Heterogeneous cluster hybrid attack defense control method and system oriented to urban confrontation environment, terminal equipment and medium

Abstract

The invention discloses a hybrid attack defense control method and system for a heterogeneous cluster in an urban confrontation environment, terminal equipment and a medium, and relates to the technical field of unmanned platform cluster control, and the method comprises the steps: constructing an ideal system model of an unmanned platform cluster comprising a leader and a plurality of followers, constructing an information physical hybrid attack model based on the model; using the attack model to simulate an attack behavior of an attacker on an ideal system to obtain an attacked system model; based on an attacked system model, constructing a distributed elastic security estimator with a compensation mechanism, compensating attack influence for each follower and estimating an expected position; and based on the expected position of the follower, constructing a distributed elastic safety controller with a compensation mechanism, and controlling the follower. By designing the estimator and the controller, attack interference is counteracted, control input is generated, and safe collaboration of the heterogeneous nonlinear unmanned cluster under the cyber-physical hybrid attack is guaranteed.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of unmanned platform cluster control, and in particular to a hybrid attack defense control method and system for a heterogeneous cluster in a city confrontation environment, a terminal device and a medium. BACKGROUND

[0002] With the development of intelligent equipment technology, unmanned clusters containing unmanned platforms such as unmanned aerial vehicles, unmanned vehicles, underwater robots, etc. are increasingly widely used in the fields of intelligent transportation, environmental monitoring, emergency rescue, etc., and their cooperative control performance determines the task execution efficiency. In the prior art, the cooperative control of unmanned clusters is mostly based on the assumption of an ideal communication environment, and state synchronization or trajectory tracking is achieved by designing distributed controllers, such as using consensus algorithms, sliding mode control, etc. to improve the cooperative accuracy.

[0003] However, in actual applications, unmanned clusters face complex information and physical security threats. For example, at the network layer, they are vulnerable to asynchronous DoS (Denial-of-Service) attacks, in which an attacker interrupts different communication links at different times, causing intermittent failure of information interaction, or at the physical layer, they may encounter FDI (False Data Injection) attacks, which inject false signals to tamper with sensor or actuator data. At the same time, the dynamic characteristics of different types of unmanned platforms in the cluster are heterogeneous and nonlinear, such as different dynamic equations and state dimensions, further increasing the difficulty of attack and defense.

[0004] Existing defense methods have obvious limitations. Specifically, most defense methods are only against a single type of attack, such as only defending against DoS attacks, lacking comprehensive response to information-physical hybrid attacks, and lacking adaptability to heterogeneous nonlinear systems, making it difficult to ensure cooperative stability under attack. The existing technology has not formed a defense mechanism of attack estimation and compensation control, resulting in weak defense robustness.

[0005] Therefore, there is an urgent need for a method that can adapt to heterogeneous nonlinear characteristics, resist information-physical hybrid attacks, and achieve safe and cooperative cluster, to fill the gap in the existing technology. SUMMARY

[0006] The technical problem to be solved by the present application is that in the technical field of unmanned cluster systems, heterogeneous nonlinear unmanned clusters face the combined threat of network layer asynchronous DoS attacks and physical layer unknown FDI attacks, and existing methods cannot adapt to the heterogeneous nonlinear characteristics of the system and cannot comprehensively resist hybrid attacks, resulting in poor cooperative stability of the cluster and difficulty in achieving safe and cooperative goals. Therefore, there is an urgent need for an effective solution to solve the above technical problems.

[0007] To solve the above technical problems, the technical solution adopted by the present application is as follows: In a first aspect, the present application provides a hybrid attack defense control method for a heterogeneous cluster in a city confrontation environment, the method comprising: constructing an ideal system model of a cluster of unmanned platforms, wherein the cluster of unmanned platforms comprises a plurality of unmanned platforms of different types, one of which is a leader and the rest are followers, the dynamic state of the unmanned platforms changes nonlinearly, the unmanned platforms communicate through a topology graph, and the communication between any two unmanned platforms has directionality; based on the ideal system model, constructing an information-physical hybrid attack model, and using the information-physical hybrid attack model to simulate the attack behavior of an attacker on the ideal system to obtain a corresponding attacked system model of the cluster of unmanned platforms, wherein the attack behavior includes an asynchronous DoS attack at the network layer and an unknown FDI attack signal injection at the physical layer, the asynchronous DoS attack is an independent attack by the attacker on different communication links of the cluster of unmanned platforms at different time periods, and the unknown FDI attack signal injection is an unknown FDI attack signal injected by the attacker into the leader; based on the attacked system model, constructing a distributed resilient safety estimator with a compensation mechanism, and for each follower in the cluster of unmanned platforms of the attacked system model, compensating for the attack effect and estimating the desired position based on the distributed resilient safety estimator, wherein the follower completes the calculation of the desired position based on its own kinematic state and local estimation state information; based on the desired position of the follower, constructing a distributed resilient safety controller with a compensation mechanism, and using the distributed resilient safety controller to control the follower, so that the leader and the follower of the cluster of unmanned platforms safely cooperate.

[0008] In an implementation manner, the constructing an ideal system model of a cluster of unmanned platforms comprises: constructing a system topology graph of the ideal system model:

[0009] wherein the topology graph is a directed graph, is a node set composed of unmanned platforms, represents the node of the leader, when , represents the node of the follower, is an edge set between nodes, and the initial topology has a directed spanning tree with the leader as the root node; constructing a system topology graph corresponding to the communication link matrix, which is represented by a Laplacian matrix:

[0010] in, This indicates that the leader himself does not have self-circulation communication. It indicates communication from followers to leaders. This indicates one-way communication from leader to follower. Indicates a communication link between followers. Representing the set of real numbers, the communication link matrix satisfies and This indicates that communication between any two unmanned platforms is directional. Indicates transpose processing; Based on the system topology diagram and corresponding communication link matrix of the ideal system model, an ideal system model for followers and an ideal system model for leaders in a secure network environment are constructed.

