Decision and guidance integrated design method and system based on Nash equilibrium search strategy

Abstract

The invention discloses a decision-making and guidance integrated design method and system based on a Nash equilibrium search strategy, and relates to the technical field of guidance. The method comprises the steps that kinetic parameters of a target and an interception missile group are acquired, and an interception model is constructed; determining an optimal guidance law based on the model and the end collision angle constraint; setting an expected collision angle, and solving through a Nash equilibrium algorithm; the missile angle decision problem is solved according to the optimal collision angle and the expected angle formation; and making a decision-making and guidance integrated control protocol. According to the method, the expected angle decision and tail end angle constraint guidance problems of the missile for the maneuvering target are solved.

Description

Technical Field

[0001] The present application relates to the field of guidance technology, and in particular to a decision-making guidance integrated design method and system based on a Nash equilibrium search strategy. Background Art

[0002] With the development of today's offensive and defensive technologies, the demand for upgrading guidance laws is becoming more and more vigorous. Traditional proportional guidance laws have been widely used since 1960 due to their high guidance accuracy and ease of implementation. However, modern guidance missions require not only precision strikes, but also require attacking targets at a specific angle range in many guidance scenarios. Attacking targets at a specific angle of incidence has many advantages in combat, such as enhancing armor-piercing effects and increasing enemy radar cross-sectional areas. Intercepting ultra-high-speed targets at a certain angle range can also increase terminal interception accuracy. In addition, multi-missiles and multi-angle coordinated attacks on high-value targets can enable the missile group to achieve multiple-to-one interception in a siege posture, thereby increasing the detection range of the missile group and improving the interception efficiency of the missile group. The need to attack targets at a specific range of incidence angles has given rise to the development of angle-constrained guidance laws.

[0003] Many existing works focus on the implementation of angle constraints. Li et al. derived the biased proportional guidance angle constraint control law using a preset performance function, obtained the closed-loop analytical expression of the lead angle based on small disturbance linearization, and then obtained the value range and update strategy of the guidance law gain. Yang et al. obtained the angle error using the collision triangle theory, and used fixed-time sliding mode control and the obstacle Lyapunov method to derive the angle guidance law with FOV constraints. Liu et al. described the cooperative guidance problem as a zero-sum differential game problem, and the optimization objectives included the miss distance and the relative collision angle error. Zhao et al. used the event trigger mechanism to reduce the communication frequency of the cooperative process, thereby reducing the computational burden of the cooperative guidance instructions, and used the finite time theory to complete the analysis of the cooperative control law.

[0004] However, whether it is a single missile or multiple missiles coordinated angle constraint guidance law research, most of the results only focus on the realization of angle constraint, and few studies discuss the decision-making problem of the expected collision angle. It is very important to combine the decision-making process of the expected collision angle with the realization process of angle constraint. Summary of the invention

[0005] The purpose of this application is to provide a decision-guidance integrated design method and system based on the Nash equilibrium search strategy, apply the decision-guidance integrated control protocol to a multi-missile system, realize the angle decision and guidance tasks of multiple missiles to maneuvering targets, and solve the expected angle decision and terminal angle constraint guidance problems of missiles for maneuvering targets.

[0006] To achieve the above objectives, this application provides the following solutions:

[0007] In a first aspect, the present application provides a decision-guiding integrated design method based on a Nash equilibrium search strategy, comprising:

[0008] Obtain the dynamic parameters of the maneuvering target and the dynamic parameters of the interceptor group;

[0009] Constructing a dynamic model for intercepting the maneuvering target according to the dynamic parameters of the maneuvering target and the dynamic parameters of the interceptor missile group;

[0010] According to the dynamic model of intercepting maneuvering targets, based on the terminal collision angle constraint, the optimal guidance law of the basic angle constraint of the maneuvering target is determined;

[0011] According to the optimal guidance law constrained by the basic angle of the maneuvering target, the optimal collision angle of the maneuvering target is determined; the optimal collision angle is the expected terminal collision angle between the maneuvering target and the interceptor group; the expected terminal collision angle is obtained by a fully distributed preset time Nash equilibrium search algorithm;

[0012] Determine the angle decision problem of each missile in the interceptor group according to the optimal collision angle of the maneuvering target and the expected angle formation of the interceptor group;

[0013] Based on the optimal collision angle of the maneuvering target and the angle decision problem of each missile in the interceptor group, a decision-guidance integrated control protocol is determined.

