Active defense cooperative penetration guidance method considering both observability and anti-interception accuracy
By structuring an expanded state observer in missile penetration technology and designing a sliding mode surface and guidance law that takes into account observability and anti-interception accuracy, the problem of difficulty in taking into account observability and anti-interception accuracy in the existing technology is solved, and a more efficient missile penetration effect is achieved.
Patent Information
- Application Number
- CN202310757678.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-06-26
- Publication Date
- 2025-03-14
- Estimated Expiration
- 2043-06-26
AI Technical Summary
The existing missile penetration technology is difficult to take into account both observability and anti-interception accuracy, especially in sliding mode control systems, which is difficult to obtain the upper boundary of system disturbances, resulting in difficult to ensure guidance accuracy and observability.
By constructing an expansion state observer, the unknown maneuver of incoming interceptors is estimated in real time and compensated for the sliding mold guidance law of the defensive bomb, weakening the sliding mode vibration and reducing the overload required by the defensive bomb to strike incoming interceptors. At the same time, a sliding mold surface and guidance law are designed that takes into account the target detectability and adrenaline guidance accuracy.
In active defense coordinated penetration scenarios, the anti-interception accuracy and observability of the defensive bullets are improved, the sliding mode vibration is reduced, the acceleration of the defensive bullets is not saturated for a long time, and the success rate of penetration is improved.
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Figure CN116795136B_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of missile guidance and control, and specifically relates to an active defense coordinated penetration guidance method taking into account both observability and anti-interception accuracy. Background Art
[0002] In recent years, with the rapid development of missile defense technology, ballistic missile penetration faces great difficulties. Missile penetration strategies are mainly divided into anti-reconnaissance and anti-interception. Active defense strategy, as an efficient anti-interception penetration means, is a defense strategy that releases defense missiles to attack incoming interceptor missiles through one's own target aircraft or accompanying flight platform. At the same time, the target missile and the defense missile can take coordinated maneuvers to improve the anti-interception performance of the defense missile and increase the probability of penetration.
[0003] In addition, in the guidance process, the state estimation information of the target is an important source of input information, and its estimation accuracy directly affects the guidance performance. Therefore, in the process of guidance law design, the guidance system is required to ensure the guidance accuracy while taking into account the target state estimation performance, which puts higher requirements on the design of the guidance law. Since the sliding mode control method has strong robustness to system uncertainty and external interference, and has the advantages of simple structure, easy implementation and fast response, it is applied to the guidance law design. However, in general, the first-order sliding mode control system requires the upper bound of the system disturbance to be known, but in actual situations, this information is difficult to obtain. In order to solve this problem, an extended state observer is constructed to estimate the unknown maneuvers of the interceptor missile in real time, and it is compensated to the sliding mode guidance law of the defense missile, which can effectively weaken the sliding mode buffeting and reduce the overload required for the defense missile to strike the incoming interceptor missile. Therefore, it is necessary to design an active defense cooperative penetration guidance law that takes into account observability and anti-interception accuracy by combining the advantages of active defense, sliding mode control and extended state observer. Summary of the invention
[0004] In view of the deficiencies in the prior art, the present invention provides an active defense cooperative penetration guidance method that takes into account both observability and anti-interception accuracy.
[0005] The specific steps of the present invention are as follows:
[0006] Step 1: Active defense nonlinear kinematics modeling
[0007] Construct an active defense nonlinear kinematic model consisting of target missiles, defense missiles, and incoming interceptor missiles;
[0008] Step 2: Construction of sliding mode state variables and sliding surface
[0009] Design the sliding mode state variable x that meets the requirements of observability and anti-interception accuracy 1 and x 2 , where x 1is the deviation between the target missile-interceptor missile sight angle difference and the expected value, and the deviation between the defense missile-interceptor missile sight angle difference and the expected value, x 2 It represents the derivative of the difference in sight angle between the target missile and the interceptor missile and the derivative of the difference in sight angle between the defense missile and the interceptor missile; then the first-order dynamic equation of the sliding mode state variable is obtained and Expression is used to construct the sliding surface s that takes into account both target detectability and penetration guidance accuracy.
