A multi-target bidirectional encirclement control method and device

Abstract

The application belongs to the technical field of two-way encirclement control, and relates to a multi-target two-way encirclement control method and device. Based on unknown nonlinear functions, input signals, output signals and unknown false data injection attack signals of followers, a dynamic model of the followers is constructed and converted into a dynamic linearization model related to the attack signals. Based on output signal errors of the followers and each leader at the time of the last triggered iteration, an iteration triggering mechanism of the followers is constructed and a triggered iteration sequence of the followers is obtained. Based on output signal errors of the followers and each leader, a two-way encirclement error of the followers is constructed. Based on the two-way encirclement error of the followers, the triggered iteration sequence and a change amount of the input signals, a control input criterion function of the followers is constructed. The control input criterion function of the followers is minimized to obtain an input signal equation of the followers so as to control the followers.

Description

Technical Field

[0001] This invention relates to the field of two-way encirclement control technology, and in particular to a multi-target two-way encirclement control method and device. Background Technology

[0002] Encirclement control is a collaborative control method for multi-target swarms. Its core objective is to dynamically form a geometrically encircling configuration among some targets, confining the encircled target within the convex hull of the surrounding group to accomplish collaborative tasks such as encirclement, blockade, and surveillance. Traditional encirclement control is typically based on the underlying assumption that the cooperative relationship between all targets is positive, with no conflicts of interest or antagonistic behavior. For example, in a collaborative control system composed of multiple robots performing a performance task, the robots move in unison and coordinate their behavior, only needing to ensure the overall formation stability and action synchronization. However, in some application scenarios (such as social network group behavior, biological species game theory, and swarm tasks with hostile intentions or internal interest disputes), multiple targets often simultaneously exhibit cooperative and competitive relationships. For instance, multiple drones may encircle a target drone, but each drone aims to seize the best attack position and reduce its own energy consumption. To describe this complex cooperative relationship, symbolic graphs were introduced, which use positive weights to represent cooperation and negative weights to represent competition. Based on this, bipartite containment control was also developed. The goal of this control is to make multiple objectives converge to two equilateral convex hulls spanned by the enclosed objective and its opposing state under the interaction of cooperation and competition.

[0003] Existing bidirectional encirclement control methods rely heavily on precise mathematical models of the controlled object. However, in practical engineering, due to the high complexity of the environment, nonlinear dynamics, and strong uncertainties, obtaining accurate nonlinear dynamic models of the target is often extremely challenging. Furthermore, multi-target cluster systems are typically deployed in open network environments, making them vulnerable to malicious data injection attacks. Maliciously injected sensing or control signals can easily disrupt the encirclement configuration, leading to formation instability or even loss of control. In addition, existing control strategies often employ continuous-time control or high-frequency sampling mechanisms, failing to consider the energy capacity and communication bandwidth limitations of the target nodes. This results in excessive energy consumption and resource consumption for control and communication, making them difficult to apply in practical equipment deployments where energy is limited and communication speeds are restricted.

[0004] In summary, existing two-way encirclement control methods suffer from problems such as strong model dependence, poor anti-attack security, and excessive consumption of energy and communication resources. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to overcome the problems of strong model dependence, poor anti-attack security, and excessive energy and communication resource consumption in the existing two-way encirclement control method.

[0006] To solve the above-mentioned technical problems, the present invention provides a multi-target bidirectional encirclement control method, comprising: Acquire two-way encirclement groups, and designate each encircled object in each encirclement group as a follower, and the encirclement target as the leader; Based on the unknown nonlinear function, the input signal and output signal of each follower, and the unknown spoof data injection attack signal, a dynamic model of each follower is constructed; the dynamic model of each follower is then converted into a dynamic linearized model related to the attack signal. Based on the error of each follower's output signal with its previous triggering iteration and the error of its output signal with each leader, an iterative triggering mechanism for each follower is constructed to obtain the triggering iteration sequence for each follower; Based on the output signal errors of each follower with other followers and with each leader, a two-way encirclement error is constructed for each follower; Based on the bidirectional encirclement error, triggering iteration sequence, and input signal change of each follower, a control input criterion function for each follower is constructed. The control input criterion function of each follower is minimized with respect to the input signal to obtain the input signal equation of each follower, thereby controlling each follower.

[0007] Preferably, the dynamic model of the follower is expressed as: , in, Indicates the first During the next iteration The output signal of the i-th follower at time i; Represents an unknown nonlinear function; Indicates the first During the next iteration The output signal of the i-th follower at time i; Indicates the first During the next iteration The input signal of the i-th follower at time i; Indicates the first During the next iteration The i-th follower at time i receives an unknown false data injection attack signal; The dynamic linearization model of the follower is represented as: , in, Indicates the first During the next iteration Time and the During the next iteration The difference in the output signal of the i-th follower at time i; Indicates the first During the next iteration The pseudo-gradient related to the attack of the i-th follower at time i; Indicates the first During the next iteration Time and the During the next iteration The difference in the input signal of the i-th follower at time i; Indicates the first During the next iteration Time and the During the next iteration The difference in unknown false data injection attack signal received by the i-th follower at time i; .

