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

Abstract

The application discloses a decision guidance integrated design method and system based on a Nash equilibrium search strategy, relates to the technical field of guidance, and comprises the following steps: acquiring the dynamic parameters of a target and a group of interceptor missiles, and constructing an interception model; determining an optimal guidance law based on the model and an end collision angle constraint; setting an expected collision angle, and solving by means of a Nash equilibrium algorithm; solving the missile angle decision problem according to the optimal collision angle and an expected angle formation; and formulating a decision guidance integrated control protocol. The application solves the problems of the expected angle decision of a missile aiming at a maneuvering target and the end angle constraint guidance.

Description

TECHNICAL FIELD

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

[0002] With the development of attack and defense technology, the demand for upgrading guidance law is becoming more and more vigorous. Since 1960, the traditional proportional guidance law has been widely used due to its high guidance accuracy and easy implementation. However, modern guidance tasks not only require precision strikes, but also need to attack targets at a specific angle range in many guidance scenarios. Attacking targets at a specific angle range has many advantages in combat, such as enhancing armor-piercing effect, increasing radar scattering cross-section of the enemy, etc. Interception of high-speed targets at a certain angle range can also increase the terminal interception accuracy. In addition, multi-missile multi-angle cooperative attack on high-value targets can make the missile group achieve multi-to-one interception in a hunting posture, thereby increasing the detection range of the missile group and improving the interception efficiency. The demand for attacking targets at a specific angle range has given rise to the development of angle-constrained guidance law.

[0003] Many existing works mostly focus on the implementation of angle constraint. Li et al. derive the angle-constrained control law of biased proportional navigation using a pre-set performance function, obtain the closed-loop analytical expression of the lead angle based on small perturbation linearization, and then obtain the value range and updating strategy of the guidance law gain. Yang et al. use the collision triangle theory to obtain the angle error, and use the fixed-time sliding mode control and barrier Lyapunov method to derive the angle guidance law with FOV constraint. Liu et al. describe the cooperative guidance problem as a zero-sum differential game problem, and the optimization objectives include miss distance and relative impact angle error. Zhao et al. use an event-triggered mechanism to reduce the communication frequency of the cooperative process, thereby reducing the computational burden of the cooperative guidance command, and use finite-time theory to complete the analysis of the cooperative control law.

[0004] However, whether it is single-missile or multi-missile cooperative angle-constrained guidance law research, most of the achievements only focus on the implementation of angle constraint, and few studies discuss the decision-making problem of expected impact angle. It is very important to combine the decision-making process of expected impact angle with the implementation process of angle constraint. SUMMARY

[0005] The purpose of the present application is to provide a decision guidance integrated design method and system based on Nash equilibrium search strategy, which applies the decision guidance integrated control protocol to a multi-missile system to achieve angle decision and guidance task of multi-missiles against maneuvering targets, and solves the problem of expected angle decision and terminal angle-constrained guidance of missiles against maneuvering targets.

[0006] To achieve the above purpose, the present application provides the following solutions:

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

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

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

[0010] determining a basic angle constraint optimal guidance law of the maneuvering target based on the terminal collision angle constraint according to the dynamic model of intercepting the maneuvering target;

[0011] determining an optimal collision angle of the maneuvering target according to the basic angle constraint optimal guidance law of the maneuvering target; the optimal collision angle is an expected terminal collision angle of the maneuvering target and the interceptor missile group; the expected terminal collision angle is obtained by a completely distributed preset time Nash equilibrium search algorithm;

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

[0013] determining 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 missile group.

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

[0015]

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

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

[0018]

[0019] wherein m is a proportional guidance coefficient, q f is a terminal predicted line-of-sight angle, q d is an expected terminal angle, V r is the relative speed size, r and q are respectively the missile-target distance and the line-of-sight angle, σr It is the relative forward angle.