[0010] Step 3: Design of one-way collaborative sliding mode guidance law between target missile and defense missile
[0011] Considering the one-way cooperative mode of target missile and defense missile, in order to meet the guidance requirements in different scenarios, the double power reaching law and the exponential reaching law with state feedback are used to design the guidance law. In order to ensure the finite time convergence of the sliding mode control system, the double power reaching law is introduced, and the one-way cooperative sliding mode guidance law G of the target missile and defense missile under double power approach is designed according to the sliding surface in step 2. 1 ; In order to weaken the sliding mode chattering phenomenon, based on the exponential approach law with state feedback, and according to the sliding surface in step 2, the one-way cooperative sliding mode guidance law G of the target missile and the defense missile under the exponential approach with state feedback is designed. 2 .
[0012] Step 4: Design of the target missile-defense missile two-way collaborative sliding mode guidance law
[0013] The two-way coordination mode between the target missile and the defense missile can reduce the overload required for the defense missile to strike the interceptor missile, and prevent the acceleration of the defense missile from being in a saturated state for a long time, resulting in anti-interception failure. The composite control law of the target missile and the defense missile is regarded as u, and the objective function J of the weighted sum of the acceleration of the target missile and the defense missile is constructed. u is brought into the objective function J, and this two-way coordination problem is expressed as an optimization problem of minimizing the acceleration of the target missile and the defense missile. When the reaching law is a double power reaching law, the two-way coordinated sliding mode guidance law G of the target missile and the defense missile under the double power reaching law is designed. 3 ; When the reaching law is an exponential reaching law with state feedback, the target missile-defense missile bidirectional cooperative sliding mode guidance law G is designed under the exponential reaching law with state feedback. 4 ;
[0014] Step 5: Design of active defense sliding mode guidance law based on extended state observer
[0015] In actual situations, the acceleration a of the incoming interceptor missile is M Usually unknown, an extended state observer is introduced to estimate the disturbance term d related to the acceleration of the incoming interceptor in real time; according to the derivative of the state variable of the sliding mode system Construct an extended state observer, Represents the derivative of the deviation between the sight angle difference and the expected value; get x 1 and the disturbance estimation value of d, and thus the active defense sliding mode cooperative guidance law based on the extended state observer is designed;
[0016] The designed extended state observer is specifically:
[0017] First, D 1 =(R DM cos(γ M -θ TM )-R TM cos(γ M -θ DM ))a M Set it as augmented state, and construct the following extended state observer according to the first-order dynamic equation of the sliding mode state variable:
[0018]
[0019] Where Ψ DT =Φ DT -Φ f , z 1 and e represent The estimated value and estimation error of z 2 D 1 The estimated value of β 1 and β 2 is the observation gain, γ j , a j The heading angle and acceleration of each missile. T, D, and M represent the target missile, defense missile, and incoming interceptor missile, respectively. R DM , R TM and θ DM ,θ TM denote the relative distance and line of sight between the defense missile and the interceptor missile and the target missile and the interceptor missile, Φ DT is the line of sight angle deviation between target missile and interceptor missile, and between defense missile and interceptor missile, Φ f is the desired line of sight angle deviation, and the fal function is defined as
[0020]
[0021] Among them, 0<τ<1, 0<δ<1.
[0022] Therefore, the estimated value of the system disturbance d is described as
[0023]
[0024] The disturbance estimate The target missile-defense missile one-way cooperative sliding mode guidance law G is introduced respectively 2and target missile-defense missile two-way cooperative sliding mode guidance law G 4 In the paper, the one-way / two-way collaborative active defense sliding mode guidance law based on the extended state observer can be obtained.
[0025] Preferably, the active defense nonlinear kinematic model is specifically as follows: the target missile, the defense missile and the incoming interceptor missile are represented by T, D and M respectively. The active defense nonlinear kinematic model is represented by two sets of relative motion models of the defense missile-interceptor missile and the interceptor missile-target missile. The active defense nonlinear kinematic model is established as
[0026]
[0027] Where, i = {T, D}, j = {T, D, M}, γ j , a j and V j Respectively represent the heading angle, acceleration and speed of each missile; R DM , R TM and θ DM ,θ TM They represent the relative distance and line of sight angle between the defense missile and the interceptor missile and between the target missile and the interceptor missile respectively.