[0014] Optionally, the formula expression of the dynamic model of intercepting the maneuvering target is:

[0015]

[0016] Among them, γ r,i is the relative velocity yaw angle of the i-th missile, a r,i is the relative overload size of the ith missile, V r,i is the relative speed of the ith missile, r i and q i are the missile-target distance and sight angle of the ith missile, σ r,i is the relative lead angle of the i-th missile.

[0017] Optionally, the formula expression of the basic angle-constrained optimal guidance law of the maneuvering target is:

[0018]

[0019] Among them, m is the proportional guidance coefficient, q f Predict the sight angle for the terminal, q d is the desired end angle, V r is the magnitude of the relative velocity, r and q are the missile-target distance and the sight angle, respectively, σr is the relative lead angle.

[0020] Optionally, determining the optimal collision angle of the maneuvering target according to the basic angle-constrained optimal guidance law of the maneuvering target specifically includes:

[0021] when According to the formula determining an optimal collision angle of the maneuvering target;

[0022] when According to the formula determining an optimal collision angle of the maneuvering target;

[0023] in, is the relative lead angle at the initial moment, is the optimal collision angle of the maneuvering target, γ t is the velocity yaw angle of the maneuvering target, is the optimal terminal missile yaw angle, s * is the index of the smallest element in the sequence y(j).

[0024] Optionally, according to the optimal collision angle of the maneuvering target and the expected angle formation of the interceptor group, the angle decision problem of each missile in the interceptor group is determined, which specifically includes:

[0025] According to the formula Determine the angle decision problem of each missile in the interceptor group;

[0026] in, is the i-th missile pair The estimate, is the i-th missile pair The estimate, is the expected end collision angle vector, h=[h1,h2,...,h N ] T is the expected angle formation of the multi-missile system, h ij =h(i)-h(j), is the expected terminal impact angle of the ith missile on the maneuvering target, β i is the weight coefficient, and N is the total number of missiles in the swarm.

[0027] Optionally, based on the optimal collision angle of the maneuvering target and the angle decision problem of each missile in the interceptor group, a decision-guidance integrated control protocol is determined, which specifically includes:

[0028] According to the formula Determine the decision-making guidance integrated control protocol for the i-th missile;

[0029] in, K i is the speed ratio of the maneuvering target to the missiles in the interceptor group, q f,i The terminal predicted sight angle for the ith missile.

[0030] Optionally, the expected terminal impact angle of the i-th missile on the maneuvering target is The solution formula is:

[0031]

[0032] Among them, Q ij (t0),α>0, c>0,T d is a constant.

[0033] Optionally, the speed ratio K of the maneuvering target and the missiles in the interceptor group is i Satisfy 0≤K i <1.

[0034] In a second aspect, the present application provides a decision-guiding integrated design system based on a Nash equilibrium search strategy, comprising:

[0035] Parameter acquisition module, used to obtain the dynamic parameters of the maneuvering target and the dynamic parameters of the interception missile group;

[0036] A dynamic model building module, used to build a dynamic model for intercepting a maneuvering target according to the dynamic parameters of the maneuvering target and the dynamic parameters of the interceptor missile group;

[0037] A basic angle constraint optimal guidance law determination module is used to determine the basic angle constraint optimal guidance law of the maneuvering target based on the terminal collision angle constraint according to the dynamic model of the intercepting maneuvering target;

[0038] An optimal collision angle determination module is used to determine the optimal collision angle of the maneuvering target according to the optimal guidance law constrained by the basic angle of the maneuvering target; the optimal collision angle is the expected terminal collision angle between the maneuvering target and the interceptor group; the expected terminal collision angle is obtained by a fully distributed preset time Nash equilibrium search algorithm;

[0039] An angle decision problem determination module, used to determine the angle decision problem of each missile in the interceptor group according to the optimal collision angle of the maneuvering target and the expected angle formation of the interceptor group;

[0040] The decision-making guidance integrated control protocol determination module is used to determine the decision-making guidance integrated control protocol based on the optimal collision angle of the maneuvering target and the angle decision problem of each missile in the interception missile group.

