embodiment, in S11, the equations of motion of the multiple aircraft relative to a single target are expressed as:

[0016]

[0017] in, This represents the distance between the i-th aircraft and the target. This represents the speed of the i-th aircraft. This represents the leading angle of the i-th aircraft. This represents the line-of-sight angle of the i-th aircraft. This represents the flight path angle of the i-th aircraft. Let represent the normal phase acceleration of the i-th aircraft.

[0018] In a preferred embodiment, in S13, the cooperative guidance problem model for the aircraft is represented as follows:

[0019]

[0020]

[0021]

[0022]

[0023]

[0024] in, Let n represent different aircraft, and n represent the total number of aircraft. Indicates the first The guidance time of the aircraft Indicates the first The constant parameters of the aircraft Indicates the first Control commands for the aircraft This represents the distance between the i-th aircraft and the target. This represents the leading angle of the i-th aircraft. This represents the guidance gain of the i-th aircraft. This represents the bias term for the i-th aircraft. For state variables, It is a constant diagonal matrix. For control commands.

[0025] In a preferred embodiment, S2 includes the following sub-steps:

[0026] S21. Based on the aircraft cooperative guidance problem model, establish the optimal consensus problem;

[0027] S22. Solve the optimal consensus problem to obtain the globally optimal solution;

[0028] S23. Based on the globally optimal solution, obtain the globally optimal consensus protocol.

[0029] In a preferred embodiment, in S21, the optimal consensus problem is expressed as:

[0030]

[0031] in, Indicates energy consumption. This indicates the guidance time when all aircraft arrive at the target simultaneously. Indicates the flight time of the aircraft. Represents a time variable. Parameters can be set. This represents the Laplace matrix.

[0032] In a preferred embodiment, in S22, the global optimal solution Represented as:

[0033]

[0034] in, This indicates the guidance time when all aircraft arrive at the target simultaneously. Indicates the flight time of the aircraft. Parameters can be set. Represents the Laplace matrix, This represents the Moore–Penrose pseudoinverse of the Laplace matrix.

[0035] In a preferred embodiment, in S23, the globally optimal consensus protocol is:

[0036]

[0037] In a preferred embodiment, in S3, the parsing near-optimal consensus protocol under the communication topology shear condition is:

[0038]

[0039] in, It is a set of weight coefficients. Let be the weighting coefficient of the i-th aircraft.

[0040] In a preferred embodiment, in S4, the multi-vehicle energy-optimal cooperative guidance law under communication topology shear is expressed as:

[0041]

[0042]

[0043] in, Let the i-th row of the Laplace matrix of the i-th aircraft be... It is a piecewise function. Let i be the guidance gain of the i-th aircraft. Let n be the distance between the nth aircraft and the target. Let be the leading angle of the nth aircraft. Let n be the remaining flight time of the nth aircraft. Let n be the speed of the nth aircraft. These are designable parameters.

[0044] The beneficial effects of this invention include:

[0045] 1) Cooperative guidance methods consume less energy;

[0046] 2) It is more effective and performs better under directed communication topology and communication topology shearing conditions. Attached Figure Description

[0047] Figure 1 This diagram illustrates a flow chart of a multi-vehicle energy-optimal cooperative guidance method under communication topology shearing conditions according to a preferred embodiment of the present invention. Figure 2 This diagram shows the communication connection switching topology between the aircraft in Example 1 and Comparative Example 1. Figure 3 The flight trajectory curve in Example 1 is shown; Figure 4 The flight trajectory curves in Comparative Example 1 are shown; Figure 5 The simulation results of the remaining flight time in Example 1 are shown; Figure 6 The simulation results of the remaining flight time in Comparative Example 1 are shown; Figure 7 The simulation results of the acceleration curves in Example 1 are shown; Figure 8 The simulation results of the acceleration curves in Comparative Example 1 are shown. Detailed Implementation

[0048] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Through these descriptions, the features and advantages of the present invention will become clearer and more apparent.

