Incremental differential game guidance law capture area solving method and device

Abstract

The invention discloses an incremental differential game guidance law capture area solving method and device, and the method comprises the following steps: considering a maneuvering target-aircraft two-dimensional plane terminal guidance model, and building a system state equation; designing an aircraft incremental differential game guidance law and a target differential game guidance law according to the system state equation; dividing a countermeasure space into different differential countermeasure scenes according to a countermeasure guidance law of pursuit and escape parties; solving an incremental Nash equilibrium solution existence condition in different differential game scenes; and solving the incremental capture region under the condition that the existence of the incremental Nash equilibrium solution is met. According to the method, the incremental differential game guidance law is designed, the capture area is solved, the obtained guidance law is higher in robustness when facing system uncertainty and external interference, the analysis of the capture area provides a theoretical basis for incremental guidance parameter selection, and the method has the advantages of being simple in analysis method, wide in application range and the like.

Description

Technical Field

[0001] The invention belongs to the field of aircraft guidance system design, and in particular, relates to a method and device for solving the capture zone of an incremental differential game guidance law. Background Art

[0002] As a method for evaluating the performance of guidance laws, the capture zone analysis of guidance laws can determine the influence of initial conditions and guidance parameters on the performance of guidance laws. Compared with proportional guidance and its derivative guidance laws, the differential game guidance law takes into account the game between the aircraft and the target, and has the advantage of ensuring the minimum performance of the entire game process in the capture zone analysis. For the capture zone analysis of differential game, existing literature considers different cost functions such as zero control miss distance and energy consumption of both parties, solves the capture zone of norm differential game and linear quadratic differential game, and analyzes the influencing factors of the capture zone such as maximum acceleration, time constant and remaining time estimation, while the influence of acceleration estimation error on the capture zone has not been analyzed. And considering that the above guidance law has low robustness, the incremental method has a smaller system residual, that is, the required guidance gain is smaller and the robustness is stronger. The existing literature combines the incremental method with other guidance methods to enhance the robustness of the system and designs incremental sliding mode guidance law, incremental adaptive sliding mode guidance law, incremental time-varying sliding mode guidance law, etc. However, the performance of the above incremental guidance law has only been verified through simulation, and the capture area solution and analysis have not yet been performed. Summary of the invention

[0003] In order to overcome the shortcomings and disadvantages of the existing methods, the present invention considers the strong robustness of the incremental method and the superiority of differential game theory in the performance analysis of the guidance law, designs an incremental differential game guidance law and solves its capture area, and the obtained guidance law is more robust when facing system uncertainty and external interference. At the same time, the present invention considers the influence of parameters such as the maximum acceleration ratio, the time constant ratio and the acceleration estimation error of the pursuit and escape parties on the capture area of ​​the incremental differential game guidance law, which can provide a theoretical basis for the selection of incremental guidance parameters, and has the characteristics of simple analysis method and wide application range.

[0004] The present invention proposes a method for solving the capture zone of an incremental differential game guidance law, comprising the following steps:

[0005] S1: Consider the two-dimensional terminal guidance model of maneuvering target-aircraft and establish the system state equation;

[0006] S2: Design the incremental differential game guidance law of the aircraft and the target differential game guidance law according to the system state equation;

[0007] S3: According to the countermeasure guidance law of both parties, the countermeasure space is divided into different differential countermeasure scenarios;

[0008] S4: Solve the existence conditions of incremental Nash equilibrium solutions in different differential game scenarios;

[0009] S5: Under the condition of existence of incremental Nash equilibrium solution, solve the incremental capture zone.

[0010] The present invention also proposes an incremental differential game guidance law capture zone solving device, comprising the following modules:

[0011] System state equation establishment module: Considering the maneuvering target-aircraft two-dimensional plane terminal guidance model, the system state equation is established;

[0012] Guidance law design module: designs the aircraft incremental differential game guidance law and target differential game guidance law according to the system state equation;

[0013] Differential countermeasure scenario division module: divides the countermeasure space into different differential countermeasure scenarios according to the countermeasure guidance laws of both parties;

[0014] Existence condition solving module: solves the existence conditions of incremental Nash equilibrium solutions in different differential game scenarios;

[0015] Capture zone solving module: solves the incremental capture zone under the condition of existence of incremental Nash equilibrium solution.

[0016] The present invention further proposes an electronic device, comprising: one or more processors; and a memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned method.

[0017] The present invention further proposes a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enables the processor to implement the above method.

