Finite-time adaptive cooperative guidance method for swarm systems facing member loss

Abstract

This invention relates to the technical field of swarm systems that can withstand member loss during engagement, and discloses a finite-time adaptive collaborative guidance method for swarm systems with member loss. Compared to existing technologies, which struggle to balance attack time and attack angle, lack precise control constraints on attack angles at the same attack time, or fail to account for the reduced attack effectiveness caused by member loss, this invention designs a dynamic integral sliding mode surface with a fast power-rate convergence law to suppress chattering and ensure finite-time convergence. After a member missile is lost during engagement, the collaborative guidance strategy can adaptively adjust the attack angle constraints online, enabling dynamic encirclement attacks on the target and ensuring attack reliability.

Description

Technical Field

[0001] The present invention relates to the technical field of cluster systems with damaged members during combat, and in particular to a limited-time adaptive collaborative guidance method for cluster systems with damaged members. Background Art

[0002] With the continuous improvement and advancement of multi-layered anti-missile defense systems, traditional one-on-one attacks against mobile targets face significant challenges. Launching multiple missiles at a target from different angles is an effective coordinated attack strategy for increasing overall lethality. However, multi-missile systems face the threat of damage to their component missiles during attack. This damage not only degrades the swarm system's performance but can even destroy the entire system.

[0003] There are two main methods for achieving simultaneous attacks on targets by multiple missile systems. One method involves first defining the initial relative relationship between the missiles and the target to predetermine the attack time for each individual missile in the multi-missile system. Then, all missiles utilize their own independent guidance laws to achieve a simultaneous attack. Another method involves coordinated, synchronized guidance based on consensus theory. Through online information exchange between missiles, attack times converge, eliminating the need for pre-determined timing. Furthermore, communication between multiple missiles can improve guidance accuracy.

[0004] Some scholars have combined the characteristics of these two methods and achieved a predetermined attack time based on consensus theory. In addition to considering the attack time, simultaneous attack tasks also need to consider the constraints of attack angles, which makes the design of collaborative guidance laws more difficult. Zhou et al. proposed a collaborative guidance method with distance as a consensus variable to attack static targets [1]; Shen et al. combined model predictive control (MPC) and collaborative proportional navigation (CPN) to carry out salvo attacks on static targets [2]; Lin et al. solved the problem of timed simultaneous attacks in three-dimensional space based on the leader-follower control scheme [3].

[0005] Many scholars have also studied cooperative guidance strategies for attacking maneuvering targets. Hou et al. considered the impact of maneuvering targets by designing a predicted intercept point (PIP), but did not discuss the communication between multiple missiles [4]. Zhang proposed two cooperative guidance schemes to attack maneuvering targets: with or without using a lead missile [5]. Chen proposed a three-dimensional cooperative guidance strategy that can attack maneuvering targets within a fixed time. The radial distance and radial relative velocity between the missile and the target are selected as consensus variables, and the maneuvering target can be attacked within a specified time [6].

[0006] Some scholars have found other methods to solve the problem of multi-missile cooperative guidance. Yan et al. conducted a reachability analysis and proposed a cooperative guidance method to attack highly maneuverable targets by establishing favorable engagement conditions [7]; Wang et al. proposed a cooperative guidance method based on dynamic encirclement to attack highly maneuverable targets, by constructing multiple virtual targets to dynamically attack a highly maneuverable target [8]. Wei et al. used the variational method and Hamiltonian optimization method to solve the problem of simultaneous attack on maneuverable targets. However, the initial relative state and terminal relative state of the target are fixed, and even the attack duration is fixed [9]. Rohit et al. designed two nonlinear guidance laws to attack maneuverable targets, but the expected attack angle should be set in advance according to the target

[10] .

[0007] [1]J.Zhou,JY ang,Distributed guidance law design for cooperativesimultaneous attacks with multiple missiles,Journal of Guidance Control&Dynamics 39(10)(2016)2436–2445.

[0008] [2] S. Kang, J. Wang, G. Li, J. Shan, IR Petersen, Optimal cooperative guidance280 law for salvo attack: An mpc-based consensus perspective, IEEE Transactions on Aerospace and Electronic Systems 54(5)(2018)2397–2410.

[0009] [3]M.Lin,

[0010] [4]Z.Hou,Y.Y ang,L.Liu,Y.Wang,Terminal sliding mode control basedimpact time and angle constrained guidance,Aerospace Science andTechnology26093(2019)105142

[0011] [5]S.Zhang,Y.Guo,Z.Liu,S.Wang,X.Hu,Finite-time cooperative guidancestrategy for impact angle and time control,IEEE Transactions on Aerospace andElectronic Systems 57(2)(2021)806–819.

[0012] [6]Z.Chen,W.Chen,X.Liu,J.Cheng,Three-dimensional fixed-time robustco-295operative guidance law for simultaneous attack with impact angleconstraint,Aerospace Science and Technology 110(2021)106523.

