Differential game capture area solving method and device for continuous and pulse guidance law

Abstract

The invention discloses a method and a device for solving a differential game capture area of a continuous and pulse guidance law, and the method comprises the following steps: considering the continuous maneuvering or pulse maneuvering condition of pursuit and escape parties, and building a two-dimensional plane pursuit and escape model by taking a zero-control miss distance as a state quantity; introducing a pursuit scene according to a differential game guidance law form of both parties; solving a differential game guidance law in different pursuit scenes, and writing a continuous guidance law and a pulse guidance law into a unified form; solving a differential game solution existence condition according to the condition that the guidance law denominator is not zero; in different scenarios, a differential game capture zone is solved. The differential game capture area solving method disclosed by the invention reveals the difference between the pulse capture area and the continuous guidance law capture area, can provide a theoretical basis for selection of continuous and pulse differential game guidance parameters with different acceleration ratios and time constant ratios, and is simple in analysis method and wide in application range.

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 differential game capture region of continuous and pulse guidance laws. Background Art

[0002] Guidance law capture zone analysis is to evaluate the performance of different guidance laws theoretically and reveal the influence of different factors on the performance of guidance laws. It has been widely studied in recent years. Guidance law capture zone analysis mainly focuses on proportional guidance and its derivative guidance laws and differential game guidance laws. Among them, the capture zone analysis of proportional guidance and its derivative guidance laws is based on the inequality transformation of physical inequality constraints. When the pursuit and escape situation is more complicated, it is difficult to derive the necessary and sufficient conditions of the capture zone. The differential game guidance law uses the optimal situation of both parties as the capture boundary, which is convenient for obtaining the necessary and sufficient conditions of the capture zone. The theoretical analysis of the capture zone of the pulse guidance law only considers the case of one continuous guidance law and one pulse guidance law, and does not consider the case of both parties being pulsed, and there is no comparative analysis of the capture zones of the continuous guidance law and the pulse guidance law.

[0003] Obviously, it is particularly important to design a method to solve the capture zone of the differential game of continuous and pulse guidance laws, while overcoming the existing conservatism, being close to engineering practice and improving the applicability of the guidance system. Summary of the invention

[0004] The technical problem to be solved by the present invention is: when both parties in the game carry pulse engines, how to obtain the capture area of ​​the continuous guidance law and the pulse guidance law. Based on this, the present invention designs a differential game capture area solution method and device for continuous and pulse guidance laws, writes the continuous guidance law and the pulse guidance law in a unified form, and performs a unified solution for the capture area. The four pursuit models considered include a continuous guidance law target and a continuous guidance law aircraft, a continuous guidance law target and a pulse guidance law aircraft, a pulse guidance law target and a continuous guidance law aircraft, and a pulse guidance law target and a pulse guidance law aircraft. Compared with the existing methods, the present invention reveals the difference between the capture areas of pulse and continuous guidance laws, and obtains the conditions that the pulse guidance laws of both parties in the pursuit can be regarded as continuous guidance laws in the design process. The obtained capture area analysis can provide a theoretical basis for the selection of continuous and pulse differential game guidance parameters with different acceleration ratios and time constant ratios, and has the characteristics of simple analysis method and wide application range.

[0005] A method for solving the capture region of a differential game of a continuous and pulse guidance law of the present invention comprises the following steps:

[0006] S1: Considering the continuous maneuvers or pulse maneuvers of both parties, a two-dimensional zero-control miss distance pursuit model is established;

[0007] S2: Based on the zero-control miss distance pursuit model, a preliminary design of the two-party differential game guidance law is conducted and the pursuit scenario is introduced;

[0008] S3: In different pursuit scenarios, solve the differential game guidance law and write the continuous guidance law and the impulse guidance law into a unified form;

[0009] S4: Based on the fact that the denominator of the guidance law is not zero, solve the existence condition of the differential game solution;

[0010] S5: Find the capture region of the differential game for continuous and impulsive guidance laws under the solution existence condition in different scenarios.

[0011] The present invention proposes a device for solving the capture zone of a differential game of continuous and pulse guidance laws, comprising the following modules:

[0012] The zero-miss pursuit model establishment module establishes a two-dimensional zero-miss pursuit model based on the continuous or pulse maneuvers of the pursuing and escaping parties.

[0013] The pursuit and escape scenario introduction module introduces the pursuit and escape scenario based on the zero-control miss distance pursuit and escape model;

[0014] Guidance law solving module, which solves the guidance law in both continuous and pulse forms in pursuit scenarios;

[0015] The existence condition solving module solves the existence condition of the differential game solution according to the fact that the denominator in the guidance law is not zero;

[0016] The continuous and pulse capture region solving module solves the continuous and pulse capture regions under the condition of satisfying the existence of differential game solutions.