[0008] Preferably, the iterative triggering mechanism of the follower is expressed as: , , , in, This indicates the iteration triggering mechanism for the i-th follower; Indicates the previous triggered iteration The output signal of the i-th follower at time s+1; Indicates triggering the first The output signal of the i-th follower at time s+1 before the next iteration; Indicates the event trigger threshold; Indicates the time s+1. The output signal of a leader; Used to determine the grouping relationship of the i-th follower. If the i-th follower belongs to the grouping relationship of the i-th follower... The encirclement group to which each leader belongs, If the i-th follower does not belong to the i-th follower The encirclement group comprised of the leaders ; Indicates the number of leaders; The triggering iteration sequence of the follower is represented as: , in, Indicates the i-th follower in the triggering iteration sequence. One trigger iteration; Indicates the i-th follower in the triggering iteration sequence. -1 trigger iteration.

[0009] Preferably, the two-way encirclement error of the follower is expressed as: , in, Indicates the first During the next iteration The bidirectional encirclement error of the i-th follower at time i; This represents the communication weight between the i-th follower and the j-th follower; This represents a symbolic function that determines whether the relationship between the i-th follower and the j-th follower is cooperative or competitive. The function is defined as follows: when the i-th follower and the j-th follower are in a cooperative relationship... When the i-th follower and the j-th follower are in a competitive relationship, ; Indicates the first During the next iteration The output signal of the j-th follower at time j; Indicates the first During the next iteration The output signal of the i-th follower at time i; express Time of the first The output signal of a leader; Used to determine the grouping relationship of the i-th follower. If the i-th follower belongs to the grouping relationship of the i-th follower... The encirclement group to which each leader belongs, If the i-th follower does not belong to the i-th follower The encirclement group comprised of the leaders ; Indicates the number of leaders; Indicates the number of followers; Indicates the relationship between the i-th follower and the i-th follower. Communication weight between leaders.

[0010] Preferably, the control input criterion function of the follower is expressed as: , in, This represents the control input criterion function for the i-th follower; Indicates the previous triggered iteration The output signal of the i-th follower at time s; Indicates triggering the first The output signal of the i-th follower at time s before the next iteration; Indicates the adjustable weighting coefficient. ; Indicates the first During the next iteration Time and the During the next iteration The difference in the input signal of the i-th follower at time i; The input signal equation for the follower is expressed as: , in, Describe the input signal equation for the i-th follower; Indicates the adjustable step size coefficient. .

[0011] Preferably, the method further includes: Based on the input signal of each follower, the unknown spoof data injection attack signal received, and the attack-related pseudo gradient, a cost function for each follower is constructed. Minimize the cost function of each follower with respect to the attack-related pseudo-gradient to obtain the attack-related pseudo-gradient equation for each follower, thereby estimating the attack-related pseudo-gradient for each follower.

[0012] Preferably, the cost function of the follower is expressed as: , in, Denotes the cost function of the i-th follower; Indicates a positive weighting parameter; Indicates the first The attack-related pseudo-gradient estimate of the i-th follower at time s during the next iteration; The pseudo-gradient equation related to the follower's attack is expressed as: , in, Indicates the first The attack-related pseudo-gradient estimate of the i-th follower at time s during the next iteration; This represents the positive step size parameter.

[0013] Preferably, the method further includes: integrating the input signal equation, cost function, and attack-related pseudo-gradient equation for each follower to obtain an encirclement control model for each follower based on attack-related compact format dynamic linearization of event-triggered distributed model-free adaptive iterative learning.

[0014] Preferably, the encirclement control model for each follower is represented as follows: , , , in, It is a constant. ; This represents the attack-related pseudo-gradient estimate of the i-th follower at time s during the first iteration.

[0015] The present invention also provides a multi-target bidirectional encirclement control device, comprising: The Encirclement Group Acquisition Module is used to acquire two-way encirclement groups, treating each encircled object in each encirclement group as a follower and the encirclement target as the leader. The thread model acquisition module is used to construct the dynamic model of each follower based on the unknown nonlinear function, the input signal and output signal of each follower, and the unknown spoof data injection attack signal received; and to convert the dynamic model of each follower into a dynamic linearized model related to the attack signal. The event-triggered iteration sequence acquisition module is used to construct the iteration triggering mechanism of each follower based on the output signal error of each follower with its previous triggering iteration and the output signal error with each leader, thereby obtaining the triggering iteration sequence of each follower; The two-way encirclement error acquisition module is used to construct the two-way encirclement error of each follower based on the output signal error of each follower with other followers and the output signal error with each leader. The control module is used to construct the control input criterion function for each follower based on the bidirectional encirclement error, trigger iteration sequence, and input signal change of each follower; and to minimize the control input criterion function of each follower with respect to the input signal to obtain the input signal equation of each follower, thereby controlling each follower.