[0049] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

[0050] According to the present invention, a method for optimal energy cooperative guidance of multiple aircraft under communication topology shear conditions is provided, such as... Figure 1 As shown, it includes the following steps:

[0051] S1. Establish a model for the cooperative guidance problem of multiple aircraft;

[0052] S2. Establish a globally optimal consensus protocol without considering communication constraints;

[0053] S3. By minimizing the Euclidean distance between the feasible set constrained by communication and the global optimal solution, an analytical near-optimal consensus protocol under communication topology uncertainty is obtained.

[0054] S4. Obtain the energy-optimal cooperative guidance law for multiple aircraft under communication topology shear based on a near-optimal distributed consensus protocol.

[0055] S5. The aircraft flies based on the multi-aircraft energy-optimal cooperative guidance law under communication topology shear.

[0056] In S1, the model for the cooperative guidance problem of the aircraft is established through the following sub-steps:

[0057] S11. Establish the equations of relative motion of multiple aircraft with respect to a single target;

[0058] S12. Set constraints to enable simultaneous interception of targets by multiple aircraft;

[0059] S13. Based on the constraints and relative motion equations, construct a model for the cooperative guidance problem of aircraft.

[0060] In S11, the equations of motion of the multiple aircraft relative to a single target are expressed as follows:

[0061]

[0062] in, This represents the distance between the i-th aircraft and the target. This represents the speed of the i-th aircraft. This represents the leading angle of the i-th aircraft. This represents the line-of-sight angle of the i-th aircraft. This represents the flight path angle of the i-th aircraft. Let represent the normal phase acceleration of the i-th aircraft.

[0063] In S12, the constraints include end-point distance constraints and time constraints, expressed as follows:

[0064]

[0065]

[0066] in, Indicates the first The terminal distance between the aircraft and the target. Indicates the first The guidance time of the aircraft This represents the total number of aircraft.

[0067] According to the present invention, Terminal range constraints ensure that the aircraft can reach the target position. To ensure that multiple aircraft reach the target location simultaneously within a time constraint.

[0068] Preferably, the constraints also include communication constraints.

[0069] Based on the properties of the Laplace matrix of strongly connected graphs, the time constraint can be expressed in matrix form as follows:

[0070]

[0071] in, Represents the Laplace matrix, .

[0072] Furthermore, since each aircraft cannot grasp the global information of the entire network, its information acquisition capability is strictly limited by communication constraints. The i-th aircraft can only perceive its own state and the state information of neighboring aircraft with which it has a direct communication link, while the dynamics of other non-neighboring nodes are unobservable. That is, the communication constraints are expressed as:

[0073]

[0074] Among them, it means The state vector of aircraft i, Represents the set of neighbors connected to aircraft i. The state vector of the aircraft in the diagram.

[0075] In S13, for a guidance problem where the target is stationary, the optimal solution is proportional navigation (PPN):

[0076]

[0077] in Indicates the guidance gain.

[0078] Combining the equations of motion of multiple aircraft relative to a single target, the flight time for the i-th aircraft using pure proportional guidance can be predicted as follows:

[0079]

[0080] For the i-th aircraft, in order to control the flight time of the aircraft, satisfy the time constraint, and achieve cooperative guidance, a bias command is introduced. Therefore, the form of biased pure proportional guidance can be obtained as follows:

[0081]

[0082] The derivative of the flight time is then expressed as:

[0083]

[0084] Based on the idea of ​​feedback linearization and combined with constraints, a model for the cooperative guidance problem of aircraft can be obtained, expressed as:

[0085]

[0086]

[0087]

[0088]

[0089]

[0090] in, , where n represents the total number of aircraft. This represents the bias term for the i-th aircraft. For state variables, It is a constant diagonal matrix. For control commands.