[0013] [7]X.Y an,M.Kuang,J.Zhu,X.Yuan,Reachability-based cooperativestrategy for intercepting a highly maneuvering target using inferiormissiles,Aerospace Sci-305ence and Technology 106(2020)106057.

[0014] [8] Z.Wang, W.Fu, Y.Fang, Z.Wu, M.Wang, Cooperative guidance law against highly maneuvering target with dynamic surrounding attack, International Journal of Aerospace Engineering 2021(2021)6623561.

[0015] [9]X.Wei, J.Yang,

[0016]

[10] R V.Nanavati, SRKumar, A.Maity, Spatial nonlinear guidancestrategies for target interception at pre-specified orientation, AerospaceScience and Technology 114(2021)106735.

[0017] According to existing research results, there are two main methods to achieve simultaneous attack of targets by multi-guided systems:

[0018] Method 1: First, the relative initial relationship between the missiles and the target is determined to predetermine the attack time for each individual in the multi-missile system. Then, all missiles use their own independent guidance laws to achieve a simultaneous attack. However, due to the diversity of initial conditions, it is difficult to perfectly set the attack time.

[0019] Method 2: Another approach is collaborative synchronous guidance based on consensus theory. Through online information exchange between missiles, attack times converge, eliminating the need for pre-determined timing. Furthermore, communication between multiple missiles can improve guidance accuracy. The success of this method hinges on accurately estimating flight time and target attack time. However, the complex engagement environment and target maneuverability significantly impact guidance performance. Therefore, we propose a finite-time adaptive collaborative guidance method for swarm systems that accommodates member loss. Summary of the Invention

[0020] (1) Technical problems solved

[0021] In view of the deficiencies of the prior art, the present invention provides a finite-time adaptive collaborative guidance method for a cluster system facing member damage, which solves the above-mentioned problems.

[0022] (2) Technical solution

[0023] To achieve the above-mentioned objectives, the present invention provides the following technical solution: a finite-time adaptive collaborative guidance method for a cluster system facing member damage, comprising the following steps:

[0024] Step 1: The corresponding equation describing the kinematics of the relative motion between the i-th missile and the target is:

[0025]

[0026]

[0027]

[0028]

[0029] Where variable q is the line of sight angle (LOS angle), r is the relative distance between the missile and the target, θ is the track angle in the inertial system, V is the velocity, and a is the horizontal acceleration. Derivatives of equations (1) and (2) yield:

[0030]

[0031]

[0032] Among them, ω ri =a tri ,ω qi =a tqi / r i , a tri and a tqi are the acceleration of the target along and perpendicular to the line of sight of the missile and target, respectively. ri and u qi are the accelerations of missile i along and perpendicular to the missile-target line of sight, respectively;

[0033] Assume that the target's maneuverability along and perpendicular to the missile-target line of sight is bounded and satisfies;

[0034]

[0035] in, and is an unknown positive constant;

[0036] Step 2: Before designing the guidance law, a finite-time stability lemma is given;

[0037] Step 3: Simultaneous attack guidance;

[0038] Step 4: By proving that the sliding surface converges to zero in a finite time, the system state reaches the designed dynamic integral sliding surface s in a finite time. 1i , prove that the state r of the multi-missile system i and It converges uniformly in finite time;

[0039] Step 5: Constrain the missile attack angle;

[0040] Step 6: Design the guidance law;

[0041] Step 7: By proving that the sliding surface converges to zero in a finite time, the system state reaches the designed dynamic integral sliding surface s in a finite time. 2i , proving the state of the multi-missile system qi and converges to zero in finite time.

[0042] Preferably, the specific content of the second step is:

[0043] Lemma 1. There exists a positive definite function y(t) that satisfies:

[0044]

[0045] Among them, η1>0, η2>0, 0<λ<1, then the function y(t) converges to zero in a finite time t and satisfies:

[0046]

[0047] Lemma 2, for λ∈(0,1), according to the feedback control law:

[0048]

[0049] Make the origin of the double integrator system in equation (11) stable within a finite time;

[0050]

[0051] Where k1>0, k2>0, 0<λ<1, sig(ξ) β =|ξ| β ·sgn(ξ);

[0052] Lemma 3. For a multi-agent system, if each agent can be represented as According to the control law of each agent, the multi-agent system can achieve finite-time uniform convergence:

[0053]

[0054] Where k1>0, k2>0, 0<λ<1, the communication topology of the multi-agent system is undirected, and the weight coefficient a is used. ij Indicates that if agent a i and agent a j If there is no connection, then a ij =0, otherwise a ij =1.

[0055] Preferably, the specific content of the third step is:

[0056] The launch time of each missile is:

[0057]

[0058] The dynamic integral sliding surface is:

[0059]

[0060] in

[0061]

[0062]

[0063] Where k r1 >0,k r2 >0,0<λ r <1.