[0016] The multi-objective two-way encirclement control method provided in this application has the following beneficial effects: First, taking into full account the threat of false data injection attacks in open network environments, a dynamic linearization method based on attack-related compact forms is used to transform complex unknown non-affine nonlinear dynamic models into data models, effectively compensating for security threats and achieving stable bidirectional encirclement control of multi-target bidirectional encirclement systems under attack interference. Second, when constructing the dynamic model, only real-time input / output data of the controlled object is used for control design, without relying on the precise mathematical model of the controlled object. This makes the system highly robust to changes in model parameters and significantly reduces the modeling difficulty and computational burden in complex environments. In addition, this application also designs an iterative event triggering mechanism, which updates the target and transmits data only when the change in tracking error meets a preset trigger threshold. Compared with traditional continuous or high-frequency sampling iterative learning control, this scheme can effectively reduce redundant information transmission, saving valuable communication bandwidth and energy consumption of target nodes. Attached Figure Description

[0017] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein: Figure 1 Flowchart of the multi-objective two-way encirclement control method provided in this application; Figure 2 This application provides a topology diagram of a multi-target bidirectional encirclement system under a fixed topology, as illustrated in the embodiments of this application. Figure 3 The output trajectory diagrams of the multi-target bidirectional encirclement system under a fixed topology provided in the embodiments of this application at different iteration numbers; wherein, Figure 3 (a) in the figure represents the output trajectory of the multi-target bidirectional encirclement system during the 10th iteration. Figure 3 (b) in the figure represents the output trajectory of the multi-objective two-way encirclement system during the 40th iteration. Figure 3 (c) in the figure represents the output trajectory of the multi-target two-way encirclement system during the 70th iteration. Figure 3 In the figure, (d) represents the output trajectory of the multi-target bidirectional encirclement system at the 100th iteration; Figure 4 Mean square tracking error diagram of a multi-target bidirectional encirclement system under a fixed topology provided in the embodiments of this application during the iterative process; Figure 5 An event triggering interval diagram for each target in a multi-target bidirectional encirclement system under a fixed topology provided in the embodiments of this application; Figure 6 This is a topology diagram of a multi-target bidirectional encirclement system under a switching topology provided in the embodiments of this application; Figure 7 Topology switching parameters provided in the embodiments of this application A schematic diagram illustrating the change with the number of iterations; Figure 8 The output trajectory diagrams of the multi-target bidirectional encirclement system under the switching topology provided in this application embodiment at different iteration numbers; wherein, Figure 8 (a) in the figure represents the output trajectory of the multi-target bidirectional encirclement system during the 10th iteration. Figure 8 (b) in the figure represents the output trajectory of the multi-objective two-way encirclement system during the 20th iteration. Figure 8 (c) in the figure represents the output trajectory of the multi-target bidirectional encirclement system during the 40th iteration. Figure 8 (d) in the figure represents the output trajectory of the multi-target bidirectional encirclement system at the 80th iteration; Figure 9 Mean square tracking error diagram of a multi-target bidirectional encirclement system under a switching topology provided in the embodiments of this application during the iterative process; Figure 10 This is a diagram showing the event triggering intervals of each target in a multi-target bidirectional encirclement system under a switching topology provided in this application embodiment. Detailed Implementation

[0018] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0019] Please see Figure 1 , Figure 1 The diagram shown is a flowchart of the multi-objective two-way encirclement control method provided in this application. The method specifically includes steps S10 to S50: S10: Obtain two-way encirclement groups, and treat each encircled object in each encirclement group as a follower, and the encirclement target as the leader.

[0020] For example, consider a class of unknown heterogeneous nonlinear multi-objective systems, where M leaders and N followers are encircled. Based on cooperation and competition, the multi-objective groups are divided into two-way encirclement groups. , Encirclement One leader and One follower Encirclement One leader and One follower.

[0021] Specifically, each follower in the two-way encirclement control system is a mechanical system equipped with a PLC controller or a dedicated controller (such as UR's PolyScope), and the two-way encirclement control of each follower is achieved using the controller. For example, in a two-way encirclement control system composed of multiple robots, the follower is a robot equipped with a dedicated controller; in a two-way encirclement control system composed of multiple small assembly robotic arms, the follower is a small assembly robotic arm equipped with a PLC controller.

[0022] S20: Based on the unknown nonlinear function, the input signal and output signal of each follower, and the unknown spoof data injection attack signal, construct the dynamic model of each follower; convert the dynamic model of each follower into a dynamic linearized model related to the attack signal.

[0023] Specifically, the dynamics model of the follower is expressed as: , in, Indicates the first During the next iteration The output signal of the i-th follower at time i; Represents an unknown nonlinear function; Indicates the first During the next iteration The output signal of the i-th follower at time i; Indicates the first During the next iteration The input signal of the i-th follower at time i; Indicates the first During the next iteration The i-th follower at time i receives an unknown false data injection attack signal.

[0024] Furthermore, by setting assumptions 1 to 3, the above dynamic model is transformed into a dynamic linearized model of a compact form related to the attack: Assumption 1: Symbolic directed graph Structural balance means that there is at least one leader to every follower with a communication path, and that the false data injection attack signal is bounded.

[0025] Assumption 2: Unknown nonlinear function about , The partial derivatives of are continuous, denoted as . , .

[0026] Assumption 3: The multi-objective system and the two-way encirclement system satisfy the generalized Lipschitz condition, that is, when Sometimes, ,in, Represents the Lipschitz constant. , .

[0027] Specifically, if If Assumptions 2 and 3 hold, then the dynamic linearization model of the follower can be expressed as: , in, Indicates the first During the next iteration Time and the During the next iteration The difference in the output signal of the i-th follower at time i; Indicates the first During the next iteration The pseudo-gradient related to the attack of the i-th follower at time i; Indicates the first During the next iteration Time and the During the next iteration The difference in the input signal of the i-th follower at time i; Indicates the first During the next iteration Time and the During the next iteration The difference in unknown false data injection attack signal received by the i-th follower at time i; .

