Multi-aircraft distributed analysis optimal cooperative guidance interception method

Abstract

The invention discloses a multi-aircraft distributed analysis optimal cooperative guidance interception method. The method comprises the following steps: predicting guidance time of aircrafts; correcting the predicted guidance time by adopting a bias acceleration item to obtain a finite time problem, and constructing an optimal problem based on the finite time problem; based on the optimal problem, an optimal control method is adopted to obtain an optimal bias acceleration item; and obtaining an optimal acceleration instruction based on the optimal bias acceleration item, and carrying out flight control on the aircraft by adopting the acceleration instruction. According to the multi-aircraft distributed analytic optimal cooperative guidance interception method disclosed by the invention, the global optimality can be reserved to the maximum extent, the energy consumption is reduced, and the guidance time difference of each aircraft can be eliminated at a relatively low acceleration.

Description

Technical Field

[0001] The present invention relates to a distributed analytical optimal cooperative guidance and interception method for multiple aircraft, belonging to the technical field of flight control. Background Art

[0002] Existing cooperative guidance methods can be divided into centralized and distributed methods. In the centralized method, generating cooperative guidance commands requires information from all team members. The advantage is that it can obtain an analytically optimal solution to minimize the total control effort. For example, the literature "Shiyu, Z., and Rui, Z., "Cooperative Guidance for Multimissile Salvo Attack," Chinese Journal of Aeronautics, Vol. 21, No. 6, 2008, pp. 533–539" designed a hierarchical guidance architecture to determine the common arrival time of salvo attacks while minimizing the total control expenditure. This literature proposed a cooperative proportional navigation method with time-varying guidance gains to eliminate the deviation of arrival times. Although the above optimal methods can effectively minimize the system control effort for consistency, the global optimality of these methods depends on the availability of global information, which usually requires the system to adopt a central calculation or full connection, increasing the communication burden of the system. The distributed method is precisely to solve this problem. For example, the literature "Nanavati, R., Kumar, S.R., 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" proposed a finite-time consensus method based on sliding mode control theory, but the convergence time of this method usually depends on the initial conditions, resulting in difficult parameter adjustment. To mitigate this problem, fixed-time and preset-time control theories have also been used to design cooperative guidance laws.

[0003] However, the above distributed methods only consider the consensus convergence mode and fail to incorporate the optimality characteristics, which may consume unnecessary maneuvering energy of the aircraft. In a distributed communication system, finding an analytical optimal solution is infeasible.

[0004] In addition, some numerical methods, such as model predictive control and distributed convex optimization methods, have been studied to find the optimal solution in a distributed system. However, these non-analytical methods usually involve multiple online communication rounds for iterative optimization, which is too time-consuming and prone to end-point miss for aircraft guidance.

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

[0006] To overcome the above problems, an in-depth study has been carried out, and a distributed analytical optimal cooperative guidance and interception method for multiple aircraft is proposed, including the following steps:

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

[0008] S2. Use the offset acceleration term to correct the predicted guidance time to obtain a finite-time problem, and construct an optimal problem based on the finite-time problem;

[0009] S3. Based on the optimal problem, use the optimal control method to obtain the optimal offset acceleration term;

[0010] S4. Based on the optimal acceleration command obtained from the optimal offset acceleration term, use this acceleration command to control the flight of the aircraft.

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

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

[0013] S12. Set the end-distance constraint and time constraint to achieve simultaneous interception of the target;

[0014] S13. Combine the control equation and the constraints, and predict the guidance time of the aircraft based on the guidance law.

[0015] In a preferred embodiment, in S11, the kinematic control equation for target interception is established as:

[0016]

[0017] Where, M i represents the i-th aircraft, represents the speed of the i-th aircraft, η i represents the speed lead angle of the i-th aircraft, r i represents the distance between the i-th aircraft and the target, σ i represents the line-of-sight angle of the i-th aircraft, represents the normal acceleration of the i-th aircraft, Denotes 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:

[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 the proportional navigation guidance law is adopted, the predicted guidance time of the aircraft is expressed as:

[0022]

[0023] where N i Denotes the guidance parameter of the i-th aircraft.

