Multi-aircraft distributed analytical optimal cooperative guidance interception method

Abstract

The application discloses a kind of multi-aircraft distributed analytical optimal cooperative guidance interception methods, comprising the following steps: predicting the guidance time of aircraft;Using bias acceleration term to correct the predicted guidance time to obtain finite time problem, optimal problem is constructed based on finite time problem;Based on optimal problem, optimal control method is used to obtain optimal bias acceleration term;Based on the optimal acceleration command obtained by optimal bias acceleration term, the acceleration command is used to carry out flight control to aircraft.The multi-aircraft distributed analytical optimal cooperative guidance interception method disclosed by the application can maximize the global optimality, and reduce energy consumption, and can eliminate the guidance time difference of each aircraft with relatively low acceleration.

Description

Technical Field

[0001] This invention relates to a distributed analytical optimal cooperative guidance and interception method for multiple aircraft, belonging to the field of flight control technology. Background Technology

[0002] Existing cooperative guidance methods can be categorized into centralized and distributed approaches. In centralized methods, generating cooperative guidance commands requires information from all team members. The advantage lies in obtaining analytically optimal solutions to minimize total control effort. For example, the paper "Shiyu, Z., and Rui, Z., 'Cooperative Guidance for Multimissile SalvoAttack,' Chinese Journal of Aeronautics, Vol. 21, No. 6, 2008, pp. 533–539" designs a hierarchical guidance architecture to determine the common arrival time of a salvo attack while minimizing total control expenditure. This paper proposes a cooperative proportional navigation method with time-varying guidance gain to eliminate arrival time deviations. Although the aforementioned optimal methods can effectively minimize the consistent system control effort, their global optimality depends on the availability of global information. This typically requires the system to employ a central computation or be fully interconnected, increasing the system's communication burden. Distributed methods are designed to address this problem. For example, the paper "Nanavati, R., Kumar, SR., and Maity, A., 'Cooperative Target Capture Using Relative Separation for Three-Dimensional Engagement,' IEEE Transactions on Aerospace and Electronic Systems, Vol. 57, No. 5, 2021, pp. 3357–3367" proposes a finite-time consensus method based on sliding mode control theory. However, the convergence time of this method typically depends on initial conditions, leading to difficulties in parameter tuning. To mitigate this problem, fixed-time and predetermined-time control theories have also been used to design cooperative guidance laws.

[0003] However, the aforementioned distributed methods only consider consistent convergence patterns and fail to incorporate optimality properties, which may consume unnecessary maneuvering energy of the aircraft. In distributed communication systems, finding analytical optimal solutions is not feasible.

[0004] In addition, some numerical methods, such as model predictive control and distributed convex optimization, have been studied to find optimal solutions in distributed systems. However, these non-analytical methods typically involve multiple rounds of online communication for iterative optimization, which can lead to excessive delays and terminal misses for aircraft guidance.

[0005] Therefore, it is necessary to conduct more in-depth research on existing cooperative guidance interception methods in order to solve the above problems. Summary of the Invention

[0006] To overcome the above problems, in-depth research was conducted, and a multi-vehicle distributed analytical optimal cooperative guidance interception method was proposed, including the following steps:

[0007] S1. Predict the guidance time of the aircraft;

[0008] S2, the bias acceleration term is used to correct the predicted guidance time to obtain a finite-time problem, and an optimal problem is constructed based on the finite-time problem;

[0009] S3. Based on the optimal problem, the optimal control method is used to obtain the optimal bias acceleration term;

[0010] S4. The optimal acceleration command obtained based on the optimal bias acceleration term is used to control the flight of the aircraft.

[0011] In a preferred embodiment, step S1 includes the following sub-steps:

[0012] S11. Establish the kinematic control equations for target interception;

[0013] S12. Set terminal distance constraints and time constraints to achieve simultaneous interception of targets;

[0014] S13. Combining the control equations and constraints, the guidance time of the aircraft is predicted based on the guidance law.

[0015] In a preferred embodiment, in S11, the target interception kinematic control equations are established as follows:

[0016]

[0017] Among them, M i This represents the i-th aircraft. Let η represent the velocity of the i-th aircraft. i Let r represent the velocity lead angle of the i-th aircraft. i σ represents the distance between the i-th aircraft and the target. i This represents the line-of-sight angle of the i-th aircraft. Represents the normal acceleration of the i-th aircraft. This represents the flight path angle of the i-th aircraft.