[0064] Then, the acceleration of missile i along the LOS direction is designed to be:

[0065]

[0066] Where, ɑ1>0, ɑ2>0, 0 <p1<1, yes valuation, The adaptive law is:

[0067]

[0068] Among them, γ r is a positive constant.

[0069] Preferably, the fourth step includes the following:

[0070] first step:

[0071] The sliding surface s of formula (14) riDerivative, substitute into the guidance law u of formula (17) ri get:

[0072]

[0073] It should be pointed out that Define a positive definite Lyapunov function as:

[0074]

[0075] Then, we take the derivative of V1 and substitute it into formula (18) to obtain:

[0076]

[0077] Obviously, the only solution for V1(t)=0 is s 1i = 0, therefore, V1 is asymptotically stable, and the sliding surface s 1i Can converge to zero, the estimated error Bounded, then, the Lyapunov function V2 is designed as:

[0078]

[0079] Taking its derivative we get:

[0080]

[0081] because and We can make Large enough to accommodate:

[0082]

[0083] Then you know From this we can get:

[0084]

[0085] The only solution for V2(t)=0 is s 1i = 0, according to Lemma 1, the designed dynamic integral sliding surface s 1i and its rate of change can converge to zero in a finite time;

[0086] Step 2: The dynamic integral sliding mode surface of missile i converges in a finite time, using T ri Indicates that T r ={T r1 ,T r2 ,T r3 ,...T rn}, then when t≥T r When , for all n missiles At this time, according to formula (14), there exists:

[0087]

[0088] According to Lemma 3, the state r of the multi-missile system i and It can reach uniform convergence in finite time.

[0089] Preferably, the specific content of the fifth step is:

[0090] The difference in trajectory angle between missile i and target is expressed as:

[0091] θ tmi =θ t -θ mi· (27)

[0092] Desired angle of attack θ pi is the attack time t f When the speed direction difference between missile i and target is obtained, therefore, θ tmi |(t=tf)=θ pi The guidance goal of the i-th missile meeting the attack angle constraint can be achieved;

[0093] The potential function between each pair of missiles is defined as:

[0094]

[0095] Where N i ={j∈[1,n]|||(θ pi -θ pj )||≤d} is the defined neighborhood set for missile i’s impact angle adjustment. Then the potential function of missile i caused by neighboring missiles is:

[0096]

[0097] Then, the potential gradient caused by the neighboring missiles is calculated for missile i as:

[0098]

[0099] Moreover, the attack angles of all missiles are concentrated within a certain range, which can enhance the attack effect. The potential function of missile i caused by the attack angle boundary is defined as:

[0100]

[0101] Among them, θ up and θ low For the preset upper and lower bounds of the desired attack angle, the potential gradient caused by the attack angle boundary of missile i is calculated as:

[0102]

[0103] Therefore, the expected attack angle θ of the i-th missile is pi The adaptive update law is:

[0104]

[0105] Where k q and k g Is a positive number.

[0106] Preferably, the specific content of the sixth step is:

[0107] According to formula (3), the terminal sight angle q of the i-th missile can be obtained f i The expected angle of attack θ pi The relationship is:

[0108]

[0109] Where θ tf For the goal in t f Track angle at time η = V t / V m is the target-bullet speed ratio, let e qi =q i -q fi ,but The dynamic integral sliding surface is designed as:

[0110]

[0111] Among them, k q1 >0,k q2 >0,0<λ q <1;

[0112] Then, the acceleration of missile i perpendicular to LOS is designed as:

[0113]

[0114] Preferably, the specific contents of the seventh step are as follows:

[0115] Step 1: Sliding surface s of formula (35) 2i Derivative, substitute into the guidance law u of formula (36) qi get:

[0116]

[0117] make Define a positive definite Lyapunov function as:

[0118]

[0119] Then, we take the derivative of V3 and substitute it into the adaptive law of formula (37) to obtain

[0120]

[0121] Available The only solution is s 1i = 0, so according to Lemma 1, the dynamic integral sliding surface s 1i and its rate of change can converge to zero in a finite time, V3 is asymptotically stable, and the sliding surface s 2i Can converge to zero, the estimated error is bounded, and the Lyapunov function V4 is:

[0122]

[0123] Taking the derivative of V4, we get:

[0124]

[0125] because and We can make Large enough to satisfy Then you know From this we can get:

[0126]

[0127] Available The only solution is s 2i = 0, so according to Lemma 1, the dynamic integral sliding surface s 2i and its rate of change can converge to zero in a finite time;

[0128] Step 2: The dynamic integral sliding mode surface of missile i converges in a finite time, using T qi Indicates that T q ={T q1 ,T q2 ,T q3 ,...T qn}, then when t≥T q When , for all n missiles At this time, according to formula (35), there exists:

[0129]

[0130] Then, according to Lemma 2, the state e of the multi-missile system qi and It can converge to zero in finite time.