[0017] The present invention also provides 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.

[0018] The present invention also provides a computer-readable storage medium on which executable instructions are stored. When the instructions are executed by a processor, the processor implements the above method.

[0019] Beneficial effects of the present invention:

[0020] (1) The present invention writes the continuous guidance law and the impulse guidance law in a unified form and performs a unified solution for the capture zone. The obtained capture zone analysis can provide a theoretical basis for the selection of continuous and impulse differential game guidance parameters with different acceleration ratios and time constant ratios, and has the characteristics of simple analysis method and wide application range.

[0021] (2) The present invention reveals the difference between the capture areas of pulse and continuous guidance laws, and obtains the conditions that must be met in the design process for the pulse guidance law of both the pursuer and the fugitive to be regarded as the continuous guidance law. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a flow chart of the method for solving the capture region of the differential game of the continuous and pulse guidance laws of the present invention;

[0023] Figure 2 It is a simulation schematic diagram of the capture area of ​​the present invention when the guidance energy weight of both the pursuit and escape parties is small;

[0024] Figure 3 It is a schematic diagram of the capture boundary difference simulation of the present invention when the guidance energy weights of the pursuit and escape parties are small;

[0025] Figure 4 This is a simulation diagram of the capture area of ​​the aircraft's continuous guidance law when the guidance energy weights of both the pursuit and escape parties are large;

[0026] Figure 5 This is a simulation diagram of the capture area of ​​the aircraft pulse guidance law when the guidance energy weights of both the pursuit and escape parties are large. DETAILED DESCRIPTION

[0027] 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.

[0028] like Figure 1 As shown, the steps of the differential strategy capture zone solution method of the continuous and pulse guidance law of the present invention are as follows:

[0029] Step S1, considering the continuous maneuvering or pulse maneuvering of both parties, a two-dimensional plane pursuit model is established with the zero control miss amount as the state quantity;

[0030] Step S2, according to the differential game guidance law form of both parties, a two-dimensional plane pursuit model is established with zero control miss amount as the state quantity, and a pursuit scenario is introduced;

[0031] Step S3, solving the differential game guidance law in different pursuit scenarios, and writing the continuous guidance law and the pulse guidance law into a unified form;

[0032] Step S4, solving the existence condition of the differential game solution according to the fact that the denominator of the guidance law is not zero;

[0033] Step S5, solving the differential game capture area in different scenarios.

[0034] 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.

[0035] The specific steps of the differential game capture zone solution method of the continuous and pulse guidance laws of the present invention are as follows:

[0036] Step S1 specifically includes: defining , , They are the initial time, current time, terminal time, and remaining time. , , and are the target maximum acceleration, guidance law and time constant respectively, , and They are respectively the maximum acceleration of the aircraft, the guidance law and the time constant, and the zero control miss distance is the terminal lateral distance without any guidance command, and its initial value is , the terminal time value is .

[0037] Considering the end-stage pursuit scenario of a two-dimensional plane approximate head-on collision, the pursuit model with zero-control miss distance as the state quantity is:

[0038] (1)

[0039] In the formula,

[0040] , .

[0041] Step S2: Design the guidance law form of the two-party differential game and introduce the pursuit scenario. The detailed implementation steps are:

[0042] Select the differential game cost function:

[0043] (2)

[0044] In the formula, the vehicle guidance energy weight , target guidance energy weight .

[0045] The following definitions are given for the continuous and pulse flags of the pursuit and escape parties: and : If the aircraft guidance law is continuous, then ; If the aircraft guidance law is pulsed, then ; If the target guidance law is continuous, then ; If the target guidance law is pulsed, then ,Right now:

[0046] .

[0047] From the above formula, we can see that if , , then the pursuit model is a continuous guidance law target and a continuous guidance law aircraft. If , , then the pursuit model is a continuous guidance law target and a pulse guidance law aircraft. If , , then the pursuit model is a pulse guidance law target and a continuous guidance law aircraft. If , , then the pursuit model is a pulse guidance law target and a pulse guidance law aircraft.

[0048] Considering the system model in equation (1) and the cost function in equation (2), the guidance law of the pursuit and escape parties is designed to achieve , solving this optimal problem can preliminarily obtain the guidance law form of the two-party differential game:

[0049] (3)

[0050] Define the allowable off-target amount , maximum acceleration ratio , time constant ratio , then the capture zone is defined as satisfying of , , and gather.