[0020] Optionally, the optimal collision angle of the maneuvering target is determined based on the optimal guidance law constrained by the basic angle of the maneuvering target, specifically including:

[0021] when According to the formula Determine the optimal collision angle for the maneuvering target;

[0022] when According to the formula Determine the optimal collision angle for the maneuvering target;

[0023] in, The relative forward angle at the initial moment. For the optimal collision angle of the maneuvering target, γ t For the speed yaw angle of the maneuvering target, For the optimal terminal missile yaw angle, s * Let y(j) be the index of the smallest element in the sequence y(j).

[0024] Optionally, based on the optimal collision angle of the maneuvering target and the expected angle formation of the interceptor missile group, the angle decision problem for each missile in the interceptor missile group is determined, specifically including:

[0025] According to the formula Determining the angle decision for each missile in the interceptor group;

[0026] in, For the i-th missile pair The estimate, For the i-th missile pair The estimate, Let h = [h1, h2, ..., h] be the desired end-collision angle vector. N ] T For the expected angle formation of multiple missile systems, h ij =h(i)-h(j), Let β be the expected terminal impact angle of the i-th missile against the maneuvering target. i is the weighting coefficient, and N is the total number of missiles in the missile swarm.

[0027] Optionally, based on the optimal collision angle of the maneuvering target and the angle decision problem of each missile in the interceptor swarm, an integrated decision-making and guidance control protocol is determined, specifically including:

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

[0029] in, K i is the speed ratio of the maneuvering target and the missiles in the interceptor missile group, q f,i is the terminal predicted line-of-sight angle of the i-th missile.

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

[0031]

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

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

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

[0035] a parameter acquisition module, configured to acquire dynamic parameters of a maneuvering target and dynamic parameters of an interceptor missile group;

[0036] a dynamic model construction module, configured to construct a dynamic model of 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, configured to determine a basic angle constraint optimal guidance law of the maneuvering target based on terminal impact angle constraint according to the dynamic model of intercepting the maneuvering target;

[0038] an optimal impact angle determination module, configured to determine an optimal impact angle of the maneuvering target according to the basic angle constraint optimal guidance law of the maneuvering target; the optimal impact angle is an expected terminal impact angle of the maneuvering target and the interceptor missile group; the expected terminal impact angle is obtained by a completely distributed preset time Nash equilibrium search algorithm;

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

[0040] a decision guidance integrated control protocol determination module, configured to determine a decision guidance integrated control protocol based on the optimal impact angle of the maneuvering target and the angle decision problem of each missile in the interceptor missile group.

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

[0042] The angle decision problem calculation submodule is used to calculate based on the formula. Determining the angle decision for each missile in the interceptor group;

[0043] in, For the i-th missile pair The estimate, For the i-th missile pair The estimate, Let h = [h1, h2, ..., h] be the desired end-collision angle vector. N ] T For the expected angle formation of multiple missile systems, h ij =h(i)-h(j), Let β be the expected terminal impact angle of the i-th missile against the maneuvering target. i is the weighting coefficient, and N is the total number of missiles in the missile swarm.

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

[0045] The application provides a decision guidance integrated design method and system based on a Nash equilibrium search strategy, which comprises the following steps: firstly, acquiring the dynamic parameters of a maneuvering target and the dynamic parameters of a group of interceptor missiles. These parameters are the basis for constructing a dynamic model of the maneuvering target. Then, a dynamic model of the maneuvering target is constructed by using the dynamic parameters. The model can describe the dynamic behavior of the maneuvering target and the group of interceptor missiles in the interception process. Then, a basic angle constraint optimal guidance law of the maneuvering target is determined based on the end collision angle constraint. The guidance law is for the maneuvering target and is used for guiding the group of interceptor missiles 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. The optimal collision angle is the expected end collision angle of the maneuvering target and the group of interceptor missiles. The expected end collision angle is obtained by a fully distributed preset time Nash equilibrium search algorithm. The algorithm can help the system find the optimal collision angle to meet the demand of multi-missile cooperative interception. Subsequently, the angle decision problem of each missile in the group of interceptor missiles is determined according to the optimal collision angle and the expected angle formation of the group of interceptor missiles. This step is to convert the optimal collision angle into specific flight angle instructions of each missile. Finally, a decision guidance integrated control protocol is determined based on the optimal collision angle and the angle decision problem of each missile. The protocol integrates the decision and guidance aspects, and ensures that the multi-missile system can work cooperatively to complete the angle decision and guidance tasks of the maneuvering target. The application applies the decision guidance integrated control protocol to the multi-missile system, and can realize the angle decision and guidance tasks of the multi-missiles to the maneuvering target, and effectively solve the expected angle decision and end angle constraint guidance problems of the missiles to the maneuvering target. BRIEF DESCRIPTION OF DRAWINGS