[0018] Beneficial effects of the present invention:

[0019] (1) The present invention takes into account the strong robustness of the incremental method and the superiority of differential game theory in the analysis of guidance law performance, and designs an incremental differential game guidance law. The upper bound of the residual of the obtained guidance law system is smaller than the upper bound of the residual of the traditional differential game system, the guidance gain required for system stability is lower, and the robustness is stronger when facing system uncertainty and external interference.

[0020] (2) The parameters considered in the present invention include acceleration ratio, time constant ratio and acceleration estimation error of both parties. The obtained capture zone analysis can provide a theoretical basis for the selection of incremental guidance parameters. It has the characteristics of simple analysis method and wide application range. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1It is a flow chart of the method for solving the capture area of ​​the incremental differential game guidance law of the present invention;

[0022] Figure 2 is the target acceleration estimation error ratio of the present invention , guidance energy weight ratio Schematic diagram of the incremental capture zone simulation when ;

[0023] Figure 3 is the aircraft acceleration estimation error ratio of the present invention , guidance energy weight ratio Schematic diagram of the incremental capture zone simulation when . DETAILED DESCRIPTION

[0024] In order to make the purpose, technical scheme and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in each embodiment of the present invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above-mentioned purpose, the present invention adopts the following technical scheme.

[0025] like Figure 1 As shown, the steps of a method for solving the capture zone of an incremental differential game guidance law of the present invention are as follows:

[0026] S1: Consider the two-dimensional terminal guidance model of maneuvering target-aircraft and establish the system state equation;

[0027] S2: Design the incremental differential game guidance law of the aircraft and the target differential game guidance law according to the system state equation;

[0028] S3: According to the countermeasure guidance law of both parties, the countermeasure space is divided into different differential countermeasure scenarios;

[0029] S4: Solve the existence conditions of incremental Nash equilibrium solutions in different differential game scenarios;

[0030] S5: Under the condition of existence of incremental Nash equilibrium solution, solve the incremental capture zone.

[0031] The present invention takes into account the strong robustness of the incremental method and the superiority of differential game theory in guidance law performance analysis, designs an incremental differential game guidance law and solves its capture area, the obtained guidance law system residual upper bound is smaller than the traditional differential game system residual upper bound, the guidance gain required for system stability is lower, and the robustness is stronger in the face of system uncertainty and external interference. The capture area analysis can provide a theoretical basis for the selection of incremental guidance parameters, and has the characteristics of simple analysis method and wide application range.

[0032] It should be understood that all variables with dots on them in the present invention are derivatives of the variables, unless the derivative of the variable has actual physical meaning.

[0033] The specific steps of the incremental differential game guidance law capture zone solution method of the present invention are as follows:

[0034] S1 is specifically: Considering the terminal guidance model of a maneuvering target with a two-dimensional plane approximate head-on collision, the system state equation is:

[0035] (1)

[0036] In the formula, , and is the target maximum acceleration, guidance law and time constant, , and is the maximum acceleration of the vehicle, the guidance law and the time constant, , , , is the initial time, current time, terminal time, and sampling interval, is the zero control miss distance, and is an intermediate process function, and its expression is as follows:

[0037] ,

[0038] .

[0039] S2 is specifically: define the initial value of zero control miss amount , the terminal time value is , the allowable off-target amount is , then the capture zone is defined as satisfying Initial zero control miss amount scope.

[0040] Select the differential game cost function:

[0041] (2)

[0042] In the formula, the vehicle guidance energy weight , target guidance energy weight .

[0043] consider , , , Indicates less than or equal to The maximum integer of , the design of the incremental differential game guidance law of the aircraft is:

[0044] (3)

[0045] In the formula, The sampling interval The incremental term of the aircraft guidance law, the auxiliary term , design adjustable guidance gain To achieve , yes Estimated value, The sampling interval The target guidance law increment term within, the aircraft estimation error ratio .

[0046] The design target differential game guidance law expression is:

[0047] (4)

[0048] In the formula, the auxiliary term , design adjustable guidance gain To achieve , yes Estimated value, target estimation error ratio .

[0049] Considering the system state equation shown in equation (1), the cost function shown in equation (2), and the guidance law forms shown in equations (3) and (4), the guidance energy weight ratio is defined as , maximum acceleration ratio , time constant ratio , the initial guidance law expression of the pursuit and escape parties is obtained:

[0050] For aircraft, if , then the incremental differential game guidance law , otherwise the guidance law ;

[0051] For the target, ,like , then the differential game guidance law , otherwise the guidance law .in,

[0052] ,

[0053] .