[0024] In a preferred embodiment, in S2, a bias acceleration term for controlling 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 with the differential of the predicted guidance time, and the constructed finite-time problem is expressed as:

[0026]

[0027] where a b,i Is 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 minimum, s.t. represents 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 represents transpose, t fc Is the moment when all aircraft finally achieve consistent guidance time, t represents the current moment, τ represents the time factor, k represents the guidance parameter, and its specific value can be freely set by those skilled in the art according to actual needs. L is the Laplacian matrix determined by the communication topology between aircraft and can be obtained in advance;

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

[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] wherein, u i represents the control command of the i-th aircraft, and b i represents the state transition vector of the i-th aircraft.

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

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

[0039] According to the distributed optimal analytical command, the bias acceleration term of the 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 to obtain the cooperative guidance acceleration command of each aircraft,

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

[0042] The beneficial effects of the present invention include:

[0043] (1) The cooperative salvo guidance problem is formulated as a high-dimensional finite-time problem in a general prediction-correction form, and then an optimal distributed guidance method for multi-aircraft salvo interception of a target is derived using the optimal control theory, maximizing the preservation of global optimality;

[0044] (2) It consumes less energy than the existing analytical distributed protocol;

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

[0046] Figure 1 ​​Shows a schematic flow chart of a multi-aircraft distributed analytical optimal cooperative guidance and interception method according to a preferred embodiment of the present invention;

[0047] Figure 2 Shows a schematic flow chart of a multi-aircraft distributed analytical optimal cooperative guidance and interception method according to a preferred embodiment of the present invention;

[0048] Figure 3 Shows the communication topology diagram between aircraft in Embodiment 1;

[0049] Figure 4 Shows the flight trajectories of the aircraft in Embodiment 1;

[0050] Figure 5 Shows the remaining guidance time curve of the aircraft in Embodiment 1;

[0051] Figure 6 Shows the acceleration curve of the aircraft in Embodiment 1;

[0052] Figure 7 Shows the flight trajectories of the aircraft in Comparative Example 1;

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

[0054] Figure 9 Shows the acceleration curve of the aircraft in Comparative Example 1. Detailed implementation manners

[0055] The present invention will be further described in detail below with reference to the drawings and embodiments. Through these descriptions, the features and advantages of the present invention will become clearer and more definite.

[0056] The special term "exemplary" here means "serving as an example, embodiment or illustration". Any embodiment described as "exemplary" here does not have to be construed as superior or better than other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings do not have to be drawn to scale unless otherwise specified.

[0057] A multi-aircraft distributed analytical optimal cooperative guidance and interception method provided by the present invention, as Figure 1 shown, includes the following steps:

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

[0059] S2. Use the offset acceleration term to correct the predicted guidance time to obtain a finite-time problem, and construct an optimal problem based on the finite-time problem;

[0060] S3. Based on the optimal problem, use the optimal control method to obtain the optimal offset acceleration term;

[0061] S4. Obtain the optimal acceleration command based on the optimal bias acceleration term, and use this acceleration command to control the flight of the aircraft.

[0062] Preferably, as Figure 2 shown, in S1, predict the guidance time according to the bias guidance acceleration command.

[0063] In S1, it includes the following sub-steps:

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

[0065] S12. Set the terminal distance constraint and time constraint to achieve simultaneous interception of the target;

[0066] S13. Combine the control equation and the constraints, and predict the guidance time of the aircraft based on the guidance law.

[0067] In S11, the established target interception kinematic control equation is:

[0068]

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

[0070] Furthermore, the speed lead angle η i satisfies:

[0071] In S12, the set terminal distance constraint and time constraint are expressed as:

[0072] r f,i = 0

[0073] t f,1 = t f,2 = … = t f,i = … = t f,n

[0074] Among them, r f,i represents the terminal distance between the i-th aircraft and the target, t f,i represents the guidance time of the i-th aircraft, and n is 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 the present invention. For example, the common proportional navigation guidance law can be adopted.

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

[0077]

[0078] where N i represents the guidance parameter of the i-th aircraft, which can be set by those skilled in the art according to actual needs. Preferably, N i ≥3.

[0079] In S2, a bias acceleration term for controlling the guidance time is introduced into the acceleration command, so as to correct the predicted guidance time.

[0080] Preferably, as Figure 2 shown, solve the dynamics of the predicted guidance time and construct a distributed finite-time optimal convergence problem.

[0081] The acceleration command is set as:

[0082]

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

[0084] According to the present invention, the finite-time problem is constructed based on the differential of the predicted guidance time.

[0085] The constructed finite-time problem is expressed as:

[0086]

[0087] where a b,i is the bias acceleration term of the i-th aircraft.

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

[0089] The optimal problem is expressed as:

[0090]

[0091] Lx(t fc )=0

[0092] Among them, min represents the minimum, s.t. 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 represents the transpose, and t fc is the moment when all aircraft finally achieve the same guidance time, t represents the current moment, τ represents the time factor, k represents the guidance parameter, and its specific value can be freely set by those skilled in the art according to actual needs. L is the Laplacian matrix determined by the communication topology between aircraft and can be obtained in advance.

[0093] Further, the state vector, control vector, and state transition matrix are respectively:

[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 represents the control command of the i-th aircraft, and b i represents 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 in a general prediction-correction form obtained based on cooperative salvo guidance. The construction of this problem can maximize the retention of global optimality and consume less energy than existing analytical distributed protocols.

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

[0101] S3 includes the following sub-steps:

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

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

[0104] ​​S33. According to the distributed optimal parsing instruction, the bias acceleration term of the optimal control guidance time can be obtained.

[0105] In S31, the optimal control instruction u opt is expressed as:

[0106]

[0107] where L + is the pseudo-inverse matrix of the Laplacian matrix L, which can be obtained by performing an inverse operation on it.

[0108] The optimal control instruction obtained from the above formula is a centralized global optimal control instruction, and all aircraft information is required to solve the instruction. Therefore, when distributed communication is adopted between aircraft, in the present invention, a distributed approximate optimal solution close to the global optimal solution is found by minimizing the upper bound of the Euclidean distance, and a distributed optimal parsing instruction is obtained.

[0109] In S32, the minimization of the upper bound of the Euclidean distance is expressed as:

[0110]

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

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

[0113]

[0114] where represents the element of the pseudo-inverse matrix of the Laplacian matrix.

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

[0116]

[0117] In S4, substituting the optimal bias acceleration term into the acceleration instruction the cooperative guidance acceleration instruction of each aircraft can be obtained, and the optimal acceleration instruction is used to control the flight of the aircraft.

[0118] Embodiment

[0119] Embodiment 1

[0120] Perform a cooperative guidance interception simulation experiment, including the following steps:

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

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

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

[0124] S4. Based on the optimal acceleration command obtained from the optimal bias acceleration term, use this acceleration command to control the flight of the aircraft.

[0125] In S11, establish the target interception kinematic control equation as:

[0126]

[0127] In S12, the set terminal distance constraint and time constraint are expressed as:

[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 navigation guidance law, the predicted guidance time of the aircraft is expressed as:

[0131]

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

[0133]

[0134] The constructed finite-time problem is expressed as:

[0135]

[0136] The optimal problem is expressed as:

[0137]

[0138] Lx(t fc ) = 0

[0139] In S3, it includes the following sub-steps:

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

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

[0142] S33. According to the distributed optimal parsing command, the bias acceleration term of the optimal control guidance time can be obtained.

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

[0144]

[0145] In S32, the obtained distributed optimal parsing command u * is expressed as:

[0146]

[0147] In S33, according to the distributed optimal parsing command, the bias acceleration term a b of the optimal control guidance time can be obtained as: b，1 a b，2 ,..., a b，n T is:

[0148]

[0149] In S4, substitute the optimal bias acceleration term into the acceleration command to obtain the cooperative guidance acceleration command of each aircraft.

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

[0151] Table 1 Initial simulation conditions

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

[0153] The simulation results are as Figures 4 - 6 shown, where Figure 4 shows the flight trajectory of the aircraft, Figure 5 shows the remaining guidance time curve of the aircraft, Figure 6 shows the acceleration curve of the aircraft.

[0154] Comparative example 1

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

[0156] The simulation results are as Figures 7 - 9 shown, where Figure 7 shows the flight trajectory of the aircraft, Figure 8 shows the remaining guidance time curve of the aircraft, Figure 9 shows the acceleration curve of the aircraft.

