A distributed optimal event-triggered collaborative guidance method

Abstract

The present invention discloses a distributed optimal event-triggered collaborative guidance method, comprising the following steps: step 1, using the relevant theories of graph theory, transforming the collaborative guidance problem into a multi-agent collaborative control problem, and constructing the communication topology of the collaborative guidance problem; step 2, deriving the collaborative guidance model based on the communication topology; step 3, establishing the local neighborhood consistency error equation based on the consistency theory and in combination with the collaborative guidance dynamics equation; step 4, using the online identification technology in combination with the model input and output data to process the unknown dynamics of the model; step 5, deriving the optimal trigger control strategy according to the neighborhood consistency error equation; step 6, using the adaptive dynamic programming technology in combination with the unknown dynamic identification data to implement the optimal trigger control strategy. The present invention saves communication bandwidth resources, improves the utilization rate of information, and reduces the cost in the process of multi-missile interception of targets.

Description

Technical Field

[0001] The invention relates to the technical field of aircraft guidance, in particular to a distributed optimal event-triggered collaborative guidance method. Background Art

[0002] The modern combat environment is becoming increasingly complex, mission targets are more intelligent and mobility is greatly improved. Under this trend, the multi-missile coordinated combat mode has become a research hotspot in recent years. Missile coordinated guidance refers to the use of multiple missiles to perform the same attack mission, breaking the traditional idea that there is no connection and cooperation between missiles during combat, and completing the combat mode of attacking targets from different directions at the same time or at the same angle to ensure the damage efficiency. As an important way to adapt to the complex battlefield environment in the future, multi-missile coordinated attack can effectively improve the missile's rapid penetration and target damage capabilities in a strong confrontation environment. Multiple missiles give full play to the advantages of cluster combat through information sharing, functional complementarity, and tactical coordination, and carry out multi-level and all-round strikes on the enemy's defense system and targets. Compared with one-to-one guided operations, coordinated interception can expand the interception area of ​​one's own missiles, expand the effective damage space of the missile group, and reduce the probability of mobile penetration of enemy targets.

[0003] While bringing combat advantages, it also poses new challenges to the design of collaborative guidance strategies. Existing collaborative control strategies rarely consider the optimality problem while designing the control strategy. Therefore, it is of practical significance to develop a distributed optimal collaborative strategy. The premise of implementing this control strategy is to solve the related Hamilton-Jacobi-Bellman (HJB) equation. However, in practice, the problem of multi-missile collaborative guidance usually exhibits nonlinear and strong coupling characteristics, which makes the solution of the HJB equation very difficult. Adaptive dynamic programming technology uses function approximation structure to estimate the cost function, which is used to solve the dynamic programming problem forward in time, and can effectively approximate the analytical solution of the HJB equation. In recent years, it has been widely used in optimal control problems. In addition, the complex battlefield environment makes it difficult to obtain complete guidance system information, which brings difficulties to the design of control strategies. In addition, the actual missile guidance and control system resources and communication bandwidth are limited, and the traditional time-triggered control requires the satellite to adjust its own state according to the periodic sampling information. The communication pressure is large, and the control input is updated frequently, resulting in a waste of resources. Therefore, in the process of designing the optimal collaborative guidance strategy, it is particularly important to consider the incomplete system information and improve the information utilization rate. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a distributed optimal event-triggered collaborative guidance method, which saves communication bandwidth resources, improves information utilization, and reduces the cost in the process of multiple missiles intercepting targets.

[0005] In order to solve the above technical problems, the present invention provides a distributed optimal event-triggered collaborative guidance method, comprising the following steps:

[0006] Step 1: Use the relevant theories of graph theory to transform the collaborative guidance problem into a multi-agent collaborative control problem and construct the communication topology of the collaborative guidance problem;

[0007] Step 2: Based on the communication topology, derive the collaborative guidance model;

[0008] Step 3: Based on the consistency theory and combined with the cooperative guidance dynamics equation, a local neighborhood consistency error equation is established;

[0009] Step 4: Use online identification technology to combine model input and output data to process unknown dynamics of the model;

[0010] Step 5: According to the neighborhood consistency error equation, derive the optimal trigger control strategy;

[0011] Step 6: Use adaptive dynamic programming technology and combine unknown dynamic identification data to implement the optimal trigger control strategy.