[0018] In a preferred embodiment, in S12, the set end distance constraint and time constraint are expressed as follows:

[0019] r f,i =0

[0020] t f,1 =t f,2 =…=t f,i =…=t f,n

[0021] In a preferred embodiment, in S13, when a proportional guidance law is used, the predicted guidance time of the aircraft is expressed as:

[0022]

[0023] Where, N i This represents the guidance parameters of the i-th aircraft.

[0024] In a preferred embodiment, in S2, an offset acceleration term that controls the guidance time is introduced into the acceleration command to correct the predicted guidance time.

[0025] In a preferred embodiment, the finite-time problem is constructed using the derivative of the predicted guidance time, and the constructed finite-time problem is expressed as:

[0026]

[0027] Among them, a b,i Let be the bias acceleration term of the i-th aircraft.

[0028] In a preferred embodiment, the optimal problem is expressed as:

[0029]

[0030] Lx(t fc ) = 0

[0031] Where min represents the minimum, st represents the constraint, X is the state vector, U is the control vector, B is the state transition matrix, J represents the energy consumption, the superscript T indicates transpose, and t fc The moment when all aircraft finally achieve the same guidance time, t represents the current time, τ represents the time factor, k represents the guidance parameters, the specific values ​​of which can be freely set by those skilled in the art according to actual needs, and L is the Laplace matrix determined by the communication topology between aircraft, which can be obtained in advance;

[0032] The state vector, control vector, and state transition matrix are as follows:

[0033] X = [t] f,1 ,t f,2 ,…,t f,i ,…,t f,n ]

[0034] U = [u1, u2, ..., u i ,…,u n ]

[0035] B = diag{b1,b2,…,b} i ,…,b n}

[0036] Among them, u i b represents the control command for the i-th aircraft. i Let represent the state transition vector of the i-th aircraft.

[0037] In a preferred embodiment, in S3, the Hamiltonian function is set to solve the optimal control problem using the optimal control method to obtain the optimal control command;

[0038] The optimal distributed parsing instruction is obtained by minimizing the upper bound of the Euclidean distance;

[0039] Based on the distributed optimal parsing instructions, the bias acceleration term for optimal control guidance time can be obtained.

[0040] In a preferred embodiment, in S4, the optimal bias acceleration term is substituted into the acceleration command. In this process, the coordinated guidance acceleration command for each aircraft can be obtained.

[0041] in, a represents the acceleration command for the i-th aircraft. b,i The bias acceleration term represents the control and guidance time of the i-th aircraft.

[0042] The beneficial effects of this invention include:

[0043] (1) The cooperative salvo guidance problem is expressed as a high-dimensional finite-time problem in the general prediction-correction form. Then, the optimal distributed guidance method for multiple aircraft to intercept targets by salvo is derived using optimal control theory, which preserves the global optimality to the maximum extent.

[0044] (2) It consumes less energy than existing parsing distributed protocols;

[0045] (3) It can eliminate the guidance time difference of each aircraft with relatively low acceleration. Attached Figure Description

[0046] Figure 1This diagram illustrates a flowchart of a multi-vehicle distributed analytical optimal cooperative guidance interception method according to a preferred embodiment of the present invention.

[0047] Figure 2 This diagram illustrates a flowchart of a multi-vehicle distributed analytical optimal cooperative guidance interception method according to a preferred embodiment of the present invention.

[0048] Figure 3 This diagram illustrates the communication topology between aircraft in Example 1.

[0049] Figure 4 The flight trajectory of the aircraft in Example 1 is shown;

[0050] Figure 5 The remaining guidance time curve of the aircraft in Example 1 is shown;

[0051] Figure 6 The acceleration curve of the aircraft in Example 1 is shown;

[0052] Figure 7 The flight trajectory of the aircraft in Comparative Example 1 is shown;

[0053] Figure 8 The remaining guidance time curve of the aircraft in Comparative Example 1 is shown;

[0054] Figure 9 The acceleration curve of the aircraft in Comparative Example 1 is shown. Detailed Implementation

[0055] 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.

[0056] 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.

[0057] According to the present invention, a multi-vehicle distributed analytical optimal cooperative guidance interception method is provided, such as... Figure 1 As shown, it includes the following steps:

[0058] S1. Predict the guidance time of the aircraft;

[0059] S2, the bias acceleration term is used to correct the predicted guidance time to obtain a finite-time problem, and an optimal problem is constructed based on the finite-time problem;

[0060] S3. Based on the optimal problem, the optimal control method is used to obtain the optimal bias acceleration term;

[0061] S4. The optimal acceleration command obtained based on the optimal bias acceleration term is used to control the flight of the aircraft.