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort on the basis of these drawings.

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

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

[0049] Figure 3 A missile group communication topology provided by an embodiment of the present application.

[0050] Figure 4This is a schematic diagram of a multi-missile system intercepting the trajectory of a moving target, provided as an embodiment of this application.

[0051] Figure 5 This is a schematic diagram of a multi-missile overload curve provided in one embodiment of this application.

[0052] Figure 6 This is a schematic diagram of the relative forward angle of multiple missiles provided in an embodiment of this application.

[0053] Figure 7 This is a schematic diagram of a multi-missile collision angle decision-guidance curve provided in one embodiment of this application.

[0054] Figure 8 This is a schematic diagram of a multi-missile line-of-sight decision-guidance curve provided in one embodiment of this application.

[0055] Figure 9 This is a schematic diagram of a multi-missile observation error curve provided in one embodiment of this application.

[0056] Figure 10 This is a schematic diagram of a multi-missile adaptive gain curve provided in one embodiment of this application.

[0057] Figure 11 This is a schematic diagram of a comparison group trajectory provided in an embodiment of this application.

[0058] Figure 12 This is a comparative overload diagram provided for an embodiment of this application.

[0059] Figure 13 This is a schematic diagram of the functional modules of an integrated design system for decision guidance based on a Nash equilibrium search strategy, provided in an embodiment of this application. Detailed Implementation

[0060] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0061] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0062] Example 1

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

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

[0065] Step 102: constructing a dynamic model of 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: determining a basic angle constraint optimal guidance law of the maneuvering target based on a terminal impact angle constraint according to the dynamic model of intercepting the maneuvering target;

[0067] Step 104: determining an optimal impact angle of the maneuvering target according to the basic angle constraint optimal guidance law of the maneuvering target; the optimal impact angle is an expected terminal impact angle of the maneuvering target and the interceptor missile group; the expected terminal impact angle is obtained by a completely distributed preset time Nash equilibrium search algorithm;

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

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

[0070] In some embodiments, when steps 101-102 are performed, the following can be specifically implemented:

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

[0072] Specifically, as shown in Figure 2 , (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. M i and T represent the mass centers of the i th missile and the target, respectively. r i and q i represent the missile-target distance and the line-of-sight angle, respectively. V m,i and V t are the speed magnitudes of the missile and the target, respectively. γ m,i and γ t represent the speed yaw angles of the missile and the target in the inertial system, respectively. The forward 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 represent the magnitude of the overloads of the missile and the target in the inertial frame, respectively. r,i is the magnitude of the relative velocity, γ r,i is the yaw angle of the relative velocity, a r,i is the magnitude of the relative overloads, σ r,i is the angle of attack of the relative velocity and satisfies σ r,i = γ r,i - q i .

[0073] Based on the above provided dynamic parameters of the interceptor swarm and the dynamic parameters of the maneuvering target, the kinematic equations of the i-th missile and the target in the two-dimensional plane are constructed as follows:

[0074]

[0075] where i = 1, 2,..., N, the angle of attack σ t,i of the target satisfies σ t,i = γ t - q i , and the angle of attack σ m,i of the i-th missile satisfies σ m,i = γ m,i - q i .