[0011] In one implementation, the construction of ideal system models for followers and leaders in a secure network environment based on the system topology diagram and corresponding communication link matrix of the ideal system model includes: Build An ideal system model with one follower:

[0012] in, and The first in a secure network environment The status and control input of a follower Indicates the first Follower status dimensionality Represents a time variable. Indicates the first The derivative of each follower state is used to describe the change in the state of the unmanned platform over time. and They represent dimensions as follows: and The follower system state matrix, This represents a Lipschitz continuous nonlinear function. It is the output dimension of the Lipschitz continuous nonlinear function; Constructing an ideal system model for leaders:

[0013] in, It is the ideal state of a leader, that is, the expected state that followers need to follow. Indicates the leader's status dimensionality; The derivative representing the leader's state, and They represent dimensions as follows: and The leader system state matrix; Among them, nonlinear functions The Lipchitz condition must be satisfied, i.e., there must exist a nonnegative constant. ,in Such that for any vector ,satisfy:

[0014] in, It is a vector function The One portion, They are vectors The Each component.

[0015] In one implementation, the step of constructing a cyber-physical hybrid attack model based on the ideal system model, and using the cyber-physical hybrid attack model to simulate the attacker's attack behavior on the ideal system, to obtain the attacked system model corresponding to the unmanned platform cluster, includes: For the aforementioned ideal system model, an asynchronous DoS attack model for the network layer is constructed:

[0016] in, for The time-varying attack model corresponding to each moment satisfies , For the set of all attack models, This represents the total number of attack models. For the edge exist A collection of periods during which the system suffered DoS attacks; Build an attack model The adjacency matrix of the attacked system model:

[0017] in, Attack model at the current moment Below Channel communication weight, if The channel is under attack, i.e. ,but ,like Channel security, i.e. Then the link weight remains unchanged, that is , Initial topology under no attack , Channel communication weight; Construct attack model The communication link matrix of the attacked system model under the attack model is represented by the Laplacian matrix:

[0018] Where, Indicates the one-way communication from leader to follower under the attack model, Indicates the communication link between followers under the attack model, and the diagonal elements of the Laplacian matrix , other elements , ; ; ; When constructing the asynchronous DoS attack model of the network layer, limit the attack duration, and the expression is:

[0019] Where, Indicates the starting point of time, Indicates the time parameter, The edge is subjected to DoS attack within , is a positive scalar describing the diversity of the attacker, is the attack intensity parameter; When constructing the asynchronous DoS attack model of the network layer, limit the attack frequency, and the expression is:

[0020] Where, is the number of DoS attacks within , is a parameter describing the behavior of the attacker, are the equivalent attenuation rates when the edge is subjected to DoS attack and normal communication, respectively, and are optional parameters, is the maximum attack model switching rate, , , Indicates the eigenvalue; Construct the dynamics model of the follower under asynchronous DoS attack:

[0021] Where, actual state of the leader under unknown FDI attack signal injection, actual state of the corresponding time actual state of the corresponding time control input dynamically adjusted with the attack model ; constructing a dynamic model of the leader under unknown FDI attack signal injection:

[0022] wherein, actual state of the leader under FDI attack, actual state of the corresponding time actual state of the corresponding time unknown bounded FDI injection signal satisfying .

[0023] In an implementation manner, the constructing, based on the attacked system model, a distributed resilient safety estimator with a compensation mechanism, and for each follower in the unmanned platform cluster of the attacked system model, compensating attack influence and estimating a desired position based on the distributed resilient safety estimator, comprises: constructing, based on the attacked system model, a distributed resilient safety estimator with a compensation mechanism, denoted as:

[0024]

[0025] wherein, estimated state of the i th estimator, i.e., an estimated desired position, is a local estimation error, is a nonlinear function satisfying:

[0026] wherein, and are a DoS attack compensation gain constant and an FDI attack compensation gain constant, respectively, is a feedback gain matrix, wherein is a given symmetric positive definite matrix, is a Lyapunov matrix satisfying:

[0027] wherein, is a Lipschitz matrix corresponding to the nonlinear function , is an optional parameter, ,​ , is an attack decay rate corresponding to the attack model .

[0028] In an implementation, the leader's desired position is used to construct a distributed resilient safety controller with compensation mechanism, and the follower is controlled using the distributed resilient safety controller, so that the leader and the follower of the unmanned platform cluster are safely coordinated, including: The leader's desired position is used to construct a distributed resilient safety controller with compensation mechanism, and the follower is controlled using the distributed resilient safety controller, so that the leader and the follower of the unmanned platform cluster are safely coordinated, including:

[0029] wherein, is the control input of the i-th follower for controlling the follower, is an estimated tracking error, , , , is a nonlinear function, satisfying:

[0030] wherein, is a control gain constant, is a compensation gain constant, is a feedback gain matrix, wherein is a given symmetric positive definite matrix, is a Lyapunov matrix, satisfying:

[0031] wherein, is a Lipschitz matrix corresponding to the nonlinear function , is an optional parameter, , is an attack decay rate.