[0062] Preferably, such as Figure 2 As shown, in S1, the guidance time is predicted based on the bias guidance acceleration command.

[0063] S1 includes the following sub-steps:

[0064] S11. Establish the kinematic control equations for target interception;

[0065] S12. Set terminal distance constraints and time constraints to achieve simultaneous interception of targets;

[0066] S13. Combining the control equations and constraints, the guidance time of the aircraft is predicted based on the guidance law.

[0067] In S11, the target interception kinematic control equations are established as follows:

[0068]

[0069] Among them, M i This represents the i-th aircraft. Let η represent the velocity of the i-th aircraft. i Let r represent the velocity lead angle of the i-th aircraft. i σ represents the distance between the i-th aircraft and the target. i This represents the line-of-sight angle of the i-th aircraft. Represents the normal acceleration of the i-th aircraft. This represents the flight path angle of the i-th aircraft.

[0070] Furthermore, the velocity lead angle η i satisfy:

[0071] In S12, the end-point distance constraint and time constraint are expressed as follows:

[0072] r f,i =0

[0073] t f,1 =t f,2 =…=t f,i =…=t f,n

[0074] Where, r f,i t represents the terminal distance between the i-th aircraft and the target. f,i Let represent the guidance time of the i-th aircraft, and n be the total number of aircraft.

[0075] In S13, the guidance law can be set by those skilled in the art according to actual needs, and is not limited in this invention. For example, the commonly used proportional guidance law can be used.

[0076] When using proportional guidance law, the predicted guidance time of the aircraft is expressed as:

[0077]

[0078] Where, N i This represents the guidance parameters of the i-th aircraft. Those skilled in the art can set these parameters according to actual needs. Preferably, N... i ≥3.

[0079] In S2, an offset acceleration term that controls the guidance time is introduced into the acceleration command, thereby correcting the predicted guidance time.

[0080] Preferably, such as Figure 2 As shown, the dynamics of predicting guidance time are solved to construct a distributed finite-time optimal convergence problem.

[0081] The acceleration command is set as follows:

[0082]

[0083] in, a represents the acceleration command for the i-th aircraft. b,i The bias acceleration term represents the control and guidance time of the i-th aircraft.

[0084] According to the present invention, the finite-time problem is constructed by using the derivative of the predicted guidance time.

[0085] The finite-time problem of construction is represented as:

[0086]

[0087] Among them, a b,i Let be the bias acceleration term of the i-th aircraft.

[0088] The problem is constructed in the form of state-space differential equations based on the finite-time problem, and the optimal problem is constructed with the criterion of optimal energy consumption control.

[0089] The optimal problem is expressed as:

[0090]

[0091] Lx(t fc ) = 0

[0092] Where min represents the minimum, st represents the constraint, X is the state vector, U is the control vector, B is the state transition matrix, J represents the energy consumption, the superscript T indicates transpose, and t fc The moment when all aircraft finally achieve the same guidance time, t represents the current time, τ represents the time factor, k represents the guidance parameters, the specific values ​​of which can be freely set by those skilled in the art according to actual needs, and L is the Laplace matrix determined by the communication topology between aircraft, which can be obtained in advance.

[0093] Furthermore, the state vector, control vector, and state transition matrix are as follows:

[0094] X = [t] f,1 ,t f,2 ,…,t f,i ,…,t f,n ]

[0095] U = [u1, u2, ..., u i ,…,u n ]

[0096] B = diag{b1,b2,…,b} i ,…,b n}

[0097] Among them, u i b represents the control command for the i-th aircraft. i Let represent the state transition vector of the i-th aircraft.

[0098]

[0099] According to the present invention, the finite-time problem is a high-dimensional finite-time problem of general prediction-correction form obtained based on cooperative salvo guidance. The construction of this problem can preserve global optimality to the maximum extent and consume less energy than existing analytical distributed protocols.

[0100] In S3, preferably, such as Figure 2 As shown, the distributed optimal bias acceleration control term is obtained by solving the optimal control method and using the Euclidean distance minimization strategy.