[0012] Preferably, in step 1, the collaborative guidance problem is transformed into a multi-agent collaborative control problem, and the communication topology of the collaborative guidance problem is constructed as follows: the collaborative guidance problem is considered as a multi-agent collaborative control problem, and its communication topology is represented by the following directed graph:

[0013]

[0014] in, Represents a collection of nodes. Represents the node communication link set, A=[a ij ]∈R N×N ,a ij ≥0 indicates the weight link matrix. If (i,j)∈ε, it means that agent j is a neighboring agent of agent i. In this case, a ij =1; otherwise, a ij = 0; denote the set of all neighboring agents of agent i as N i ={j:(i,j)∈ε}, define the in-degree matrix D = diag{d1,d2,…,d N},in represents the number of neighboring agents of agent i, and defines the graph The Laplacian matrix of is L = DA and the sum of all rows is zero. Consider the figure is a strongly connected directed graph and a ii = 0; In addition, the connection matrix between agent i and the leader is expressed as B = diag{b1, b2, …, b N}, where bi =1 indicates that agent i can receive leader information; otherwise, b i =0.

[0015] Preferably, in step 2, based on the communication topology, the collaborative guidance model is derived specifically as follows: the collaborative interception model of N missiles on a two-dimensional plane with the same target is expressed as the following relative motion equation:

[0016]

[0017] Among them, M i represents the i-th missile, T represents the target, and the motion of all missiles and targets is considered to be point motion with constant velocity. V i and V T Represent the speed of the i-th missile and the target respectively; and γ T They represent the track inclination of the target of the i-th missile; γ MiT represents the line of sight angle between the ith missile and the target; r i represents the distance between the i-th missile and the target, and its relative speed is expressed as u i and ν are the accelerations of the ith missile and the target perpendicular to the velocity vector, respectively. The missiles communicate with each other through a communication topology network, i.e., the ith missile communicates only with its neighboring missiles;

[0018] The i-th missile and target both behave as first-order autopilots as follows:

[0019]

[0020] in represents the coordinate position of the i-th interceptor missile; a i represents the lateral acceleration of the interceptor missile; represents the interceptor missile autopilot time constant, which is set to 0.1s; the corresponding target autopilot expression is:

[0021]

[0022] Where (x T ,y T ) represents the coordinate position of the target; a T represents the lateral acceleration of the target; τ T Indicates the target autopilot time constant, and sets the time constant to 0.1s.

[0023] Preferably, in step 3, based on the consistency theory and combined with the cooperative guidance dynamics equation, a local neighborhood consistency error equation is established, specifically: based on the explicit cooperative guidance method, the remaining distance is used as the cooperative variable, and the remaining distances r1,…,r N , so that they tend to zero at the same time, thus ensuring that all missiles hit the target at the same time, defining the state variable Then the cooperative interception guidance model can be expressed as the following affine nonlinear dynamics:

[0024]

[0025] in is the state function of the system, and the leader model expression is:

[0026]

[0027] The specific structure of the leader model is the same as that of the interceptor missile, and in order to ensure the success of the coordinated interception guidance, the leader adopts a proportional guidance method to ensure that the leader can successfully intercept the maneuvering target;

[0028] Combined with graph theory, the following local neighborhood consistent error system of the i-th node is established:

[0029]

[0030] in as well as The missile cooperative guidance law design problem is transformed into the control problem of the nonlinear system (7). By designing the control law for the system (7), it is ensured that the local neighborhood consistent error of the i-th node tends to zero, thereby ensuring the success of the cooperative interception guidance.

