An anti-interference penetration game control method for hypersonic aircraft

Abstract

The present invention relates to an anti-interference penetration game control method for a hypersonic aircraft, and belongs to the field of aerospace. First, a hypersonic aircraft penetration game model and a measurement error interference model are established; second, an interference observer is designed to estimate and compensate for the measurement error interference in the penetration game model in real time; then, a differential game three-dimensional guidance law is designed to achieve maneuver avoidance of the hypersonic aircraft; finally, the differential game guidance law and the anti-interference control law are combined to ensure the stability of the closed-loop system by reasonably selecting the observer and controller parameters. The present invention designs an anti-interference penetration game control algorithm based on differential game and interference observer, realizes intelligent penetration under measurement error interference through active maneuvering under the optimal strategy of both the attacking and defending sides, and improves the anti-interference capability and penetration efficiency of the hypersonic aircraft.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace, and in particular relates to an anti-interference penetration game control method for a hypersonic aircraft. Background Art

[0002] Hypersonic vehicles are the ultimate weapon that will revolutionize future warfare. Their supersonic speeds allow them to rapidly strike military targets thousands or even tens of thousands of kilometers away in a short period of time. Therefore, they are a key technology in the international arms race and hold immense strategic significance. However, the characteristics of large airspace, wide speed range, high dynamics, and diverse missions make hypersonic vehicles, their environments, and their missions fraught with interference and uncertainty, making their penetration control challenging.

[0003] Research on methods for hypersonic vehicle penetration control has been conducted both domestically and internationally. Existing ballistic penetration technologies primarily rely on pre-programmed ballistic maneuvers, lacking intelligence. Once the interceptor identifies the maneuvering pattern, the probability of interception increases significantly. While game-based penetration technology can intelligently adapt to enemy maneuvers, it fails to fully consider the impact of various interference and fault factors on the game strategy. Traditional penetration control methods are insufficiently resistant to interference and, under interference, cannot meet the requirements for ultra-stable, ultra-fast, and ultra-accurate control of hypersonic vehicles. To ensure successful penetration, identifying interceptor missile maneuver information is a critical prerequisite. This identification directly impacts interceptor missile trajectory prediction. However, in actual combat scenarios, errors often exist in the measurement of interceptor missile motion information. Further research is needed to design interference-resistant game-based penetration control strategies that are susceptible to measurement errors.

[0004] In summary, the existing methods for the penetration control problem of hypersonic aircraft are still insufficient in terms of interference characterization, influence mechanism analysis and compensation control. In order to further improve the penetration intelligence, safety and success rate of hypersonic aircraft, it is urgent to propose a new anti-interference penetration game control method for hypersonic aircraft. Summary of the Invention

[0005] In view of the fact that existing hypersonic aircraft penetration strategies are unable to solve the problem of measurement errors in the motion state of enemy interceptor missiles, the present invention provides an anti-interference penetration game control method for hypersonic aircraft. The method is an anti-interference penetration strategy that combines differential game and nonlinear interference observer. It can estimate and compensate for measurement error interference in real time, thereby improving the penetration success rate of hypersonic aircraft under measurement errors, and can be used for penetration strategy design in battlefield environments.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] In view of the hypersonic aircraft penetration situation in which there is a measurement error in the motion state of the enemy interceptor missile, a hypersonic aircraft anti-interference penetration game control method of the present invention includes the following steps:

[0008] The first step is to establish a relative kinematic model of the penetration missile and the interceptor missile based on the kinematic and dynamic models of the hypersonic vehicle. On this basis, the penetration game model is solved and the mathematical representation and modeling of the measurement error are completed.

[0009] The second step is to design an adaptive disturbance observer and anti-disturbance control law based on the upper bound of the measurement error disturbance to ensure real-time estimation and compensation of the disturbance.

[0010] The third step is to design a differential game guidance law based on the penetration game model to obtain the Nash equilibrium solution for both the attack and defense game.