[0032] In an implementation, the defense control method further includes: For the distributed resilient safety estimator, a Lyapunov function is constructed based on the estimation error for evaluating the convergence of the estimation error of the distributed resilient safety estimator, represented as:

[0033] wherein, , represents a Kronecker product, and the distributed resilient safety estimator can realize the decay of the Lyapunov function, i.e. ; wherein, the decay rate of the Lyapunov function satisfy the following conditions:

[0034]

[0035]

[0036] wherein, is an attack intensity parameter, and are equivalent attenuation rates when edges suffer DoS attacks and normal communication, respectively; based on the attenuation condition and the attack behavior, the convergence of the estimation error of the distributed resilient security estimator is obtained , that is, , the estimation error asymptotically converges; for the distributed resilient security controller, a Lyapunov function is constructed based on the tracking error, for evaluating the convergence of the tracking error of the distributed resilient security controller, expressed as:

[0037] wherein, is the tracking error of the th follower unmanned platform, denotes the transpose at time ; based on the control input, the convergence of the tracking error of the distributed resilient security controller is obtained , that is, , the tracking error asymptotically converges, indicating that the state of the unmanned platform follower is able to track the leader state .

[0038] In a second aspect, the embodiments of the present application also provide a hybrid attack defense control system for a heterogeneous cluster in a city confrontation environment, the system comprising: an ideal system model construction module, configured to construct an ideal system model of an unmanned platform cluster, wherein the unmanned platform cluster comprises a plurality of unmanned platforms of different types, one of which is a leader and the rest are followers, the dynamic state of the unmanned platform changes nonlinearly, the unmanned platforms communicate through a topology graph, and the communication between any two unmanned platforms has directionality; an information-physical hybrid attack model construction module, configured to construct an information-physical hybrid attack model based on the ideal system model, and simulate attack behaviors of an attacker on the ideal system using the information-physical hybrid attack model to obtain an attacked system model corresponding to the UAV cluster, wherein the attack behaviors include an asynchronous DoS attack at a network layer and unknown FDI attack signal injection at a physical layer, the asynchronous DoS attack is an independent attack by the attacker on different communication links of the UAV cluster in different time periods, and the unknown FDI attack signal injection is unknown FDI attack signal injection by the attacker into the leader; an elastic security estimator construction module, configured to construct a distributed elastic security estimator with a compensation mechanism based on the attacked system model, and compensate for attack effects and estimate a desired position of each follower in the UAV cluster of the attacked system model based on the distributed elastic security estimator; an elastic security controller construction module, configured to construct a distributed elastic security controller with a compensation mechanism based on the desired position of the follower, and control the follower using the distributed elastic security controller so that the leader and the follower of the UAV cluster are safely coordinated.

[0039] In a third aspect, an embodiment of the present application further provides a terminal device, which comprises a memory, a processor, and a hybrid attack defense control program for a heterogeneous cluster in a city confrontation environment stored in the memory and executable on the processor; when the processor executes the hybrid attack defense control program for the heterogeneous cluster in the city confrontation environment, steps of the hybrid attack defense control method for the heterogeneous cluster in the city confrontation environment in any of the above solutions are implemented.

[0040] In a fourth aspect, an embodiment of the present application further provides a computer readable storage medium, which stores a hybrid attack defense control program for a heterogeneous cluster in a city confrontation environment; when a processor executes the hybrid attack defense control program for the heterogeneous cluster in the city confrontation environment, steps of the hybrid attack defense control method for the heterogeneous cluster in the city confrontation environment in any of the above solutions are implemented.

[0041] Beneficial effects: A hybrid attack defense control method, system, terminal device and medium for heterogeneous clusters in urban counter-environment, relating to unmanned platform cluster control technology field, the method first constructs an ideal system model of unmanned platform cluster, wherein the unmanned platform cluster includes several different types of unmanned platforms, one of which is a leader and the rest are followers, the dynamic state change of the unmanned platform is nonlinear, the unmanned platforms communicate through a topology graph, and the communication between any two unmanned platforms has directionality. Thereafter, based on the ideal system model, an information-physical hybrid attack model is constructed, and the attack behavior of the attacker on the ideal system is simulated using the information-physical hybrid attack model to obtain the corresponding attacked system model of the unmanned platform cluster, wherein the attack behavior includes asynchronous DoS attack at the network layer and unknown FDI attack signal injection at the physical layer, the asynchronous DoS attack is an independent attack by the attacker on different communication links of the unmanned platform cluster at different time periods, and the unknown FDI attack signal injection is the injection of unknown FDI attack signals by the attacker into the leader. Then, based on the attacked system model, a distributed resilient security estimator with compensation mechanism is constructed, and for each follower in the unmanned platform cluster of the attacked system model, the expected position is estimated based on the distributed resilient security estimator to compensate for the attack effect, wherein the follower completes the calculation of the expected position based on its own kinematic state and local estimation state information. Finally, based on the expected position of the follower, a distributed resilient security controller with compensation mechanism is constructed, and the follower is controlled using the distributed resilient security controller, so that the leader and follower of the unmanned platform cluster are safely coordinated. The present application aims at the technical problem of information-physical hybrid attack of heterogeneous nonlinear unmanned platform cluster, based on the mixed model covering asynchronous DoS attack at the network layer and unknown FDI attack at the physical layer, a distributed resilient security estimator and controller with compensation mechanism are designed to offset the attack interference and reconstruct the leader information, so that the follower can complete the expected position estimation and control without centralized scheduling, finally realizing the safe cooperative tracking of the cluster, improving the robustness and autonomy of the system under complex interference and composite attack, and providing technical support for the reliable operation of the unmanned cluster. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 The flowchart of the specific implementation mode of the hybrid attack defense control method for heterogeneous clusters in urban counter-environment provided by the embodiments of the present application is provided.