[0031] Preferably, in step 4, the online identification technology is used in combination with the model input and output data to process the unknown dynamics of the model as follows: considering the system function f i (x i ) is unknown, then system (5) is approximated as follows:

[0032]

[0033] in represents the expected weight of the neural network, represents the activation function, represents the approximation error;

[0034] To reconstruct the unknown function, define Design the following adaptive compensation online identifier

[0035]

[0036] And the following weight update law and adaptive law:

[0037]

[0038]

[0039] in Respectively represent the estimated values ​​of the state and neural network weights, sgn(δ i ) represents the symbolic function, M i ,E i ,G i is the designed constant matrix, α i For the designed gain constant, the local neighborhood consistent error system is rewritten as:

[0040]

[0041] in

[0042] Preferably, in step 5, based on the neighborhood consistency error equation, the optimal trigger control strategy is derived as follows: define the following local performance indicators

[0043]

[0044] Where Q i ,R ii ,R ij is the designed positive definite symmetric matrix;

[0045] The following Hamilton function is defined as:

[0046]

[0047] in represents the partial derivative of the performance index with respect to the state;

[0048] Introduce an event trigger mechanism and define a monotonically increasing sequence of time instants for the i-th node The system state at the moment of measurement sampling is recorded as The error between the latest state measurement sampling instant and the current state is defined as follows:

[0049]

[0050] Correspondingly, the event-based local neighborhood consistent error system and the trigger measurement error are:

[0051]

[0052]

[0053] According to the optimal control theory, the optimal trigger control strategy is derived as follows:

[0054]

[0055] in Substituting the control strategy of (18) into (14), we obtain the following triggering HJB equation:

[0056]

[0057] Preferably, in step 6, the optimal trigger control strategy is implemented by using adaptive dynamic programming technology and combining unknown dynamic identification data. Specifically, the following evaluation network approximate cost function is constructed in combination with neural network theory, and its expected approximate form is:

[0058]

[0059] in To evaluate the expected weight of the network, To evaluate the network activation function, ε i (z i ) represents the approximation error;

[0060] The partial derivative of (20) with respect to the state is expressed as:

[0061]

[0062] in

[0063] The following practical approximation is adopted:

[0064]

[0065]

[0066] in, and is the estimated value of the cost function and weight;

[0067] Then, from equation (23), the expression of the approximate triggering optimal control strategy is derived as follows:

[0068]

[0069] Combining (22)-(24) and substituting into (19), we get the HJB approximate error equation:

[0070]

[0071] The purpose of evaluating network design is to design a suitable weight update law so that the weight estimate Close to expected value That is to minimize the following error function:

[0072]

[0073] In order to ensure the boundedness of the closed-loop system during the entire learning process, a continuously differentiable radially unbounded Lyapunov function J is designed. i (z i ), and the function satisfies the following conditions in Indicates J i (z i ) with respect to time, Indicates J i (z i ) i The partial derivative of

[0074] Based on the gradient descent method and taking into account the stability of the closed-loop system, the following trigger evaluation network update law is designed:

[0075]

[0076] where β i >0 is the network weight learning rate, Defined as the following expression:

[0077]

[0078] And design the following trigger conditions:

[0079]

[0080] The beneficial effects of the present invention are as follows: (1) The present invention takes into account the optimal control strategy design problem for the coordinated guidance control of multiple missiles, and uses the adaptive dynamic programming technology to effectively solve the problem of solving the nonlinear strongly coupled HJB equation, and the single evaluation network structure greatly reduces the complexity of the control strategy design; (2) The present invention takes into account the optimal control strategy design problem for the coordinated guidance control of multiple missiles, and uses the adaptive dynamic programming technology to effectively solve the problem of solving the nonlinear strongly coupled HJB equation, and the single evaluation network structure greatly reduces the complexity of the control strategy design; (3) The present invention saves communication bandwidth resources, improves the utilization rate of information, and reduces the cost of multiple missiles intercepting targets through the introduction of an event trigger mechanism, which is of practical significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 It is a schematic diagram of the relative motion of multiple missiles in the coordinated guidance of the present invention in a two-dimensional plane.

[0082] Figure 2 It is a schematic flow chart of the guidance method of the present invention. DETAILED DESCRIPTION

[0083] like Figure 1 and Figure 2 As shown, a distributed optimal event-triggered collaborative guidance method comprises the following steps:

[0084] Step 1: Use relevant graph theory to transform the collaborative guidance problem into a multi-agent collaborative control problem and construct the communication topology of the collaborative guidance problem.