[0131] (3) Beneficial effects

[0132] Compared with the existing technology, the present invention provides a finite-time adaptive collaborative guidance method for cluster systems facing member damage, which has the following beneficial effects:

[0133] This finite-time adaptive collaborative guidance method for swarm systems facing member loss utilizes a dynamic integral sliding mode surface with a fast power-rate reaching law to suppress chattering and ensure finite-time convergence. If a member missile is lost during engagement, the collaborative guidance strategy adaptively adjusts the attack angle constraints online, enabling dynamic attack against the surrounding system and ensuring attack reliability.

[0134] 2. This finite-time adaptive collaborative guidance method for swarm systems designed for member loss investigates an adaptive collaborative guidance strategy for multi-missile systems attacking maneuvering targets. Simultaneous attack missions are implemented based on finite-time consensus theory. Collision angle constraints are met by solving the line-of-sight angle tracking problem within a finite time. To address the loss of member missiles during engagement, a dynamic encirclement attack strategy is proposed by adaptively adjusting the desired attack angles of the remaining missiles. BRIEF DESCRIPTION OF THE DRAWINGS

[0135] Figure 1 A geometric diagram of multiple missiles engaging a maneuvering target;

[0136] Figure 2 Schematic diagram of the trajectory of the missile and target in Case 1;

[0137] Figure 3 Schematic diagram of missile states related to simultaneous attacks in Case 1;

[0138] Figure 4 Schematic diagram of the missile state related to the attack angle constraint in Case 1;

[0139] Figure 5 This is a schematic diagram of the guidance instructions for the missile in Case 1;

[0140] Figure 6 Schematic diagram of the trajectory of the missile and target in case 2;

[0141] Figure 7 Schematic diagram of missile states related to simultaneous attacks in case 2;

[0142] Figure 8 Schematic diagram of missile status related to attack angle constraint in case 2;

[0143] Figure 9 Schematic diagram of the guidance law of the missile in Case 2. DETAILED DESCRIPTION

[0144] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0145] The method for finite-time adaptive collaborative guidance of a cluster system facing member damage includes the following steps:

[0146] The geometry of multiple missiles engaging a maneuvering target is shown in the figure below. Figure 1 As shown;

[0147] The corresponding equation describing the kinematics of the relative motion between the i-th missile and the target is:

[0148]

[0149]

[0150]

[0151]

[0152] Where variable q is the line of sight angle (LOS angle), r is the relative distance between the missile and the target, θ is the track angle of the inertial system, V is the velocity, and a is the horizontal acceleration. Derivatives of equations (1) and (2) yield:

[0153]

[0154]

[0155] Among them, ω ri =a tri ,ω qi =a tqi / r i , a tri and a tqi are the acceleration of the target along and perpendicular to the line of sight of the missile and target, respectively. ri and u qi are the accelerations of missile i along and perpendicular to the missile-target line of sight, respectively.

[0156] Assume that the target's maneuverability along and perpendicular to the missile-target line of sight is bounded and satisfies.

[0157]

[0158] in, and is an unknown positive constant.

[0159] System stability within a limited time

[0160] Before designing the guidance law, some lemmas on finite-time stability are given.

[0161] Lemma 1. There exists a positive definite function y(t) such that:

[0162]

[0163] Among them, η1>0, η2>0, 0<λ<1. Then, the function y(t) converges to zero in a finite time t and satisfies:

[0164]

[0165] Lemma 2. For λ∈(0,1), according to the feedback control law:

[0166]

[0167] Make the origin of the double integrator system in equation (11) stable within a finite time.

[0168]

[0169] Where k1>0, k2>0, 0<λ<1, sig(ξ) β =|ξ| β ·sgn(ξ).

[0170] Lemma 3. For a multi-agent system, if each agent can be represented as According to the control law of each agent, the multi-agent system can achieve finite-time uniform convergence:

[0171]

[0172] Where k1>0, k2>0, 0<λ<1. The communication topology of the multi-agent system is undirected, and the weight coefficient a is used. ij Indicates that if agent a i and agent a j If there is no connection, then a ij =0, otherwise a ij =1.

[0173] Simultaneous Attack Guidance

[0174] To increase overall lethality, all missiles should attack the target simultaneously. The launch time of each missile is:

[0175]

[0176] The dynamic integral sliding surface is:

[0177]

[0178] in

[0179]

[0180]

[0181] Where k r1 >0,k r2 >0,0<λ r <1.

[0182] Then, the acceleration of missile i along the LOS direction is designed to be:

[0183]

[0184] Where, ɑ1>0, ɑ2>0, 0 <p1<1。 yes valuation, The adaptive law is:

[0185]

[0186] Among them, γ r is a positive constant.

[0187] Theorem 4

[0188] For the multi-missile system using undirected and connected communication topologies as shown in Equations (1)-(6), the integral sliding mode surface designed for each missile in Equation (14) and the acceleration along the LOS direction in Equation (17) can achieve simultaneous attack on the target within a finite time.