[0043] Figure 2 The principle block diagram of the hybrid attack defense control device for heterogeneous clusters in urban counter-environment provided by the embodiments of the present application is provided.

[0044] Figure 3is an internal structure principle block diagram of a terminal device provided by an embodiment of the present application. DETAILED DESCRIPTION

[0045] To make the objects, technical solutions and effects of the present application clearer and more explicit, the present application is further described in detail below with reference to the drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application and do not limit the present application.

[0046] The flowchart shown in the drawings is only an example and does not necessarily include all contents and operations or steps, nor does it necessarily execute in the order described. For example, some operations or steps can be further divided, combined or partially merged, so the actual execution order may be changed according to the actual situation.

[0047] It should be understood that the terms used in the present application are only for the purpose of describing specific examples and are not intended to limit the present application. As used in the present application specification and the appended claims, unless the context clearly indicates otherwise, the singular forms "a", "an" and "the" are intended to include the plural forms.

[0048] It should be understood that, in order to facilitate the clear description of the technical solutions of the embodiments of the present application, in the embodiments of the present application, the terms "first", "second" and the like are used to distinguish the same or similar items with basically the same function and role. For example, the first control information and the second control information are only used to distinguish different control information and do not limit the order.

[0049] Those skilled in the art can understand that the terms "first", "second" and the like do not limit the quantity and execution order, and the terms "first", "second" and the like do not necessarily mean different.

[0050] It should also be understood that the term "and / or" used in the present application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes these combinations.

[0051] The unmanned cluster system is a large-scale complex system composed of multiple intelligent unmanned platforms such as unmanned aerial vehicles, unmanned vehicles and unmanned boats. Each platform interacts and cooperates based on a communication network to perform special tasks, with characteristics such as autonomy, distribution, collaboration and robustness. Based on the above advantages, the system has been widely used in various fields, especially in collaborative emergency management and control scenarios in urban confrontation environments. The distributed collaboration mechanism between unmanned platforms reduces the computational load in the cooperative deployment problem and significantly improves the overall performance of the system, but at the same time, this collaborative control mechanism also puts higher requirements on the information security of the system.

[0052] Large-scale unmanned swarm is a typical cyber-physical system, in which platforms share information and make collaborative decisions through a distributed network. Although this interaction architecture improves the flexibility and scalability of the system, the open task execution environment in urban combat scenarios also exposes the unmanned swarm system to dual security threats at the network and physical layers. Therefore, while ensuring emergency response efficiency, how to achieve rapid and secure collaborative deployment and effectively resist external attacks is a key problem for the reliable operation of large-scale unmanned swarm systems in urban combat environments. At the physical layer, false data injection (FDI) attacks are a typical security threat. Attackers inject malicious signals into each unmanned platform to compromise data integrity and disrupt the normal operation of the system. At the network layer, the system is often affected by denial-of-service (DoS) attacks. Attackers block communication channels maliciously, causing some or all components of the control system to lose contact, thereby endangering the stability of the system. Existing network layer security control researches mostly focus on periodic DoS attacks and non-periodic DoS attacks, considering that all communication links face the same attack mode. This homogeneous attack model ignores the heterogeneity of channels and the diversity of attackers. Asynchronous DoS attacks consider the existence of multiple heterogeneous attackers, allowing each attacker to perform asynchronous and independent attacks on different communication links at different times. This attack model can more accurately capture the complex communication situation in actual urban combat environments. In addition, current security collaborative control methods mainly focus on the research of a single attack type. However, in large-scale unmanned swarm systems with deep integration of communication networks and physical components, system security threats often take more diversified composite forms. The establishment of an information-physical hybrid attack model can effectively address this challenge by establishing a joint mathematical model for composite attacks at the network and physical layers, accurately simulating the security threat situation faced by large-scale unmanned swarm systems in complex urban combat environments.

[0053] At the same time, most existing unmanned swarm collaborative control methods linearize the actual system dynamics of unmanned platforms, obtaining an approximate dynamic model near the system equilibrium point through mathematical techniques such as Taylor expansion or small perturbation methods, and then simplifying the controller design. However, in complex urban combat environments, multiple external environmental disturbances such as electromagnetic noise, building obstructions, and dynamic obstacles may cause the system to deviate from equilibrium, reducing the prediction accuracy of the linearized model and undermining the practical applicability of traditional control algorithms. The establishment of a heterogeneous nonlinear unmanned swarm system model can effectively capture the individual differences of unmanned platforms and real external disturbance models, and then depict more realistic system operation rules, laying a theoretical foundation for unmanned swarm collaborative defense in complex urban combat environments.

[0054] Therefore, based on the compensation and estimation mechanism, the distributed resilient security controller under the hybrid attack can accurately reconstruct the leader information and perform safe cooperative control under the information-physical complex threat situation, better cope with the interference of complex environment, and the complexity and diversity of network attacks in urban confrontation scenes, and provide a practical solution for urban security cooperative defense in conflict situations, which has important theoretical and practical value for improving the autonomous ability and robustness of large-scale clusters in complex environments.

[0055] The hybrid attack defense control method for heterogeneous clusters in urban confrontation environment provided by the embodiment comprises the steps of: Figure 1 As shown in the figure, the method comprises the following steps: Step S100, an ideal system model of an unmanned platform cluster is constructed, wherein the unmanned platform cluster comprises a plurality of unmanned platforms of different types, one of which is a leader and the others are followers, the dynamic state change of the unmanned platforms is nonlinear, the unmanned platforms communicate through a topology graph, and the communication between any two unmanned platforms has directionality.