[0028] It should be noted that this application further proves the boundedness of attack-related pseudo-gradients: From the follower dynamics model and assumption 3, we can obtain: , in, , They are respectively In the interval About a certain point inside , The partial derivatives of .

[0029] remember: , Consider variables Then the above formula can be transformed into: , because It is guaranteed that at least one solution exists that satisfies ,make Then the equations obtained from the follower dynamics model and hypothesis 3 can be rewritten as an attack-related compact dynamic linearization model. The boundedness of the attack-related pseudo-gradient is a direct result of hypothesis 3 and the dynamic linearization model.

[0030] Definition 1: If a directed symbolic graph There is a bidirectional vertex mapping ,satisfy , so that for any have For any If the structure of the directed symbolic graph is balanced, then the graph is said to be in equilibrium. (Grouping matrix) Used to represent the relationship between followers and groups, if follower i belongs to... ,but ,otherwise .

[0031] Since the control objective is to design an event-triggered, distributed, model-free, adaptive iterative learning bidirectional encirclement control scheme, this scheme aims to stably achieve bidirectional encirclement control in an unknown nonlinear multi-objective bidirectional encirclement system susceptible to spurious data injection attacks. That is: , , Among them, the convex hulls corresponding to the two-way encirclement group are respectively , .

[0032] S30: Based on the error of each follower's output signal with its previous triggering iteration and the error of its output signal with each leader, construct the iteration triggering mechanism for each follower to obtain the triggering iteration sequence for each follower.

[0033] Specifically, the iterative triggering mechanism of the follower is represented as follows: , , , in, This indicates the iteration triggering mechanism for the i-th follower; Indicates the previous triggered iteration The output signal of the i-th follower at time s+1; Indicates triggering the first The output signal of the i-th follower at time s+1 before the next iteration; Indicates the event trigger threshold; Indicates the time s+1. The output signal of a leader; Used to determine the grouping relationship of the i-th follower. If the i-th follower belongs to the grouping relationship of the i-th follower... The encirclement group to which each leader belongs, If the i-th follower does not belong to the i-th follower The encirclement group comprised of the leaders ; Indicates the number of leaders; The triggering iteration sequence of the follower is represented as: , in, Indicates the i-th follower in the triggering iteration sequence. One trigger iteration; Indicates the i-th follower in the triggering iteration sequence. -1 trigger iteration.

[0034] Lemma 1: Let Given the set of all irreducible subrandom matrices, iterate over the correlation matrix. ,from If elements are randomly selected from the middle and the diagonal elements are non-negative, then there exists a fixed value. ,satisfy .

[0035] Lemma 2: Each element is positive, and the sum of the elements in each row is 1.

[0036] S40: Construct a two-way encirclement error for each follower based on the output signal errors of each follower with other followers and with each leader.

[0037] Specifically, assuming the leader's dynamics are independent of iteration, the follower's two-way encirclement error is expressed as: , in, Indicates the first During the next iteration The bidirectional encirclement error of the i-th follower at time i; This represents the communication weight between the i-th follower and the j-th follower; This represents a symbolic function that determines whether the relationship between the i-th follower and the j-th follower is cooperative or competitive. The function is defined as follows: when the i-th follower and the j-th follower are in a cooperative relationship... When the i-th follower and the j-th follower are in a competitive relationship, ; Indicates the first During the next iteration The output signal of the j-th follower at time j; Indicates the first During the next iteration The output signal of the i-th follower at time i; express Time of the first The output signal of a leader; Used to determine the grouping relationship of the i-th follower. If the i-th follower belongs to the grouping relationship of the i-th follower... The encirclement group to which each leader belongs, If the i-th follower does not belong to the i-th follower The encirclement group comprised of the leaders ; Indicates the number of leaders; Indicates the number of followers; Indicates the relationship between the i-th follower and the i-th follower. Communication weight between leaders.

[0038] S50: Based on the bidirectional encirclement error, triggering iteration sequence, and input signal change of each follower, construct the control input criterion function for each follower; minimize the control input criterion function of each follower with respect to the input signal to obtain the input signal equation of each follower, thereby controlling each follower.

[0039] Specifically, the control input criterion function for the follower is expressed as: , in, This represents the control input criterion function for the i-th follower; Indicates the previous triggered iteration The output signal of the i-th follower at time s; Indicates triggering the first The output signal of the i-th follower at time s before the next iteration; These represent adjustable weighting coefficients, used to limit the amount of change in the input signal between iterations. ; Indicates the first During the next iteration Time and the During the next iteration The difference in the input signal of the i-th follower at time i; The input signal equation for the follower is expressed as: , in, Describe the input signal equation for the i-th follower; Indicates the adjustable step size coefficient. .

[0040] Furthermore, the method also includes steps S60-S70: S60: Construct the cost function for each follower based on the input signal of each follower, the unknown spoof data injection attack signal received, and the attack-related pseudo gradient.

[0041] Specifically, the cost function of the follower is expressed as: , in, Denotes the cost function of the i-th follower; Indicates a positive weighting parameter; Indicates the first The attack-related pseudo-gradient estimate of the i-th follower at time s during the next iteration.

