Topology switching decentration differential game collaborative guidance method

Abstract

The invention discloses a decentralized differential game cooperative guidance method for a missile cluster under a switching communication topological structure, and the method comprises the steps: introducing a virtual leading missile-slave missile architecture, enabling each missile to construct a virtual leading missile from an initial position, enabling nodes in a simplified virtual leading missile group system to interact through the state information of a topological structure, coordinating a virtual state, and achieving the cooperative guidance of the missile cluster under the switching communication topological structure. And generating a virtual consensus state track so as to realize decentration control. Communication topological structure switching is considered, an optimal control scheme for tracking an expected trajectory is solved in combination with a differential game theory and self-adaptive dynamic programming, and a network weight updating mechanism is designed in the process of solving an optimal control strategy for a nonlinear system line. According to the scheme, the average residence time limiting condition of switching signals is put forward, hypotheses and conditions needing to be met by part of parameters and variables are given, under the scheme, the designed multi-Lyapunov function can achieve exponential convergence, and the stability performance of a missile cluster using the guidance scheme under the topology switching condition is guaranteed.

Description

Technical Field

[0001] The present invention relates to the field of multi-missile cooperative guidance, and in particular to a decentralized differential game cooperative guidance method for a missile cluster under communication topology switching. Background Art

[0002] In recent years, as modern warfare presents increasingly strong non-contact, precision, information, and systematization characteristics, precision-guided weapons, as the main equipment for achieving modern battlefield target strikes, have attracted great attention from countries around the world in terms of their related technologies and equipment development, and are booming at an unprecedented speed, playing an irreplaceable role. At the same time, with the complexity of missile-target attack and defense, the limitations of single missile operations in modern warfare are becoming increasingly prominent. At the same time, the development of cluster intelligent cooperative control theory has attracted considerable attention to various issues in the cooperative control of multi-agent systems, which has prompted the study of missile cluster cooperative guidance strategies in the modern warfare environment, and the consideration of attacks on missile clusters such as enemy denial of service (DoS) on the battlefield, in order to enhance the combat effectiveness of missiles under various threats on the battlefield, has become the key to designing advanced missile systems.

[0003] Different from the general multi-agent swarm control problem, the required cooperative control method requires higher real-time performance and less communication data due to the high speed and high maneuverability of missiles. The control result should make the flight trajectory smoother and avoid circling or stationary phenomena. Secondly, as an offensive weapon, the results of missile actions often involve military strategy, security and other issues. Therefore, in the problem of multi-missile cooperative control, in addition to considering technical factors, more complex non-technical factors need to be considered, such as strategic decision-making, combat command, political influence, etc. These factors make the problem of multi-missile cooperative control more complex and sensitive, and require more comprehensive and in-depth research. Due to problems such as dynamic limitations, different mission requirements and complex non-technical factors involved, the application of swarm control technology in missile guidance requires in-depth research and the search for effective solutions to achieve efficient cooperative control of missiles and achieve the expected combat effect.

[0004] For multi-agent cooperative control problems including missile cluster cooperative interception of targets, the current mainstream method is to use the "leader-follower" structure, design distributed observers for followers to achieve time coordination; or to estimate the given virtual leader information by designing distributed observers, and combine reinforcement learning methods to achieve synchronous control under nonlinearity and actuator failure. However, in the above leader-follower architecture, or the method of adding a given input virtual leader signal to the topological structure, the lack of key central nodes can easily lead to the failure of the missile cluster, so it is necessary to achieve decentralization to meet the requirements of missile cluster node autonomy. At the same time, since the battlefield target maneuvers are usually unknown, differential countermeasures have been widely used in problems such as missile interception guidance. Through this multi-party optimal control theory, the guidance strategy of the target under our non-ideal maneuvers can be studied. Adaptive Dynamics Programming (ADP) combines neural networks and has been widely used to solve problems such as the Hamilton-Jacobi-Isaacs (HJI) equation, which is difficult to solve for nonlinear systems. If the impact of cyber attacks on the above-mentioned missile cluster collaborative guidance is considered, it is mainly reflected in the fact that the connectivity of the communication network is damaged to a certain extent, that is, under the action of cyber attack signals that can be expressed as switching topology signals, the missile cluster system will change, and the analysis method of the stability of the switching system cannot be directly applied to the multi-agent system with switching topology. Regarding this type of problem, many scholars have studied the consistency problem of multi-agents under the semi-Markov switching topology process, and analyzed the conditions and convergence performance of the state consensus of various types of linear and nonlinear multi-agent systems under the switching topology. However, when using the ADP method under differential games to solve multi-agent control problems including missile cluster interception guidance, there is still a lack of improved solutions for the switching topology situation and research on the consensus convergence performance of the system under this method. Therefore, it is necessary to conduct research on the decentralized collaborative control of missile clusters based on differential games in view of the impact of switching communication topology structures on the consistency collaborative control of missile clusters. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention discloses a switching topology decentralized differential game collaborative guidance method. Aiming at the problem of the change of the communication topology structure of a missile cluster during combat, the invention designs a decentralized collaborative guidance law for the missile cluster under the switching topology. Combined with the virtual leader-slave architecture, each missile constructs a virtual leader starting from its own initial position, and the simplified multi-virtual leader system interacts with state information based on the communication topology structure to realize the coordination of virtual states, thereby generating a virtual consensus state trajectory, thereby realizing decentralization. Based on the process of tracking the expected trajectory, the switching of the communication topology structure of the missile cluster is considered, and combined with the differential game theory, the optimal control strategy is solved for the nonlinear system using ADP, and an evaluation network weight update scheme is designed. The restriction condition of the averaged well time (ADT) of the switching signal under certain parameter settings is given, and under this method, the influence of the switching signal is considered, and the designed multiple Lyapunov functions (MLF) can achieve exponential convergence.

[0006] In order to achieve the above technical objectives, the technical solution adopted by the present invention includes the following steps:

[0007] Step 1: Create a missile cluster limited switching atlas Topology switching signal defined in time series is a set of switching signals 1 to p. At the same time, the time domain [t ini ,t) The average dwell time limit of the switching signal:

[0008]

[0009] Where t>t ini >0, is δ(t) in the time domain [t,t ini ), N0>0 is the frequency hopping limit of the switching signal δ(t).

[0010] Step 2: Create a two-dimensional plane containing M1~M N In the combat scenario where a missile cluster including N missiles intercepts a maneuvering target T, the relative motion relationship between the missile and the target is designed to design the guidance law (Impact Time Control Guidance, ITCG) with the missile cluster attack time coordination as the goal. As a state cooperative variable, the cooperative guidance interception system can be described as a nonlinear state equation:

[0011]

[0012] Among them, Vi is the flight speed of missile i, α i is the track angle of missile i, u i is the missile i control lateral acceleration signal, V T is the target’s flight speed, β is the target’s track angle, v T is the target control lateral acceleration signal, θ i is the sight angle of missile i to the target, a Mi0 , r i0 , α i0 ,θ i0 are the normal acceleration of the virtual missile i, the distance to the target, the track angle and the sight angle. In addition, define σ i is the rate of change of the sight angle of missile i to the target. Assuming that in the final guidance stage, the missile flight speed is constant at V M , the target flight speed is constant at V T At the same time, the design objectives of the missile cluster distributed cooperative control law based on virtual missile output are summarized as follows:

[0013] The relative distance between the projectile and the target converges to 0:

[0014] Coordination of missile strike times:

[0015] Step 3: Combine the feedback linearization method to simplify the virtual missile cluster system into a second-order integral system:

[0016]

[0017] in

[0018] Design the control quantity of virtual cooperative control law:

[0019]

[0020] in, To simulate a Mi0 Virtual control under action, the second is a coordination term, where C = [ρτ], ρ and τ are adjustable parameters in the vector C. This term is used to ensure that the state error between nodes to the virtual leader converges quickly. At this time, the virtual control quantity can make the virtual leader group output the ideal state target:

[0021]

[0022] Step 4: Assume that the virtual lead satisfies the state equation The missile i satisfies the nonlinear state equation:

[0023]

[0024] Assume that the system formula is referred to here in formula (6), the nonlinear function f i (x i ) on the set containing the origin satisfies f i (0) = 0, and locally Lipschitz continuous, and the control matrix g i (x) and k i (x) are all bounded functions, among which, it is defined that there exists a positive constant g m ,g M (0<g m <g M ) makes the inequality g m <||g i (x)||<g M Established;

[0025] Based on the virtual trajectory x i0 , establish the missile cluster consensus deviation signal e i and e are:

[0026]

[0027] in Then the time interval [t k ,t k+1 ), k∈N, let , D δ(t) The elements of the nonlinear state equation (6) are used to input the relevant term k i (x i )v T is regarded as a disturbance term to the nonlinear system, that is, z i (x i ,v T ) = k i (x i )v T (z is used later i Indicates), the performance indicators considered at this time are:

[0028]

[0029] Where Q i ,R ii ,R ij ,T ii ,T ij is a positive definite matrix of corresponding dimension, and the optimal performance index

[0030] According to differential game control theory, the Hamiltonian function satisfies the following HJI equation:

[0031]

[0032] According to the Nash-Pound-Lyakin maximum-minimum principle, assuming that the solution of equation (9) exists and is unique, the necessary condition of equation (9) can be Solve for the optimal control law:

[0033]

[0034] Step 5: Use the neural network to fit the optimal performance index function and construct an evaluation network to approximate the ideal weights. The actual output of the evaluation network is:

[0035]

[0036] in To evaluate the network, we estimate the weights. To evaluate the network output based on the estimated weights;

[0037] The actual control law output is:

[0038]

[0039] Considering the influence of the switching signal δ(t), the evaluation network adopts the weight update law shown in formula (13):

[0040]

[0041] in ∑(·) is defined as:

[0042]

[0043] F 1i ,F 2i is an adjustable parameter, taking ( K∈R n×n is a positive definite diagonal matrix), then define A matrix with diagonal elements is a diagonal matrix that changes with the switching topology model, and ψ δ(t) ∈{ψ 1 ,ψ 2 ,…,ψ p There is always ψ δ(t) >0,ψ δ(t) Need to meet the specified selection conditions, first define:

[0044]

[0045] Where K is the adjustable parameter matrix, and the matrix Ω δ(t) It can be obtained by solving the following linear matrix inequality (LinearMatrix Inequality, LMI):

[0046]

[0047] in I N is an N-dimensional unit matrix, θ, α1, Λ, l is an adjustable parameter;

[0048] Combined with the bisection method to optimize ψ δ(t) Matrix to reduce MLF:

[0049]

[0050] At the switching time t k The upper bound of the ratio between before and after:

[0051]

[0052] in Augmentation Vector λ max (·) and λ min (·) are the maximum and minimum eigenvalues ​​of the corresponding matrices. The time-varying matrix Π(t) is defined as:

[0053]

[0054] in

[0055] Furthermore, in step 5, to solve ψ δ(t) The design optimization steps are as follows:

[0056] Step 5-1: When the system is acted upon by a switching topology signal k, k∈{1,2,…,p}, the parameters are initialized c k =0, Current number of iterations h = 0, maximum number of iterations h max ;

[0057] Step 5-2: Solve the LMI equation, let c k =λ min (ψ k ), definition andc k The lower bound of the ratio m l =1, upper bound

[0058] Step 5-3 Command

[0059] Step 5-4: Determine whether the LMI equation (16) has a solution under the added constraint condition (20):

[0060] st1λ max (ψ k )≤m mid λ min (ψ k )

[0061] st2λ max (ψ k )≤c mid Formula (20);

[0062] Step 5-5: If the constrained LMI equation in step 5-3 has a solution, let And return to step 5-3; if the constrained LMI equation in step 5-3 does not have a solution, but has a solution only when constrained by st1, then let m h =m mid , c k =c mid , and return to step 5-3; if the constrained LMI equation in step 5-3 does not have a solution, but has a solution only when subject to the st2 constraint, then let m l =m mid , And return to step 5-3; otherwise, let m l =m mid , c k =c mid ;

[0063] Step 5-6: Let h = h + 1, if h ≤ h max , and continue back to step 5-3.

[0064] In addition, you need to ensure that some parameters or variables meet the following conditions:

[0065] (1) For the missile i system (6) and the optimal control strategy of the differential game (10), there exists a continuously differentiable Lyapunov function Function satisfies And there exists a positive definite matrix such that

[0066] (2) For missile i in the missile cluster, its ideal weight of the evaluation network is Activation function σ i (e i ) and its effect on e i The partial derivative of Fitting error ε i (e i ) and its effect on e i The partial derivative of are all constrained, that is

[0067] (3) In e i A value range Inside, At zero point e i =0 or so like Bounded, the selected activation function σ i (e i ) and the weight update law can make the optimal performance index estimation error For i The partial derivative is continuous within the assigned range and satisfies The parameter matrix and For the corresponding e i An n×n-dimensional diagonal matrix of parameters.

[0068] Based on the above conditions, for missile i, the optimal control strategy (10) of the system (6) and the differential game exists as a continuously differentiable Lyapunov function Function satisfies And there exists a positive definite matrix such that

[0069] When ∑(.)=0, the condition is satisfied

[0070]

[0071] in

[0072] for ||Ψ i The upper bound of ||, that is

[0073] When Σ(.)=1, when α s =1 / α i When , the additional condition of formula (21) is satisfied so that

[0074]

[0075] Where [tk ,t k+1 ),k∈N Initial value is bounded The matrices are The corresponding eigenvalue upper bound is

[0076] Under the conditions corresponding to the above two situations, for the initial t k time The initial value of Considering Continuity, then for [t k ,t k+1 ), at any time in k∈N, we have The upper bound of exists, and the topological structure remains unchanged The consensus error e of all agents in the missile swarm i and weight estimation error are uniformly bounded and stable. Based on the above analysis, the network weight estimation error is evaluated as In the time interval [t k ,t k+1 ), k∈N converges, assuming that it is subject to positive real numbers Constraints, i.e.

[0077] The lower bound of the residence time is The adjustable parameter β must ensure that the LMI equation (16) has a solution. At this time, when the average residence time of the switching signal When there is lim t→∞ L1(t)=0, and for ψ δ(t) Optimization can reduce

[0078] At this time, when the communication topology between the system agents switches to the atlas All images Each of them contains at least one spanning tree containing all nodes. In the case of switching the missile cluster communication topology, the missile cluster can be synchronized with the switching signal δ(t) by evaluating the network weight update law combined with the optimization algorithm. The system can achieve exponential stability.

[0079] Compared with the general missile cluster guidance scheme, this invention has the following technical effects:

[0080] (1) Decentralized collaborative guidance of missile clusters is realized. Combined with the virtual leader-follower architecture, each missile builds its own virtual leader. Multiple virtual leaders exchange state information based on the communication topology structure to achieve virtual state coordination and form a virtual consensus state trajectory, thus realizing the decentralization of missile clusters without additional leadership signals.

[0081] (2) For the process of tracking the virtual consensus state trajectory, the target is considered to perform intelligent maneuvers, and the ADP is used to solve the optimal guidance law in combination with differential games. Different from the conventional ADP algorithm application, the present invention designs a weight update method for the evaluation network in response to the change of the communication topology structure when the missile cluster is attacked by malicious networks. By solving the LMI equation and combining the optimization method, the stability of the system under the weight update rate is guaranteed;

[0082] (3) The assumptions that some variables need to meet under certain parameter settings are given, and the constraints on the average residence time under this guidance method are given. Under this method, the exponential convergence of the designed multi-Lyapunov function can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0084] Figure 1 This is the overall flow chart of a switching topology decentralized differential game collaborative guidance method.

[0085] Figure 2 Schematic diagram of the relative motion between the missile cluster and the target under the virtual leader-follower architecture.

[0086] Figure 3 This is a schematic diagram of the virtual missile-decentralized collaborative guidance scheme from the missile architecture.

[0087] Figure 4 A collection of topological structures.

[0088] Figure 5 The following are the trajectory results of the projectile-target motion in the simulation example.

[0089] Figure 6 This is the curve of the relative distance between the projectile and the target changing with time in the simulation example.

[0090] Figure 7 This is the curve of the relative velocity between the projectile and the target changing with time in the simulation example.

[0091] Figure 8This is the result of the missile-target motion trajectory in the simulation example (a missile is randomly damaged). DETAILED DESCRIPTION

[0092] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work are within the scope of protection of the present invention.

[0093] like Figure 1 As shown, the embodiment of the present application provides a switching topology decentralized differential game collaborative guidance method, including the following steps:

[0094] Step 1: For the communication topology composed of missile i, its topology switching signal on the defined time sequence is the set of switching signals 1 to p. Corresponding to the finite switching graph set Switching time t k Satisfies 0<t1<t2<…<t k <t k+1 <…, the system topology is in the time interval Remains unchanged, and the minimum residence time τ of the topological structure satisfies τ=inf k (t k+1 -t k )>0, the topology switching process conforms to the semi-Markov process. To relax the switching signal in the time domain [t ini ,t), the definition of ADT is introduced here: if we let the positive constant τ a is the ADT of the switching signal δ(t), then it satisfies:

[0095]

[0096] Where t>t ini >0, is δ(t) in the time domain [t,t ini ), N0>0 is the frequency hopping limit of the switching signal δ(t);

[0097] A δ(t) , D δ(t) are the adjacency matrix and in-degree matrix of the missile cluster under the switching signal, L δ(t) =A δ(t) -D δ(t) is the Laplace matrix under the topology switching signal, is the deviation weighted coefficient matrix between cluster nodes and virtual consensus.

[0098] Step 2: See Figure 2 , consider the two-dimensional plane containing M1~M N A combat scenario in which a missile cluster with a total of N missiles intercepts a maneuvering target T is established, and the relative motion relationship between the missile and the target is established in this scenario. i is the flight speed of missile i; α i is the track angle of missile i; u i V is the lateral acceleration signal for missile i control; T is the target’s flight speed; β is the target’s track angle; v T The lateral acceleration signal for target control; r i is the distance between missile i and the target; θ i is the sight angle of missile i to the target; a Mi0 , r i0 , α i0 ,θ i0 are the normal acceleration of the virtual missile i, the distance to the target, the track angle and the sight angle; in addition, define σ i is the rate of change of the sight angle of missile i to the target. Assume that in the final guidance stage, the missile flight speed is constant at V M , the target flight speed is constant at V T , the relative kinematic equation of projectile and target can be established:

[0099]

[0100] In order to design the guidance law for missile cluster attack time coordination (Impact Time Control Guidance, ITCG), the missile-target distance and its derivative are used As a state cooperative variable, the cooperative guidance interception system can be described as a nonlinear state equation:

[0101]

[0102] At the same time, the design objectives of the distributed cooperative control law of missile clusters based on virtual missile output are summarized as follows:

[0103] The relative distance between the projectile and the target converges to 0:

[0104] Coordination of missile strike times:

[0105] Step 3: See Figure 3 Build a missile cluster system under the framework of virtual leader-slave missile, 10 ~M N0 The virtual leading group system composed of the selected state quantity r i0 , And output to missile i as the estimation of virtual consensus state trajectory for collaborative tracking. Each missile i assumes that the virtual leader i starts from its initial position, so that the error between the virtual leader state quantities converges quickly to the consensus as the goal: without considering the game between the virtual leader system and the target, the missile-target kinematic model is adopted, so that r i0 = 0 is the asymptotically stable equilibrium point of the system. The system (25) can be simplified to a second-order integral system:

[0106]

[0107] in

[0108] Design the control quantity of virtual cooperative control law:

[0109]

[0110] in, To simulate a Mi0 Virtual control under action, the second is a coordination term, where C = [ρτ], ρ, τ are adjustable parameters in vector C. This term is used to ensure that the state error between nodes converges quickly to the virtual leader, based on the system virtual control signal u i0 , decompose system (26) into the following two systems:

[0111]

[0112] Among them, the error between the state of missile i and the neighboring nodes in system S1 converges asymptotically, and when the communication topology of the missile cluster contains at least one spanning tree, is the only state equilibrium point of the system. Therefore, when system S1 can ensure that the system is bounded under the control law (27), we can have For system S2, the control component needs to be designed Make the system under the premise that the state quantity is asymptotically stable or uniformly bounded, that is, r i0 →0 and When bounded, simulate a Mi0 Virtual control under the action. At this time, the virtual control amount can make the virtual leading group output the ideal state target:

[0113]

[0114] Step 4: Assume that the virtual lead satisfies the state equation The missile i satisfies the nonlinear state equation:

[0115]

[0116] Assumption 1 System formula Reference Here In formula (30), the nonlinear function f i (x i ) on the set containing the origin satisfies f i (0) = 0, and locally Lipschitz continuous, and the control matrix g i (x) and k i (x) are all bounded functions, among which, it is defined that there exists a positive constant g m ,g M (0<g m <g M ) makes the inequality g m <||g i (x)||<g M Established;

[0117] Based on the virtual trajectory x i0 , establish the missile cluster consensus deviation signal e i and e are:

[0118]

[0119] in Then the time interval [t k ,t k+1 ), within k∈N, missile i has a local area combat consensus deviation equation:

[0120]

[0121] in The target control input related term k in the nonlinear state equation (30) is i (x i )v T is regarded as a disturbance term to the nonlinear system, that is, z i (x i ,v T ) = k i (x i )v T (z is used later i Indicates), the performance indicators considered at this time are:

[0122]

[0123] Where Q i ,R ii ,R ij ,T ii ,T ij is a positive definite matrix of corresponding dimension, and the optimal performance index

[0124] Define the Hamiltonian function:

[0125]

[0126] in It represents the derivative of the performance index function with respect to the consensus deviation signal. According to the differential game control theory, the Hamiltonian function satisfies the following HJI equation:

[0127]

[0128] According to the Nash-Pound-Lyakin maximum-minimum principle, assuming that the solution of equation (35) exists and is unique, the necessary condition of equation (35) can be Solve for the optimal control law:

[0129]

[0130] Step 5: Use the neural network to fit the optimal performance index function and build an evaluation network. Under the ideal weights, and its effect on consensus error e i The partial derivative of for:

[0131]

[0132] in p>0 is the ideal weight of the neural network, σ i (e i ) is the activation function of the neural network, ε i (e i ) is the fitting error of the neural network for the optimal performance index function. For the actual evaluation network, it is necessary to design a certain weight update law to make the actual weights close to the ideal weights. The real output of the evaluation network is:

[0133]

[0134] in To evaluate the network, we estimate the weights. To evaluate the network output based on the estimated weights, i The partial derivative is:

[0135]

[0136] At this time, according to formula (36), the actual control law output is:

[0137]

[0138] in The optimal control law for the differential game is The estimated value of . Ideal evaluation network With ideal control law satisfy Therefore, the network Estimated error:

[0139]

[0140] Design residuals:

[0141]

[0142] Considering the influence of the switching signal δ(t), the evaluation network adopts the weight update law shown in formula (43):

[0143]

[0144] in Defined as:

[0145]

[0146] F 1i ,F 2i is an adjustable parameter, taking ( K∈R n×n is a positive definite diagonal matrix), then define A matrix with diagonal elements is a diagonal matrix that changes with the switching topology model, and ψ δ(t) ∈{ψ 1 ,ψ 2 ,…,ψ p There is always ψ δ(t) >0,ψ δ(t) Need to meet the specified selection conditions, first define:

[0147]

[0148] Where K is the adjustable parameter matrix, and the matrix Ω δ(t) It can be obtained by solving the following linear matrix inequality (LinearMatrix Inequality, LMI):

[0149]

[0150] in I N is an N-dimensional unit matrix, θ, α1, Λ, l is an adjustable parameter.

[0151] Combined with the bisection method to optimize ψδ(t) Matrix to reduce MLF:

[0152]

[0153] At the switching time t k The upper bound of the ratio between before and after:

[0154]

[0155] in Augmentation Vector λ max (·) and λ min (·) are the maximum and minimum eigenvalues ​​of the corresponding matrices. The time-varying matrix Π(t) is defined as:

[0156]

[0157] in

[0158] Furthermore, in step 5, to solve ψ δ(t) The design optimization steps are as follows:

[0159] Step 5-1: When the system is acted upon by a switching topology signal k, k∈{1,2,…,p}, the parameters are initialized c k =0

[0160] , Current number of iterations h = 0, maximum number of iterations h max ;

[0161] Step 5-2: Solve the LMI equation (46) and let c k =λ min (ψ k ), definition and c k The lower bound of the ratio m l =1, upper bound

[0162] Step 5-3 Command

[0163] Step 5-4: Determine whether the LMI equation (46) has a solution under the added constraint (50):

[0164]

[0165] Step 5-5: If the constrained LMI equation in step 5-3 has a solution, let m h=m mid , And return to step 5-3; if the constrained LMI equation in step 5-3 does not have a solution, but has a solution only when constrained by st1, then let m h =m mid , c k =c mid , and return to step 5-3; if the constrained LMI equation in step 5-3 does not have a solution, but has a solution only when subject to the st2 constraint, then let m l =m mid , And return to step 5-3; otherwise, let m l =m mid , c k =c mid ;

[0166] Step 5-6: Let h = h + 1, if h ≤ h max , and continue back to step 5-3.

[0167] The evaluation network weight error is defined as:

[0168]

[0169] definition Then the weight error derivative is:

[0170]

[0171] In addition, you need to ensure that some parameters or variables meet the following conditions:

[0172] Assumption 2 For the missile i system (30) and the optimal control strategy (36) for both differential games, there exists a continuously differentiable Lyapunov function Function satisfies And there exists a positive definite matrix such that

[0173] Assumption 3 For missile i in a missile cluster, the ideal weight of its evaluation network is Activation function σ i (e i ) and its effect on e i The partial derivative of Fitting error ε i (e i ) and its effect on e i The partial derivative of are all constrained, that is

[0174] Assumption 4 In e i A value range Inside, At zero point e i =0 or so like Bounded, the selected activation function σ i (e i ) and the weight update law can make the optimal performance index estimation error For i The partial derivative is continuous within the assigned range and satisfies The parameter matrix and For the corresponding e i An n×n-dimensional parameter diagonal matrix of dimension .

[0175] Based on Assumptions 2-4:

[0176] When ∑(.)=0, the condition is satisfied:

[0177]

[0178] in for ||Ψ i The upper bound of ||, that is

[0179] When ∑(.)=1, when α s =1 / α i When , the additional condition of formula (53) is satisfied so that

[0180]

[0181] Where: k ,t k+1 ),k∈N Initial value is bounded The matrices are The corresponding eigenvalue upper bound is

[0182] Under the conditions corresponding to the above two situations, for the initial t k time The initial value of Considering Continuity, then for [t k ,t k+1 ), at any time in k∈N, we have The upper bound of exists, and the topological structure remains unchanged The consensus error e of all agents in the missile swarm i and weight estimation error are uniformly bounded and stable. Based on the above analysis, the network weight estimation error is evaluated as In the time interval [t k ,t k+1 ), k∈N converges, assuming that it is subject to positive real numbers Constraints, i.e.

[0183] The lower bound of the residence time is The adjustable parameter β must ensure that the LMI equation (46) has a solution. At this time, when the average residence time of the switching signal When there is lim t→∞ L1(t)=0, and for ψ δ(t) Optimization can reduce

[0184] At this time, when the communication topology between the system agents switches to the atlas All images Each of them contains at least one spanning tree containing all nodes. In the case of switching the missile cluster communication topology, the missile cluster can be synchronized with the switching signal δ(t) by evaluating the network weight update law combined with the optimization algorithm. The system can achieve exponential stability.

[0185] Example:

[0186] This embodiment considers the combat scenario of three missiles intercepting a maneuvering target in terminal maneuver, and sets the initial conditions as follows: missile initial position (x1, y1) = (700, 250), (x2, y2) = (2 000, 0), (x3, y3) = (250, 700), initial track angle α1 = α2 = α3 = 60°, speed V1 = V2 = V3 = 600 m / s, target initial position (x T ,y T )=(4 000,3 000), initial track angle β=120°, speed V T =400m / s. Adjustable parameter setting C = [1 1], performance index function parameter R 11 =R 22 =R 33 =0.1, T 11 =T 22 =T 33 =0.1, evaluation network weight update coefficient α c =1,α s =1,α a =0.3, F 11 =F12 =F 13 =[0.5 0.5 0.5 0.5 0.5] T , F 21 =F 21 =F 22 =F 23 =0.5, LMI equation parameters α1 = 1, Λ = 100I6, β = 1, θ = 1, l = 0.5, K=0.01I2. Initial values ​​of missile evaluation network parameters B δ(t) =I3. See Figure 3 Limited switching atlas for missile swarm communication topology

[0187] It is stipulated that after missile i hits the target or is set to fail due to damage, A δ(t) With B δ(t) Set the i-th row and i-th column of 0. Design control law components The target adopts the optimal guidance law under the 10g constraint. The simulation results are shown in Figure 4-Figure 7 . Under random topology switching signals, all switching times t k ,exist and ι = 1.03, Therefore, the lower limit of the average residence time τ a When lnυ / β=0.38, L1(t) exponential convergence can be guaranteed. At the same time, the three missiles realize the state quantity r i , The coordination can further achieve the estimated remaining attack time The maximum time interval between hits is 0.156s, which meets the interception requirements. And when a missile is randomly damaged in battle, see Figure 7 At t = 5s, missile 2 is damaged and its state quantity r2 = 0. The node is deleted in the topology graph. The results show that after missile 2 is damaged, the state quantities of missiles 1 and 3 can still be coordinated, achieving the design goal of decentralization.

[0188] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of complete hardware embodiments, complete software embodiments, or embodiments in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code. The scheme in the embodiments of the present application can be implemented in various computer languages, for example, object-oriented programming language Java and literal scripting language JavaScript, etc.

[0189] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0190] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0191] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0192] Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0193] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A switching topology decentralized differential game collaborative guidance method, characterized in that: The method comprises the following steps: Step 1: Model the semi-Markov switching topology process on the time series, set the random topology switching atlas and related topology information, and define the random topology switching signal on the time series; Step 2: Establish a virtual leader-follower architecture model. Each missile establishes a virtual leader based on its initial position. Multiple virtual leaders are combined with the communication topology to form a virtual leader group system. The state consensus trajectory generated by virtual state collaboration is used as the target, and the virtual state is fed back to the corresponding missile for tracking; Step 3: Simplify the virtual leading group system into a second-order integral system, and construct a virtual cooperative control law. Then decompose the second-order integral system, and the virtual leading group system outputs the ideal state target; Step 4: Combined with step 3, a virtual consensus state trajectory tracking process is given, and a consensus deviation signal is constructed for the nonlinear state equation of a general missile cluster. A performance index function is established by combining the consensus deviation, control input, and the missile's own state. The optimal guidance law of the missile cluster is solved by combining the optimal performance index function. Step 5: Construct the optimal performance index function for fitting the evaluation network, use the Hamiltonian function to construct the residual, construct the weight update law of the evaluation network, and obtain the parameter matrix of the Lyapunov function in the stable term of the weight update law by solving the LMI equation combined with the optimization algorithm to reduce the minimum residence time limit.

2. A switching topology decentralized differential game collaborative guidance method as claimed in claim 1, characterized in that: The semi-Markov switching topology process modeling in step 1 includes the following steps: Step 1.1: Create a missile cluster limited switching atlas Topology switching signal defined in time series is a set of switching signals 1 to p; A δ(t) , D δ(t) are the adjacency matrix and in-degree matrix of the missile cluster under the switching signal, L δ(t) =A δ(t) -D δ(t) is the Laplace matrix under the topology switching signal, is the deviation weighted coefficient matrix between cluster nodes and virtual consensus; Step 1.2: Use formula (1) to introduce in the time domain [t ini ,t) The average dwell time limit of the switching signal: Where t>t ini >0, is δ(t) in the time domain [t ini ,t), N0>0 is the frequency hopping limit of the switching signal δ(t), τ a Is a positive constant.

3. A switching topology decentralized differential game collaborative guidance method as claimed in claim 1, characterized in that: The step 2 specifically includes: Establish a two-dimensional plane containing M1~M N The relative motion relationship between missiles and targets in a combat scenario where a missile cluster with a total of N missiles intercepts a maneuvering target T is designed to design a guidance law with the goal of time coordination of missile cluster attack. As a state cooperative variable, the cooperative guidance interception system is described in the form of the nonlinear state equation of formula (2): Among them, α i is the track angle of missile i, u i is the lateral acceleration signal of missile i, β is the target track angle, v T is the target control lateral acceleration signal, θ i is the sight angle of missile i to the target, r i is the distance between missile i and the target, a Mi0 、r i0 , α i0 and θ i0 are the normal acceleration, distance from the target, track angle and sight angle of the virtual missile i respectively. Assuming that in the terminal guidance stage, the missile flight speed is constant at V M , the target flight speed is constant at V T At the same time, the design objectives of the distributed cooperative control law of missile clusters based on virtual missile output are: The relative distance between the projectile and the target converges to 0: Coordination of missile strike times:

4. A switching topology decentralized differential game collaborative guidance method as claimed in claim 1, characterized in that: The step 3 specifically includes the following steps: Step 3.1: Combine the feedback linearization method to simplify the virtual missile cluster system into a second-order integral system: in is a virtual track, For M 10 ~M N0 The state quantity selected by the virtual missile cluster system composed of u i0 It is the system virtual control signal; Step 3.2: Design the control quantity of the virtual cooperative control law: Among them, a Mi0 、r i0 , α i0 and θ i0 are the normal acceleration of the virtual missile i, the distance to the target, the track angle and the sight angle, To simulate a Mi0 Virtual control under action, the second is a collaborative term, is the adjacency matrix A of the missile cluster under the switching signal δ(t) , C = [ρτ], ρ, τ are adjustable parameters in vector C, which are used to ensure that the state error between nodes to the virtual leader converges quickly. At this time, the virtual control amount can make the virtual leader group output the ideal state target:

5. The switching topology decentralized differential game collaborative guidance method according to claim 1, characterized in that: The step 4 specifically comprises the following steps: Step 4.1: Assume that the virtual lead satisfies the state equation in is the virtual trajectory, u i0 is the system virtual control signal, v T The lateral acceleration signal of the target is controlled, and the missile i satisfies the nonlinear state equation: System formula: refer to formula (6), x i is the state cooperative variable, u i is the lateral acceleration signal of missile i, and the nonlinear function f i (x i ) on the set containing the origin satisfies f i (0) = 0, and locally Lipschitz continuous, and the control matrix g i (x) and k i (x) are all bounded functions, among which, it is defined that there exists a positive constant g m ,g M (0<g m <g M ) makes the inequality g m <||g i (x)||<g M If true, then based on the virtual trajectory x i0 , establish the missile cluster consensus deviation signal e i and e are: in is the adjacency matrix A of the missile cluster under the switching signal δ(t) The element L δ(t) =A δ(t) -D δ(t) is the Laplace matrix of the topology switching signal, D δ(t) is the in-degree matrix of the missile cluster under the switching signal, is the deviation weighted coefficient matrix between cluster nodes and virtual consensus, and the time interval [t k ,t k+1 ), k∈N, let D δ(t) The elements of the nonlinear state equation (6) are used to input the target control related terms k i (x i )v T is regarded as a disturbance term to the nonlinear system, that is, z i (x i ,v T ) = k i (x i )v T (z is used later i express); Step 4.2: Consider the performance indicators as: Where Q i ,R ii ,R ij ,T ii ,T ij is a positive definite matrix of corresponding dimension, and the optimal performance index According to differential game control theory, the Hamiltonian function satisfies the following HJI equation: According to the Nash-Pound-Lyakin maximum-minimum principle, assuming that the solution of equation (9) exists and is unique, the necessary condition of equation (9) can be Solve for the value of the optimal control law 6. A switching topology decentralized differential game collaborative guidance method as claimed in claim 1, characterized in that: The step 5 specifically comprises the following steps: Step 5.1: Use the neural network to fit the optimal performance index function and construct an evaluation network to approximate the ideal weights. Under the ideal weights, in is the ideal weight of the neural network, σ i (e i ) is the activation function of the neural network, ε i (e i ) is the fitting error of the neural network for the optimal performance index function, e i is the missile cluster consensus deviation signal, is the optimal performance indicator, and the true output of the evaluation network is: in To evaluate the network, we estimate the weights. To evaluate the network output based on the estimated weights, i The partial derivative is The actual control law output is: in They are the optimal control laws for the corresponding differential games. The estimated value of is the deviation weighted coefficient matrix between cluster nodes and virtual consensus, is the in-degree matrix D of the missile cluster under the switching signal δ(t) The element R ii and T ii is a positive definite matrix of the corresponding dimension, and the control matrix g i (x) is a bounded function; Step 5.2: Considering the influence of the switching signal δ(t), the evaluation network adopts the weight update law shown in formula (13): in, is the adjacency matrix A of the missile cluster under the switching signal δ(t) The elements of Σ(·) are defined as: F 1i ,F 2i is an adjustable parameter, in formula (14) K∈R n×n is a positive definite diagonal matrix), define The diagonal matrix is a diagonal matrix that changes with the switching topology model, and ψ δ(t) ∈{ψ 1 ,ψ 2 ,…,ψ p There is always ψ δ(t) >0; Step 5.3: ψ δ(t) Need to meet the specified selection conditions, first define Where K is the adjustable parameter matrix, and the matrix Ω δ(t) It can be obtained by solving the LMI equation shown in formula (16): in I N is an N-dimensional unit matrix, θ, α1, Λ, l is an adjustable parameter, A δ(t) is the adjacency matrix of the missile cluster under the switching signal, D δ(t) is the in-degree matrix of the missile cluster under the switching signal, L δ(t) =A δ(t) -D δ(t) is the Laplace matrix under the topology switching signal; Step 5.4: Optimize ψ by combining bisection δ(t) Matrix to reduce MLF: At the switching time t k The upper bound of the ratio between before and after: in Augmentation Vector λ max (·) and λ min (·) are the maximum and minimum eigenvalues ​​of the corresponding matrices, respectively. The time-varying matrix Π(t) is defined as: in is the deviation weighted coefficient matrix between cluster nodes and virtual consensus.

7. A switching topology decentralized differential game collaborative guidance method as claimed in claim 6, characterized in that: The parameter matrix of the function ψ δ(t) The optimization method includes the following steps: Step 5.4-1: When the system is acted upon by a switching topology signal k, k∈{1,2,…,p}, the initialization parameters c k =0, Current number of iterations h = 0, maximum number of iterations h max ; Step 5.4-2: Solve the LMI equation in equation (16) and let definition With c k The lower bound of the ratio m l =1, upper bound Step 5.4-3: Order Step 5.4-4: Determine whether the LMI equation of formula (16) has a solution under the added constraint condition formula (20); st1λ max (ψ k )≤m mid l min (ψ k ) s.t. 2λ max (ψ k ) ≤ c mid Equation (20) Step 5.4-5: If the constrained LMI equation in step 5.4-3 has a solution, let m h =m mid , And return to step 5.4-3. If the constrained LMI equation in step 5.4-3 does not have a solution, but has a solution only when constrained by st1, then let m h =m mid ,c k =c mid , and return to step 5.4-3. If the constrained LMI equation in step 5.4-3 does not have a solution, but has a solution only when subject to the st2 constraint, then let m l =m mid , And return to step 5.4-3, otherwise let m l =m mid ,c k =c mid ; Step 5.4-6: Let h = h + 1, if h ≤ h max , and continue back to (3).

8. A switching topology decentralized differential game collaborative guidance method as claimed in claim 6, characterized in that: For the missile i system (6) and the optimal control strategy of the differential game (10), there exists a continuously differentiable Lyapunov function Function satisfies And there exists a positive definite matrix such that For missile i in the missile cluster, its ideal weight of the evaluation network is Activation function σ i (e i ) and its effect on e i The partial derivative of ▽σ i (e i ), fitting error ε i (e i ) and its effect on e i The partial derivative of ▽ε i (e i ) are subject to constraints, namely In e i A value range Inside, At zero point e i =0 or so Define the evaluation network weight error as like Bounded, the selected activation function σ i (e i ) and the weight update law can make the optimal performance index estimation error For i The partial derivative is continuous within the assigned range and satisfies The parameter matrix ρ = diag{ρ1,ρ2,…,ρ n }and For the corresponding e i An n×n-dimensional parameter diagonal matrix of dimension .

9. A switching topology decentralized differential game collaborative guidance method as claimed in claim 8, characterized in that: During the operation of the missile cluster, the following variable constraints must be met: When ∑(.)=0, the condition is satisfied: in for ||Ψ i The upper bound of ||, that is When Σ(.)=1, when α s =1 / α i When , the additional condition of formula (21) is satisfied so that Where [t k ,t k+1 ),k∈N Initial value is bounded The matrices are The upper bound of the eigenvalue corresponding to M3j is Then under the conditions corresponding to the above two situations, for the initial t k time The initial value of Considering Continuity, then for [t k ,t k+1 ), at any time in k∈N, we have The upper bound of exists, and the topological structure remains unchanged The consensus error e of all agents in the missile swarm i and weight estimation error are uniformly bounded and stable. Based on the above analysis, the network weight estimation error is evaluated as In the time interval [t k ,t k+1 ), k∈N converges, assuming that it is subject to positive real numbers Constraints, i.e. The lower bound of the residence time is The adjustable parameter β must ensure that the LMI equation has a solution. When there is lim t→∞ L1(t)=0, and for ψ δ(t) Optimization can reduce At this time, when the communication topology between the system agents switches to the atlas All images Each of them contains at least one spanning tree containing all nodes. In the case of switching the missile cluster communication topology, the missile cluster can be synchronized with the switching signal δ(t) by evaluating the network weight update law combined with the optimization algorithm. The system can achieve exponential stability.

Images