[0056] In the embodiment, the heterogeneous nonlinear unmanned platform cluster refers to a cluster system composed of two or more different types of unmanned platforms such as unmanned aerial vehicles, unmanned vehicles, and unmanned boats. The heterogeneity of the unmanned platform cluster is reflected in the differences in the dynamic parameters of each unmanned platform, such as the differences in the state matrix, input dimension, and other parameters of each unmanned platform. The nonlinearity of the unmanned platform cluster refers to the fact that the change of the dynamic state of the unmanned platform with time does not satisfy a linear relationship, for example, influenced by electromagnetic interference, load fluctuation, environmental resistance, and other factors, the state change needs to be described by a Lipschitz continuous nonlinear function. Compared with traditional homogeneous linear cluster systems, this is more in line with the actual operating characteristics of unmanned platforms in urban confrontation environments. In addition, the unmanned platform cluster referred to in the embodiment is generally a leader and follower architecture, which includes a leader unmanned platform responsible for providing global target instructions such as cooperative defense path and task area coordinates. The leader unmanned platform is the reference for the follower unmanned platforms, and the follower unmanned platforms are responsible for executing specific tasks by communicating with the leader or other followers to obtain information. This leader and follower architecture can reduce the computational complexity of cluster cooperation, avoid system paralysis caused by single node failure, and meet the reliability requirements in urban confrontation scenarios.

[0057] In the ideal system model of the unmanned platform cluster constructed in this embodiment, a directed topology graph is used to simulate the communication between unmanned platforms. The topology is a directed topology graph, indicating that the communication link between any two unmanned platforms has unidirectionality. For example, due to the shielding of urban buildings, the signal transmission direction is limited, unmanned platform A can send data to unmanned platform B, but unmanned platform B cannot feedback to unmanned platform A, which is different from the bidirectional interaction of undirected communication. In this ideal system model, the initial topology has a directed spanning tree with the leader as the root node, indicating that there is at least one communication path from the leader that can cover part of the followers, ensuring that the basic instructions of the leader can be delivered to the cluster, providing an initial connected basis for information reconstruction and cooperative control under subsequent attacks, and avoiding information islands in the initial state.

[0058] In the specific implementation process of this embodiment, first, the cluster size and platform type need to be determined, including determining the specific number of followers, such as 10 followers and 1 leader, and including determining the platform type, such as 3 unmanned aerial vehicles and 7 unmanned vehicles. Then, the dynamic nonlinear characteristics of each platform are determined based on the maximum speed, load capacity and other hardware parameters, and finally the directed topology graph is constructed based on the communication distance, obstacle distribution and other communication conditions of the urban confrontation environment, to ensure that the initial topology meets the condition of the leader as the root of the directed spanning tree, thereby establishing an ideal system model that can reflect the actual cluster characteristics. It should be understood that this model serves as a benchmark for subsequent analysis of attack effects and design of defense strategies, and needs to exclude non-ideal factors such as attacks and interference, and only depict the communication and dynamic state of the cluster in a non-threatening environment.

[0059] In one implementation, the ideal system model of the unmanned platform cluster is constructed, specifically including the following steps: Step S110, constructing a system topology graph of the ideal system model:

[0060] Wherein, the topology graph is a directed graph, is a node set composed of unmanned platforms, indicates the node of the leader, when , indicates the node of the th follower, is an edge set between nodes, and the initial topology has a directed spanning tree with the leader as the root node; Step S120, constructing a system topology graph corresponding to the communication link matrix, which is represented by a Laplacian matrix:

[0061] in, This indicates that the leader himself does not have self-circulation communication. It indicates communication from followers to leaders. This indicates one-way communication from leader to follower. Indicates a communication link between followers. Representing the set of real numbers, the communication link matrix satisfies and This indicates that communication between any two unmanned platforms is directional. Indicates transpose processing; Step S130: Based on the system topology diagram and corresponding communication link matrix of the ideal system model, construct the ideal system model of the follower and the ideal system model of the leader in a secure network environment.

[0062] In this embodiment, a directed topological graph is used to characterize the communication relationships between unmanned platforms. Unlike undirected graphs where communication is bidirectional and peer-to-peer, the edges of a directed topological graph have a definite direction. For example, in an urban combat environment, a drone can send signals to a ground-based unmanned vehicle due to its altitude advantage, but the unmanned vehicle cannot respond to the drone due to building obstructions. This unidirectional communication relationship needs to be mathematically expressed using directed edges. In one implementation, in the node set of the constructed system topological graph, each node uniquely corresponds to one unmanned platform. As a leader node, it can specifically be a command drone with global positioning capabilities. As follower nodes, these can specifically be unmanned vehicles performing patrol missions or reconnaissance drones; the total number of nodes... The specific details are determined based on the requirements of the urban combat mission. Furthermore, in the edge set of the system topology graph, edges represent the data transmission capability between the sending node and the receiving node. The existence of an edge depends on urban environmental factors such as communication distance, signal obstruction, and electromagnetic interference; if there is no effective communication, the edge is not included in the edge set. When constructing the system topology graph, the initial topology is built. The directed spanning tree in the initial topology refers to the existence of at least one directed path from the leader node that covers the follower nodes. This is the connectivity condition of an ideal system, used to ensure that the leader's basic instructions can be transmitted to the cluster, preventing some followers from becoming information islands in the initial state.