[0041] Optionally, the angle decision problem determination module includes:

[0042] The angle decision problem calculation submodule is used to calculate the angle decision problem according to the formula Determine the angle decision problem of each missile in the interceptor group;

[0043] in, is the i-th missile pair The estimate, is the i-th missile pair The estimate, is the expected end collision angle vector, h=[h1,h2,...,h N ] T is the expected angle formation of the multi-missile system, h ij =h(i)-h(j), is the expected terminal impact angle of the ith missile on the maneuvering target, β i is the weight coefficient, and N is the total number of missiles in the swarm.

[0044] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0045] The present application provides a decision-guidance integrated design method and system based on a Nash equilibrium search strategy, the method comprising: first, obtaining the dynamic parameters of a maneuvering target and the dynamic parameters of an interceptor group. These parameters are the basis for constructing a dynamic model for intercepting a maneuvering target. Then, using these dynamic parameters to construct a dynamic model for intercepting a maneuvering target. This model can describe the dynamic behavior of a maneuvering target and an interceptor group during the interception process. Then, based on the terminal collision angle constraint, the basic angle constraint optimal guidance law of the maneuvering target is determined. This guidance law is for maneuvering targets and is used to guide the interceptor group on how to adjust the flight path to achieve the expected collision angle. According to the basic angle constraint optimal guidance law, the optimal collision angle of the maneuvering target is further determined. This optimal collision angle is the expected terminal collision angle between the maneuvering target and the interceptor group. The expected terminal collision angle is obtained by a fully distributed preset time Nash equilibrium search algorithm. This algorithm can help the system find the optimal collision angle to meet the needs of multi-missile coordinated interception. Subsequently, according to the optimal collision angle and the expected angle formation of the interceptor group, the angle decision problem of each missile in the interceptor group is determined. This step is to convert the optimal collision angle into a specific flight angle instruction for each missile. Finally, based on the optimal collision angle and the angle decision problem of each missile, the decision-guidance integrated control protocol is determined. This protocol combines the two aspects of decision-making and guidance to ensure that multiple missile systems can work together to complete the angle decision and guidance tasks for maneuvering targets. This application applies the decision-guidance integrated control protocol to multiple missile systems, which can realize the angle decision and guidance tasks of multiple missiles for maneuvering targets, and effectively solve the expected angle decision and terminal angle constraint guidance problems of missiles for maneuvering targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0047] Figure 1 A flowchart of a decision-guidance integrated design method based on a Nash equilibrium search strategy is provided in accordance with an embodiment of the present application.

[0048] Figure 2 A schematic diagram of a guidance model in a two-dimensional plane provided in one embodiment of the present application.

[0049] Figure 3 A bullet-swarm communication topology diagram provided for one embodiment of the present application.

[0050] Figure 4A schematic diagram of the trajectory of a moving target intercepted by a multi-missile system provided in one embodiment of the present application.

[0051] Figure 5 A schematic diagram of a multi-missile overload curve provided in an embodiment of the present application.

[0052] Figure 6 A schematic diagram of the relative lead angles of multiple missiles provided in one embodiment of the present application.

[0053] Figure 7 A schematic diagram of a multi-missile collision angle decision-guidance curve provided in one embodiment of the present application.

[0054] Figure 8 A schematic diagram of a multi-missile sight angle decision-guidance curve provided for an embodiment of the present application.

[0055] Fig. 9 A schematic diagram of a multi-missile observation error curve provided in an embodiment of the present application.

[0056] Fig.10 A schematic diagram of a multi-missile adaptive gain curve provided in an embodiment of the present application.

[0057] Fig.11 A schematic diagram of a comparison group trajectory provided in an embodiment of the present application.

[0058] Fig.12 A schematic diagram of a comparison group overload provided in an embodiment of the present application.