[0189] prove

[0190] The proof of Theorem 4 consists of two steps. The first step is to prove that the sliding surface converges to zero in a finite time, so that the system state reaches the designed dynamic integral sliding surface s in a finite time. 1i The second step is to prove that the state r of the multi-missile system i and It converges uniformly in finite time.

[0191] Step 1:

[0192] The sliding surface s of formula (14) ri Derivative, substitute into the guidance law u of formula (17) ri get

[0193]

[0194] It should be pointed out that Define a positive definite Lyapunov function as:

[0195]

[0196] Then, we take the derivative of V1 and substitute it into formula (18) to obtain:

[0197]

[0198] Obviously, the only solution for V1(t)=0 is s 1i = 0. Therefore, V1 is asymptotically stable. Sliding surface s 1i Can converge to zero, the estimated error Bounded. Then, the Lyapunov function V2 is designed as:

[0199]

[0200] Taking its derivative we get:

[0201]

[0202] because and We can make Large enough to accommodate:

[0203]

[0204] Then you know From this we can get:

[0205]

[0206] The only solution for V2(t)=0 is s 1i = 0. Therefore, according to Lemma 1, the designed dynamic integral sliding surface s 1i and its rate of change can converge to zero in a finite time.

[0207] Step 2

[0208] The dynamic integral sliding mode surface of missile i converges in a finite time, using T ri Let T r ={T r1 ,T r2 ,T r3 ,...T rn}. Then when t≥T r When , for all n missiles At this time, according to formula (14), there exists:

[0209]

[0210] Then, according to Lemma 3, the state r of the multi-missile system i and It can reach uniform convergence in finite time. Therefore, multiple missiles can attack at the same time, and the theorem is proved.

[0211] Attack Angle Constraint

[0212] Attack angle adjustment

[0213] The difference in track angle between missile i and target is expressed as:

[0214] ≥

[0215] Desired angle of attack θ pi is the attack time t f When , the speed direction difference between missile i and target is obtained. Therefore, satisfying θ tmi |(t=tf)=θ pi The guidance goal of the i-th missile meeting the attack angle constraint can be achieved.

[0216] Multi-missile system failures are a common problem in practical coordinated guidance, potentially degrading system performance and even destroying the entire system. With the advancement of multi-layered anti-missile defense systems, the sacrifice of component missiles is one of the most serious flaws of multi-layered missile systems. Therefore, when sacrificing some missiles during an engagement, the attack angle constraints of the remaining missiles need to be adjusted to maximize overall lethality. This is followed by the use of a dynamic encirclement attack strategy.

[0217] The potential function between each pair of missiles is defined as:

[0218]

[0219] Where N i ={j∈[1,n]|||(θ pi -θ pj )||≤d} is the defined neighborhood set for missile i’s impact angle adjustment. Then the potential function of missile i caused by neighboring missiles is:

[0220]

[0221] Then, the potential gradient caused by the neighboring missiles is calculated for missile i as:

[0222]

[0223] Moreover, the attack angles of all missiles are concentrated within a certain range, which can enhance the attack effect. Then, the potential function of missile i caused by the attack angle boundary is defined as:

[0224]

[0225] Among them, θ up and θ low are the preset upper and lower bounds of the desired attack angle. Then, the potential gradient caused by the attack angle boundary of missile i is calculated as:

[0226]

[0227] Therefore, the expected attack angle θ of the i-th missile is pi The adaptive update law is:

[0228]

[0229] Where k q and k g Is a positive number.

[0230] Guidance law design

[0231] According to formula (3), the terminal sight angle q of the i-th missile can be obtained fi The expected angle of attack θ pi The relationship is:

[0232]

[0233] Where θ tf For the goal in t f Track angle at time η = V t / V m is the target-projectile velocity ratio. Therefore, the collision angle constraint can be satisfied by solving the LOS angle tracking problem in a finite time. Let e qi =q i -q fi ,but The dynamic integral sliding surface is designed as:

[0234]

[0235] Among them, k q1 >0,k q2 >0,0<λ q <1.

[0236] Then, the acceleration of missile i perpendicular to LOS is designed as:

[0237]

[0238] Theorem 5

[0239] For the multi-missile system of Equations (1)-(6), the integral sliding mode surface of each missile in Equation (35) and the acceleration perpendicular to the LOS in Equation (36) can realize the attack angle constraint of cooperative guidance within a finite time.

[0240] prove

[0241] The proof of the theorem consists of two steps. In the first step, by proving that the sliding surface converges to zero in a finite time, the system state reaches the designed dynamic integral sliding surface s in a finite time. 2i The second step is to prove the state of the multi-missile system qi and converges to zero in finite time.