[0028] As a preferred method, in step 2, let Φ DT is the line of sight angle deviation between target missile and interceptor missile, and between defense missile and interceptor missile, satisfying Φ DT =θ TM -θ DM ,θ DM ,θ TM They represent the sight angles between the defense missile and the interceptor missile and between the target missile and the interceptor missile respectively; the target flight state estimation accuracy is affected by the observability of the measurement information, and the observability of the measurement information has a certain relationship with the spatial configuration between the target aircraft and the sensor. When the angle between the two sensors and the target aircraft is large, the two angle information can better determine and estimate the target state. Therefore, the sight angle difference Φ between the target missile and the interceptor missile and the defense missile and the interceptor missile is increased. DT Enhance the observability of target angle detection information;
[0029] The sliding mode state variables are defined as follows
[0030]
[0031] In the formula, Φ f For the desired sight angle deviation, the first-order dynamic equation of the sliding mode state variable is as follows:
[0032]
[0033] Where d is the unknown disturbance;
[0034]
[0035] In the formula, and Respectively represent the interception time t f The distance between the target missile-interceptor missile and the defense missile-interceptor missile.
[0036] The sliding surface designed to take into account both target detectability and penetration guidance accuracy is:
[0037] s=x 2 +ηx 1 ,η>0 (8).
[0038] As a preferred method, in step 3, the one-way coordination mode between the target missile and the defense missile is considered. In order to ensure the finite time convergence of the sliding mode control system, the double power reaching law is introduced.
[0039]
[0040] Where η 1 >0;η 2 >0;0<a 1 <1; a 2 >1; The double power reaching law has the global fixed time convergence characteristic, ensuring that the sliding mode state quantity converges to the steady-state error bound in a finite time.
[0041] According to the sliding surface in step 2 and the double power reaching law in step 3, the one-way cooperative sliding mode guidance law G of the target missile and the defense missile is designed. 1 for
[0042]
[0043] In the formula,
[0044] Since the double-power approaching sliding mode guidance law of formula (10) will produce large chattering on the sliding mode switching surface, an exponential approaching law with state feedback is introduced to weaken the sliding mode chattering phenomenon. The approaching law expression is:
[0045]
[0046] In the formula, h 1 >0;h 2 >0; α>0; 0<β<1; 0<β<1, x is a selectable system state variable, such as x=x 1 Or x=x 2 ; The saturation function of the switching control satisfies
[0047]
[0048] Where Ω is the boundary layer thickness of the saturation function.
[0049] Sliding mode cooperative guidance law based on exponential reaching law with state feedback 2 Expressed as
[0050]
[0051] As a preferred method, in step 4, the two-way coordination mode of target missile and defense missile is considered, the sliding surface s is derived and the first-order dynamic equation of the sliding mode state variable is brought into the equation to obtain:
[0052]
[0053] Where F = cos(γ T -θ TM ) / R TM , G = cos(γ D -θ DM ) / R DM , represents a double power reaching law or an exponential reaching law with state feedback, and u is regarded as a composite control law of the target missile and the defense missile.
[0054]
[0055] In order to avoid the overload saturation problem of the acceleration of the target missile and the defense missile, the acceleration objective function is introduced, and the two-way coordination problem is expressed as an optimization problem of minimizing the acceleration of the target missile-defense missile based on equation (14).
[0056] Construct the following objective function
[0057] J=[|κ 1 a T | p +|κ 2 a D | p ] 1 / p (15) In the formula, p represents a positive integer greater than 1, κ 1 and κ 2 represents the positive weight coefficient, respectively
[0058]
[0059] In the formula, and are the maximum accelerations of the defense projectile and the target projectile, respectively.
[0060] Substituting equation (14) into equation (15), the optimization problem is now described as
[0061]
[0062] Substituting the double power reaching law into the guidance law G of the defense missile and the target missile 3 for
[0063]
[0064] Substituting the exponential reaching law with state feedback into the guidance law G of the defense missile and the target missile 4 for
[0065]
[0066] The present invention has the following beneficial effects:
[0067] 1. Aiming at the active defense coordination scenario consisting of target missiles and defense missiles, the present invention introduces the problem of observability of target detection information during the penetration process, converts the target observability problem into a line of sight angle deviation control problem, and designs the corresponding sliding surface to ensure detectability and coordinated penetration performance.