[0091] S2 includes the following sub-steps:

[0092] S21. Based on the aircraft cooperative guidance problem model, establish the optimal consensus problem;

[0093] S22. Solve the optimal consensus problem to obtain the globally optimal solution;

[0094] S23. Based on the globally optimal solution, obtain the globally optimal consensus protocol.

[0095] In S21, within the aircraft cooperative guidance problem model, the magnitude of the control input directly affects the system's energy consumption. To reduce overall energy consumption while achieving system consistency, the performance index is chosen as a weighted integral quadratic form, thus establishing an optimal consensus problem:

[0096]

[0097] in, Indicates energy consumption. This indicates the guidance time when all aircraft arrive at the target simultaneously. Indicates the flight time of the aircraft. Represents a time variable. Parameters can be set. This represents the Laplace matrix.

[0098] In S22, based on the optimal consensus problem, its Hamiltonian function can be obtained:

[0099]

[0100]

[0101] in, Represents the Hamiltonian function. It is a constant costate vector.

[0102] According to the first-order optimality condition The optimal control command can be obtained as follows:

[0103]

[0104] Combining this with the optimal consensus problem, we can obtain:

[0105]

[0106] Multiply both sides by the Laplace matrix L on the left, and combine with the terminal condition. The constant costate vector can be obtained as follows:

[0107]

[0108] in This represents the Moore–Penrose pseudoinverse of the Laplace matrix.

[0109] And for any Laplace matrix, we have:

[0110]

[0111] in and Let represent the n-dimensional identity matrix and the matrix whose elements are all 1, respectively.

[0112] By combining the optimal control commands, the global optimal solution can be obtained. :

[0113]

[0114] In S23, based on the global optimal solution combined with the aircraft cooperative guidance problem model, the globally optimal consensus protocol can be obtained as follows:

[0115]

[0116] As can be seen from the global optimal solution, the control commands for each aircraft will be generated by the states of all aircraft. Therefore, the global optimal consensus protocol requires global information and can only be implemented in a fully connected network, and cannot be applied to the case of communication topology switching.

[0117] In S3, since the performance index in the optimal consensus problem is selected as a weighted integral quadratic form, a similar method is used in this invention to find a feasible approximate solution. .

[0118] Specifically, for the i-th aircraft, it can obtain the state information of its neighboring aircraft, and the i-th row of its corresponding Laplace matrix... Since this is known, we can apply the idea of ​​local optimal approximation to construct the local approximate optimal solution for the i-th aircraft in a form similar to the global optimal solution:

[0119]

[0120] in, Let represent the local approximate optimal solution for the i-th aircraft. Let be the weighting coefficient of the i-th aircraft.

[0121] In this invention, by introducing weighting coefficients, the pseudo-inverse matrix is ​​optimized in the absence of global communication topology information. Approximate compensation is performed to improve the accuracy of local approximate optimal solutions.

[0122] Then, for the entire aircraft swarm, the candidate approximate optimal solution can be expressed as:

[0123]

[0124]

[0125] in, It is a set of weighting coefficients.

[0126] According to the present invention, by minimizing the approximate optimal solution With the global optimal solution The approximate optimal solution is obtained at the supremum of the Euclidean distance. , represented as:

[0127]

[0128] in, This represents all feasible control instructions that satisfy the communication constraints. The set that constitutes the composition.

[0129] Furthermore, the above equation can be transformed into finding a condition such that... and Minimize the Euclidean distance between them , represented as:

[0130]

[0131] in, The set of weight coefficients Approximate value.

[0132] Furthermore, since the Euclidean norm of a matrix is ​​compatible with the Euclidean modulus of a vector, therefore The supremum can be represented as:

[0133]

[0134] in, This represents the Euclidean norm.

[0135] This inequality means that for any , The supremum of the matrix is The Euclidean norm is determined by neglecting the constant diagonal matrix. It can be transformed into:

[0136]

[0137] Will Matrix writing Therefore, there is

[0138]

[0139] but The solution can be transformed into a line-by-line problem, that is:

[0140]

[0141] in, for An approximate solution.