[0054] Consider system uncertainty and external interference , sampling interval Internal system uncertainty and external disturbances , Substituting the guidance law forms shown in equations (3) and (4) into the system state equation shown in equation (1), the system residual can be obtained:

[0055] ,

[0056] In the formula, , , In the guidance law design process, , , The nominal value of The remainder is the Taylor expansion.

[0057] Similarly, the residual of the traditional differential game system can be obtained:

[0058] .

[0059] Design of Lyapunov functions , in order to achieve system stability, that is , the guidance gain needs to satisfy and Theoretical analysis shows that there is a small sampling interval Make Upper bound is less than The upper bound, that is, the upper bound of the residual of the incremental differential game system is smaller than the upper bound of the residual of the differential game system. The guidance gain required for system stability is lower, and the system is more robust in the face of system uncertainty and external interference.

[0060] S3: Conditions for dividing the target guidance law shown in S2 After analysis, we can know:

[0061] (a) If any of the following conditions is met, then :(a1) ; (a2) and ;

[0062] (b) If any of the following conditions is met, then :(b1) ; (b2) and .

[0063] The switching time of the guidance law of both parties from saturation value to non-saturation value is defined as , and ,Right now: , and satisfy:

[0064] ,

[0065] ,

[0066] ,

[0067] Among them, the process variable , , , , is greater than or equal to The smallest integer.

[0068] Consider capture zone boundaries , switching time , and satisfy:

[0069] ,

[0070] ,

[0071] .

[0072] Depending on whether the guidance law reaches saturation, the following differential game scenario is introduced:

[0073] Differential game scenario A: And the above condition (a) is established.

[0074] Differential game scenario B: And the above condition (b) is established.

[0075] Differential game scenario C: And the above condition (a) is established.

[0076] Differential game scenario D: And the above condition (b) is established.

[0077] In differential game scenario A:

[0078] Define the differential game scenario A1 to satisfy: ;

[0079] Differential game scenario A2 satisfies: ;

[0080] Differential game scenario A3 satisfies: ;

[0081] Differential game scenario A4 satisfies: and ;

[0082] Differential strategy scenario A5 satisfies: and .

[0083] In differential game scenario B:

[0084] Define the differential game scenario B1 to satisfy: ;

[0085] Differential game scenario B2 satisfies: .

[0086] In differential game scenario C:

[0087] Define the differential game scenario C1 to satisfy: ;

[0088] Differential game scenario C2 satisfies: .

[0089] In differential game scenario D:

[0090] Define the differential game scenario D1 to satisfy: ;

[0091] Differential game scenario D2 satisfies: and ,or ;

[0092] Differential game scenario D3 satisfies: and ,or .

[0093] In the differential game scenario B, the guidance law of the pursuit and escape parties is and , at the border In the above figure, the aircraft guidance law does not reach saturation in the differential game scenario B1, but is saturated in the differential game scenario B2.

[0094] In the differential game scenario C, the guidance law of both the pursuit and escape parties is and , at the border In the above figure, the target guidance law does not reach saturation in the differential game scenario C1, but is saturated in the differential game scenario C2.

[0095] In the differential game scenario D, the guidance law of the pursuit and escape parties is , zero control miss amount In the differential strategy scenario D1, the initial value remains unchanged, in the differential strategy scenario D2, it eventually becomes a monotone decreasing function, and in the differential strategy scenario D3, it eventually becomes a monotone increasing function.

[0096] S4: For any initial time , , define the parameters , define the following process function:

[0097] ,

[0098] ,

[0099] ,

[0100] ,

[0101] in, ,function Maximum satisfy:

[0102] like and ,but .

[0103] when When , , ,and ,but ,otherwise .

[0104] like and ,but .

[0105] when When , , ,and ,but , , ,otherwise .

[0106] For the differential game scenario described in S3, the existence condition of the differential game solution is obtained based on the fact that the denominator of the guidance law of both parties is not 0, as shown below:

[0107] Differential game scenario A1: , .

[0108] Differential game scenario A2: , .

[0109] Differential game scenario A3: , , .

[0110] Differential game scenario A4: , , .

[0111] Differential game scenario A5: , , .

[0112] Differential game scenario C1: .

[0113] Differential game scenario C2: .

[0114] Differential game scenario B and differential game scenario D: The optimal solution always exists.