[0068] 2. In the one-way collaborative mode, two typical convergence laws are used to derive the sliding mode guidance law of the defense missile. In the two-way collaborative mode, based on the one-way collaborative sliding mode guidance, the sliding mode control theory and optimization theory are used to derive the optimization of the control energy of the target-defense missile and the target missile, so that the defense missile can strike the lethal interceptor missile with a smaller control.
[0069] 3. An extended state observer is designed to estimate the disturbance term caused by target maneuvering, thereby weakening the sliding mode chattering phenomenon caused by it. BRIEF DESCRIPTION OF THE DRAWINGS
[0070] Figure 1 This is a schematic diagram of active defense attack and defense confrontation;
[0071] Figure 2 It is a schematic diagram of the attack and defense confrontation curve of one-way collaboration based on different convergence laws;
[0072] Figure 3 It is a schematic diagram of the convergence curve of s under different convergence laws of one-way collaboration;
[0073] Figure 4 It is a schematic diagram of the change of sight angle deviation under different convergence laws of one-way collaboration;
[0074] Figure 5 It is a schematic diagram of active defense attack and defense confrontation under two-way coordination with different convergence laws;
[0075] Figure 6 It is a schematic diagram of the convergence curve of s under different convergence laws of bidirectional collaboration;
[0076] Figure 7It is a schematic diagram of the change of sight angle deviation under different reaching laws of bidirectional collaboration;
[0077] Figure 8 It is a schematic diagram of the disturbance estimation curve under the exponential reaching law of one-way cooperation with state feedback;
[0078] Fig. 9 Schematic diagram of the disturbance estimation curve under the exponential reaching law of bidirectional cooperation with state feedback. DETAILED DESCRIPTION
[0079] The present invention is further described below in conjunction with a specific application example; Figure 1 , establish the nonlinear kinematic model of active defense; set the initial information of target missile, defense missile and incoming interceptor missile as shown in Table 1, the sliding surface parameter of formula (8) is η = 0.8, and the expected line of sight angle difference is Φ f =10°, the simulation step is 0.001s, the incoming interceptor missile uses proportional guidance, and the proportional guidance coefficient is 5. First, consider the scenario of one-way coordination between the target missile and the defense missile, and let the acceleration of the target missile be a T =0m / s 2 , the parameters of the double-power sliding mode guidance law shown in formula (10) are set to η 1 =0.05,η 2 =2.3, a 1 =0.3, a 2 =2; the parameter of the exponential approaching guidance law with state feedback shown in equation (13) is set to h 1 =10,h 2 =0.015, β=0.01, δ=0.01, α=20, Ω=20, the defense missile adopts the above two unidirectional cooperative sliding mode guidance laws for anti-interception, such as Figure 8 In the disturbance scenario shown in Figure 2 to Figure 4 From the simulation results, it can be seen that the one-way sliding mode cooperative guidance law under different approaching laws can enable the defense missile to successfully intercept the incoming interceptor missile, and at the same time make the actual line of sight angle deviation gradually approach the expected value Φ f =10° and maintained at the expected value.
[0080] Next, considering the scenario of two-way coordination between target missile and defense missile, the bi-power guidance law parameter shown in equation (18) is set to η 1 =0.075,η 2 =8; the exponential reaching law parameter with state feedback shown in formula (19) is set to h 1 =10,h 2 =1.7; the other parameters are consistent with the simulation parameters under unidirectional coordination, such as Fig. 9 In the disturbance scenario shown in the figure, the simulation results of the target missile-defense missile adopting the above two bidirectional cooperative sliding mode guidance laws are as follows: Figure 5 to Figure 7 As shown in the figure. According to the simulation results, under the action of the two-way cooperative guidance law with different approaching laws, the target missile and the defense missile successfully penetrate the incoming interceptor missile through cooperation, and the actual line of sight angle deviation can converge to the expected value. The above results all meet the requirements of the defense missile for precise strikes on incoming interceptor missiles and enhanced state observability.