[0059] Fig.13 A schematic diagram of functional modules of a decision-guidance integrated design system based on a Nash equilibrium search strategy provided in one embodiment of the present application. DETAILED DESCRIPTION

[0060] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0061] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0062] Embodiment 1

[0063] like Figure 1 As shown, this embodiment provides a decision-guiding integrated design method based on a Nash equilibrium search strategy, including:

[0064] Step 101: Obtaining dynamic parameters of the maneuvering target and dynamic parameters of the interceptor group;

[0065] Step 102: constructing a dynamic model for intercepting the maneuvering target according to the dynamic parameters of the maneuvering target and the dynamic parameters of the interceptor missile group;

[0066] Step 103: According to the dynamic model of the intercept maneuvering target and based on the terminal collision angle constraint, determine the basic angle constraint optimal guidance law of the maneuvering target;

[0067] Step 104: determining the optimal collision angle of the maneuvering target according to the basic angle-constrained optimal guidance law of the maneuvering target; the optimal collision angle is the expected terminal collision angle between the maneuvering target and the interceptor group; the expected terminal collision angle is obtained by a fully distributed preset time Nash equilibrium search algorithm;

[0068] Step 105: determining the angle decision problem of each missile in the interceptor group according to the optimal collision angle of the maneuvering target and the expected angle formation of the interceptor group;

[0069] Step 106: Determine a decision-guidance integrated control protocol based on the optimal collision angle of the maneuvering target and the angle decision problem of each missile in the interceptor group.

[0070] In some embodiments, when executing steps 101-102, the specific steps may be as follows:

[0071] Considering the scenario where the i-th missile intercepts a single maneuvering target in a two-dimensional plane, the guidance model can be seen as Figure 2 .

[0072] Specifically, Figure 2 As shown, (X,Y) and (X r ,Y r ) represent the inertial coordinate system and the line of sight coordinate system respectively. The subscript i represents the i-th missile in the missile group. i and T represent the center of mass of the ith missile and the target, respectively. i and q i represent the missile-target distance and the sight angle, V m,i and V t are the speeds of the missile and the target respectively. m,i and γ t They represent the velocity yaw angle of the missile and the target in the inertial system. The lead angles of the missile and the target are σ m,i =γ m,i -q i and σ t =γ t -q i.a m,i , a t Respectively represent the overload size of the missile and the target in the inertial system. r,i is the magnitude of the relative velocity, γ r,i is the relative velocity yaw angle, a r,i is the relative overload size, σ r,i is the relative lead angle and satisfies σ r,i =γ r,i -q i .

[0073] Among them, based on the dynamic parameters of the interceptor group and the dynamic parameters of the maneuvering target provided above, the kinematic equation of the i-th missile and the target in the two-dimensional plane is constructed as follows:

[0074]

[0075] Where i = 1, 2, ..., N, the lead angle of the target σ t,i Satisfy σ t,i =γ t -q i , the lead angle σ of the i-th missile m,i Satisfy σ m,i =γ m,i -q i .

[0076] Therefore, the kinematic equations of the i-th missile and target in the two-dimensional plane can be further expressed as:

[0077]

[0078] Among them, according to the dynamic parameters of the interceptor group and the dynamic parameters of the maneuvering target, the following parameter relationship can also be obtained.

[0079]

[0080] In this embodiment, it is assumed that the moment when the interceptor group starts guiding is marked as t=t0, and the initial moment of the relative lead angle satisfies The speeds of the missile and the target are constant, and the speed ratio of the target and the i-th missile is K i Satisfy 0≤K i <1, that is, the speed of the missile must be greater than the speed of the target.

[0081] In some embodiments, when executing step 103, the specific steps may be as follows:

[0082] In order to achieve the terminal collision angle constraint, the basic optimal angle guidance law should be designed.

[0083] Among them, the zero-control miss amount can be expressed as:

[0084] z=-rsinσ r (4).

[0085] Specifically, the basic proportional guidance law can be expressed as The proportional guidance coefficient m≥0. Substituting this proportional guidance law into formula (4), we can get γ r (t f )-γ r (t0) = (m + 3)(q(t f )-q(t0)), where t f is the terminal impact time. Due to the nature of the proportional guidance law, we can get

[0086] According to the parameter relationship in formula (3), r (t f )-γ r (t0) = (m + 3)(q(t f )-q(t0)) is transformed to obtain:

[0087]

[0088] Therefore, the terminal predicts the sight angle q f It can be expressed as q f =(m+3)q / (m+2)-γ r / (m+2).