[0085] The collaborative guidance problem is considered as a multi-agent collaborative control problem, and its communication topology is represented by the following directed graph:

[0086]

[0087] in, Represents a collection of nodes. Represents the node communication link set, A=[a ij ]∈R N×N ,a ij ≥0 indicates the weight link matrix. If (i,j)∈ε, it means that agent j is a neighboring agent of agent i. In this case, a ij =1; otherwise, a ij = 0; denote the set of all neighboring agents of agent i as N i ={j:(i,j)∈ε}, define the in-degree matrix D = diag{d1,d2,…,d N},in represents the number of neighboring agents of agent i, and defines the graph The Laplacian matrix of is L = DA and the sum of all rows is zero. Consider the figure is a strongly connected directed graph and a ii = 0; In addition, the connection matrix between agent i and the leader is expressed as B = diag{b1, b2, …, b N}, where b i =1 indicates that agent i can receive leader information; otherwise, b i =0.

[0088] Step 2: Based on the communication topology, derive the cooperative guidance model; the two-dimensional plane N missiles cooperatively intercept the same target model is expressed as the following relative motion equation:

[0089]

[0090] Among them, M irepresents the i-th missile, T represents the target, and the motion of all missiles and targets is considered to be point motion with constant velocity. V i and V T denote the speed of the i-th missile and the target respectively; and γ T They represent the track inclination angle of the target of the i-th missile respectively; represents the line of sight angle between the ith missile and the target; r i represents the distance between the i-th missile and the target, and its relative speed is expressed as u i and ν are the accelerations of the ith missile and the target perpendicular to the velocity vector, respectively. The missiles communicate with each other through a communication topology network, i.e., the ith missile communicates only with its neighboring missiles;

[0091] The i-th missile and target both behave as first-order autopilots as follows:

[0092]

[0093] in represents the coordinate position of the i-th interceptor missile; a i represents the lateral acceleration of the interceptor missile; represents the interceptor missile autopilot time constant, which is set to 0.1s; the corresponding target autopilot expression is:

[0094]

[0095] Where (x T ,y T ) represents the coordinate position of the target; a T represents the lateral acceleration of the target; τ T Indicates the target autopilot time constant, and sets the time constant to 0.1s.

[0096] Step 3: Based on the consistency theory and combined with the cooperative guidance dynamics equation, establish the local neighborhood consistency error equation; based on the explicit cooperative guidance method, take the remaining distance as the cooperative variable and define the state variable Then the cooperative interception guidance model can be expressed as the following affine nonlinear dynamics:

[0097]

[0098] in is the state function of the system, and the leader model expression is:

[0099]

[0100] The specific structure of the leader model is the same as that of the interceptor missile, and in order to ensure the success of the coordinated interception guidance, the leader adopts a proportional guidance method to ensure that the leader can successfully intercept the maneuvering target;

[0101] Combined with graph theory, the following local neighborhood consistent error system of the i-th node is established:

[0102]

[0103] in as well as The missile cooperative guidance law design problem is transformed into the control problem of the nonlinear system (7). By designing the control law for the system (7), it is ensured that the local neighborhood consistent error of the i-th node tends to zero, thereby ensuring the success of the cooperative interception guidance.

[0104] Step 4: Use online identification technology to combine model input and output data to process unknown dynamics of the model; consider the system function f i (x i ) is unknown, then system (5) is approximated as follows:

[0105]

[0106] in represents the expected weight of the neural network, represents the activation function, represents the approximation error;

[0107] To reconstruct the unknown function, define Design the following adaptive compensation online identifier

[0108]

[0109] And the following weight update law and adaptive law:

[0110]

[0111]

[0112] in Respectively represent the estimated values ​​of the state and neural network weights, sgn(δ i ) represents the symbolic function, M i ,E i ,G i is the designed constant matrix, α i For the designed gain constant, the local neighborhood consistent error system is rewritten as:

[0113]

[0114] in

[0115] Step 5: According to the neighborhood consistency error equation, derive the optimal trigger control strategy; define the following local performance indicators