[0101] S3 includes the following sub-steps:

[0102] S31. Set the Hamiltonian function and use the optimal control method to solve the optimal control problem and obtain the optimal control command;

[0103] S32. Obtain the distributed optimal parsing instruction by minimizing the upper bound of the Euclidean distance;

[0104] S33. Based on the distributed optimal parsing instruction, the bias acceleration term for the optimal control guidance time can be obtained.

[0105] In S31, the optimal control command u opt Represented as:

[0106]

[0107] Where L + It is the pseudo-inverse of the Laplace matrix L, which can be obtained by inverting it.

[0108] The optimal control command obtained from the above equation is a centralized globally optimal control command, which requires information from all aircraft to solve for. Therefore, when distributed communication is used between aircraft, in this invention, a distributed approximate optimal solution close to the globally optimal solution is found by minimizing the upper bound of the Euclidean distance, thus obtaining a distributed optimal analytical command.

[0109] In S32, the upper bound for minimizing the Euclidean distance is expressed as:

[0110]

[0111] Among them, u * This represents the distributed optimal parsing instruction, and sup represents the supremum distance.

[0112] The obtained distributed optimal parsing instruction u * Represented as:

[0113]

[0114] in, The elements represent the pseudo-inverse of the Laplace matrix.

[0115] In S33, the bias acceleration term a for optimal control guidance time can be obtained according to the distributed optimal analysis instruction. b =[a b，1 a b，2 , ..., a b，n ] T for:

[0116]

[0117] In S4, the optimal bias acceleration term is substituted into the acceleration command. In this process, the coordinated guidance acceleration command for each aircraft can be obtained, and the optimal acceleration command can be used to control the flight of the aircraft.

[0118] Example

[0119] Example 1

[0120] Conducting a cooperative guidance interception simulation experiment includes the following steps:

[0121] S1. Predict the guidance time of the aircraft;

[0122] S2, the bias acceleration term is used to correct the predicted guidance time to obtain a finite-time problem, and an optimal problem is constructed based on the finite-time problem;

[0123] S3. Based on the optimal problem, the optimal control method is used to obtain the optimal bias acceleration term;

[0124] S4. The optimal acceleration command obtained based on the optimal bias acceleration term is used to control the flight of the aircraft.

[0125] In S11, the target interception kinematic control equations are established as follows:

[0126]

[0127] In S12, the end-point distance constraint and time constraint are expressed as follows:

[0128] r f,i =0

[0129] t f,1 =t f,2 =…=t f,i =…=t f,n

[0130] In S13, when using the proportional guidance law, the predicted guidance time of the aircraft is expressed as:

[0131]

[0132] In S2, the acceleration command is set as follows:

[0133]

[0134] The finite-time problem of construction is represented as:

[0135]

[0136] The optimal problem is expressed as:

[0137]

[0138] Lx(t fc ) = 0

[0139] S3 includes the following sub-steps:

[0140] S31. Set the Hamiltonian function and use the optimal control method to solve the optimal control problem and obtain the optimal control command;

[0141] S32. Obtain the distributed optimal parsing instruction by minimizing the upper bound of the Euclidean distance;

[0142] S33. Based on the distributed optimal parsing instruction, the bias acceleration term for the optimal control guidance time can be obtained.

[0143] In S31, the optimal control command u opt Represented as:

[0144]

[0145] In S32, the distributed optimal parsing instruction u is obtained. * Represented as:

[0146]

[0147] In S33, the bias acceleration term a for optimal control guidance time can be obtained according to the distributed optimal analysis instruction. b =[a b，1 a b，2 , ..., a b，n ] T for:

[0148]

[0149] In S4, the optimal bias acceleration term is substituted into the acceleration command. In the process, the coordinated guidance acceleration command for each aircraft is obtained.

[0150] During the simulation, N is set i =4, k=4, a total of 5 aircraft are set up using distributed communication. The initial position and track angle conditions of the simulation are shown in Table 1. The communication topology between the aircraft is as follows: Figure 3 As shown.

[0151] Table 1 Initial Simulation Conditions

[0152] <![CDATA[M1]]> <![CDATA[M2]]> <![CDATA[M3]]> <![CDATA[M4]]> <![CDATA[M5]]> Target Location (kilometers) (0.4,6) (0,1) (0,0) (0,-4) (0.4,-6) (10,0) Track angle (degrees) 40 30 60 -40 -30 /

[0153] Simulation results are as follows Figures 4-6 As shown, where, Figure 4 The flight path of the aircraft is shown. Figure 5 The remaining guidance time curve of the aircraft is shown. Figure 6 The acceleration curve of the aircraft is shown.

