A method and device for solving the capture region of differential game for continuous and pulse guidance laws

Abstract

The present invention discloses a method and device for solving the differential game capture zone of continuous and pulse guidance laws, comprising the following steps: considering the continuous or pulse maneuvers of both the pursuer and the escaper, establishing a two-dimensional plane pursuit model with zero-control miss distance as the state variable; introducing pursuit scenarios based on the differential game guidance law form of both parties; solving the differential game guidance law in different pursuit scenarios, and writing the continuous guidance law and the pulse guidance law in a unified form; solving the existence condition of the differential game solution based on the fact that the denominator of the guidance law is not zero; and solving the differential game capture zone in different scenarios. The differential game capture zone solution method in the present invention reveals the difference between the capture zones of pulse and continuous guidance laws, and can provide a theoretical basis for the selection of continuous and pulse differential game guidance parameters with different acceleration ratios and time constant ratios. The analysis method is simple and has a wide range of applications.

Description

Technical Field

[0001] The present invention belongs to the field of aircraft guidance system design, and in particular relates to a method and device for solving the capture region of a differential game of continuous and pulse guidance laws. Background Art

[0002] Guidance law capture zone analysis theoretically evaluates the performance of different guidance laws and reveals the impact of various factors on their performance. It has been widely studied in recent years. This analysis primarily focuses on proportional guidance and its derivatives, as well as differential game guidance laws. The capture zone analysis for proportional guidance and its derivatives is based on inequality transformations constrained by physical inequalities. This makes it difficult to derive necessary and sufficient conditions for the capture zone when the pursuit and escape scenario is complex. However, differential game guidance laws, which use the optimal capture boundary for both pursuers and escapees, facilitate the determination of necessary and sufficient conditions for the capture zone. Theoretical analysis of the capture zone for pulsed guidance laws has only considered the cases of one continuous guidance law and one pulsed guidance law, ignoring the case where both parties are pulsed. Furthermore, no comparative analysis of the capture zones for continuous and pulsed guidance laws has been conducted.

[0003] Obviously, it is particularly important to design a differential game capture zone solution method for continuous and pulse guidance laws, which can overcome the existing conservatism, be close to engineering practice, and improve the applicability of the guidance system. Summary of the Invention

[0004] The technical problem to be solved by the present invention is how to obtain the capture zones for continuous and pulsed guidance laws when both players in the game are equipped with pulse engines. Based on this, the present invention designs a method and apparatus for solving the capture zones for continuous and pulsed differential game guidance laws. The method unifies the continuous and pulsed guidance laws into a unified form and performs a unified capture zone solution. Four pursuit models are considered: a continuous guidance law target and a continuous guidance law aircraft, a continuous guidance law target and a pulsed guidance law aircraft, a pulsed guidance law target and a continuous guidance law aircraft, and a pulsed guidance law target and a pulsed guidance law aircraft. Compared with existing methods, the present invention reveals the difference between the capture zones for pulsed and continuous guidance laws and derives the conditions that must be met for the pulsed guidance laws of both pursuers and evaders to be considered continuous guidance laws during the design process. The resulting capture zone analysis provides a theoretical basis for selecting guidance parameters for continuous and pulsed differential game guidance with different acceleration ratios and time constant ratios. The method is characterized by its simplicity and wide applicability.

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

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

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

[0008] S3: Solve the differential game guidance law in different pursuit scenarios and express the continuous guidance law and the impulse guidance law in a unified form;

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

[0010] S5: Determine the capture region of the differential game for continuous and impulse guidance laws under the solution existence conditions in different scenarios.

[0011] The present invention proposes a device for solving the capture region of differential games for continuous and impulse 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 fleeing parties.

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

[0014] The guidance law solving module 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 based on 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 existence conditions 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 having executable instructions stored thereon, which, when executed by a processor, enables the processor to implement the above method.

[0019] Beneficial effects of the present invention:

[0020] (1) This invention unifies the continuous and impulse guidance laws and performs a unified solution for the capture region. The resulting capture region analysis provides a theoretical basis for selecting guidance parameters for continuous and impulse differential game systems with different acceleration ratios and time constant ratios. It has the advantages of a simple analysis method and a wide range of applicability.

[0021] (2) The present invention reveals the difference between the capture zones 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 pursuit and escape parties to be regarded as a continuous guidance law. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 Flowchart 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 A schematic diagram of the capture zone simulation of the present invention when the guidance energy weights of both the pursuer and the fugitive are relatively small;

[0024] Figure 3 This 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 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 objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are intended only to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other. To achieve the above-mentioned objectives, the present invention adopts the following technical solutions.

[0028] like Figure 1 As shown, the steps of the differential game capture zone solution method for continuous and pulse guidance laws 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 distance as the state quantity;

[0030] Step S2, based on the dual differential game guidance law, a two-dimensional plane pursuit model is established with zero-control miss distance as the state variable, and a pursuit scenario is introduced;

[0031] Step S3: Solve the differential game guidance law in different pursuit scenarios and write the continuous guidance law and the impulse guidance law into a unified form;

[0032] Step S4, solving the existence condition of the differential game solution based on 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 method for solving the capture region of the differential game of the continuous and pulse guidance laws of the present invention are as follows:

[0036] Step S1 is specifically as follows: 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 its initial value is , the terminal time value is .

[0037] Considering the final stage of pursuit and escape scenario with a two-dimensional plane approximating head-on collision, the pursuit and escape model with zero-control miss distance as the state variable is:

[0038] (1)

[0039] Where,

[0040] , .

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

[0042] Select the differential game cost function:

[0043] (2)

[0044] Where, the aircraft guidance energy weight is , target guidance energy weight .