[0116]

[0117] Where Q i ,R ii ,R ij is the designed positive definite symmetric matrix;

[0118] The following Hamilton function is defined as:

[0119]

[0120] in represents the partial derivative of the performance index with respect to the state;

[0121] Introduce an event trigger mechanism and define a monotonically increasing sequence of time instants for the i-th node The system state at the moment of measurement sampling is recorded as The error between the latest state measurement sampling instant and the current state is defined as follows:

[0122]

[0123] Correspondingly, the event-based local neighborhood consistent error system and the trigger measurement error are:

[0124]

[0125]

[0126] According to the optimal control theory, the optimal trigger control strategy is derived as follows:

[0127]

[0128] in Substituting the control strategy of (18) into (14), we obtain the following triggering HJB equation:

[0129]

[0130] Step 6: Use adaptive dynamic programming technology and combine unknown dynamic identification data to implement the optimal trigger control strategy; combine neural network theory to construct the following evaluation network approximate cost function, and its expected approximate form is:

[0131]

[0132] in To evaluate the expected weight of the network, To evaluate the network activation function, ε i (z i ) represents the approximation error;

[0133] The partial derivative of (20) with respect to the state is expressed as:

[0134]

[0135] in

[0136] The following practical approximation is adopted:

[0137]

[0138]

[0139] in, and is the estimated value of the cost function and weight;

[0140] Then, from equation (23), the expression of the approximate triggering optimal control strategy is derived as follows:

[0141]

[0142] Combining (22)-(24) and substituting into (19), we get the HJB approximate error equation:

[0143]

[0144] The purpose of evaluating network design is to design a suitable weight update law so that the weight estimate Close to expected value That is to minimize the following error function:

[0145]

[0146] In order to ensure the boundedness of the closed-loop system during the entire learning process, a continuously differentiable radially unbounded Lyapunov function J is designed. i (z i ), and the function satisfies the following conditions in Indicates J i (z i ) with respect to time, Indicates J i (z i ) i The partial derivative of

[0147] Based on the gradient descent method and taking into account the stability of the closed-loop system, the following trigger evaluation network update law is designed:

[0148]

[0149] where β i >0 is the network weight learning rate, Π(·) is defined as the following expression:

[0150]

[0151] And design the following trigger conditions:

[0152]