[0142] Obviously, It has a quadratic form and is a convex function. Its extrema can be obtained by solving the following equation.

[0143]

[0144] Note the original function right The second derivative is Therefore, the original function has a local minimum, which gives us... The solution is:

[0145]

[0146] According to the characteristics of the Laplace matrix, we know that...

[0147]

[0148] but

[0149] According to the property that the sum of each row of the Laplace matrix is ​​zero, we have:

[0150]

[0151] In summary, the solution is as follows:

[0152]

[0153] but The numerator is the i-th element in the i-th row of the Laplace matrix, i.e. The i-th diagonal element corresponds to the in-degree of the i-th aircraft; The denominator is the square of the 2-norm of the i-th row of the Laplace matrix. Since the non-zero elements in the i-th row of the Laplace matrix only appear at node i itself and its adjacent nodes, only the local information of the i-th aircraft and its neighboring nodes is needed to calculate the value. There is no need to know the global communication topology or the number of aircraft.

[0154] based on The near-optimal control command can be obtained, and based on the optimal consensus problem, the analytical near-optimal consensus protocol under the communication topology shear condition can be derived as follows:

[0155] .

[0156] In S4, based on the near-optimal distributed consensus protocol and combined with the aircraft cooperative guidance problem model, the bias term vector can be obtained. :

[0157]

[0158] As can be seen from the bias term vector, its generation requires a common... Ideally, this This equals the final consensus flight time of the aircraft. However, in distributed systems, the future consensus time is often unpredictable. In practical applications, the common time for the i-th aircraft is... Its predicted flight time can be used Approximate substitution; therefore, the bias term can be transformed into the following form:

[0159]

[0160] Although at the initial moment However, as time went on, converges to Therefore, the bias term in the above form can realize the proposed cooperative guidance in a distributed context.

[0161] Furthermore, when When the end becomes too small, it has The denominator may lead to singularities. To address this issue, a piecewise function is introduced in this invention. To replace

[0162]

[0163] in, These are designable parameters.

[0164] The energy-optimal cooperative guidance law for multiple aircraft under communication topology shear is expressed as:

[0165]

[0166] in, Let be the i-th row of the Laplace matrix of the i-th aircraft.

[0167] Example

[0168] Example 1

[0169] Conducting a multi-vehicle cooperative guidance simulation experiment includes the following steps:

[0170] S1. Establish a model for the cooperative guidance problem of multiple aircraft;

[0171] S2. Establish a globally optimal consensus protocol without considering communication constraints;

[0172] S3. By minimizing the Euclidean distance between the feasible set constrained by communication and the global optimal solution, an analytical near-optimal consensus protocol under communication topology uncertainty is obtained.

[0173] S4. Obtain the energy-optimal cooperative guidance law for multiple aircraft under communication topology shear based on the near-optimal distributed consensus protocol.

[0174] In S1, the model for the cooperative guidance problem of the aircraft is established through the following sub-steps:

[0175] S11. Establish the equations of relative motion of multiple aircraft with respect to a single target;

[0176] S12. Set constraints to enable simultaneous interception of targets by multiple aircraft;

[0177] S13. Based on the constraints and relative motion equations, construct a model for the cooperative guidance problem of aircraft.

[0178] In S11, the equations of motion of the multiple aircraft relative to a single target are expressed as follows:

[0179]

[0180] In S12, the constraints include

[0181]

[0182]

[0183]

[0184] In S13, the model for the cooperative guidance problem of aircraft is represented as follows:

[0185]

[0186]

[0187]

[0188]

[0189]

[0190] S2 includes the following sub-steps:

[0191] S21. Based on the aircraft cooperative guidance problem model, establish the optimal consensus problem;

[0192] S22. Solve the optimal consensus problem to obtain the globally optimal solution;

[0193] S23. Based on the globally optimal solution, obtain the globally optimal consensus protocol.