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

[0077]

[0078] According to the dynamic parameters of the interceptor swarm and the dynamic parameters of the maneuvering target, the following parameter relationships can also be obtained.

[0079]

[0080] In this embodiment, it is assumed that the time when the interceptor swarm starts to guide is marked as t = t0, and the initial time of the relative angle of attack satisfies The velocities of the missile and the target are constant, and the velocity ratio K i of the target and the i-th missile satisfies 0 ≤ K i < 1, i.e., the velocity of the missile is greater than that of the target.

[0081] In some embodiments, when step 103 is performed, the following can be specifically implemented:

[0082] In order to realize the terminal impact angle constraint, a basic optimal angle guidance law is designed.

[0083] The zero-control miss distance can be expressed as:

[0084] z = -rsinσ r (4).

[0085] Specifically, the basic proportional guidance law can be expressed as where the proportional guidance coefficient m ≥ 0. Substituting this proportional guidance law into equation (4), 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, it can be obtained that

[0086] According to the parameter relationship in equation (3), γ r (t f )-γ r (t0) = (m+3)(q(t f )-q(t0)) can be transformed as follows:

[0087]

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

[0089] Integrating both sides of the zero-control miss distance and terminal predicted angle equation with respect to the missile-target distance and using the small perturbation assumption theorem, i.e., sinσ r ≈ptanσ r where p > 0, the following optimal control problem can be obtained:

[0090]

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

[0092]

[0093] In the equation, λ z , are the corresponding Lagrange parameters. By using the minimum value principle, it can be obtained that:

[0094]

[0095] where C1, C2 are constants. Substituting u in equation (8) into the equation expression (6) of the optimal control problem and integrating with respect to the relative distance, the expressions of C1, C2 are obtained as follows:

[0096]

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

[0098]

[0099] Taking the current time as the initial time t0, r, z can be used to replace the initial state r0, z0, and at the current time, p = cos σ r , so the basic angle constraint optimal guidance law can be expressed as:

[0100]

[0101] In some embodiments, when step 104 is performed, specifically as follows:

[0102] First, substituting the equation expression (10) of the closed-loop input command into the equation expression (6) of the optimal control problem can obtain equation (12), specifically as follows:

[0103]

[0104] Taking J u as a function of , that is, Let , then Since m ≥ 0, the optimal line-of-sight angle satisfies only if According to the derivation process of equation (3) and the equation expression (11) of the optimal guidance law, it can be obtained that:

[0105]

[0106] where is the optimal terminal missile yaw angle. Define where

[0107] x ∈ [-1, 1], Let B = -Kcos γ t , and C = -Ksin γ t , then (13) can be further expressed as:

[0108]

[0109] Solving (14) gives

[0110]

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

[0112] Because And Therefore, the formula (11) of the basic optimal guidance law can be transformed into Based on formula (3) and formula (4), there is dz / dr=(m+3)z / r, then the integral of both sides with respect to the missile-target distance can be obtained:

[0113]

[0114] Substituting and formula (16) into formula (3) gives formula (17), which is:

[0115]

[0116] Because σ r ∈(-π / 2,π / 2) and dr / dt<0, so It can be further known that

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

[0118]

[0119] Therefore, it can be known that Because V m >V t , γ r -γ m ∈(-π / 2,π / 2), further

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

[0121]

[0122] When The optimal terminal impact angle satisfies formula (20):

[0123]

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

[0125] Where, in some embodiments, when step 105 is performed, it can be specifically as follows:

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

[0127]

[0128] Where, represents the expected terminal impact angle vector. h = [h1, h2,..., h N ] T represents the expected angular formation of the multi-missile system, where h ij = h(i) - h(j). Let It is 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||x - k|| (22).