[0089] The two sides of the equation of zero-control miss distance and terminal prediction angle are integrated according to the missile-target distance, and the small disturbance hypothesis theorem is adopted, that is, sinσ r ≈ptanσ r , where p>0, we can get the following optimal control problem:

[0090]

[0091] The subscript "0" in formula (6) represents the initial moment. Using the idea of ​​small perturbation linearization, let sinσ≈ptanσ r Where p>0. Let where q d is the desired end angle. The Hamiltonian equation for the optimal control problem can be expressed as:

[0092]

[0093] In the formula, λ z , is the corresponding Lagrangian parameter. By using the minimum principle, we can get:

[0094]

[0095] Where C1 and C2 are constants. Substituting u in formula (8) into the optimal control problem formula (6) and integrating the relative distance, we can get the expressions of C1 and C2 as follows:

[0096]

[0097] Substituting equation (9) into equation (8) can further obtain the closed-loop input command. Specifically, it is as follows:

[0098]

[0099] Considering the current time as the initial time t0, we can use r, z replaces the initial state r0, z0, and at the current moment p=cosσ r , so the basic angle constraint optimal guidance law can be expressed as:

[0100]

[0101] In some embodiments, when executing step 104, the specific steps may be as follows:

[0102] First, substitute the closed-loop input command formula (10) into the optimal control problem formula (6) to obtain formula (12), which is as follows:

[0103]

[0104] J u See The function of make Available Since m ≥ 0, then if and only if The optimal sight angle is satisfy According to the derivation process of formula (3) and the optimal guidance law formula expression (11), we can get:

[0105]

[0106] in is the optimal terminal missile yaw angle. Definition in

[0107] x∈[-1,1], make B=-Kcosγ t , and C = -Ksinγ t , then (13) can be further expressed as:

[0108]

[0109] Solving (14) yields:

[0110]

[0111] in, According to formula (15), All of them can satisfy formula (13), but since the basic optimal guidance law formula (11) is fixed, the trajectory generated by this guidance law is unique, so there is only one Make Where j is 1 or 2.

[0112] because and Therefore, the basic optimal guidance law formula (11) can be transformed into Based on formula (3) and formula (4), we have dz / dr = (m+3)z / r. Then, integrating both sides of the equation with respect to the distance between the projectile and the target yields:

[0113]

[0114] Will Substituting formula (16) into formula (3) yields formula (17), which is:

[0115]

[0116] Due to σ r ∈(-π / 2,π / 2) and dr / dt<0, so Further information

[0117] The sign(·) function satisfies that when x>0, sign(x)=1; when x=0, sign(x)=0; when x<0, sign(x)=-1. The optimal form of guidance law under the condition The following formula (18) is satisfied:

[0118]

[0119] Therefore, it can be known that Since V m >V t , there is γ r -γ m ∈(-π / 2,π / 2), and then we can get

[0120] Based on the above analysis, it can be inferred that The optimal end collision angle satisfies formula (19):

[0121]

[0122] when The optimal end collision angle satisfies formula (20):

[0123]

[0124] In the formula, where s * is the serial number of the smallest element in the sequence y(j), marked as

[0125] In some embodiments, when executing step 105, the specific steps may be as follows:

[0126] Determine the cost function of the i-th missile, which can be defined as:

[0127]

[0128] in, represents the expected end impact angle vector. h=[h1,h2,...,h N ] T represents the expected angular formation of the multiple missile system, where h ij =h(i)-h(j). Let It can be known that i J i (x) is differentiable at x, so there exists l1 such that:

[0129] |▽ i J i (x)-▽ i J i (k)|≤l1||xk|| (22).

[0130] in, i=1,2,...,N,l1>0. exist is convex, so the following inequality holds:

[0131] (xy) T (▽J(x)-▽J(y))≥l2||xy|| 2 (twenty three).

[0132] in, Based on (22) and (23), we know that the Nash equilibrium point is is the only one that can make

[0133] Since real collaborative operations may use distributed communications, vector It is unknown for the missiles in the swarm. For practicality, the cost function of the i-th missile can be constructed as formula (24), as follows:

[0134]

[0135] in Represents the i-th missile pair The estimate, Represents the i-th missile pair Estimates.