[0051] 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 , , , If the capture zone boundary is considered , then the switching time between the pursuit and escape parties is and ,Right now and Satisfy , , where the process variables are:

[0052] ,

[0053] As shown in equation (3), in the differential game guidance law form, the terminal zero control miss distance is To solve the terminal zero control miss amount and the specific expression of the guidance law, the following five pursuit scenarios are introduced according to whether the guidance law reaches saturation:

[0054] Chase scene 1: ;

[0055] Chase scene 2: ;

[0056] Chase scene 3: ;

[0057] Chase scene 4: ,and ;

[0058] Chase scene 5: ,and .

[0059] Among them, in pursuit scenarios 2, 4, and 5, the target guidance law will reach saturation, and in pursuit scenarios 3, 4, and 5, the aircraft guidance law will reach saturation.

[0060] Step S3: For the five pursuit scenarios described in S2, a continuous and impulse unified differential game guidance law is obtained. The specific pursuit scenarios are as follows:

[0061] Pursuit Scenario 1: Aircraft Guidance Law , target guidance law ,in: , , ;

[0062] Pursuit scenario 2: Guidance law for both parties:

[0063] ,

[0064] In the formula,

[0065] ;

[0066] Pursuit scenario 3: Guidance law for both parties:

[0067] ,

[0068] In the formula,

[0069] ;

[0070] Pursuit Scenario 4: Guidance Laws for Both Pursuit and Escape:

[0071] ;

[0072] Pursuit Scenario 5: Guidance Laws for Both Pursuit and Escape:

[0073] ;

[0074] S4: For the five pursuit scenarios described in S2, according to the fact that the denominator of the guidance law described in S3 is not 0, the existence conditions of the differential game solution are obtained as follows:

[0075] Chase scene 1: , ;

[0076] Chase scene 2: , ;

[0077] Chase scene 3:

[0078] , , ;

[0079] Chase scene 4: , ;

[0080] Chase scene 5:

[0081] , , .

[0082] Step S5: For the five pursuit scenarios described in S2, when the optimal solution existence condition described in S4 is met, the differential strategy capture area of ​​continuous maneuver and impulse maneuver is obtained. and non-capture zone , ,as follows:

[0083] (4)

[0084] in, , It is the capture zone boundary value of pursuit scenario 1-5, and the expression is as follows:

[0085] , ,

[0086] ,

[0087] ,

[0088] ,

[0089] ,

[0090] ,

[0091] ,

[0092] ,

[0093] .

[0094] For the above capture area , Theoretical analysis and comparison show that for aircraft, when the guidance energy weight is small, the difference between the continuous and pulse capture areas is negligible, and when the guidance energy weight is large, the continuous guidance law capture area is larger than the pulse guidance law capture area; for targets, when the guidance energy weight is small, the difference between the continuous and pulse capture areas is negligible, and when the guidance energy weight is large, the continuous guidance law capture area is smaller than the pulse guidance law capture area.

[0095] The following simulation results under different guidance energy weights are used as examples to illustrate the effectiveness of the method proposed in the present invention. , , , , , , . Figure 2 This is a simulation diagram of the capture zone when the guidance energy weight is relatively small. Figure 3 This is a simulation diagram of the capture boundary difference when the guidance energy weight is relatively small. Figure 4 This is a simulation diagram of the capture area of ​​the aircraft continuous guidance law when the guidance energy weight is large. Figure 5 It is a schematic diagram of the simulation of the capture area of ​​the aircraft pulse guidance law when the guidance energy weights of both the pursuit and escape parties are large. Figure 2 and Figure 3 The weight of the guided energy of both sides , , Figure 4 and Figure 5 The weight of the guided energy of both sides , . Figure 3 middle, express , The capture zone boundary and , The difference between the capture zone boundaries at express , The capture zone boundary and , The difference between the capture zone boundaries at .

[0096] Figure 2 According to the optimal solution existence condition described in step 4, if the aircraft guidance law is pulsed and the target guidance law is continuous, that is, , , then the condition There is an optimal solution when , but the above simulation parameters do not meet this condition and the solution does not exist. Figure 2 and Figure 3 As shown, except , In addition, the capture areas of the other three cases are slightly different, that is, when the solution existence condition is met, if the guidance energy weights of the chasing and escaping parties are small, the difference between the continuous and pulse capture areas is small and can be ignored. Figure 4 and Figure 5 It can be seen that when the aircraft guidance energy weight is large, the capture area of ​​the continuous guidance law is larger than the capture area of ​​the pulse guidance law. Figure 4 and Figure 5 As shown in , when the target guidance energy weight is large, the capture area of ​​the continuous guidance law is smaller than that of the pulse guidance law. Figure 2-Figure 5 As shown, when other conditions are the same, the capture area changes with the acceleration ratio increases with the increase of .