[0130] Where, i = 1, 2,..., N, l1 > 0. Since is convex on , the following inequality holds:

[0131] (x - y) T (▽J(x) - ▽J(y)) ≥ l2||x - y|| 2 (23).

[0132] Where, Based on (22) and (23), it can be known that the Nash equilibrium point is unique, which can make

[0133] Since the real cooperative engagement can employ distributed communication, the vector is unknown to the missiles in the missile group. For practicality, the cost function of the ith missile can be constructed as formula (24), as follows:

[0134]

[0135] where represents the estimate of the ith missile to represents the estimate of the ith missile to represents the estimate of the ith missile to represents the estimate of the ith missile to

[0136] According to the theory of steps 101 to 104, the decision guidance integrated control protocol of the ith missile can be designed as:

[0137]

[0138] where the solution equations of and in formula (25) are as follows:

[0139]

[0140] The desired end impact angle can be obtained by 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, so as to meet the preset time convergence condition.

[0143] In this embodiment, the decision guidance integrated control law (25) based on Nash equilibrium search designed can achieve the decision and strike task of the maneuvering target. The process of decision guidance integration design of the ith missile in the missile group can be described as follows:

[0144] 1) Select the navigation ratio parameter m e (0, 3], determine the basic angle constraint optimal guidance law formula (11), and determine

[0145] 2) Based on the initial state of the guidance phase and obtain and Then determine

[0146] 3) Determine the minimum time-to-go based on the initial state of the guidance phase The minimum time-to-go can be determined by

[0147]

[0148] If the minimum time-to-go of all missiles in the missile group is known, then Otherwise, let where is the minimum missile-target distance when the missile group starts the guidance phase, and represent the maximum speed limit of the missile and the target, respectively.

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

[0150] Embodiment Two

[0151] As shown in Figure 13 , the embodiment provides a decision-making and integrated guidance design system based on a Nash equilibrium search strategy, comprising:

[0152] A parameter acquisition module 1301 is configured to acquire the dynamic parameters of the maneuvering target and the dynamic parameters of the missile group.

[0153] A dynamic model construction module 1302 is configured to construct a dynamic model for intercepting the maneuvering target based on the dynamic parameters of the maneuvering target and the dynamic parameters of the missile group.

[0154] A basic angle constraint optimal guidance law determination module 1303 is configured to determine a basic angle constraint optimal guidance law for the maneuvering target based on an end collision angle constraint based on the dynamic model for intercepting the maneuvering target.

[0155] An optimal collision angle determination module 1304 is configured to determine an optimal collision angle for the maneuvering target based on the basic angle constraint optimal guidance law for the maneuvering target; the optimal collision angle is an expected end collision angle for the maneuvering target and the missile group; the expected end collision angle is obtained by a fully distributed preset time Nash equilibrium search algorithm.

[0156] An angle decision problem determination module 1305 is configured to determine an angle decision problem for each missile in the missile group based on the optimal collision angle for the maneuvering target and the expected angle formation of the missile group.

[0157] The decision-guidance integrated control protocol determination module 1306 is used to determine the 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 missile group.

[0158] This application also verifies the effectiveness of the proposed method through a specific example of a multi-missile system consisting of five missiles attacking a moving 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 as follows:

[0160] [X T ,Y T [1500m, 1000m]. Initial velocity 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 yaw angle is 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 missile group is as follows: Figure 3 As 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 is... d =10s, the expected formation can be set to h=[-15°,-30°,0°,30°,15°]. Other guidance parameters are set as follows: α=4, Q ij (t0)=20, β i =0.8, where i,j = 1,2,...,N. The comparison group does not use a decision-making process, but directly sets a fixed angle formation h = [6.75°, -1.50°, 15.00°, 31.50°, 23.25°], with all other parameters remaining the same.

[0162] Finally, the results are analyzed: the simulation results for the pursuit scenario are as follows... Figures 4-10 As shown. The coordinated guidance trajectory without angle decision-making and overload are as follows. Figures 11-12 As shown.