[0157] Comparing the simulation results in Example 1 and Comparative Example 1, it can be seen from Figures 4 - 6 the comparison with Figures 7 - 9 that the method in Example 1 eliminated the guidance time difference of each aircraft with a relatively low acceleration: the peak acceleration of the method in Example 1 was almost lower than 5g, while the peak acceleration of the method in Comparative Example 1 exceeded the maximum available acceleration limit of the flight, which was 10g.

[0158] From the comparison results, it can be known that the method in Example 1 can save flight energy and thus improve the guidance interception accuracy.

[0159] The present invention has been described above in combination with preferred embodiments, but these embodiments are only exemplary and only serve an illustrative purpose. On this basis, various substitutions and improvements can be made to the present invention, and these all fall within the protection scope of the present invention.

Claims

1. A multi-aircraft distributed analytical optimal cooperative guidance interception method, characterized in that: The following steps are involved: S1. Predict the guidance time of the aircraft; S2, using the bias acceleration term to correct the predicted guidance time to obtain a finite time problem, and constructing an optimal problem based on the finite time problem; S3. Based on the optimal problem, an optimal control method is used to obtain the optimal bias acceleration term; S4. An optimal acceleration instruction is obtained based on the optimal bias acceleration term, and the aircraft is controlled by using the acceleration instruction.

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

3. The multi-aircraft distributed analytical optimal cooperative guidance interception method according to claim 2 is characterized in that: In S11, the target interception kinematic control equation is established as: Among them, M i represents the i-th aircraft, represents the speed of the i-th aircraft, η i represents the velocity lead angle of the ith aircraft, r i represents the distance between the i-th aircraft and the target, σ i represents the sight angle of the ith aircraft, represents the normal acceleration of the ith aircraft, represents the flight path angle of the ith aircraft.

4. The multi-aircraft distributed analytical optimal cooperative guidance interception method according to claim 3 is characterized in that: In S12, the terminal distance constraint and time constraint are set as follows: r f,i ＝0 t f,1 =t f,2 =…=t f,i =…=t f,n 。 5. The multi-aircraft distributed analytical optimal cooperative guidance interception method according to claim 4 is characterized in that: In S13, when the proportional guidance law is used, the predicted aircraft guidance time is expressed as: Among them, N i represents the guidance parameters of the ith aircraft.

6. The multi-aircraft distributed analytical optimal cooperative guidance interception method according to claim 1 is characterized in that: In S2, a bias acceleration term for controlling the guidance time is introduced into the acceleration command, thereby correcting the predicted guidance time.

7. The multi-aircraft distributed analytical optimal cooperative guidance interception method according to claim 6 is characterized in that: The finite time problem is constructed by predicting the differential of the guidance time. The constructed finite time problem is expressed as: Among them, a b,i is the bias acceleration term of the ith aircraft.

8. The multi-aircraft distributed analytical optimal cooperative guidance interception method according to claim 1 is characterized in that: The optimal problem is expressed as: Lx(t fc )=0 Where min means minimum, st means constraint, X is the state vector, U is the control vector, B is the state transfer matrix, J is the energy consumption, superscript T means transpose, and f tc is the moment when all aircraft finally reach the same guidance time, t represents the current moment, τ represents the time factor, k represents the guidance parameter, and its specific value can be freely set by technicians in this field according to actual needs. L is the Laplace matrix determined by the communication topology between aircrafts and can be obtained in advance; The state vector, control vector and state transfer matrix are: X=[t f,1 ,t f,2 ,…,t f,i ,…,t f,n ] U=[u1,u2,…,u i ,…,u n ] B=diag{b1,b2,…,b i ,…,b n } Among them, u i represents the control command of the ith aircraft, b i Represents the state transition vector of the i-th aircraft.

9. The multi-aircraft distributed analytical optimal cooperative guidance interception method according to claim 1, characterized in that: In S3, the Hamiltonian function is set to use the optimal control method to solve the optimal control problem and obtain the optimal control instruction; The distributed optimal parsing instructions are obtained by minimizing the upper bound of the Euclidean distance; According to the distributed optimal analytical instructions, the bias acceleration term of the optimal control guidance time can be obtained.

10. The multi-aircraft 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 the above example, the coordinated guidance acceleration command of each aircraft can be obtained. in, represents the acceleration command of the ith aircraft, a b,i Represents the bias acceleration term of the control guidance time of the i-th aircraft.

Images