[0194] In S21, the optimal consensus problem is established:

[0195]

[0196] In S22, the global optimal solution :

[0197]

[0198] in, .

[0199] In S23, the globally optimal consensus protocol is:

[0200]

[0201] In S3, the analytical near-optimal consensus protocol under communication topology shearing conditions is:

[0202]

[0203] In S4, the energy-optimal cooperative guidance law for multiple aircraft under communication topology shear is expressed as follows:

[0204]

[0205] .

[0206] in, , .

[0207] The simulation included five aircraft and one target, with the target's location being... = 8km = 0km, maximum acceleration amplitude is During the simulation, the communication connection switching topology between aircraft is as follows: Figure 2 As shown.

[0208] The simulation conditions are set as shown in Table 1.

[0209] Table 1

[0210] Comparative Example 1 The same experiment as in Example 1 was conducted, except that the aircraft used the following guidance law:

[0211]

[0212] Its parameter selection is as follows , , , The maximum acceleration amplitude of the aircraft is .

[0213] Comparing the simulation results of the methods in Example 1 and Comparative Example 1, the results are as follows: Figures 3-8 As shown, where, Figure 3 The flight trajectory curve in Example 1 is shown. Figure 4 The flight trajectory curves in Comparative Example 1 are shown; Figure 5 The simulation results of the remaining flight time in Example 1 are shown. Figure 6 The simulation results of the remaining flight time in Comparative Example 1 are shown; Figure 7 The simulation results of the acceleration curve in Example 1 are shown. Figure 8 The simulation results of the acceleration curves in Comparative Example 1 are shown.

[0214] from Figures 3 to 8 It can be seen that the methods in Example 1 and Comparative Example 1 can both achieve coordinated strikes on the target, with basically the same strike time. Moreover, the peak acceleration of the method in Example 1 is significantly smaller than that in Comparative Example 1, and the stability of the aircraft in Example 1 is better.

[0215] The energy consumption indicators of Example 1 and Comparative Example 1 are shown in Table 2, where energy consumption is defined as:

[0216]

[0217] Table 2

[0218] Guidance methods E1 E2 E3 E4 E5 Total Example 1 2.245 6.327 7.231 5.949 9.215 30.968 Comparative Example 1 3.720 6.036 7.811 9.218 14.593 41.378

[0219] Comparing the energy consumption in Example 1 and Comparative Example 1, it can be seen that the energy consumption of almost every aircraft in Example 1 is less than that of the aircraft in Comparative Example 1, and the total energy consumption of the aircraft in Example 1 is much less than that of Comparative Example 1.

[0220] In the description of this invention, it should be noted that the terms "upper," "lower," "inner," "outer," "front," and "rear," etc., indicate the orientation or positional relationship based on the orientation or positional relationship in the working state of this invention, and are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention. Furthermore, the terms "first," "second," "third," and "fourth" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0221] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0222] The present invention has been described above with reference to preferred embodiments; however, these embodiments are merely exemplary and illustrative. Various substitutions and modifications can be made to the present invention based on these embodiments, all of which fall within the scope of protection of the present invention.

Claims

1. A method for optimal energy cooperative guidance of multiple aircraft under communication topology shear conditions, characterized in that, Includes the following steps: S1. Establish a model for the cooperative guidance problem of multiple aircraft; S2. Establish a globally optimal consensus protocol without considering communication constraints; S3. By minimizing the Euclidean distance between the feasible set constrained by communication and the global optimal solution, an analytical near-optimal consensus protocol under communication topology uncertainty is obtained. S4. Obtain the energy-optimal cooperative guidance law for multiple aircraft under communication topology shear based on a near-optimal distributed consensus protocol. S5. The aircraft flies based on the multi-aircraft energy-optimal cooperative guidance law under communication topology shear.