[0242] Step 1:

[0243] The sliding surface s of formula (35) 2i Derivative, substitute into the guidance law u of formula (36) qi get

[0244]

[0245] make Define a positive definite Lyapunov function as:

[0246]

[0247] Then, we take the derivative of V3 and substitute it into the adaptive law of formula (37) to obtain

[0248]

[0249] Available The only solution is s 1i = 0. Therefore, according to Lemma 1, the designed dynamic integral sliding surface s 1i and its rate of change can converge to zero in a finite time. V3 is asymptotically stable. The sliding surface s 2i Can converge to zero, the estimated error is bounded. Then, the Lyapunov function V4 is:

[0250]

[0251] Taking the derivative of V4, we get:

[0252]

[0253] because and We can make Large enough to satisfy Then you know From this we can get:

[0254]

[0255] Available The only solution is s 2i = 0. Therefore, according to Lemma 1, the designed dynamic integral sliding surface s 2i and its rate of change can converge to zero in a finite time.

[0256] Step 2:

[0257] The dynamic integral sliding mode surface of missile i converges in a finite time, using T qi Let T q ={T q1 ,T q2 ,T q3 ,...T qn}. Then when t≥T q When , for all n missiles At this time, according to formula (35), there exists:

[0258]

[0259] Then, according to Lemma 2, the state e of the multi-missile system qi and It can converge to zero in a finite time. Therefore, the LOS angle q of each missile is i and its rate It can converge to the expected value in a finite time. Then, the target can be attacked at the desired attack angle, and the theorem is proved.

[0260] Implementation Case 1:

[0261] Table 1 Initial simulation settings of the missile

[0262] Table 1: Initial conditions and expected impact angle

[0263]

[0264] Coordinated Attack

[0265] In Case 1, we will show that four missiles 160 can achieve a synchronized attack mission with a desired attack angle within a limited time. The simulation results of the coordinated attack are shown in Table 2. The trajectory of the missiles and the target is shown in Figure 2 As shown in Figure 1, four missiles can simultaneously attack a maneuvering target with a miss distance of less than 1 meter. The attack angle constraints are all satisfied with an error of less than 1°. The missiles are connected in the topological adjacency matrix as follows:

[0266]

[0267] Table 2 Coordinated attack simulation results

[0268] Table 2: Results of cooperative attack in case 1

[0269]

[0270] The missile states related to simultaneous attacks in Case 1 are as follows: Figure 3 shown. Figure 3 (a) in the figure is the missile's take-off time. Figure 3 (b) and Figure 3 (c) in the figure are the relative distance and radial relative velocity between the missile and the target. Figure 3 (d) in the figure is the sliding surface s1. The results show that the missile's relative distance to the target and its radial relative velocity are consistent within a finite time. This achieves a consensus about the future time. Therefore, the four missiles can simultaneously attack the maneuvering target.

[0271] The missile state related to the attack angle constraint in Case 1 is as follows: Figure 4 As shown, Figure 4 (a) is the track angle difference between the missile and the target, Figure 4 (b) in the figure is the LOS angle tracking error, Figure 4 (c) is the missile speed, Figure 4 (d) in the figure is the sliding surface s2. The results show that the state e of the multi-elastic system qi It can converge to zero in a finite time. Therefore, all four missiles can attack the target at the desired attack angle.

[0272] The guidance instructions for the missile in Case 1 are as follows: Figure 5 As shown. Due to the different initial conditions of the missile, the initial missile-target relative distance and the radial relative velocity of the missile are very different. Therefore, Figure 5 In (a), the guidance command and sliding surface s1 along the LOS direction fluctuate greatly in the early stage. The sliding surface s1 converges to zero after about 5 seconds, and the guidance command along the LOS direction stabilizes after about 6.5 seconds, which means that the synchronous attack mission is achieved. Due to the large LOS angle error and its rate of change of the missile, Figure 5 (b) Guidance instruction u q The sliding surface s2 fluctuates greatly in the early stage. The sliding surface s2 converges to zero after about 5 seconds, and the guidance command perpendicular to the impact point stabilizes after about 9 seconds, indicating that the missile's attack angle constraint is satisfied.

[0273] Implementation Case 2:

[0274] Coordinated attack with member destruction

[0275] In the engagement of Case 2, one missile was destroyed. Then, by adaptively adjusting the attack angle constraints of the remaining missiles, a dynamic encirclement attack strategy was employed to maximize overall lethality. All initial settings were the same as in Case 1.

[0276] Missile 4 is set to be destroyed during the engagement at t=4s. Then, the topological adjacency matrix of the remaining missiles becomes:

[0277]

[0278] Using the attack angle adjustment strategy, the expected attack angle of the remaining missiles is adjusted to θ p1 =150°、θ p2 =180°、θ p3 =210°. The simulation results of the coordinated attack of Case 2 are shown in Table 3. The trajectory of the missile and the target is shown in Figure 6 As shown, the remaining three missiles can simultaneously attack the maneuvering target with a miss distance of less than 1 meter. The attack angle constraints are all met with an error of less than 1°.

[0279] The missile states related to simultaneous attacks in Case 2 are as follows: Figure 7 shown.