[0163] By Figure 4 It can be seen that the cluster composed of multiple missiles can realize multi-angle guidance to the maneuvering target. Figure 5 It can be seen that the relative overload of the terminal missile can converge to zero, and has a good terminal interception posture. Figure 6 It can be seen that the relative lead angle of the terminal converges to zero, and the decision-making and guidance integrated control protocol degenerates into a proportional guidance law. Figure 7 And Figure 8 It can be seen that the missile can realize angle decision-making within the preset time, and can realize angle constraint at the interception terminal. Based on Figure 9 And Figure 10 It can be seen that the optimal collision angle observation error of the missile can converge to zero, and the derivative of the adaptive curve is zero in the later period, verifying the effectiveness of the decision-making link. From Figures 4-5 And Figures 11-12 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 motion process and increase the energy loss.

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

[0165] The present application establishes a relative motion model of the missile and the target in a two-dimensional plane, and gives a basic angle constraint optimal guidance law for the maneuvering target; the optimal collision angle is determined according to the proposed guidance law; the angle decision-making problem is established according to the optimal collision angle and the expected angle formation; the decision-making and guidance integrated control protocol is proposed based on the above analysis and design. The designed decision-making and guidance integrated control protocol is applied to the multi-missile system, realizing the angle decision-making and guidance task of multiple missiles to the maneuvering target, and solving the expected angle decision-making and terminal angle constraint guidance problem of the missile to the maneuvering target.

[0166] The technical features of the above embodiments can be combined in any way. In order to make the description concise, not all possible combinations of the technical features in the above embodiments are described, but as long as the combinations of the technical features do not exist contradictory, they should be considered as the scope of the present application.

[0167] In this paper, specific examples are used to illustrate the principles and implementation methods of the present application. The above description of the embodiments is only used to help understand the method and its core idea; at the same time, for those skilled in the art, according to the idea of the present application, the specific implementation and application range will be changed. In summary, the content of the specification should not be understood as a limitation of the present application.

Claims

1. A decision-guidance integrated design method based on a Nash equilibrium search strategy, characterized in that, The decision-guidance integrated design method based on Nash equilibrium search strategy includes: Acquire the dynamic parameters of the maneuvering target and the dynamic parameters of the interceptor missile group; Based on the dynamic parameters of the maneuvering target and the dynamic parameters of the interceptor missile group, a dynamic model for intercepting the maneuvering target is constructed. Based on the dynamic model of intercepting maneuvering targets, and based on the terminal collision angle constraint, the optimal guidance law for the basic angle constraint of the maneuvering target is determined; Based on 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 missile group; the expected terminal collision angle is obtained by a fully distributed preset time Nash equilibrium search algorithm. Based on the optimal collision angle of the maneuvering target and the expected angle formation of the interceptor missile group, the angle decision problem of each missile in the interceptor missile group is determined. Based on the optimal collision angle of the maneuvering target and the angle decision-making problem of each missile in the interceptor group, an integrated decision-making and guidance control protocol is determined. Based on the optimal collision angle of the maneuvering target and the expected angle formation of the interceptor missile group, the angle decision problem for each missile in the interceptor missile group is determined, specifically including: According to the formula Determining the angle decision for each missile in the interceptor group; in, For the i-th missile pair The estimate, For the i-th missile pair The estimate, Let h = [h1, h2, ..., h] be the desired end-collision angle vector. N ] T For the expected angle formation of multiple missile systems, h ij =h(i)-h(j), Let β be the expected terminal impact angle of the i-th missile against the maneuvering target. i Here, N is the weighting coefficient, and N is the total number of missiles in the missile swarm. Based on the optimal collision angle of the maneuvering target and the angle decision-making problem of each missile in the interceptor group, an integrated decision-making and guidance control protocol is determined, specifically including: According to the formula Determine the integrated decision-making, guidance, and control protocol for the i-th missile; in, K i q is the ratio of the speed of the maneuvering target to the speed of the missiles in the interceptor swarm. f,i γ is the terminal prediction line-of-sight angle for the i-th missile. r,i Let V be the relative velocity yaw angle of the i-th missile. r,i Let r be the magnitude of the relative velocity of the i-th missile. i and q i These are the missile-target distance and line-of-sight angle of the i-th missile, respectively, σ r,i Let γ be the relative lead angle of the i-th missile, m be the proportional guidance coefficient, and γ be the relative lead angle of the i-th missile. t The yaw angle is the speed of the maneuvering target.