[0115] S5: For the differential game scenario described in S3, when the optimal solution existence condition described in S4 is met, the incremental capture area is solved as follows:

[0116] In differential game scenario A, differential game scenarios A1-A5 capture area - for:

[0117] ,

[0118] In the formula, , is the capture zone boundary value of the differential game scenario A1-A5, expressed as:

[0119] ,

[0120] ,

[0121] ,

[0122] ,

[0123] ,

[0124] ,

[0125] ,

[0126] ,

[0127] ,

[0128] ,

[0129] ,

[0130] In the differential game scenario B, the differential game scenarios B1 and B2 capture the region and for:

[0131] ,

[0132] In the formula, , is the capture zone boundary value of the differential game scenario B1-B2, and the expression is as follows:

[0133] ,

[0134] ,

[0135] ,

[0136] In the differential game scenario C, the differential game scenarios C1 and C2 capture the region and for:

[0137] ,

[0138] In the formula, , is the capture zone boundary value of the differential game scenario C1-C2, and the expression is as follows:

[0139] ,

[0140] ,

[0141] ,

[0142] In the differential game scenario D, the differential game scenarios D1-D3 capture the area - for:

[0143] ,

[0144] ,

[0145] .

[0146] Comparison of the above capture zone theoretical analysis shows that if ,but ,Right now When other parameters are the same, the capture area increases with increases or remains unchanged. , , ,but , that is, the capture area increases with increases or remains unchanged with the increase of increases and decreases or remains unchanged.

[0147] The following simulation results under different guidance parameters are used as examples to illustrate the effectiveness of the method proposed in the present invention. , , , , , , , , . Figure 2 is the target estimation error ratio , guidance energy weight ratio Simulation diagram of the capture area, the aircraft estimation error ratio . Figure 3 Estimated error ratio for the aircraft , guidance energy weight ratio Simulation diagram of the capture area, .

[0148] Figure 2 middle, , , for an aircraft, if ,but ,otherwise ; For the target, if ,but ,otherwise .when When , then the capture area changes with the guidance energy weight ratio Increase and decrease, if , the capture zone boundary value is 10m, if , then the capture zone boundary value is 9.9986m; when When , then the capture area Increase and decrease, if , then the capture zone boundary value is 9.9986m. Figure 3 middle, , , for an aircraft, if ,but ,otherwise ; For the target, if ,but ,otherwise .when When , then the capture area If , then the capture zone boundary value is 10m, if , then the capture zone boundary value is 9.9986m; when When , then the capture area Increase and decrease, if , then the capture zone does not exist. , then the capture zone boundary value is 9.9986m.

[0149] According to the above analysis and description, the incremental differential game guidance law system designed by the present invention has a small upper bound on the residual and is more robust in the face of system uncertainty and external interference. The capture zone analysis can provide a theoretical basis for the selection of incremental guidance parameters, and has the characteristics of simple analysis method and wide application range.

[0150] The above applications are only some implementation methods of the present application. For those skilled in the art, several modifications and improvements can be made without departing from the creative concept of the present application, and these all belong to the protection scope of the present application.

Claims

1. A method for solving the capture zone of an incremental differential game guidance law, characterized in that: The following steps are involved: S1: Consider the two-dimensional terminal guidance model of maneuvering target-aircraft and establish the system state equation; S2: Design the incremental differential game guidance law of the aircraft and the target differential game guidance law according to the system state equation; S3: According to the countermeasure guidance law of both parties, the countermeasure space is divided into different differential countermeasure scenarios; S4: Solve the existence conditions of incremental Nash equilibrium solutions in different differential game scenarios; S5: Under the condition of existence of incremental Nash equilibrium solution, solve the incremental capture zone.