Claims

1. A distributed optimal event-triggered collaborative guidance method, characterized in that: The steps include: Step 1: Using the relevant theories of graph theory, transform the collaborative guidance problem into a multi-agent collaborative control problem and construct the communication topology of the collaborative guidance problem; consider the collaborative guidance problem as a multi-agent collaborative control problem, and its communication topology is represented by the following directed graph: in, Represents a collection of nodes. Represents the node communication link set, A=[a ij ]∈R N×N ,a ij ≥0 indicates the weight link matrix. If (i,j)∈E, it means that agent j is a neighboring agent of agent i. In this case, a ij =1; otherwise, a ij = 0; denote the set of all neighboring agents of agent i as N i ={j:(i,j)∈E}, define the in-degree matrix D=diag{d1,d2,…,d N },in represents the number of neighboring agents of agent i, and defines the graph The Laplace matrix of is L = DA and the sum of all rows is zero. Consider that graph g is a strongly connected directed graph and a ii = 0; In addition, the connection matrix between agent i and the leader is expressed as B = diag{b1, b2, …, b N }, where b i =1 indicates that agent i can receive leader information; otherwise, b i =0; Step 2: Based on the communication topology, derive the cooperative guidance model; the two-dimensional plane N missiles cooperatively intercept the same target model is expressed as the following relative motion equation: Among them, M i represents the i-th missile, T represents the target, and the motion of all missiles and targets is considered to be point motion with constant velocity. V i and V T Represent the speed of the i-th missile and the target respectively; and γ T They represent the track inclination angle of the target of the i-th missile respectively; represents the line of sight angle between the ith missile and the target; r i represents the distance between the i-th missile and the target, and its relative speed is expressed as u i and ν are the accelerations of the ith missile and the target perpendicular to the velocity vector, respectively. The missiles communicate with each other through a communication topology network, i.e., the ith missile communicates only with its neighboring missiles; The i-th missile and target both behave as first-order autopilots as follows: in represents the coordinate position of the i-th interceptor missile; a i represents the lateral acceleration of the interceptor missile; represents the interceptor missile autopilot time constant, which is set to 0.1s; the corresponding target autopilot expression is: Where (x T ,y T ) represents the coordinate position of the target; a T represents the lateral acceleration of the target; τ T Indicates the target autopilot time constant, and sets the time constant to 0.1s; Step 3: Based on the consistency theory and combined with the cooperative guidance dynamics equation, the local neighborhood consistency error equation is established; based on the explicit cooperative guidance method, the remaining distance is used as the cooperative variable, and the remaining distances r1,…,r N , so that they tend to zero at the same time, thus ensuring that all missiles hit the target at the same time, defining the state variable Then the cooperative interception guidance model can be expressed as the following affine nonlinear dynamics: in is the state function of the system, and the leader model expression is: The specific structure of the leader model is the same as that of the interceptor missile, and in order to ensure the success of the coordinated interception guidance, the leader adopts a proportional guidance method to ensure that the leader can successfully intercept the maneuvering target; Combined with graph theory, the following local neighborhood consistent error system of the i-th node is established: in as well as The missile cooperative guidance law design problem is transformed into the control problem of the nonlinear system (7). By designing the control law for the system (7), the local neighborhood consistent error of the i-th node is guaranteed to be zero, thus ensuring the success of the cooperative interception guidance. Step 4: Use online identification technology to combine model input and output data to process unknown dynamics of the model; consider the system function f i (x i ) is unknown, then system (5) is approximated as follows: Where K fi represents the expected weight of the neural network, represents the activation function, represents the approximation error; To reconstruct the unknown function, define Design the following adaptive compensation online identifier And the following weight update law and adaptive law: in Respectively represent the estimated values ​​of the state and neural network weights, sgn(δ i ) represents the symbolic function, M i ,E i ,G i is the designed constant matrix, α i For the designed gain constant, the local neighborhood consistent error system is rewritten as: in Step 5: According to the neighborhood consistency error equation, derive the optimal trigger control strategy; define the following local performance indicators Where Q i ,R ii ,R ij is the designed positive definite symmetric matrix; The following Hamilton function is defined as: in represents the partial derivative of the performance index with respect to the state; Introduce an event trigger mechanism and define a monotonically increasing sequence of time instants for the i-th node The system state at the moment of measurement sampling is recorded as The error between the latest state measurement sampling instant and the current state is defined as follows: Correspondingly, the event-based local neighborhood consistent error system and the trigger measurement error are: According to the optimal control theory, the optimal trigger control strategy is derived as follows: in Substituting the control strategy of (18) into (14), we obtain the following triggering HJB equation: Step 6: Use adaptive dynamic programming technology and combine unknown dynamic identification data to implement the optimal trigger control strategy; combine neural network theory to construct the following evaluation network approximate cost function, and its expected approximate form is: in To evaluate the expected weight of the network, To evaluate the network activation function, ε i (z i ) represents the approximation error; The partial derivative of (20) with respect to the state is expressed as: in The following practical approximation is adopted: in, and is the estimated value of the cost function and weight; Then, from equation (23), the expression of the approximate triggering optimal control strategy is derived as follows: Combining (22)-(24) and substituting into (19), we get the HJB approximate error equation: The purpose of evaluating network design is to design a suitable weight update law so that the weight estimate Close to expected value That is to minimize the following error function: In order to ensure the boundedness of the closed-loop system during the entire learning process, a continuously differentiable radially unbounded Lyapunov function J is designed. i (z i ), and the function satisfies the following conditions in Indicates J i (z i ) with respect to time, Indicates J i (z i ) i The partial derivative of Based on the gradient descent method and taking into account the stability of the closed-loop system, the following trigger evaluation network update law is designed: where β i >0 is the network weight learning rate, Π(·) is defined as the following expression: And design the following trigger conditions:

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