[0063] In the constructed system topology diagram, communication links are represented using a block structure of Laplace matrices. Specifically, in the communication link matrix, the top-left diagonal block... This indicates that the leader node has no self-loop communication, meaning the leader does not need to send data to itself. It signifies that the leader's state commands are generated by its own decision-making system, without internal loop transmission. (The rest of the first line is missing.) yes zero vector, indicating that the follower in the ideal system cannot send a communication signal to the leader, and only receives the control signal of the leader to complete the control follower-leader communication block expressing the strength of one-way communication from the leader to the follower, wherein, expressing the leader, expressing the follower. The leader-to-follower one-way communication strength can be expressed as expressing the first follower receiving the control signal data sent by the leader, using expressing that the follower cannot directly receive the control signal data of the leader due to factors such as too long communication distance, and the number of non-zero elements is consistent with the coverage range of the directed spanning tree of the initial topology. The follower-to-follower communication block is used to quantify the one-way communication relationship between the followers, for example expressing that the first follower can pass information to the first follower, expressing that the first follower can pass information to the first follower, and expressing that communication is not possible. The matrix satisfies and , indicating that the matrix is asymmetric, and is used to express the one-way nature presented by the communication link in the urban confrontation environment due to factors such as shielding and signal direction limitation, for example, the downlink communication from the unmanned aerial vehicle to the ground unmanned vehicle is possible, and the uplink communication is not possible.

[0064] After the overall system topology graph is constructed, based on the node relationship in the system topology graph, a dynamic model expressing the state change of the leader and the follower in a secure network environment is further constructed, which is an ideal system model of the follower and an ideal system model of the leader.

[0065] In one implementation, the system topology graph and the corresponding communication link matrix based on the ideal system model are used to construct the ideal system model of the follower and the ideal system model of the leader in a secure network environment, and the specific steps include the following steps: Step S131, constructing an ideal system model of the first follower:

[0066] wherein, and are the state and control input of the first follower in a secure network environment, indicates the dimension of the state of the first follower, Represents a time variable. Indicates the first The derivative of each follower state is used to describe the change in the state of the unmanned platform over time. and They represent dimensions as follows: and The follower system state matrix, This represents a Lipschitz continuous nonlinear function. It is the output dimension of the Lipschitz continuous nonlinear function; Step S132: Construct an ideal system model for the leader:

[0067] in, It is the ideal state of a leader, that is, the expected state that followers need to follow. Indicates the leader's status dimensionality; The derivative representing the leader's state, and They represent dimensions as follows: and The leader system state matrix; Among them, nonlinear functions The Lipchitz condition must be satisfied, i.e., there must exist a nonnegative constant. ,in Such that for any vector ,satisfy:

[0068] in, It is a vector function The One portion, They are vectors The Each component.

[0069] In this embodiment, in the constructed ideal system model of the follower, the state vector This represents the ideal state of a follower in a secure network environment. State dimension, for example, for unmanned vehicles, can be 3, representing two-dimensional coordinates and operating speed. For drones, the state dimension can be 6, representing three-dimensional coordinates, operating speed, roll angle, pitch angle, and other states. These state components directly reflect the operating state of the follower and serve as the benchmark for state comparison under subsequent attacks. Control input refers to the instruction signal driving the follower's movement in a safe environment, such as the throttle opening of an unmanned vehicle, the steering angle, the motor speed of a drone. There is a pure input in the ideal model without attack interference, and the subsequent attacked model will adjust the input to offset the attack. System state matrix expresses the follower's own dynamic characteristics, such as the speed attenuation of an unmanned vehicle due to ground friction, which can be used to express the attenuation coefficient. Different types of followers have differences, such as the air resistance coefficient of a drone and the ground resistance coefficient of an unmanned vehicle, which reflect the heterogeneous characteristics of the unmanned platform cluster in this embodiment. Another matrix associates control input and state change, such as using elements to represent that the state component is affected by the control input, and the speed state row of the unmanned vehicle corresponds to the non-zero coefficient of the throttle input. Among them, is a nonlinear function output dimension, and together constitute the basic dynamics framework of the follower.

[0070] Further, using nonlinear function, the non-ideal factors such as electromagnetic interference, gust resistance, and load fluctuation in the actual environment are quantified, and Lipschitz continuity is used for constraint. Specifically, by using a non-negative constant limit the nonlinearity, avoid model divergence due to too strong nonlinearity, and ensure the designability of the subsequent attack model and defense strategy, which conforms to the actual scene in urban confrontation. In one embodiment, when constructing the ideal model of the follower, the platforms can be grouped by type first, such as a drone group and an unmanned vehicle group. The parameters of platforms in the same group are similar, reducing the amount of calculation, and then the parameters are calibrated according to the measured data of a single platform, such as the speed attenuation rate of an unmanned vehicle on a flat road. Finally, the Lipschitz condition is verified to ensure that the model can reflect the true movement law of the follower without attack.

[0071] Similarly, the ideal system model of the leader constructed does not have a control input corresponding to the control input in the follower model because the leader, as the target benchmark of the cluster, generates its own decision system to generate the state such as the task area coordinate and the cruise path, without the need for external control instructions, so only the state self-evolution item and the nonlinear disturbance term are retained in the model, which expresses the architecture logic of the leader providing a global target and the follower tracking. In addition, the ideal state is the expected tracking target of all followers, such as the real-time position of the leader, which is the rendezvous point of the follower, and the dimension is consistent with that of the follower, ensuring that the state can be compared. And in the leader model, the nonlinear function The same set of Lipschitz matrices shared with the follower ensures consistent quantization criteria for nonlinear disturbance in the cluster, avoids tracking deviation caused by differences in disturbance models between the leader and the follower, and lays a foundation for unified compensation under subsequent attacks.