[0042] S70: Minimize the cost function of each follower with respect to the attack-related pseudo-gradient to obtain the attack-related pseudo-gradient equation of each follower, thereby estimating the attack-related pseudo-gradient of each follower.

[0043] Specifically, the pseudo-gradient equation related to the follower's attack is expressed as: , in, Indicates the first The attack-related pseudo-gradient estimate of the i-th follower at time s during the next iteration; This represents the positive step size parameter.

[0044] Furthermore, by integrating the input signal equation, cost function, and attack-related pseudo-gradient equation for each follower, we can obtain an encirclement control model for each follower based on attack-related compact format dynamic linearization of event-triggered distributed model-free adaptive iterative learning.

[0045] Specifically, the encirclement control model for each follower is represented as follows: , , , in, It is a constant. ; This represents the attack-related pseudo-gradient estimate of the i-th follower at time s during the first iteration.

[0046] Assumption 4: The sign of all elements in the attack-related pseudo-gradient remains unchanged across all time points, iterations, and followers, i.e. (or )and (or ), For small normal numbers, this application analyzes and The situation.

[0047] The following verification Boundedness and Convergence: 1. Boundedness: Scenario 1: That is, the event triggering condition is triggered, and if the input signal equation of the follower is satisfied, then Bounded; otherwise, define the attack-related pseudo-gradient estimation error. ,but: , in, .

[0048] Substituting the attack-related compact form dynamic linearization model into the above formula, we can transform it into: , Theorem 1 has been proven. The maximum value is Obviously, its range is limited. Taking the norm of both sides of the above equation, we get: , Squaring the norm term on the right side of the above equation, we get: , because and For a positive parameter, the following inequality holds: .

[0049] Combining the above squares and inequalities, we get: , Therefore, there exists a fixed value. ,satisfy:

[0050] Furthermore, we can obtain: , The above formula proves Bounded, Theorem 1 is proved Bounded, therefore It also has boundaries.

[0051] Scenario 2: This means that the event triggering condition was not triggered, and the parameter estimates within this interval are... To maintain consistency with the previous triggered iteration, because It has been proven to be bounded, and It remains unchanged, therefore The iteration is bounded throughout.

[0052] 2. Convergence: Scenario 1: That is, the event triggering condition is triggered, denoted as a set vector: , , , , , , , The two-way encirclement error can be rewritten as:

[0053] remember ,but: , According to Lemma 2, lie in Inside the convex hull, if If it is bounded, then Bounded, the following proof Boundedness: , in, , , .

[0054] Similarly, the attack-related compact form dynamic linearization model can be rewritten as: , in, , , , .

[0055] Depend on We can obtain: , Combination and The definitions are as follows: , Furthermore, we can obtain: , because , ,therefore, It can be simplified to: , remember: , , ,but: .

[0056] Theorem 1 shows For constants and ,when At that time, there were: , .

[0057] Because the structure of the symbolic directed graph is balanced, therefore Uncancellable, Selection satisfy ,but The reciprocal of the i-th diagonal element is greater than Because for all have Therefore At least one row has a sum less than 1, meaning the matrix is ​​an irreducible subrandom matrix with positive diagonal elements. Theorem 1 guarantees... and Bounded; Part 1 has been proven Elements are bounded; Assumption 2 guarantees Bounded. Obviously. Bounded, that is .

[0058] remember ,but: , Combining Lemma 1, we get: , Furthermore, we can obtain: , .

[0059] Scenario 2: That is, the event triggering condition was not triggered, and , ,Right now , therefore: , , remember When satisfied Sometimes, .

[0060] Furthermore, we can obtain: , Combining Lemma 1, we get: .

[0061] Furthermore, this application also presents the design and proof of an event-triggered distributed model-free adaptive iterative learning bidirectional encirclement control scheme under topology switching.

[0062] Symbolic directed graph is denoted as , The number of iterations represents the communication topology in a set of symbolic directed graphs. Switching between time slots This represents the total number of directed graphs.

[0063] Assumption 5: Set Each directed graph in The structure is balanced in each iteration.

[0064] Assumption 6: The leader's trajectory varies within the upper and lower bounds, i.e. ,in , It is a constant.

[0065] Based on the above adjustments, the bidirectional encirclement error of the i-th follower is modified as follows: , in , Adjacency matrix As can be seen from the above formula, compared to the bidirectional encirclement error provided in the previous embodiment, the leader's reference trajectory in the modified bidirectional encirclement error also changes with iteration. It becomes an iterative time-varying signal. To overcome this problem, a new variable is introduced. The model is reconstructed as follows: , in, , According to the analysis of Theorem 1, the matrix It is also bounded.

[0066] For the i-th follower, the improved encirclement control model based on attack-related compact format dynamic linearization of event-triggered distributed model-free adaptive iterative learning is modified as follows: , , , in, yes initial value, yes The estimated value, the analysis process for this case is consistent with Theorem 2, the difference is that During the stability analysis, It will change with iteration.

[0067] Furthermore, Proof of Boundedness and Theorem 2 The boundedness proof is similar.

[0068] Further proof Convergence: Scenario 1: That is, the event triggering condition is triggered, denoted as: , , Furthermore, , .

[0069] This leads to the following relationship: , in, , , .