[0136] According to the theory of step 101 to step 104, the decision-making guidance integrated control protocol of the i-th missile can be designed as follows:

[0137]

[0138] Among them, in formula (25) and The solution equation is as follows:

[0139]

[0140] Expected end impact angle It can be obtained through the following fully distributed preset time Nash equilibrium search algorithm:

[0141]

[0142] Where c>0, T d is a constant, which is a relatively small value, thus satisfying the condition of convergence within the preset time.

[0143] In this embodiment, the decision-making and attack tasks of maneuvering targets can be achieved by using the designed decision-making and guidance integrated control law (25) based on Nash equilibrium search. The process of decision-making and guidance integrated design of the i-th missile in the missile group can be described as follows:

[0144] 1) Select the navigation ratio parameter m∈(0,3], determine the optimal guidance law of the basic angle constraint analytical formula (11), and determine it through formula (12):

[0145] 2) Based on the initial state of the guidance phase and According to formula (15), and Then, based on formulas (19)-(20),

[0146] 3) Determine the minimum remaining flight time based on the initial state of the guidance phase The minimum remaining flight time can be determined by the following formula:

[0147]

[0148] If the minimum remaining flight time of all missiles in a swarm is known, then Otherwise, let in The minimum distance between the missile group and the target for the missile group to start the guidance phase. and Represents the maximum speed limits of the missile and target respectively.

[0149] Finally, choose α,Q ij (t0),c>0,β i ∈(0,1), and let j=1,2,...,N, and execute the decision-making guidance integrated control protocol, i.e., formula (25)-formula (30).

[0150] Embodiment 2

[0151] like Fig.13 As shown, this embodiment provides a decision-guiding integrated design system based on a Nash equilibrium search strategy, including:

[0152] The parameter acquisition module 1301 is used to acquire the dynamic parameters of the maneuvering target and the dynamic parameters of the interception missile group;

[0153] A dynamic model building module 1302 is used to build a dynamic model for intercepting a maneuvering target according to the dynamic parameters of the maneuvering target and the dynamic parameters of the interceptor missile group;

[0154] A basic angle constraint optimal guidance law determination module 1303 is used to determine the basic angle constraint optimal guidance law of the maneuvering target based on the terminal collision angle constraint according to the dynamic model of the intercepting maneuvering target;

[0155] The optimal collision angle determination module 1304 is used to determine the optimal collision angle of the maneuvering target according to the optimal guidance law constrained by the basic angle of the maneuvering target; the optimal collision angle is the expected terminal collision angle between the maneuvering target and the interceptor group; the expected terminal collision angle is obtained by a fully distributed preset time Nash equilibrium search algorithm;

[0156] Angle decision problem determination module 1305, for determining the angle decision problem of each missile in the interceptor group according to the optimal collision angle of the maneuvering target and the expected angle formation of the interceptor group;

[0157] The decision-making guidance integrated control protocol determination module 1306 is used to determine the decision-making guidance integrated control protocol based on the optimal collision angle of the maneuvering target and the angle decision problem of each missile in the interceptor group.

[0158] The present application also verifies the effectiveness of the method proposed by the present invention through a specific example of a multi-missile system consisting of five missiles attacking a mobile target. The specific implementation steps of this example are as follows:

[0159] First, set the missile simulation conditions: the initial positions of the 5 missiles and the target are set to

[0160] [X T ,Y T ]=[1500m,1000m]. The initial speed is set to V T =80m / s,V m,1 =180m / s, V m,2 =170m / s, V m,3 =155m / s, V m,4 =165m / s, V m,5 =160m / s. The initial velocity and yaw angle are set to γ t =20°,γ m,1 (t0) = 30°, γ m,2 (t0) = 15°, γ m,3 (t0) = 5°, γ m,4 (t0) = 5°, γ m,5 (t0) = 20°. The communication topology of the missiles in the swarm is as follows: Figure 3 shown.