[0072] In a specific implementation, parameter calibration of the ideal model of the leader can adopt a strategy of prioritizing stability, verify the rationality of the state through field testing, and ultimately form an ideal collaborative foundation with stable output targets of the leader and trackable followers.

[0073] Step S200, based on the ideal system model, an information-physical hybrid attack model is constructed, and the attacker's attack behavior on the ideal system is simulated using the information-physical hybrid attack model to obtain an attacked system model corresponding to the unmanned platform cluster, wherein the attack behavior includes asynchronous DoS attack at the network layer and unknown FDI attack signal injection at the physical layer, the asynchronous DoS attack is an independent attack by the attacker on different communication links of the unmanned platform cluster at different time periods, and the unknown FDI attack signal injection is an unknown FDI attack signal injected by the attacker into the leader.

[0074] In this embodiment, the information-physical hybrid attack refers to a composite attack acting on the network layer and the physical layer of the unmanned platform cluster at the same time, which is different from the traditional single attack. The network layer affects information interaction by blocking communication, and the physical layer destroys dynamic stability by tampering with device state. The superposition of the two is more in line with the actual scene of multi-dimensional destruction by attackers in urban confrontation environment, for example, the attacker first interrupts the communication between the unmanned aerial vehicle and the unmanned vehicle through DoS attack, and then injects false signals to tamper with the leader's position, resulting in chaotic cluster defense.

[0075] The core feature of asynchronous DoS attack is that the attacker independently attacks different communication links at different time periods, for example, attacking the links between unmanned aerial vehicle 1 and unmanned vehicle 2 at t1, and attacking the links between unmanned vehicle 2 and unmanned vehicle 3 at t2, rather than simultaneously attacking all links as in traditional DoS attack. This attack conforms to the characteristics of heterogeneous communication links in urban confrontation due to building shielding and signal power differences, because different links have different anti-interference capabilities, the attacker will selectively attack weak links at different times.

[0076] Unknown FDI attack signal injection refers to the specific waveform and amplitude of the false signal injected by the attacker, which is the same as the actual attack where the details of the attack signal cannot be predicted in advance. The injection object of this FDI attack signal is the leader, because the leader is the target reference of the cluster, and tampering with its state will cause tracking deviation of all followers.

[0077] In this embodiment, the attacked system model corresponding to the unmanned platform cluster is a dynamic model with the attack impact superimposed on the ideal system model. This model is used to transform abstract attacks into quantifiable mathematical expressions. Specifically, by modifying the adjacency matrix and setting the link weight to 0 to simulate a DoS attack, and by adding an attack term to the model, the model can reflect the actual operating state of the cluster under attack. This provides a quantitative basis for the attack impact in the subsequent design of resilient security estimators and controllers, preventing defense strategies from deviating from actual attack scenarios.

[0078] In one implementation, the step of constructing a cyber-physical hybrid attack model based on the ideal system model, and using the cyber-physical hybrid attack model to simulate the attacker's attack behavior on the ideal system to obtain the attacked system model corresponding to the unmanned platform cluster, specifically includes the following steps: Step S210: For the ideal system model, construct an asynchronous DoS attack model at the network layer:

[0079] in, for The time-varying attack model corresponding to each moment satisfies , For the set of all attack models, This represents the total number of attack models. For the edge exist A collection of periods during which the system suffered DoS attacks; Build an attack model The adjacency matrix of the attacked system model:

[0080] in, Attack model at the current moment Below Channel communication weight, if The channel is under attack, i.e. ,but ,like Channel security, i.e. Then the link weight remains unchanged, that is , Initial topology under no-attack conditions In Channel communication weights; Step S220: Constructing an attack model The communication link matrix of the attacked system model is represented by a Laplace matrix:

[0081] in, representing the leader-to-follower unidirectional communication under the attack model representing the communication links between followers under the attack model , other elements , ; Step S230, when constructing the asynchronous DoS attack model of the network layer, limit the attack duration, the expression is:

[0082] wherein, represents the time starting point, represents the time parameter, is the edge set of time periods within which the follower suffers DoS attack, is a positive scalar describing the diversity of the attacker, is the attack intensity parameter; Step S240, when constructing the asynchronous DoS attack model of the network layer, limit the attack frequency, the expression is: wherein,

[0083] is the number of times of DoS attack within is a parameter describing the behavior of the attacker, are the equivalent decay rates when the edge suffers DoS attack and normal communication respectively, and are optional parameters, is the maximum attack model switching rate, wherein , represents the eigenvalue; Step S250, construct the dynamics model of the follower under asynchronous DoS attack: wherein, is the actual state of the

[0084] th follower under network attack, is the actual state at the corresponding time is the control input dynamically adjusted with the attack model ; Step S260, construct the dynamics model of the leader under unknown FDI attack signal injection: ​​​​​

[0085] in, The actual state of the leader under an FDI attack. For the corresponding time The actual state under the following conditions Inject a signal into an unknown bounded FDI, satisfying .

[0086] In this embodiment, in the constructed asynchronous DoS attack model, yes The current set of attack links at any given time represents the time-sharing characteristics of asynchronous attacks. All possible combinations of attack links are included, covering all possible attack strategies employed by the attacker, ensuring the model can handle scenarios where attackers flexibly adjust attack links in urban warfare. The set of attack time periods represents all time intervals during which a particular edge suffers a DoS attack throughout the entire runtime, serving as the basis for calculating subsequent attack duration and frequency limits. Specifically, by statistically analyzing the length and intervals of the attack time period set, the sustained intensity and density of the attack can be quantified, preventing the attack model from being unconstrained. Without constraints, attacks may continuously interrupt links, leading to complete system paralysis and rendering defense meaningless. The attacked adjacency matrix... This indicates that the link state determines the weight value. Attack model at the current moment Below Channel communication weight, if The channel is under attack, i.e. ,but ,like Channel security, i.e. Then the link weight remains unchanged, that is , Initial topology under no-attack conditions In The channel communication weights are set to reflect the communication disruption effect of a DoS attack. The communication link matrix of the attacked system model is consistent with the form of the communication link matrix of the ideal system model, but the element values ​​change due to the attack.