[0280] Figure 7 (a) in the figure is the launch time of the missile. Figure 7 (b) and Figure 7 (c) in the figure are the relative distance and radial relative velocity between the missile and the target. Figure 7 (d) in the figure is the sliding surface s1. The results show that the relative distances and radial relative velocities of the remaining three missiles are consistent within a finite time. This achieves consistent attack timing. Therefore, the remaining three missiles can still attack the maneuvering target simultaneously.

[0281] The missile state related to the attack angle constraint in case 2 is as follows: Figure 8 As shown, Figure 8 (a) is the track angle difference between the missile and the target, Figure 8 (b) in the equation is the tracking error of the viewing angle. Figure 8 (c) is the missile speed, Figure 8 (d) is the sliding surface s2. The results show that the state e of the multi-missile system qi It can converge to zero in a finite time. Therefore, the target can still be attacked by the remaining three missiles after adjusting the desired attack angle.

[0282] Table 3. Coordinated attack simulation results

[0283] Table 3: Results of cooperative attack in case 2

[0284]

[0285] The guidance instructions for the missile in case 2 are as follows: Figure 9 As shown. Due to the different initial conditions of the missile, the initial missile-target relative distance and the radial relative velocity of the missile are very different. Figure 9 In (a), the guidance command and sliding surface s1 along the LOS direction fluctuate greatly in the early stage. The sliding surface s1 converges to zero after about 5 seconds, and the guidance command along the LOS direction tends to stabilize after about 6 seconds, which means that the synchronous attack mission is achieved. Due to the large LOS angle error and its rate of change of the missile, Figure 9 The guidance instruction u in (b) q In the early stage, the sliding surface s2 fluctuates greatly. After sacrificing missile 4 at t=4s, the relevant states and guidance instructions of missiles 2 and 3 fluctuate greatly, while the relevant states and guidance instructions of missile 1 are almost unaffected. This is because the expected attack angle of missile 1 does not change, while the expected attack angles of missiles 2 and 3 increase. Finally, the sliding surface s2 converges to zero after about 8s, and the guidance instructions u q It stabilizes after about 9 seconds, indicating that the attack angle constraints of the remaining three missiles are met.

[0286] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A finite-time adaptive collaborative guidance method for cluster systems facing member damage, characterized by: The following steps are involved: Step 1: Describe the corresponding equations of the kinematics of the relative motion between the i-th missile and the target; Step 2: Before designing the guidance law, a finite-time stability lemma is given; Step 3: Simultaneous attack guidance; Step 4: By proving that the sliding surface converges to zero in a finite time, the system state reaches the designed dynamic integral sliding surface s in a finite time. 1i , proving the status of the multi-missile system i and i It converges uniformly in finite time; The dynamic integral sliding surface is: in Where k r1 >0,k r2 >0, 0 <λ r < 1; Step 5: Constrain the missile attack angle; Step 6: Design the guidance law and design the acceleration of missile i perpendicular to LOS as: ； Step 7: By proving that the sliding surface converges to zero in a finite time, the system state reaches the designed dynamic integral sliding surface s in a finite time. 2i , proving the state of the multi-missile system qi and qi converges to zero in finite time.

2. The method for finite-time adaptive collaborative guidance of a cluster system facing member loss according to claim 1, characterized in that: The specific contents of the second step are: Lemma 1. There exists a positive definite function y(t) that satisfies: Among them, η1>0, η2>0, 0 < λ < 1, then the function y(t) converges to zero in a finite time t and satisfies: Lemma 2, for λ∈(0,1), according to the feedback control law: Make the origin of the double integrator system in equation (11) stable within a finite time; where k1 > 0, k2 > 0, 0 < λ < 1, ; Lemma 3. For a multi-agent system, if each agent can be represented as ; According to the control law of each agent, the multi-agent system can achieve finite-time uniform convergence: Where k1>0, k2>0, 0 < λ < 1, the communication topology of the multi-agent system is undirected, and the weight coefficient a is used ij Indicates that if agent a i and agent a j If there is no connection, then a ij =0, otherwise a ij =1.

3. The method for finite-time adaptive collaborative guidance of a cluster system facing member loss according to claim 1, characterized in that: The specific content of the third step is: The launch time of each missile is: The dynamic integral sliding surface is: in Where k r1 >0,k r2 >0, 0 <λ r < 1; Then, the acceleration of missile i along the LOS direction is designed to be: Where ɑ1>0, ɑ2>0, 0 <p1< 1, ri yes ri valuation, ri The adaptive law is: Among them, γ r is a positive constant.