[0081] Table 1 Initial information of each active defense aircraft
[0082]
Claims
1. An active defense cooperative penetration guidance method that takes into account both observability and anti-interception accuracy, characterized in that: The following steps are involved: Step 1: Active defense nonlinear kinematics modeling Construct an active defense nonlinear kinematic model consisting of target missiles, defense missiles, and incoming interceptor missiles; Step 2: Construction of sliding mode state variables and sliding surface Design sliding mode state variables x1 and x2 that meet the requirements of observability and anti-interception accuracy, where x1 is the deviation between the sight angle difference between the target missile and the interceptor missile and the expected value, and the deviation between the sight angle difference between the defense missile and the interceptor missile and the expected value, and x2 represents the derivative of the sight angle difference between the target missile and the interceptor missile and the derivative of the sight angle difference between the defense missile and the interceptor missile; then solve the first-order dynamic equation of the sliding mode state variable and Expression, construct the sliding surface s that takes into account both target detectability and penetration guidance accuracy; Step 3: Design of one-way collaborative sliding mode guidance law between target missile and defense missile Considering the one-way cooperative cooperation mode between target missile and defense missile, in order to meet the guidance requirements in different scenarios, the double power reaching law and the exponential reaching law with state feedback are respectively applied to design the guidance law; in order to ensure the finite time convergence of the sliding mode control system, the double power reaching law is introduced, and the one-way cooperative sliding mode guidance law G1 of the target missile and defense missile under the double power approach is designed according to the sliding surface in step 2; in order to weaken the sliding mode chattering phenomenon, based on the exponential reaching law with state feedback, the one-way cooperative sliding mode guidance law G2 of the target missile and defense missile under the exponential approach with state feedback is designed according to the sliding surface in step 2; Step 4: Design of the target missile-defense missile two-way collaborative sliding mode guidance law The target missile-defense missile two-way coordination mode can reduce the overload required for the defense missile to strike the interceptor missile, and prevent the defense missile acceleration from being in a saturated state for a long time, resulting in anti-interception failure; the composite control law of the target missile and the defense missile is regarded as u, and the objective function J of the weighted sum of the acceleration of the target missile-defense missile is constructed, and u is brought into the objective function J. This two-way coordination problem is expressed as an optimization problem of minimizing the acceleration of the target missile-defense missile; when the reaching law is a double power reaching law, a target missile-defense missile two-way coordinated sliding mode guidance law G3 under the double power reaching law is designed; when the reaching law is an exponential reaching law with state feedback, a target missile-defense missile two-way coordinated sliding mode guidance law G4 under the exponential reaching law with state feedback is designed; Step 5: Design of active defense sliding mode guidance law based on extended state observer In actual situations, the acceleration a of the incoming interceptor missile is M Usually unknown, an extended state observer is introduced to estimate the disturbance term d related to the acceleration of the incoming interceptor in real time; according to the derivative of the state variable of the sliding mode system Construct an extended state observer, The derivative of the deviation between the line of sight angle difference and the expected value is expressed; the disturbance estimation values of x1 and d are obtained, and the active defense sliding mode cooperative guidance law based on the extended state observer is designed; The designed extended state observer is specifically: First, D1=(R DM cos(γ M -θ TM )-R TM cos(γ M -θ DM ))a M Set it as augmented state, and construct the following extended state observer according to the first-order dynamic equation of the sliding mode state variable: Where Ψ DT =Φ DT -Φ f , z1 and e represent The estimated value and estimation error of , z2 is the estimated value of D1, β1 and β2 are the observed gains, γ j , a j The heading angle and acceleration of each missile. T, D, and M represent the target missile, defense missile, and incoming interceptor missile, respectively. R DM , R TM and θ DM ,θ TM denote the relative distance and line of sight between the defense missile and the interceptor missile and the target missile and the interceptor missile, Φ DT is the line of sight angle deviation between target missile and interceptor missile, and between defense missile and interceptor missile, Φ f is the desired line of sight angle deviation, and the fal function is defined as Among them, 0<τ<1, 0<δ<1; Therefore, the estimated value of the system disturbance d is described as The disturbance estimate By respectively substituting them into the target missile-defense missile unidirectional collaborative sliding mode guidance law G2 and the target missile-defense missile bidirectional collaborative sliding mode guidance law G4, we can obtain the unidirectional / bidirectional collaborative active defense sliding mode guidance law based on the extended state observer.