2. The method according to claim 1, characterized in that In step S1, considering the terminal guidance scenario of a maneuvering target with a two-dimensional plane approximate head-on collision, the system state equation is: （1） In the formula, , and is the target maximum acceleration, guidance law and time constant, , and is the maximum acceleration of the vehicle, the guidance law and the time constant, is the zero control miss distance, , , are the initial time, current time, and terminal time, is the sampling interval, and is an intermediate process function, and its expression is as follows: ， 。 3. The method according to claim 2, characterized in that In step S2, the initial value of zero control miss distance is defined as , the terminal time value is , the allowable off-target amount is , then the capture zone is defined as satisfying Initial zero control miss amount scope; Select the differential game cost function: （2） In the formula, the vehicle guidance energy weight , target guidance energy weight ; Considering the system state equation shown in formula (1) and the cost function shown in formula (2), , , , Indicates less than or equal to The maximum integer that defines the guidance energy weight ratio , and The sampling intervals are The guidance law increments for the internal vehicle and the target, is the incremental term of the guidance law of the aircraft to the target Estimated value, aircraft estimation error ratio , Guidance law for target aircraft Estimated value, target estimation error ratio , then we get the following guidance law expression for both the pursuit and escape parties: For aircraft, if , then the incremental differential game guidance law ,otherwise ; Maximum acceleration ratio ; For the target, ,like ,but ,otherwise ,in: ， 。 4. The method according to claim 3, characterized in that In step S3, the time constant ratio , the target guidance law division conditions described in step S2 After analysis, we can know: (a) If any of the following conditions is met, then :(a1) ; (a2) and ; (b) If any of the following conditions is met, then :(b1) ; (b2) and ; The switching time of the guidance law of both parties from saturation value to non-saturation value is defined as and ,Right now and satisfy: ， ， ， Among them, the process variable , , , , is greater than or equal to The smallest integer of ; Consider capture zone boundaries , switching time and satisfy: ， ， ； Depending on whether the guidance law reaches saturation, the following differential game scenario is introduced: Differential game scenario A: and the above condition (a) is met; Differential game scenario B: and the above condition (b) is met; Differential game scenario C: and the above condition (a) is met; Differential game scenario D: and the above condition (b) is met; In differential game scenario A: Define the differential game scenario A1 to satisfy: ; Differential game scenario A2 satisfies: ; Differential strategy scenario A3 satisfies ; Differential game scenario A4 satisfies: and ; Differential strategy scenario A5 satisfies: and ; In differential game scenario B: Define the differential game scenario B1 to satisfy: ; Differential game scenario B2 satisfies: ; In differential game scenario C: Define the differential game scenario C1 to satisfy: ; Differential game scenario C2 satisfies: ; In differential game scenario D: Define the differential game scenario D1 to satisfy: ; Differential game scenario D2 satisfies and ,or ; Differential game scenario D3 satisfies: and ,or .

5. The method according to claim 4, characterized in that In step S4, for any initial time , , define the process parameters , define the following process function: ， ， ， ； in, ,function Maximum satisfy: like and ,but ; when When , , ,and ,but ,otherwise ; like and ,but ; when When , , ,and ,but , , ,otherwise ; For the differential game scenario described in step S3, the following differential game solution existence conditions are obtained: Differential game scenario A1: , ; Differential game scenario A2: , ; Differential game scenario A3: , , ; Differential game scenario A4: , , ; Differential game scenario A5: , , ; Differential game scenario C1: ; Differential game scenario C2: ; Differential game scenario B and differential game scenario D: The optimal solution always exists.

6. The method according to claim 5, characterized in that In step S5, for the differential game scenario described in step S3, when the optimal solution existence condition described in step S4 is met, the incremental capture area is solved as follows: In differential game scenario A, differential game scenarios A1-A5 capture area - for: ； In the formula, , is the capture area boundary value of scene A1-A5, expressed as: ， ， ， ， ， ， ， ， ， ， ， In the differential game scenario B, the differential game scenarios B1 and B2 capture the region and for: ， In the formula, , is the capture zone boundary value of the differential game scenario B1-B2, and the expression is as follows: ， ， ， In the differential game scenario C, the differential game scenarios C1 and C2 capture the region and for: ， In the formula, , is the capture zone boundary value of the differential game scenario C1-C2, and the expression is as follows: ， ， ， In the differential game scenario D, the differential game scenarios D1-D3 capture the area - for: ， ， 。 7. An incremental differential game guidance law capture zone solving device, characterized in that: Includes the following modules: System state equation establishment module: Considering the maneuvering target-aircraft two-dimensional plane terminal guidance model, the system state equation is established; Guidance law design module: designs the aircraft incremental differential game guidance law and target differential game guidance law according to the system state equation; Differential countermeasure scenario division module: divides the countermeasure space into different differential countermeasure scenarios according to the countermeasure guidance laws of both parties; Existence condition solving module: solves the existence conditions of incremental Nash equilibrium solutions in different differential game scenarios; Capture zone solving module: solves the incremental capture zone under the condition of existence of incremental Nash equilibrium solution.

8. An electronic device, characterized in that: include: one or more processors; A memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the method according to any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that: Executable instructions are stored thereon, and when the instructions are executed by a processor, the processor implements the method according to any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

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