[0154] Comparative Example 1

[0155] The same experiment as in Example 1 was conducted, except that a distributed consensus-based cooperative guidance (DCG) method was used, where the guidance parameters were set to N. i =4, the control parameters in DCG are selected as c1=0.2, c2=0.8, w ij =0.8.

[0156] Simulation results are as follows Figures 7-9 As shown, where, Figure 7 The flight path of the aircraft is shown. Figure 8 The remaining guidance time curve of the aircraft is shown. Figure 9 The acceleration curve of the aircraft is shown.

[0157] Comparing the simulation results in Example 1 and Comparative Example 1, from Figures 4-6 and Figures 7-9 The comparison shows that the method in Example 1 eliminates the guidance time difference for each aircraft with relatively low acceleration: the peak acceleration of the method in Example 1 is almost below 5g, while the peak acceleration of the method in Comparative Example 1 exceeds the maximum available acceleration limit of 10g.

[0158] The comparison results show that the method in Example 1 can save flight energy, thereby improving the accuracy of guidance and interception.

[0159] 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 multi-aircraft distributed analytical optimal cooperative guidance interception method, characterized in that, Includes the following steps: S1. Predict the guidance time of the aircraft; S2, the bias acceleration term is used to correct the predicted guidance time to obtain a finite-time problem, and an optimal problem is constructed based on the finite-time problem; S3. Based on the optimal problem, the optimal control method is used to obtain the optimal bias acceleration term; S4. The optimal acceleration command obtained based on the optimal bias acceleration term is used to control the flight of the aircraft. In S2, an offset acceleration term that controls the guidance time is introduced into the acceleration command to correct the predicted guidance time. The finite-time problem is constructed by using the derivative of the predicted guidance time. The constructed finite-time problem is expressed as: wherein, is the bias acceleration term for the th aircraft; The optimal problem is expressed as: Where min denotes minimum, st denotes constraint, X is the state vector, U is the control vector, and B is the state transition matrix. J Indicates energy consumption, superscript T Indicates transpose. The moment when all aircraft finally achieve the same guidance timing. Indicates the current moment. τ Indicates the time factor. These represent guidance parameters, the specific values ​​of which can be freely set by those skilled in the art according to actual needs. It is the Laplace matrix determined by the communication topology between aircraft and can be obtained in advance; The state vector, control vector, and state transition matrix are as follows: wherein, represents a control instruction for the th aircraft, represents a state transition vector for the th aircraft; In S3, the Hamiltonian function is set to use the optimal control method to solve the optimal control problem and obtain the optimal control command; The optimal distributed parsing instruction is obtained by minimizing the upper bound of the Euclidean distance; Based on the distributed optimal parsing instructions, the bias acceleration term for optimal control guidance time can be obtained.

2. The multi-vehicle distributed analytical optimal cooperative guidance interception method according to claim 1, characterized in that, S1 includes the following sub-steps: S11. Establish the kinematic control equations for target interception; S12. Set terminal distance constraints and time constraints to achieve simultaneous interception of targets; S13. Combining the control equations and constraints, the guidance time of the aircraft is predicted based on the guidance law.

3. The multi-vehicle distributed analytical optimal cooperative guidance interception method according to claim 2, characterized in that, In S11, the target interception kinematic control equations are established as follows: in, Indicates the first One aircraft, Indicates the first The speed of the aircraft Indicates the first The velocity lead angle of the aircraft Indicates the first The distance between the aircraft and the target Indicates the first The line-of-sight angle of an aircraft Indicates the first The normal acceleration of the aircraft Indicates the first The flight path angle of the aircraft.

4. The multi-vehicle distributed analytical optimal cooperative guidance interception method according to claim 3, characterized in that, In S12, the end-point distance constraint and time constraint are expressed as follows: 。 5. The multi-vehicle distributed analytical optimal cooperative guidance interception method according to claim 4, characterized in that, In S13, when the proportional guidance law is used, the predicted guidance time of the aircraft is expressed as: in, Indicates the first The guidance parameters of an aircraft.

6. The multi-vehicle distributed analytical optimal cooperative guidance interception method according to claim 1, characterized in that, In S4, the optimal bias acceleration term is substituted into the acceleration command. In this process, the coordinated guidance acceleration command for each aircraft can be obtained. in, Indicates the first Acceleration commands for each aircraft Indicates the first The bias acceleration term of the control and guidance time of an aircraft.

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