2. The decision-guidance integrated design method based on Nash equilibrium search strategy according to claim 1, characterized in that, The formula for the dynamic model of intercepting maneuvering targets is as follows: Among them, a r,i Let be the relative overload size of the i-th missile.

3. The decision-guidance integrated design method based on Nash equilibrium search strategy according to claim 2, characterized in that, The formula for the optimal guidance law based on the fundamental angle constraint of the maneuvering target is as follows: Where, q f To predict the viewing angle for the terminal, q d For the desired end angle, V r Let r be the relative velocity, q be the missile-target distance and line-of-sight angle, respectively, and σ be the relative velocity. r It is the relative forward angle.

4. The decision-guidance integrated design method based on Nash equilibrium search strategy according to claim 3, characterized in that, Based on the optimal guidance law constrained by the fundamental angle of the maneuvering target, the optimal collision angle of the maneuvering target is determined, specifically including: when According to the formula Determine the optimal collision angle for the maneuvering target; when According to the formula Determine the optimal collision angle for the maneuvering target; in, The relative lead angle at the initial moment of guidance. The optimal collision angle for a maneuvering target. For the optimal terminal missile yaw angle, s * Let y(j) be 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 1, characterized in that, The expected terminal impact angle of the i-th missile against the maneuvering target The solution formula is: Among them, Q ij (t0), α>0, c > 0, T d It is a constant.

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

7. A decision-guidance integrated design system based on a Nash equilibrium search strategy, used to implement the decision-guidance integrated design method based on a Nash equilibrium search strategy as described in any one of claims 1-6, characterized in that, include: The parameter acquisition module is used to acquire the dynamic parameters of maneuvering targets and the dynamic parameters of interceptor missile groups; The dynamics model construction module is used to construct a dynamics model for intercepting the maneuvering target based on the dynamics parameters of the maneuvering target and the dynamics parameters of the interceptor missile group. The module for determining the optimal guidance law under basic angle constraints is used to determine the optimal guidance law under basic angle constraints for a maneuvering target based on the dynamic model of intercepting the maneuvering target and the terminal collision angle constraint. The optimal collision angle determination module is used to determine the optimal collision angle of the maneuvering target based on 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 missile group; the expected terminal collision angle is obtained by a fully distributed preset time Nash equilibrium search algorithm. Angle decision problem determination module is used to determine the angle decision problem of each missile in the interceptor missile group based on the optimal collision angle of the maneuvering target and the expected angle formation of the interceptor missile group; The integrated decision-making and guidance control protocol determination module is used to determine the integrated decision-making and guidance control protocol based on the optimal collision angle of the maneuvering target and the angle decision problem of each missile in the interceptor missile group.

8. The decision-guidance integrated design system based on Nash equilibrium search strategy according to claim 7, characterized in that, The angle decision problem determination module includes: The angle decision problem calculation submodule is used to calculate based on the formula. Determining the angle decision for each missile in the interceptor group; in, For the i-th missile pair The estimate, For the i-th missile pair The estimate, Let h = [h1, h2, ..., h] be the desired end-collision angle vector. N ] T For the expected angle formation of multiple missile systems, h ij =h(i)-h(j), Let β be the expected terminal impact angle of the i-th missile against the maneuvering target. i is the weighting coefficient, and N is the total number of missiles in the missile swarm.

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