[0070] According to hypothesis 6, the graph remains strongly connected in each iteration, which means that the matrix It is not revocable; if selected... Meet the conditions ,but The reciprocal of the i-th diagonal element will be greater than Similar to the logic of Theorem 2, it can be deduced correctly. At that time, matrix It is still an irreducible subrandom matrix, because and Both are bounded and can be obtained. ,in It is a fixed constant. Clearly, there exists a fixed value. We can obtain: .

[0071] Scenario 2: That is, the event triggering condition was not triggered, denoted as: , When satisfied At that time, it can be obtained Furthermore: , Combining Lemma 1, we can obtain: , in conclusion: Case 1: For a multi-target bidirectional encirclement system under a fixed topology satisfying Assumptions 1-4, the encirclement control model based on the improved attack-related compact format dynamic linearization event-triggered distributed model-free adaptive iterative learning is used. If there exists a constant... Step size coefficient Event trigger threshold satisfy: , , This allows the control objective to be achieved.

[0072] Case 2: For a multi-target bidirectional encirclement system under the switching topology satisfying Assumptions 2-6, an improved encirclement control model based on attack-related compact format dynamic linearization and event-triggered distributed model-free adaptive iterative learning is adopted. If a constant exists... Step size coefficient Event trigger threshold satisfy: , , This will enable the control objective to be achieved.

[0073] The following two specific numerical simulation examples will demonstrate the effectiveness of the control method provided in this application: Step 1: Determine the dynamic mathematical expression model of the follower in a multi-objective two-way encirclement system under a fixed topology: , , , , The mathematical expression for the fake data injection attack signal is: , , , , Encirclement Group The leader trajectory in the middle is as follows: , , Encirclement Group The leader trajectory in the middle is as follows: , , like Figure 2 As shown, the symbolic directed graph contains 8 targets, denoted as the encirclement team. Encirclement group Specifically: follower nodes 1 to 4, leader nodes 5 to 8, +1 indicates collaborative interaction, -1 indicates adversarial relationship.

[0074] Step 2: The initial conditions for the followers are: , , , ; , , The controller parameters are set as follows: , , , , , Event trigger threshold .

[0075] Step 3: Build a Simulink model of a multi-objective bidirectional encirclement system under a fixed topology, obtain simulation results, and use bidirectional inclusion mean square deviation (MBD) simulation. , , (time step) and root mean square deviation ( As quantitative evaluation indicators, the lower these indicator values, the better the control performance.

[0076] like Figure 3 The figure shows the output trajectory of the multi-target bidirectional encirclement system under a fixed topology provided in this application embodiment at different iteration numbers; wherein, Figure 3 (a) in the figure represents the output trajectory of the multi-target bidirectional encirclement system during the 10th iteration. Figure 3 (b) in the figure represents the output trajectory of the multi-objective two-way encirclement system during the 40th iteration. Figure 3 (c) in the figure represents the output trajectory of the multi-target two-way encirclement system during the 70th iteration. Figure 3 In the figure, (d) represents the output trajectory of the multi-target bidirectional encirclement system at the 100th iteration; like Figure 4 The figure shown is a mean square tracking error diagram of a multi-target bidirectional encirclement system under a fixed topology provided in an embodiment of this application during the iterative process. like Figure 5 The diagram shown is a diagram of the event triggering intervals of each target in a multi-target bidirectional encirclement system under a fixed topology provided in an embodiment of this application.

[0077] It should be noted that, Figure 4 and Figure 5 Agent 1 to Agent 4 correspond to Figure 2 Follower nodes 1 through 4 in the network.

[0078] The simulation results above show that as the number of iterations increases, the root mean square error gradually decreases to a small range, indicating the effectiveness of the control method provided in this application under a fixed topology. In addition, the triggering conditions for different followers are different, and the number of iterations is also different. This is because the controller update and data transmission are only triggered when the change in the tracking error exceeds the set threshold, thereby reducing the computational and communication burden.

[0079] Step 4: Further extend the above simulation to an iterative time-varying topology. The follower dynamics model and the spoofed data injection attack signal are the same as in Step 1, such as... Figure 6 As shown, the communication topology includes 10 followers. Random switching between them, irregular switching in a directed graph is caused by... This indicates that, as the number of iterations increases, the topological change of the bidirectional encirclement system changes from... Decide, Figure 7for A schematic diagram showing the change with the number of iterations. The specific mathematical expression is: , , , , The mathematical expression for the fake data injection attack signal is: , , , , Encirclement Group The leader trajectory in the middle is as follows: , , , Encirclement Group The leader trajectory in the middle is as follows: , , .

[0080] Step 5: The initial conditions for the followers are: , , , , , , The controller parameters are set as follows: , , , , , Event trigger threshold .

[0081] Step 6: Build a Simulink model of the multi-objective bidirectional encirclement system under the switching topology, obtain simulation results, and use bidirectional inclusion mean square deviation (MBD) simulation. , , (time step) and root mean square deviation ( As quantitative evaluation indicators, the lower these indicator values, the better the control performance.

[0082] like Figure 8The figure shows the output trajectory of the multi-target bidirectional encirclement system under the switching topology provided in this application embodiment at different iteration numbers; wherein, Figure 8 (a) in the figure represents the output trajectory of the multi-target bidirectional encirclement system during the 10th iteration. Figure 8 (b) in the figure represents the output trajectory of the multi-objective two-way encirclement system during the 20th iteration. Figure 8 (c) in the figure represents the output trajectory of the multi-target bidirectional encirclement system during the 40th iteration. Figure 8 In the figure, (d) represents the output trajectory of the multi-objective bidirectional encirclement system during the 80th iteration.