[0097] Based on the above analysis and description, the present invention reveals the difference between the capture areas of pulse and continuous guidance laws. The obtained capture area analysis can provide a theoretical basis for the selection of continuous and pulse differential strategy guidance parameters with different acceleration ratios and time constant ratios. It has the characteristics of simple analysis method and wide application range.

[0098] 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 region of differential game for continuous and impulse guidance laws, characterized in that: The following steps are involved: S1: According to the continuous maneuvers or pulse maneuvers of the pursuers and fugitives, a two-dimensional zero-control miss distance pursuit model is established; S2: Based on the zero-control miss distance pursuit model, the pursuit scenario is introduced; S3: In the pursuit scenario, solve the guidance law that unifies the continuous and pulse forms; S4: According to the guidance law, the denominator is not zero, and the existence condition of the solution of the differential game is solved; S5: Under the existence condition of differential game solution, solve the continuous and pulse capture regions.

2. The method according to claim 1, characterized in that In step S1, define , , They are the initial time, current time, terminal time, and remaining time. , , and are the target maximum acceleration, guidance law and time constant respectively, , and They are respectively the maximum acceleration of the aircraft, the guidance law and the time constant, and the zero control miss distance is the terminal lateral distance without any guidance command, and the initial value of zero control miss distance is The terminal time value of zero control miss distance is , considering the end-stage pursuit scenario of a two-dimensional plane approximate head-on collision, the pursuit model with zero-control miss distance as the state quantity is: （1） In the above formula, ， 。 3. The method according to claim 2, characterized in that In step S2, the cost function is selected: （2） In the formula, the aircraft guidance energy weight , target guidance energy weight ; The following definitions are given for the continuous and pulse flags of the pursuit and escape parties: and : If the aircraft guidance law is continuous, then ; If the aircraft guidance law is pulsed, then ; If the target guidance law is continuous, then ; If the target guidance law is pulsed, then ,Right now: ， Define the allowable off-target amount , maximum acceleration ratio , time constant ratio , then the capture zone is defined as satisfying of , , and gather; 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: ， ， in, , ; If the capture zone boundary is considered , then the switching time between the pursuit and escape parties is and ,Right now and Respectively meet: ， ， The process variables are: ， Depending on whether the guidance law has reached saturation, the following five pursuit scenarios are introduced: Chase scene 1: ; Chase scene 2: ; Chase scene 3: ; Chase scene 4: ,and ; Chase scene 5: ,and .

4. The method according to claim 3, characterized in that In step S3, for the five pursuit scenarios described in step S2, a unified continuous and impulse differential game guidance law is obtained: Pursuit Scenario 1: Aircraft Guidance Law , target guidance law ,in: ， ， ， Pursuit scenario 2: Guidance law for both parties: ， ， Pursuit scenario 3: Guidance law for both parties: ， ， Pursuit Scenario 4: Guidance Laws for Both Pursuit and Escape: ， Pursuit scenario 5: Guidance law for both parties: 。 5. The method according to claim 4, characterized in that In step S4, according to the fact that the denominator of the guidance law in step S3 is not 0, the existence condition of the differential game solution is obtained: Chase scene 1: , ; Chase scene 2: , ; Chase scene 3: ， ， ； Chase scene 4: , ; Chase scene 5: ， ， 。 6. The method according to claim 5, characterized in that In step S5, when the existence condition of step S4 is satisfied, the capture area is obtained. and non-capture zone , : （4） in, , It is the capture zone boundary value of pursuit scenario 1-5, and the expression is as follows: ， ， ， ， ， ， ， ， ， 。 7. A device for solving the capture zone of differential game of continuous and pulse guidance laws, characterized in that: Includes the following modules: The zero-miss pursuit model establishment module establishes a two-dimensional zero-miss pursuit model based on the continuous or pulse maneuvers of the pursuing and escaping parties. The pursuit and escape scenario introduction module introduces the pursuit and escape scenario based on the zero-control miss distance pursuit and escape model; Guidance law solving module, which solves the guidance law in both continuous and pulse forms in pursuit scenarios; The existence condition solving module solves the existence condition of the differential game solution according to the fact that the denominator in the guidance law is not zero; The continuous and pulse capture region solving module solves the continuous and pulse capture regions under the condition of satisfying the existence of differential game solutions.

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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