[0045] The following definitions are given for the continuous and pulsed guidance laws of both 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 target with continuous guidance law and an aircraft with pulse guidance law. 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 respectively , , 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 distance and the specific expression of the guidance law, the following five pursuit scenarios are introduced according to whether the guidance law has reached 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 unified continuous and impulse 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] ,

[0063] ,

[0064] ;

[0065] Pursuit Scenario 2: Guidance Laws for Both Pursuers and Escapers:

[0066] ,

[0067] Where,

[0068] ;

[0069] Pursuit Scenario 3: Guidance Laws for Both Pursuers and Escapers:

[0070] ,

[0071] Where,

[0072] ;

[0073] Pursuit Scenario 4: Guidance Laws for Both Pursuers and Escapers:

[0074] ;

[0075] Pursuit Scenario 5: Guidance Laws for Both Pursuers and Escapers:

[0076] ;

[0077] S4: For the five pursuit scenarios described in S2, based on the fact that the denominator of the guidance law described in S3 is not zero, the existence conditions of the differential game solution are obtained as follows:

[0078] Chase scene 1: , ;

[0079] Chase scene 2: , ;

[0080] Chase scene 3:

[0081] , , ;

[0082] Chase scene 4: , ;

[0083] Chase scene 5:

[0084] , , .

[0085] 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 maneuvering and impulse maneuvering is obtained. and non-capture zones , ,as follows:

[0086] (4)

[0087] in, , It is the capture zone boundary value for pursuit scenarios 1-5, and is expressed as follows:

[0088] , ,

[0089] ,

[0090] ,

[0091] ,

[0092] ,

[0093] ,

[0094] ,

[0095] ,

[0096] .

[0097] For the capture zone , 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.

[0098] The following simulation results under different guidance energy weights are used as an example to illustrate the effectiveness of the method proposed in the present invention. , , , , , , . Figure 2 This is a simulation diagram of the capture area 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 Schematic diagram of the capture zone simulation of the aircraft pulse guidance law when the guidance energy weights of both the pursuing and escaping parties are large. Figure 2 and Figure 3 The guidance energy weight of both sides , , Figure 4 and Figure 5 The guidance energy weight of both sides , . Figure 3 middle, express , The capture zone boundary and , The difference between the capture zone boundaries when express , The capture zone boundary and , The difference between the capture zone boundaries at .

[0099] Figure 2 According to the optimal solution existence condition described in the fourth step, 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 area differences of the other three cases are small, 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 .

[0100] Based on the above analysis and explanation, 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 guidance parameters of continuous and pulse differential countermeasures with different acceleration ratios and time constant ratios. It has the characteristics of simple analysis method and wide applicability.

[0101] The above applications are only some embodiments of the present application. For those skilled in the art, without departing from the inventive concept of the present application, several modifications and improvements can be made, which all fall within the scope of protection of the present application.

Claims

1. A method for solving the capture region of differential game for continuous and impulse guidance laws, characterized by: The following steps are involved: S1: Based on the continuous or pulse maneuvers of the pursuing and fleeing parties, a two-dimensional zero-miss distance pursuit model is established; S2: Based on the zero-miss pursuit model, a pursuit scenario is introduced; S3: In pursuit scenarios, solve the guidance law that unifies continuous and pulse forms; S4: According to the guidance law, the denominator is not zero, solve the existence condition of the differential game solution; S5: Solve the continuous and impulse capture regions under the existence conditions of differential game solutions; 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 applying any guidance command, and the initial value of the zero control miss distance is The terminal moment value of the zero-control miss distance is , considering the two-dimensional plane near-head-on collision pursuit and escape scenario, the pursuit and escape model with zero-control miss distance as the state quantity is: （1） In the above formula, ， 。 2. The method according to claim 1, wherein In step S2, the cost function is selected: （2） Where, the aircraft guidance energy weight is , target guidance energy weight ; The following definitions are given for the continuous and pulsed guidance laws of both 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 Satisfy respectively: ， ， 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 .

3. The method according to claim 2, wherein 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 Laws for Both Pursuers and Escapers: ， ， Pursuit Scenario 3: Guidance Laws for Both Pursuers and Escapers: ， ， Pursuit Scenario 4: Guidance Laws for Both Pursuers and Escapers: ， Pursuit Scenario 5: Guidance Laws for Both Pursuers and Escapers: 。 4. The method according to claim 3, wherein In step S4, according to the fact that the denominator of the guidance law in step S3 is not zero, 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: ， ， 。 5. The method according to claim 4, wherein In step S5, when the existence condition of step S4 is satisfied, the capture zone is obtained. and non-capture zones , : （4） in, , It is the capture zone boundary value for pursuit scenarios 1-5, and is expressed as follows: ， ， ， ， ， ， ， ， ， 。 6. A device for solving the capture region of differential game of continuous and impulse 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 fleeing parties. The pursuit scenario introduction module introduces the pursuit scenario based on the zero-control miss distance pursuit model; The guidance law solving module 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 based on the fact that the denominator in the guidance law is not zero; Continuous and pulse capture region solving module, which solves continuous and pulse capture regions under the existence condition of differential game solutions; definition , , 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 applying any guidance command, and the initial value of the zero control miss distance is The terminal moment value of the zero-control miss distance is , considering the two-dimensional plane near-head-on collision pursuit and escape scenario, the pursuit and escape model with zero-control miss distance as the state quantity is: （1） In the above formula, ， 。 7. 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 are enabled to implement the method according to any one of claims 1 to 5.

8. 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 5.

9. 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 5 is implemented.

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