[0083] like Figure 9 The figure shown is a mean square tracking error diagram of a multi-target bidirectional encirclement system under a switching topology provided in this application embodiment during the iterative process.

[0084] like Figure 10 The diagram shown is a diagram of the event triggering intervals of each target in a multi-target bidirectional encirclement system under a switching topology provided in an embodiment of this application.

[0085] Simulation results show that the improved encirclement control model based on attack-related compact format dynamic linearization, which is used to control a multi-target bidirectional encirclement system under a switching topology, gradually stabilizes the system output as the number of iterations increases, and the mean square error of each follower also gradually decreases to a small range, demonstrating the effectiveness of the improved control method under the switching topology.

[0086] Based on the multi-target bidirectional encirclement control method provided in the above embodiments, this application also provides a multi-target bidirectional encirclement control device, which includes: The Encirclement Group Acquisition Module is used to acquire two-way encirclement groups, treating each encircled object in each encirclement group as a follower and the encirclement target as the leader. The thread model acquisition module is used to construct the dynamic model of each follower based on the unknown nonlinear function, the input signal and output signal of each follower, and the unknown spoof data injection attack signal received; and to convert the dynamic model of each follower into a dynamic linearized model related to the attack signal. The event-triggered iteration sequence acquisition module is used to construct the iteration triggering mechanism of each follower based on the output signal error of each follower with its previous triggering iteration and the output signal error with each leader, thereby obtaining the triggering iteration sequence of each follower; The two-way encirclement error acquisition module is used to construct the two-way encirclement error of each follower based on the output signal error of each follower with other followers and the output signal error with each leader. The control module is used to construct the control input criterion function for each follower based on the bidirectional encirclement error, trigger iteration sequence, and input signal change of each follower; and to minimize the control input criterion function of each follower with respect to the input signal to obtain the input signal equation of each follower, thereby controlling each follower.

[0087] In summary, this application fully considers the threat of false data injection attacks in open network environments. By employing the Attack-Related Compact Form Dynamic Linearization (ArCFDL) method, it transforms complex, unknown non-affine nonlinear dynamic models into data models, effectively compensating for security threats and achieving stable bidirectional encirclement control of a multi-target bidirectional encirclement system under attack interference. Simultaneously, an iterative event triggering mechanism is designed, where updates to the controllers (each controller executes the aforementioned control method, thereby outputting the input signals of each follower to control them) and data transmission are only performed when the change in tracking error meets a preset trigger threshold. Compared to traditional continuous or high-frequency sampling iterative learning control, this scheme effectively reduces redundant information transmission, saving valuable communication bandwidth and target node energy consumption. Furthermore, this scheme belongs to data-driven control technology, utilizing only the real-time input / output data of the controlled object for control design, without relying on the precise mathematical model of the controlled object. This makes the system highly robust to changes in model parameters and significantly reduces the modeling difficulty and computational burden in complex environments.

[0088] In addition, this application extends the control method and convergence analysis to the case of iterative topology switching. For situations where the communication structure changes dynamically, the scheme can adjust the control parameters in real time to ensure that the system can maintain stability and achieve the bidirectional encirclement control objective even under switching graphs with strong connectivity or structural balance.

[0089] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0090] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0091] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0092] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0093] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A multi-objective, two-way encirclement control method, characterized in that, include: Acquire two-way encirclement groups, and designate each encircled object in each encirclement group as a follower, and the encirclement target as the leader; Based on the unknown nonlinear function, the input signal and output signal of each follower, and the unknown spoof data injection attack signal, a dynamic model of each follower is constructed; the dynamic model of each follower is then converted into a dynamic linearized model related to the attack signal. Based on the error of each follower's output signal with its previous triggering iteration and the error of its output signal with each leader, an iterative triggering mechanism for each follower is constructed to obtain the triggering iteration sequence for each follower; Based on the output signal errors of each follower with other followers and with each leader, a two-way encirclement error is constructed for each follower; Based on the bidirectional encirclement error, triggering iteration sequence, and input signal change of each follower, a control input criterion function for each follower is constructed. Minimize the control input criterion function for each follower with respect to the input signal to obtain the input signal equation for each follower, thereby controlling each follower.

2. The multi-target bidirectional encirclement control method according to claim 1, characterized in that, The dynamic model of the follower is expressed as: ， in, Indicates the first During the next iteration The output signal of the i-th follower at time i; Represents an unknown nonlinear function; Indicates the first During the next iteration The output signal of the i-th follower at time i; Indicates the first During the next iteration The input signal of the i-th follower at time i; Indicates the first During the next iteration The i-th follower at time i receives an unknown false data injection attack signal; The dynamic linearization model of the follower is represented as: ， in, Indicates the first During the next iteration Time and the During the next iteration The difference in the output signal of the i-th follower at time i; Indicates the first During the next iteration The pseudo-gradient related to the attack of the i-th follower at time i; Indicates the first During the next iteration Time and the During the next iteration The difference in the input signal of the i-th follower at time i; Indicates the first During the next iteration Time and the During the next iteration The difference in unknown false data injection attack signal received by the i-th follower at time i; .