[0161] Then, the decision guidance parameters are set: the navigation ratio parameter in the guidance law is set to m = 1.2, and the expected decision convergence time T d = 10s, the expected formation can be set to h = [-15°, -30°, 0°, 30°, 15°]. The other guidance parameters are set to: α = 4, Q ij (t0) = 20, β i = 0.8, where i, j = 1, 2, ..., N. The comparison group did not use the decision link, and directly set the fixed angle formation h = [6.75°, -1.50°, 15.00°, 31.50°, 23.25°], and the other parameters remained the same.

[0162] Finally, the results are analyzed: the simulation results of the pursuit situation are as follows Figure 4-Figure 10 The coordinated guidance trajectory and overload without taking angle decisions are shown in Figure 11-Figure 12 shown.

[0163] pass Figure 4 It can be seen that a cluster of multiple missiles can achieve multi-incident angle guidance for maneuvering targets. Figure 5 It can be seen that the relative overload of the terminal missile can converge to zero, and it has a good terminal interception situation. Figure 6 It can be seen that the terminal relative lead angle converges to zero, and the decision-guidance integrated control protocol degenerates into a proportional guidance law. Figure 7 and Figure 8 It can be seen that the missile can make an angle decision within the preset time and can achieve angle constraint at the end of the interception. Fig. 9 and Fig.10 It can be seen that the observation error of the optimal collision angle of the missile can converge to zero, and the late derivative of the adaptive curve is zero, which verifies the effectiveness of the decision-making link. Figure 4-Figure 5 as well as Figure 11-Figure 12 It can be seen that if the preset angle formation is set unreasonably, the decision-making link of the expected angle may increase the overload demand of the movement process and increase energy loss.

[0164] In summary, this application has the following technical effects:

[0165] This application establishes a relative motion model of missiles and targets in a two-dimensional plane, and gives the optimal guidance law with basic angle constraints for maneuvering targets; determines the optimal collision angle based on the proposed guidance law; establishes the angle decision problem based on the optimal collision angle and the expected angle formation; and proposes a decision-guidance integrated control protocol based on the above analysis and design. The designed decision-guidance integrated control protocol is applied to a multi-missile system to achieve the angle decision and guidance tasks of multiple missiles against maneuvering targets, solving the expected angle decision and terminal angle constraint guidance problems of missiles against maneuvering targets.

[0166] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0167] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A decision-guidance integrated design method based on Nash equilibrium search strategy, characterized in that: The decision-making guidance integrated design method based on the Nash equilibrium search strategy includes: Obtain the dynamic parameters of the maneuvering target and the dynamic parameters of the interceptor group; Constructing a dynamic model for intercepting the maneuvering target according to the dynamic parameters of the maneuvering target and the dynamic parameters of the interceptor missile group; According to the dynamic model of intercepting maneuvering targets, based on the terminal collision angle constraint, the optimal guidance law of the basic angle constraint of the maneuvering target is determined; According to the optimal guidance law constrained by the basic angle of the maneuvering target, the optimal collision angle of the maneuvering target is determined; the optimal collision angle is the expected terminal collision angle between the maneuvering target and the interceptor group; the expected terminal collision angle is obtained by a fully distributed preset time Nash equilibrium search algorithm; Determine the angle decision problem of each missile in the interceptor group according to the optimal collision angle of the maneuvering target and the expected angle formation of the interceptor group; Based on the optimal collision angle of the maneuvering target and the angle decision problem of each missile in the interceptor group, a decision-guidance integrated control protocol is determined.

2. The decision-guidance integrated design method based on Nash equilibrium search strategy according to claim 1 is characterized in that: The formula expression of the dynamic model of intercepting the maneuvering target is: Among them, γ r,i is the relative velocity yaw angle of the i-th missile, a r,i is the relative overload size of the ith missile, V r,i is the relative speed of the ith missile, r i and q i are the missile-target distance and sight angle of the ith missile, σ r,i is the relative lead angle of the i-th missile.

3. The decision-guidance integrated design method based on Nash equilibrium search strategy according to claim 2 is characterized in that: The formula expression of the optimal guidance law of the basic angle constraint of the maneuvering target is: Among them, m is the proportional guidance coefficient, q f Predict the sight angle for the terminal, q d is the desired end angle, V r is the magnitude of the relative velocity, r and q are the missile-target distance and the sight angle, respectively, σ r is the relative lead angle.