[0011] In the fourth step, based on the adaptive dynamic programming technology and the evaluation neural network, the optimal cost function is estimated, and the anti-interference penetration game strategy is obtained based on the interference observer.

[0012] The beneficial effects of the present invention compared with the prior art are:

[0013] The present invention proposes an anti-interference penetration game control method for a hypersonic aircraft. The controller includes two parts with a composite structure. The anti-interference controller is used for real-time estimation and compensation of measurement errors, thereby ensuring the robust performance of the closed-loop system. The differential game controller is used for active maneuvering according to the enemy's interception strategy, thereby ensuring avoidance of interception under measurement errors and improving the penetration success rate of the hypersonic aircraft in complex battlefield environments. The present invention can not only enable the hypersonic aircraft to intelligently and autonomously adjust the penetration guidance law according to the enemy's maneuvering strategy to actively avoid interception, but also can perform real-time compensation and estimation of the measurement error of the enemy interceptor missile motion state during the penetration process, thereby increasing the robust performance of the hypersonic aircraft system and improving the penetration success rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 The present invention is a flowchart of an anti-interference penetration game control method for a hypersonic aircraft. DETAILED DESCRIPTION

[0015] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0016] like Figure 1As shown, the anti-interference penetration game control method of a hypersonic aircraft of the present invention is specifically implemented in the following steps:

[0017] The first step is to establish a relative kinematic model of the penetration missile and the interceptor missile based on the kinematic and dynamic models of the hypersonic vehicle. On this basis, the penetration game model is solved and the mathematical representation and modeling of the measurement error are completed.

[0018] According to the dynamics of gliding hypersonic aircraft, the system model is as follows:

[0019] (1)

[0020] Among them, the superscript represents the derivative of a variable, , and Represents the horizontal two-dimensional coordinates and altitude of the hypersonic aircraft; , and Indicates the speed, track angle and heading angle of the aircraft; represents the acceleration due to gravity and satisfies ,in is the acceleration due to gravity at sea level, represents the radius of the Earth; Indicates the roll angle; and It represents the lift and drag of a hypersonic vehicle. The specific expressions are as follows:

[0021] (2)

[0022] in, represents the atmospheric density, satisfying , is the atmospheric density at sea level, is the standard height; represents the reference characteristic area of ​​a gliding hypersonic vehicle; and Denotes the lift and drag coefficients. Define the lower right corner is the variable related to the bulletproof defense, with the lower right corner marked is the variable related to the interceptor missile. The relative distance between the penetration missile and the interceptor missile in three-dimensional space is defined as , the lateral sight angle is , the vertical sight angle is According to the geometric relationship between the attacking and defending aircraft, the projection of the speed of the penetration missile and the interceptor missile in the line of sight coordinate can be obtained as follows:

[0023] (3)

[0024] Among them, among them, Respectively represent the penetration missile in the line of sight coordinates Speed ​​in the axis direction, The speed in the axial direction and the speed in the longitudinal direction, Respectively represent the interceptor missile in the line of sight coordinates Speed ​​in the axis direction, The speed in the axial direction and the speed in the longitudinal direction, The conversion matrix is ​​specifically expressed as follows:

[0025] (4)

[0026] Consider the measurement error interference as follows:

[0027] (5)

[0028] in, Indicates the true relative distance between the penetration missile and the interceptor missile, the longitudinal sight angle and the lateral sight angle; represents a measurement error coefficient greater than 0. The relative motion relationship between the penetration missile and the interceptor missile under the interference of measurement error can be expressed as:

[0029] (6)

[0030] The concept of zero-control miss distance is introduced, and its expression is as follows:

[0031] (7)

[0032] in, represents the relative velocity along the line of sight; Indicates the longitudinal line of sight angular rate. Under the premise of controlling the longitudinal sight angular rate If the line of sight angular rate is set to 0, the target can be intercepted in the longitudinal plane. As the state quantity of the attack and defense game model, the longitudinal line of sight angular rate model under the interference of measurement error can be expressed as:

[0033] (8)

[0034] in, Indicates measurement error interference; sudden bulletproof virtual controller and interceptor missile virtual controller for:

[0035] (9)

[0036] in, They represent the lift of interceptor missile and penetration missile respectively; Respectively represent the roll angles of interceptor missiles and penetration missiles; Respectively represent the mass of interceptor missile and penetration missile; They represent the gravitational acceleration of the interceptor missile and the penetration missile respectively; They represent the track angles of interceptor missiles and penetration missiles respectively. The expression is as follows:

[0037] ;

[0038] The second step is to design an adaptive disturbance observer and anti-disturbance control law based on the upper bound of the measurement error disturbance to ensure real-time estimation and compensation of the disturbance.

[0039] according to The expression of :

[0040] (10)

[0041] in, represents an unknown constant; represents a continuous function, and its expression is:

[0042] (11)

[0043] For unknown constants , design disturbance observer as follows:

[0044] (12)

[0045] in, and represents an observer gain greater than 0; ,function Defined as ,symbol represents partial differential; function Defined as .

[0046] Design the anti-interference controller as follows:

[0047] (13)

[0048] in, Represents any positive number greater than 0.

[0049] The third step is to design a differential game guidance law based on the penetration game model to obtain the Nash equilibrium solution for both the attack and defense game.

[0050] For both the attacker and the defender, the following zero-sum differential game cost function is designed:

[0051] (14)

[0052] in,

[0053] (15)

[0054] is a weight coefficient greater than 0, is a control gain greater than 0.

[0055] The Hamiltonian function of the zero-sum differential game between the attacker and the defender is designed as:

[0056] (16)

[0057] in, Represents the cost function Line of sight angular velocity The partial derivative of . Then the Nash equilibrium solution for both the attacker and the defender is:

[0058] (17)

[0059] The fourth step is to estimate the optimal cost function based on the adaptive dynamic programming technology and the evaluation neural network, and obtain the anti-interference penetration game strategy based on the interference observer.

[0060] The evaluation neural network is defined as follows:

[0061] (18)

[0062] in, Represents the activation function vector, the superscript symbol Represents the transpose of a vector or matrix; represents the ideal weight vector; Represents the approximation error. Then the evaluation network estimation function is designed as follows:

[0063] (19)

[0064] Finally, the differential game control strategy is:

[0065] (20)

[0066] Among them, the ideal weight vector The adaptive estimation update law is designed as:

[0067] (twenty one)

[0068] Error term The design is as follows:

[0069] (twenty two)

[0070] Finally, combining equations (13) and (20), the guidance law applied to the penetration ballistic missile is for:

[0071] (twenty three)

[0072] The contents not described in detail in the specification of the present invention belong to the prior art known to those skilled in the art.

Claims

1. A hypersonic vehicle anti-interference penetration game control method, characterized in that: The following steps are involved: The first step is to establish a relative kinematic model of the penetration missile and the interceptor missile based on the kinematic and dynamic models of the hypersonic vehicle. On this basis, the penetration game model is solved and the mathematical representation and modeling of the measurement error are completed. The second step is to design an adaptive disturbance observer and anti-disturbance control law based on the upper bound of the measurement error disturbance to ensure real-time estimation and compensation of the disturbance. The third step is to design a differential game guidance law based on the penetration game model to obtain the Nash equilibrium solution for both the attack and defense game. The fourth step is to estimate the optimal cost function based on adaptive dynamic programming and evaluation neural network, and obtain the anti-interference penetration game strategy based on the interference observer. The first step comprises: The dynamic model of hypersonic aircraft is as follows: （1） Among them, the superscript represents the derivative of a variable, , and Represents the horizontal two-dimensional coordinates and altitude of the hypersonic aircraft; , and Indicates the speed, track angle and heading angle of the aircraft; represents the acceleration due to gravity and satisfies ,in is the acceleration due to gravity at sea level, represents the radius of the Earth; Indicates the roll angle; and It represents the lift and drag of a hypersonic vehicle. The specific expressions are as follows: （2） in, represents the atmospheric density, satisfying , is the atmospheric density at sea level, is the standard height; represents the reference characteristic area of ​​a gliding hypersonic vehicle; and Indicates lift and drag coefficients, defining the lower right corner is the variable related to the bulletproof defense, with the lower right corner marked is the relevant variable of the interceptor missile, and the relative distance between the penetration missile and the interceptor missile in three-dimensional space is defined as , the lateral sight angle is , the vertical sight angle is According to the geometric relationship between the attacking and defending aircraft, the projection of the speed of the penetration missile and the interceptor missile in the line of sight coordinate is: （3） in, Respectively represent the penetration missile in the line of sight coordinates Speed ​​in the axis direction, The speed in the axial direction and the speed in the longitudinal direction, Respectively represent the interceptor missile in the line of sight coordinates Speed ​​in the axis direction, The speed in the axial direction and the speed in the longitudinal direction, The conversion matrix is ​​specifically expressed as follows: （4） Consider the measurement error interference as follows: （5） in, They represent the relative distance between the penetration missile and the interceptor missile, the longitudinal sight angle and the lateral sight angle respectively; represents a measurement error coefficient greater than 0. The relative motion relationship between the penetration missile and the interceptor missile under the interference of measurement error is expressed as: （6） Introducing zero miss distance , that is, the minimum deviation distance when the penetration missile and the interceptor missile no longer exert control, its mathematical expression is defined as follows: （7） in, represents the relative velocity along the line of sight; represents the longitudinal line of sight angular rate, Under the premise of controlling the longitudinal sight angular rate Converges to 0, that is, it is possible to intercept the target in the longitudinal plane. Therefore, in the longitudinal plane, the line of sight angular rate is selected As the state quantity of the game model, the longitudinal line of sight angular rate model under the interference of measurement error is expressed as: （8） in, Indicates measurement error interference; sudden bulletproof virtual controller and interceptor missile virtual controller for: （9） in, They represent the lift of interceptor missile and penetration missile respectively; Respectively represent the roll angles of interceptor missiles and penetration missiles; Respectively represent the mass of interceptor missile and penetration missile; They represent the gravitational acceleration of the interceptor missile and the penetration missile respectively; They represent the track angles of interceptor missiles and penetration missiles respectively; The expression is as follows: ； In formula (8), ,in represents the differential game guidance law, represents the control law used to compensate for the measurement error disturbance.

2. The anti-interference penetration game control method for a hypersonic aircraft according to claim 1, characterized in that: The second step includes: according to The expression of : （10） in, represents an unknown constant; represents a continuous function, and its expression is: （11） For unknown constants , design disturbance observer as follows: （12） in, and represents an observer gain greater than 0; ,function Defined as ,symbol represents partial differential; function Defined as ; Design the anti-interference controller as follows: （13） in, Represents any positive number greater than 0.

3. The anti-interference penetration game control method for a hypersonic aircraft according to claim 2, characterized in that: The third step includes: Design the following zero-sum differential game cost function: （14） in, （15） is a weight coefficient greater than 0, is a control gain greater than 0; The Hamiltonian function of the zero-sum differential game between the attacker and the defender is designed as: （16） in, Represents the cost function Line of sight angular velocity The partial derivative of , then the Nash equilibrium solution for both the attacker and the defender is: （17）。 4. The anti-interference penetration game control method for a hypersonic aircraft according to claim 3, characterized in that: The fourth step includes: The evaluation neural network is defined as follows: （18） in, Represents the activation function vector, the superscript symbol Represents the transpose of a vector or matrix; represents the ideal weight vector, with the superscript represents the ideal value; Represents the approximation error, then the evaluation network estimation function is designed as follows: （19） The differential game control strategy is: （20） Among them, the ideal weight vector The adaptive estimation update law is designed as: （21） and Represents the gain coefficient of the adaptive update law, the error term The design is as follows: （22） Finally, combining equations (13) and (20), the guidance law applied to the penetration ballistic missile is for: （23）。

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