3. The multi-target bidirectional encirclement control method according to claim 2, characterized in that, The iterative triggering mechanism of followers is represented as: ， ， ， in, This indicates the iteration triggering mechanism for the i-th follower; Indicates the previous triggered iteration The output signal of the i-th follower at time s+1; Indicates triggering the first The output signal of the i-th follower at time s+1 before the next iteration; Indicates the event trigger threshold; Indicates the time s+1. The output signal of a leader; Used to determine the grouping relationship of the i-th follower. If the i-th follower belongs to the grouping relationship of the i-th follower... The encirclement group to which each leader belongs, If the i-th follower does not belong to the i-th follower The encirclement group comprised of the leaders ; Indicates the number of leaders; The triggering iteration sequence of the follower is represented as: ， in, Indicates the i-th follower in the triggering iteration sequence. One trigger iteration; Indicates the i-th follower in the triggering iteration sequence. -1 trigger iteration.

4. The multi-target bidirectional encirclement control method according to claim 3, characterized in that, The two-way encirclement error of the follower is expressed as: ， in, Indicates the first During the next iteration The bidirectional encirclement error of the i-th follower at time i; This represents the communication weight between the i-th follower and the j-th follower; This represents a symbolic function that determines whether the relationship between the i-th follower and the j-th follower is cooperative or competitive. The function is defined as follows: when the relationship between the i-th follower and the j-th follower is cooperative... When the i-th follower and the j-th follower are in a competitive relationship, ; Indicates the first During the next iteration The output signal of the j-th follower at time j; Indicates the first During the next iteration The output signal of the i-th follower at time i; express Time of the first The output signal of a leader; Used to determine the grouping relationship of the i-th follower. If the i-th follower belongs to the grouping relationship of the i-th follower... The encirclement group to which each leader belongs, If the i-th follower does not belong to the i-th follower The encirclement group comprised of the leaders ; Indicates the number of leaders; Indicates the number of followers; Indicates the relationship between the i-th follower and the i-th follower. Communication weight between leaders.

5. The multi-target bidirectional encirclement control method according to claim 4, characterized in that, The control input criterion function of the follower is expressed as: ， in, This represents the control input criterion function for the i-th follower; Indicates the previous triggered iteration The output signal of the i-th follower at time s; Indicates triggering the first The output signal of the i-th follower at time s before the next iteration; Indicates the adjustable weighting coefficient. ; Indicates the first During the next iteration Time and the During the next iteration The difference in the input signal of the i-th follower at time i; The input signal equation for the follower is expressed as: ， in, Describe the input signal equation for the i-th follower; Indicates the adjustable step size coefficient. .

6. The multi-target bidirectional encirclement control method according to claim 5, characterized in that, The method further includes: Based on the input signal of each follower, the unknown spoof data injection attack signal received, and the attack-related pseudo gradient, a cost function for each follower is constructed. Minimize the cost function of each follower with respect to the attack-related pseudo-gradient to obtain the attack-related pseudo-gradient equation for each follower, thereby estimating the attack-related pseudo-gradient for each follower.

7. The multi-target bidirectional encirclement control method according to claim 6, characterized in that, The cost function of the follower is expressed as: ， in, Denotes the cost function of the i-th follower; Indicates a positive weighting parameter; Indicates the first The attack-related pseudo-gradient estimate of the i-th follower at time s during the next iteration; The pseudo-gradient equation related to the follower's attack is expressed as: ， in, Indicates the first The attack-related pseudo-gradient estimate of the i-th follower at time s during the next iteration; This represents the positive step size parameter.

8. The multi-target bidirectional encirclement control method according to claim 7, characterized in that, The method further includes: integrating the input signal equation, cost function, and attack-related pseudo-gradient equation for each follower to obtain an encirclement control model for each follower based on attack-related compact format dynamic linearization of event-triggered distributed model-free adaptive iterative learning.

9. The multi-target bidirectional encirclement control method according to claim 8, characterized in that, The encirclement control model for each follower is represented as follows: ， ， ， in, It is a constant. ; This represents the attack-related pseudo-gradient estimate of the i-th follower at time s during the first iteration.

10. A multi-target bidirectional encirclement control device, characterized in that, include: The Encirclement Group Acquisition Module is used to acquire two-way encirclement groups, treating each encircled object in each encirclement group as a follower and the encirclement target as the leader. The thread model acquisition module is used to construct the dynamic model of each follower based on the unknown nonlinear function, the input signal and output signal of each follower, and the unknown spoof data injection attack signal received; and to convert the dynamic model of each follower into a dynamic linearized model related to the attack signal. The event-triggered iteration sequence acquisition module is used to construct the iteration triggering mechanism of each follower based on the error of each follower's output signal with its previous triggering iteration and the error of its output signal with each leader, thereby obtaining the triggering iteration sequence of each follower; The two-way encirclement error acquisition module is used to construct the two-way encirclement error of each follower based on the output signal error of each follower with other followers and the output signal error with each leader. The control module is used to construct the control input criterion function for each follower based on the bidirectional encirclement error, trigger iteration sequence, and input signal change of each follower. Minimize the control input criterion function for each follower with respect to the input signal to obtain the input signal equation for each follower, thereby controlling each follower.

Images