4. The method for finite-time adaptive collaborative guidance of a cluster system facing member loss according to claim 3, characterized in that: The fourth step includes the following: first step: The sliding surface s of formula (14) ri Derivative, substitute into the guidance law u of formula (17) ri get: It should be pointed out that ri = ri − ri , define a positive definite Lyapunov function as: Then, take the derivative of V1 and substitute it into formula (18), and we get: Obviously, the only solution for V1(t) = 0 is s 1i = 0, therefore, V1 is asymptotically stable and the sliding surface s 1i Can converge to zero, the estimated error ri Bounded, then, the Lyapunov function V2 is designed as: Taking its derivative we get: because ri =γ r | s 1i |≥0 and ri (0)>0, we can make ri (0) is large enough to satisfy: Then you know ri | s 1i |- ri | s 1i |≤0, from this we can get: The only solution for V2(t) = 0 is s 1i = 0, according to Lemma 1, the designed dynamic integral sliding surface s 1i and its rate of change li can converge to zero in a finite time; Step 2: The dynamic integral sliding mode surface of missile i converges in a finite time, using T ri Indicates that T r ={T r1 ,T r2 ,T r3 ,...T rn }, then when t≥T r When all n missiles have s 1i = li =0, then according to formula (14), there exists: According to Lemma 3, the state r of the multi-missile system i and i It can reach uniform convergence in finite time.

5. The method for finite-time adaptive collaborative guidance of a cluster system facing member loss according to claim 4, characterized in that: The specific contents of the fifth step are: The difference in track angle between missile i and target is expressed as: Desired angle of attack θ pi is the attack time t f When , the speed difference between missile i and target is obtained, so it satisfies θ tmi |(t = tf)=θ pi The guidance goal of the i-th missile meeting the attack angle constraint can be achieved; The potential function between each pair of missiles is defined as: Where N i = {j∈[1,n]| ||(θ pi −θ pj )||≤d} is the definition neighborhood set for missile i’s impact angle adjustment; then the potential function of missile i caused by neighboring missiles is: Then, the potential gradient caused by the neighboring missiles is calculated for missile i as: Moreover, the attack angles of all missiles are concentrated within a certain range, which can enhance the attack effect. The potential function of missile i caused by the attack angle boundary is defined as: Among them, θ up and θ low For the preset upper and lower bounds of the desired attack angle, the potential gradient caused by the attack angle boundary of missile i is calculated as: Therefore, the expected attack angle θ of the i-th missile is pi The adaptive update law is: Where k q and k g Is a positive number.

6. The method for finite-time adaptive collaborative guidance of a cluster system facing member loss according to claim 5, characterized in that: The specific contents of the sixth step are: According to formula (3), the terminal sight angle q of the i-th missile can be obtained f i The expected angle of attack θ pi The relationship is: Where θ tf For the goal in t f Track angle at time η = V t / V m is the target-bullet speed ratio, let e qi = q i −q fi ,but qi = i ; The dynamic integral sliding surface is designed as: Among them, k q1 > 0 , k q2 > 0, 0 < λ q < 1; Then, the acceleration of missile i perpendicular to LOS is designed as: 。 7. The method for finite-time adaptive collaborative guidance of a cluster system facing member loss according to claim 6, characterized in that: The specific contents of step 7 are as follows: Step 1: Sliding surface s of formula (35) 2i Derivative, substitute into the guidance law u of formula (36) qi get: make ri = ri − ri， Define a positive definite Lyapunov function as: Then, we take the derivative of V3 and substitute it into the adaptive law of formula (37) to obtain Available The only solution for 3(t) = 0 is s 1i = 0, so according to Lemma 1, the dynamic integral sliding surface s 1i and its rate of change li can converge to zero in a finite time, V3 is asymptotically stable, and the sliding surface s 2i Can converge to zero, the estimated error qi is bounded, and the Lyapunov function V4 is: Taking the derivative of V4, we get: because qi =γ q | s 2i |≥0 and qi (0)>0, we can make qi (0) Large enough to satisfy qi (0)> qi (0), then we know ri | s 1i |- ri | s 1i |≤0, from this we can get: Available The only solution for 4(t) = 0 is s 2i = 0, so according to Lemma 1, the dynamic integral sliding surface s 2i and its rate of change 2i can converge to zero in a finite time; Step 2: The dynamic integral sliding mode surface of missile i converges in a finite time, using T qi Indicates that T q ={T q1 ,T q2 ,T q3 ,...T qn }, then when t≥T q When all n missiles have s 2i = 2i =0, then according to formula (35), there exists: Then, according to Lemma 2, the state e of the multi-missile system qi and qi It can converge to zero in finite time.

8. The method for finite-time adaptive collaborative guidance of a cluster system facing member damage according to claim 7, characterized in that: The corresponding equations describing the kinematics of the relative motion between the i-th missile and the target include: Among them, the variable is the sight angle, is the relative distance between the missile and the target, is the track angle of the inertial system, For speed, is the horizontal acceleration; taking the derivative of equation (1) and equation (2), we get: Among them, ω ri =a tri ,ω ｑi =a tqi / r i , a tri and a tqi are the acceleration of the target along and perpendicular to the line of sight of the missile; u ri and u qi are the accelerations of missile i along and perpendicular to the missile-target line of sight, respectively; Assume that the target's maneuverability along and perpendicular to the missile-target line of sight is bounded and satisfies; in, ri and qi is an unknown positive constant.

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