2. The method for optimal energy cooperative guidance of multiple aircraft under communication topology shearing conditions according to claim 1, characterized in that, In S1, the model for the cooperative guidance problem of the aircraft is established through the following sub-steps: S11. Establish the equations of relative motion of multiple aircraft with respect to a single target; S12. Set constraints to enable simultaneous interception of targets by multiple aircraft; S13. Based on the constraints and relative motion equations, construct a model for the cooperative guidance problem of aircraft.

3. The method for optimal energy cooperative guidance of multiple aircraft under communication topology shearing conditions according to claim 2, characterized in that, In S11, the equations of motion of the multiple aircraft relative to a single target are expressed as follows: ， in, This represents the distance between the i-th aircraft and the target. This represents the speed of the i-th aircraft. This represents the leading angle of the i-th aircraft. This represents the line-of-sight angle of the i-th aircraft. This represents the flight path angle of the i-th aircraft. Let represent the normal acceleration of the i-th aircraft.

4. The method for optimal energy cooperative guidance of multiple aircraft under communication topology shearing conditions according to claim 2, characterized in that, In S13, the model for the cooperative guidance problem of the aircraft is expressed as follows: ， ， ， ， ， in, Let n represent different aircraft, and n represent the total number of aircraft. Indicates the first The guidance time of the aircraft Indicates the first The constant parameters of the aircraft Indicates the first Control commands for the aircraft This represents the distance between the i-th aircraft and the target. This represents the leading angle of the i-th aircraft. This represents the guidance gain of the i-th aircraft. This represents the bias term for the i-th aircraft. For state variables, It is a constant diagonal matrix. For control commands.

5. The method for optimal energy cooperative guidance of multiple aircraft under communication topology shearing conditions according to claim 1, characterized in that, S2 includes the following sub-steps: S21. Based on the aircraft cooperative guidance problem model, establish the optimal consensus problem; S22. Solve the optimal consensus problem to obtain the globally optimal solution; S23. Based on the globally optimal solution, obtain the globally optimal consensus protocol.

6. The method for optimal energy cooperative guidance of multiple aircraft under communication topology shearing conditions according to claim 5, characterized in that, In S21, the optimal consensus problem is expressed as: ， in, Indicates energy consumption. This indicates the guidance time when all aircraft arrive at the target simultaneously. Indicates the flight time of the aircraft. Represents a time variable. Parameters can be set. This represents the Laplace matrix.

7. The method for optimal energy cooperative guidance of multiple aircraft under communication topology shearing conditions according to claim 5, characterized in that, In S22, the global optimal solution Represented as: ， in, This indicates the guidance time when all aircraft arrive at the target simultaneously. Indicates the flight time of the aircraft. Parameters can be set. Represents the Laplace matrix, This represents the Moore–Penrose pseudoinverse of the Laplace matrix.

8. The method for optimal energy cooperative guidance of multiple aircraft under communication topology shearing conditions according to claim 7, characterized in that, In S23, the globally optimal consensus protocol is: 。 9. The method for optimal energy cooperative guidance of multiple aircraft under communication topology shearing conditions according to claim 1, characterized in that, In S3, the analytical near-optimal consensus protocol under communication topology shearing conditions is: ， in, It is a set of weight coefficients. Let be the weighting coefficient of the i-th aircraft.

10. The method for optimal energy cooperative guidance of multiple aircraft under communication topology shearing conditions according to claim 1, characterized in that, In S4, the energy-optimal cooperative guidance law for multiple aircraft under communication topology shear is expressed as follows: ， ， in, Let the i-th row of the Laplace matrix of the i-th aircraft be... It is a piecewise function. Let i be the guidance gain of the i-th aircraft. Let n be the distance between the nth aircraft and the target. Let be the leading angle of the nth aircraft. Let n be the remaining flight time of the nth aircraft. Let n be the speed of the nth aircraft. These are designable parameters.

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