4. The decision-guidance integrated design method based on Nash equilibrium search strategy according to claim 3 is characterized in that: Determining the optimal collision angle of the maneuvering target according to the basic angle constraint optimal guidance law of the maneuvering target specifically includes: when According to the formula determining an optimal collision angle of the maneuvering target; when According to the formula determining an optimal collision angle of the maneuvering target; in, is the relative lead angle at the initial moment of guidance, is the optimal collision angle of the maneuvering target, γ t is the velocity yaw angle of the maneuvering target, is the optimal terminal missile yaw angle, s * is the index of the smallest element in the sequence y(j).

5. The decision-guidance integrated design method based on Nash equilibrium search strategy according to claim 4 is characterized in that: According to the optimal collision angle of the maneuvering target and the expected angle formation of the interceptor group, the angle decision problem of each missile in the interceptor group is determined, which specifically includes: According to the formula Determine the angle decision problem of each missile in the interceptor group; in, is the i-th missile pair The estimate, is the i-th missile pair The estimate, is the expected end collision angle vector, h=[h1,h2,...,h N ] T is the expected angle formation of the multi-missile system, h ij =h(i)-h(j), is the expected terminal impact angle of the ith missile on the maneuvering target, β i is the weight coefficient, and N is the total number of missiles in the swarm.

6. The decision-guidance integrated design method based on Nash equilibrium search strategy according to claim 5, characterized in that: Based on the optimal collision angle of the maneuvering target and the angle decision problem of each missile in the interceptor group, a decision-making guidance integrated control protocol is determined, which specifically includes: According to the formula Determine the decision-making guidance integrated control protocol for the i-th missile; in, K i is the speed ratio of the maneuvering target to the missiles in the interceptor group, q f,i The terminal predicted sight angle for the ith missile.

7. The decision-guidance integrated design method based on Nash equilibrium search strategy according to claim 5, characterized in that: The expected terminal impact angle of the i-th missile on the maneuvering target The solution formula is: Among them, Q ij (t0),α>0, c>0,T d is a constant.

8. The decision-guidance integrated design method based on Nash equilibrium search strategy according to claim 1, characterized in that: The speed ratio K of the maneuvering target and the missiles in the interceptor group i Satisfy 0≤K i <1.

9. A decision-making guidance integrated design system based on Nash equilibrium search strategy, characterized in that: include: Parameter acquisition module, used to obtain the dynamic parameters of the maneuvering target and the dynamic parameters of the interception missile group; A dynamic model building module, used to build a dynamic model for intercepting a maneuvering target according to the dynamic parameters of the maneuvering target and the dynamic parameters of the interceptor missile group; A basic angle constraint optimal guidance law determination module is used to determine the basic angle constraint optimal guidance law of the maneuvering target based on the terminal collision angle constraint according to the dynamic model of the intercepting maneuvering target; An optimal collision angle determination module is used to determine the optimal collision angle of the maneuvering target according to the optimal guidance law constrained by the basic angle of the maneuvering target; the optimal collision angle is the expected terminal collision angle between the maneuvering target and the interceptor group; the expected terminal collision angle is obtained by a fully distributed preset time Nash equilibrium search algorithm; An angle decision problem determination module, used to determine the angle decision problem of each missile in the interceptor group according to the optimal collision angle of the maneuvering target and the expected angle formation of the interceptor group; The decision-making guidance integrated control protocol determination module is used to determine the decision-making guidance integrated control protocol based on the optimal collision angle of the maneuvering target and the angle decision problem of each missile in the interception missile group.

10. The decision-making guidance integrated design system based on Nash equilibrium search strategy according to claim 9, characterized in that: The angle decision problem determination module includes: The angle decision problem calculation submodule is used to calculate the angle decision problem according to the formula Determine the angle decision problem of each missile in the interceptor group; in, is the i-th missile pair The estimate, is the i-th missile pair The estimate, is the expected end collision angle vector, h=[h1,h2,...,h N ] T is the expected angle formation of the multi-missile system, h ij =h(i)-h(j), is the expected terminal impact angle of the ith missile on the maneuvering target, β i is the weight coefficient, and N is the total number of missiles in the swarm.

Images