2. The active defense cooperative penetration guidance method taking into account both observability and anti-interception accuracy according to claim 1 is characterized in that: The active defense nonlinear kinematic model is specifically as follows: the target missile, the defense missile and the incoming interceptor missile are represented by T, D and M respectively; the active defense nonlinear kinematic model is represented as two sets of relative motion models of the defense missile-interceptor missile and the interceptor missile-target missile; the active defense nonlinear kinematic model is established as Where, i = {T, D}, j = {T, D, M}, γ j , a j and V j Respectively represent the heading angle, acceleration and speed of each missile; R DM , R TM and θ DM ,θ TM They represent the relative distance and line of sight angle between the defense missile and the interceptor missile and between the target missile and the interceptor missile respectively.
3. The active defense cooperative penetration guidance method taking into account both observability and anti-interception accuracy according to claim 1 is characterized in that: In step 2, let Φ DT is the line of sight angle deviation between target missile and interceptor missile, and between defense missile and interceptor missile, satisfying Φ DT =θ TM -θ DM ,θ DM ,θ TM They represent the sight angles between the defense missile and the interceptor missile and between the target missile and the interceptor missile respectively; the target flight state estimation accuracy is affected by the observability of the measurement information, and the observability of the measurement information has a certain relationship with the spatial configuration between the target aircraft and the sensor; the sight angle difference Φ between the target missile and the interceptor missile and the defense missile and the interceptor missile is increased DT Enhance the observability of target angle detection information; The sliding mode state variables are defined as follows In the formula, Φ f For the desired sight angle deviation, the first-order dynamic equation of the sliding mode state variable is as follows: Where d is the unknown disturbance; In the formula, and They represent the interception time t f The distances between the target missile and the interceptor missile and between the defense missile and the interceptor missile; The sliding surface designed to take into account both target detectability and penetration guidance accuracy is: s=x2+ηx1,η>0 (8).
4. The active defense cooperative penetration guidance method taking into account both observability and anti-interception accuracy according to claim 1 is characterized in that: In step 3, the one-way coordination mode between target missile and defense missile is considered. In order to ensure the finite time convergence of the sliding mode control system, the double power reaching law is introduced. Where η1>0; η2>0; 0 <a1<1;a2> 1. The bi-power reaching law has the global fixed time convergence characteristic, ensuring that the sliding mode state quantity converges to the steady-state error bound in a finite time; According to the sliding surface in step 2 and the double power reaching law in step 3, the one-way cooperative sliding mode guidance law G1 of the target missile and the defense missile is designed as follows: In the formula, Since the double-power approaching sliding mode guidance law of formula (10) will produce large chattering on the sliding mode switching surface, an exponential approaching law with state feedback is introduced to weaken the sliding mode chattering phenomenon. The approaching law expression is: Where h1>0; h2>0; α>0; 0<β<1; 0<δ<1, x=x1 or x=x2; the saturation function of the switching control satisfies Where Ω is the boundary layer thickness of the saturation function; The sliding mode cooperative guidance law G2 based on the exponential reaching law with state feedback is expressed as 5. The active defense cooperative penetration guidance method taking into account both observability and anti-interception accuracy according to claim 1 is characterized in that: In step 4, the two-way coordination mode between target missile and defense missile is considered, the sliding surface s is derived and the first-order dynamic equation of the sliding state variable is substituted into it to obtain Where F = cos(γ T -θ TM ) / R TM , G = cos(γ D -θ DM ) / R DM , represents a double power reaching law or an exponential reaching law with state feedback, and u is regarded as a composite control law of the target missile and the defense missile. In order to avoid the overload saturation problem of the acceleration of the target missile and the defense missile, the acceleration objective function is introduced, and the two-way coordination problem is expressed as an optimization problem of minimizing the acceleration of the target missile-defense missile based on equation (14); Construct the following objective function J=[|κ1a T | p +|κ2a D | p ] 1 / p (15) In the formula, p represents a positive integer greater than 1, κ1 and κ2 represent positive weight coefficients, which are In the formula, and are the maximum accelerations of the defense projectile and the target projectile, respectively; Substituting equation (14) into equation (15), the optimization problem is now described as Substituting the double power approaching law, the guidance law G3 of the defense missile and the target missile is obtained as follows: Substituting the exponential reaching law with state feedback into the guidance law G4 of the defense missile and the target missile is: