A collaborative guidance method for decentralized differential games with switching topology

Abstract

This invention discloses a decentralized differential game collaborative guidance method for missile swarms under switching communication topologies. By introducing a virtual leader-follower architecture, each missile constructs a virtual leader from its initial position. Nodes in the simplified virtual leader swarm system interact through topological state information, coordinate virtual states, and generate a virtual consensus state trajectory, thereby achieving decentralized control. Considering communication topology switching, this method combines differential game theory with adaptive dynamic programming to solve an optimal control scheme for tracking the desired trajectory. In this process of solving the optimal control strategy for the nonlinear system, a network weight update mechanism is designed. By proposing an average dwell time constraint for the switching signal and providing assumptions and conditions that must be met for some parameters and variables, this scheme enables exponential convergence of the designed multi-Lyapunov function, ensuring the stable performance of missile swarms using this guidance scheme under topology switching.

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 missile clusters under communication topology switching. Background Art

[0002] In recent years, as modern warfare has become increasingly non-contact, precise, information-based, and systematized, precision-guided weapons, as the primary means of achieving target strikes on the modern battlefield, have attracted significant attention worldwide. The development of related technologies and equipment for precision-guided weapons, as the primary means of achieving target strikes on the modern battlefield, has flourished at an unprecedented rate, playing an irreplaceable role. Simultaneously, the increasing complexity of missile-target attack and defense has highlighted the limitations of single-missile operations in modern warfare. Furthermore, the development of swarm intelligence cooperative control theory has drawn considerable attention to various issues in the cooperative control of multi-agent systems. This has prompted the study of missile swarm cooperative guidance strategies in modern warfare environments, including consideration of battlefield attacks against missile swarms, such as enemy Denial of Service (DoS), to enhance missile combat effectiveness under various battlefield threats, becoming a key to the design of advanced missile systems.

[0003] Unlike general multi-agent swarm control problems, the required coordinated control approach, constrained by the high speed and maneuverability of missiles, requires higher real-time performance and less communication data. The resulting control should result in a smoother flight trajectory and avoid circling or stalling. Furthermore, as offensive weapons, the consequences of missile actions often involve military strategy, security, and other issues. Therefore, in addition to technical considerations, the coordinated control of multiple missiles also requires consideration of more complex non-technical factors, such as strategic decision-making, operational command, and political influence. These factors make the coordinated control of multiple missiles more complex and sensitive, requiring more comprehensive and in-depth research. Due to dynamic constraints, varying mission requirements, and the complex non-technical factors involved, the application of swarm control technology to missile guidance requires in-depth research and the search for effective solutions to achieve efficient coordinated control of missiles and the desired combat effectiveness.

[0004] For multi-agent cooperative control problems, including missile swarm coordinated interception, the current mainstream approaches use a "leader-follower" architecture, designing distributed observers for the followers to achieve temporal coordination; or designing distributed observers to estimate information about a given virtual leader, combined with reinforcement learning methods to achieve synchronous control under nonlinearities and actuator failures. However, in these leader-follower architectures, or by adding a given virtual leader signal to the topology, the absence of key central nodes can easily lead to missile swarm failure. Therefore, decentralization is necessary to meet the requirements for node autonomy in missile swarms. Furthermore, because battlefield target maneuvers are often unknown, differential games have been widely used in missile interception and guidance. This multi-party optimal control theory can be used to study guidance strategies for targets under nonideal maneuvers. Adaptive dynamic programming (ADP), combined with neural networks, has been widely applied to solve problems such as the difficult-to-solve partially differential Hamilton-Jacobi-Isaacs (HJI) equations for nonlinear systems. Considering the impact of cyberattacks on the coordinated guidance of missile swarms, this primarily manifests itself in a certain degree of disruption in the connectivity of the communication network. Specifically, under the influence of cyberattack signals, which can manifest as switching topology signals, the missile swarm system will undergo transformations. However, analytical methods for the stability of switching systems cannot be directly applied to multi-agent systems with switching topologies. Regarding this issue, many researchers have studied the consensus of multi-agents under semi-Markov switching topology processes, analyzing the conditions and convergence performance of state consensus for various linear and nonlinear multi-agent systems under switching topologies. However, when using the ADP method under differential games to solve multi-agent control problems, including missile swarm interception guidance, there is a lack of improved solutions for switching topologies and research on the consensus convergence performance of the system under this method. Therefore, it is necessary to investigate the impact of switching communication topologies on the consensus coordinated control of missile swarms and to conduct research on decentralized coordinated control of missile swarms based on differential games. Summary of the Invention

[0005] In response to the deficiencies in the prior art, the present invention discloses a switching topology decentralized differential game collaborative guidance method. Aiming at the problem of changes in 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 a virtual leader-follower architecture, each missile constructs a virtual leader starting from its own initial position. The simplified multi-virtual leader system interacts with state information based on the communication topology structure to achieve virtual state collaboration, thereby generating a virtual consensus state trajectory and achieving decentralization. Based on the process of tracking the expected trajectory, the switching of the missile cluster communication topology is considered. Combined with differential game theory, the optimal control strategy is solved for the nonlinear system using ADP, and an evaluation network weight update scheme is designed. Constraints on the average dwell time (ADT) of the switching signal are given under certain parameter settings. Furthermore, under this method, considering the influence of the switching signal, the designed multiple Lyapunov functions (MLF) can achieve exponential convergence.

[0006] 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) Average dwell time limit of 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 consisting of 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 the missile's flight speed is constant at V in the terminal guidance stage, M , the target flight speed is constant at V T At the same time, the design objectives of the distributed cooperative control law for missile clusters 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 time:

[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 the action of the second is a collaborative term, where C = [ρτ], where ρ and τ are adjustable parameters in the vector C. This term is used to ensure that the state error between nodes converges quickly to the virtual leader. At this time, the virtual control quantity can enable the virtual leader group to 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 ) satisfies f on the set containing the origin i (0) = 0, and locally Lipschitz continuous, and the control matrix g i (x) and k i (x) are all bounded functions, among which, 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 ), within k∈N, let , D δ(t) The elements of the nonlinear state equation (6) are input into the target control related terms k i (x i )v T is considered as a disturbance term to the nonlinear system, i.e. 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, 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 obtained. Solve for the optimal control law:

[0033]

[0034] Step 5: Use the neural network to fit the optimal performance index function and build 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, and is taken as ( 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 under the action of the switching topology signal, 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 (LMI):

[0046]

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

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

[0049]

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

[0051]

[0052] 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:

[0053]

[0054] in

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

[0056] Step 5-1: When the system is subjected to the 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

[0059] Step 5-4: Determine whether the LMI equation (16) has a solution under the added constraint (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 when only 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 when only constrained by st2, 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 must ensure that some parameters or variables meet the following conditions:

[0065] (1) For the missile i system (6) and the optimal control strategy (10) for both differential games, 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, i.e.

[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 e 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 conditions of formula (21) are satisfied so that

[0074]

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

[0076] Under the conditions corresponding to the above two situations, for the initial t k time The initial value of Taking into account Continuity, then for [t k ,t k+1 ), at any time in k∈N, there is The upper bound 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 is 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 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 general missile cluster guidance solutions, this invention has the following technical effects:

[0080] (1) Realize the decentralized collaborative guidance of missile clusters. 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 relying on additional leadership signals.

[0081] (2) In the process of tracking the trajectory of the virtual consensus state, the target is considered to perform intelligent maneuvers, and the ADP is used to solve the optimal guidance law in combination with differential games. Unlike conventional ADP algorithm applications, the present invention designs a weight update method for the evaluation network in response to the situation where the communication topology structure changes when the missile cluster is attacked by malicious networks. By solving the LMI equation and combining it with 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. In addition, the exponential convergence of the designed multi-Lyapunov function can be achieved under this method. 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 following briefly introduces the drawings required for use in the embodiments or the description of the prior art. 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 any 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 diagram of the virtual missile leadership-decentralized collaborative guidance scheme from the missile architecture.

[0087] Figure 4 A collection of topological structures.

[0088] Figure 5 The trajectory results of the projectile and target in the simulation example are shown in Figure 2.

[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 (one missile is randomly damaged). DETAILED DESCRIPTION

[0092] 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.

[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 consisting 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 Satisfying 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) on the minimum residence time limit, here we introduce the definition of ADT: if we let the positive constant τ a is the ADT of the switching signal δ(t), which 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 weighted coefficient matrix of the deviation 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 consisting of N missiles intercepts a maneuvering target T is established, and the relative motion relationship between the missile and the target is established. 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; T is the target’s flight speed; β is the target’s track angle; v T Target control lateral acceleration signal; 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 respectively 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 to calculate the target range. 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 for missile swarms 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 time:

[0105] Step 3: See Figure 3 Build a missile cluster system under the virtual missile leader-missile framework to 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. Without considering the game between the virtual leader system and the target, the missile-target kinematic model is adopted to make r i0 = 0 is the asymptotically stable equilibrium point of the system. 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 the action of the second is a collaborative 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 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 its 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 the 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 The virtual control under the action of the virtual control quantity 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 refers to the formula (30) where the nonlinear function f i (x i ) satisfies f on the set containing the origin 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 considered as a disturbance term to the nonlinear system, i.e. 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, 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 obtained. 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, there are and its effect on the consensus error e i 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 actual 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, and is taken as ( 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 under the action of the switching topology signal, 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 (LMI):

[0149]

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

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

[0152]

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

[0154]

[0155] 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:

[0156]

[0157] in

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

[0159] Step 5-1: When the system is subjected to the 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

[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 when only 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 when only constrained by st2, 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 must 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 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, i.e.

[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 e 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.

[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: [t k ,t k+1 ),k∈N Initial value is bounded The matrices The corresponding upper bound of the eigenvalue is

[0182] Under the conditions corresponding to the above two situations, for the initial t k time The initial value of Taking into account Continuity, then for [t k ,t k+1 ), at any time in k∈N, there is The upper bound 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 is 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 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 during terminal maneuvering. The initial conditions are set as follows: missile initial position (x1, y1) = (700, 250), (x2, y2) = (2000, 0), (x3, y3) = (250, 700), initial track angle α1 = α2 = α3 = 60°, speed V1 = V2 = V3 = 600 m / s, target ... 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 the missile i hits the target or the set damage fails, A δ(t) With B δ(t) Set row i and column i 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 realize 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 from 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 application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the 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 embodiment of the present application can be implemented in various computer languages, for example, object-oriented programming language Java and literal translation 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 produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. 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 that can direct a computer or other programmable data processing device to work 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 The 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 the instructions for executing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0192] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional 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 that fall within the scope of the present application.

[0193] Obviously, those skilled in the art may make various changes and modifications to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalents, this application is 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, combined with a communication topology, form a virtual leader group system. The virtual state collaboratively generated state consensus trajectory 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 to construct a consensus deviation signal for the nonlinear state equation of a general missile cluster. Combining the consensus deviation, control input, and the missile's own state, a performance index function is established. Combined with the optimal performance index function, the optimal guidance law of the missile cluster is solved. Step 5: Construct the evaluation network to fit the optimal performance indicator function, use the Hamiltonian function to construct the residual, construct the evaluation network weight update law, and solve the LMI equation combined with the optimization algorithm to reduce the minimum residence time limit to obtain the parameter matrix of the Lyapunov function in the stability term of the weight update law.

2. A switching topology decentralized differential game collaborative guidance method according to 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 the 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 weighted coefficient matrix of the deviation between cluster nodes and virtual consensus; Step 1.2: Use formula (1) to introduce the time domain [t ini ,t) Average dwell time limit of 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 according to 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 consisting 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 (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 of the virtual missile i, the distance to the target, the track angle and the sight angle, assuming that the missile flight speed is constant at V in the terminal guidance stage. 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 time:

4. The switching topology decentralized differential game collaborative guidance method according to 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 trajectory, 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 variables of the virtual cooperative control law: Among them, a Mi0 、r i0 , α i0 and θ i0 are respectively 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 the action of the second is a collaborative term, is the adjacency matrix A of the missile cluster under the switching signal δ(t) , C = [ρτ], ρ and τ are adjustable parameters in the 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 includes 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 reference (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 ) satisfies f on the set containing the origin 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 under 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, time interval [t k ,t k+1 ), within k∈N, let D δ(t) The elements of the nonlinear state equation (6) are the target control input related terms k i (x i )v T is considered as a disturbance term to the nonlinear system, i.e. 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, 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 obtained. Solve for the value of the optimal control law 6. A switching topology decentralized differential game collaborative guidance method according to claim 1, characterized in that: The step 5 specifically includes the following steps: Step 5.1: Use the neural network to fit the optimal performance index function and build an evaluation network to approximate the ideal weight. Under the ideal weight, there is 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 the 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 Upper bound of the ratio of 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 weighted coefficient matrix of the deviation between cluster nodes and virtual consensus.

7. A switching topology decentralized differential game collaborative guidance method according to 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 subjected to the switching topology signal k, k∈{1,2,…,p}, initialize the 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 formula (16) and let definition with c k The lower bound of the ratio m l =1, upper bound Step 5.4-3: Make 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 constrained by st2, 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 to return to (3).

8. The switching topology decentralized differential game collaborative guidance method according to claim 6, characterized in that: For the missile i system (6) and the optimal control strategy (10) for both differential games, there exists a continuously differentiable Lyapunov function Function satisfies And there exists a positive definite matrix such that For missile i in a 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 chosen activation function σ i (e i ) and the weight update law can make the optimal performance index estimation error For e 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 diagonal matrix of parameters.

9. A switching topology decentralized differential game collaborative guidance method according to 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 conditions of formula (21) are satisfied so that where [t k ,t k+1 ),k∈N Initial value is bounded The matrices 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 Taking into account Continuity, then for [t k ,t k+1 ), at any time in k∈N, there is The upper bound 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. At this time, when the average residence time of the switching signal is 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 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