[0087] After building the asynchronous DoS attack model, the attack duration and attack frequency of the asynchronous DoS attack need to be limited. If the attack duration is not limited, the attacker may continuously attack the critical link, such as the link between the leader and the core follower, causing the system to be unable to recover communication. This constraint ensures that the attack has a gap and the defense has a time window, which conforms to the actual situation that the attacker's resources are limited and cannot attack continuously in the city confrontation. Similarly, high-frequency attacks will cause the system to frequently switch the communication topology, and the traditional controller cannot adjust in time. The constraint of attack frequency ensures that the attack frequency is within the response range of the system, providing feasibility for the dynamic adjustment of the subsequent resilient security controller, because the controller needs to adjust the input based on the attack model. If the frequency is too high, it will cause control lag.

[0088] Based on the asynchronous DoS attack model, the dynamics model of the follower under attack is built. The control input of the follower under attack is changed from to , Dynamic adjustment means that the control input will be adjusted in real time according to the current attack model, for example, when a certain link is attacked, it will be adjusted to compensate for the missing information, which embodies the resilience characteristic. In addition, the state is no longer equal to the ideal state . Attack causes interruption of information interaction, and deviation occurs between the two. The model needs to retain the nonlinear function to ensure that it can still reflect the influence of environmental disturbance on the state, avoiding model distortion caused by only considering attack and ignoring environmental disturbance.

[0089] For unknown FDI attack signal injection, the leader's dynamics model adds an term to the ideal model, which is an unknown bounded FDI injection signal. The reason for using an unknown bounded FDI injection signal is that complete unknown will cause the defense to be unable to design, and unbounded will cause the model to diverge. This constraint not only conforms to the actual situation that the maximum error of the leader's sensor can be measured, but also provides a design basis for the subsequent FDI compensation gain. At the same time, the FDI attack signal is only injected into the leader, that is, the term is added to the leader model rather than the follower, because the state of the leader is the expected tracking target of all followers. Tampering with the state of the leader will cause tracking errors of all followers, and the attack will have the largest impact range, which conforms to the attacker's goal of maximizing damage with the least cost.

[0090] Step S300, based on the attacked system model, a distributed resilient security estimator with compensation mechanism is constructed, and for each follower in the unmanned platform cluster of the attacked system model, the attack influence is compensated and the expected position is estimated based on the distributed resilient security estimator, wherein the follower completes the calculation of the expected position based on the kinematic state and local estimated state information.

[0091] In this embodiment, a distributed resilient security estimator with a compensation mechanism is specifically constructed. This resilient security estimator differs from centralized estimation that relies on a central node for computation. Each follower estimates its desired position based solely on its own kinematic state and information from its directly communicating neighbors, without requiring global information exchange. This design aligns with the requirement in urban warfare that link interruptions due to partial node failures do not affect the overall system. This is because centralized estimation completely fails if a centralized node is attacked; distributed systems avoid this problem. Furthermore, the resilient estimator can dynamically adapt to attack changes. For example, during a DoS attack link switch, it can quickly adjust its compensation strategy. Security refers to offsetting the attack's impact through a built-in compensation mechanism, rather than passively enduring the attack. The goal is to ensure that the estimated result after an attack still approximates the leader's true desired position, providing a reliable target benchmark for subsequent controllers. The compensation mechanism of this resilient security estimator is the core of its defense, employing layered compensation logic designed to address the dual threats of cyber-physical hybrid attacks. Specifically, for asynchronous DoS attacks at the network layer (i.e., information loss due to link interruption), compensation is achieved by adjusting the communication weight and the ratio of neighbor information fusion. For unknown FDI attacks at the physical layer (i.e., the leader's state is tampered with), compensation is achieved through attack signal boundary estimation. The two compensation methods work in parallel to ensure effective estimation under both single and combined attacks, avoiding estimation failure due to omission of attack types.

[0092] Furthermore, the estimated desired position refers to the leader's non-attack state that the followers need to track. However, due to the attack, the leader's actual state has been tampered with by the FDI attack. Therefore, the core task of the estimator is to reconstruct an approximate value of the leader's non-attack state from the tampered leader state and the interrupted local estimated state information. This estimate directly determines the control accuracy of the subsequent controller. If the estimation deviation is too large, the followers will track the wrong target, leading to cluster coordination failure.

[0093] In one implementation, the step of constructing a distributed resilient security estimator with a compensation mechanism based on the attacked system model, and compensating for the attack impact and estimating the desired location for each follower in the unmanned platform cluster of the attacked system model based on the distributed resilient security estimator, specifically includes the following steps: Step S310: Based on the attacked system model, construct a distributed resilient security estimator with a compensation mechanism, expressed as:

[0094]

[0095] in, For the first The estimated state of each estimator, i.e., the estimated desired position. It is a local estimation error. is a nonlinear function satisfying

[0096] where and are DoS attack compensation gain constant and FDI attack compensation gain constant, respectively, is feedback gain matrix, where is a given symmetric positive definite matrix, is Lyapunov matrix satisfying

[0097] where is Lipschitz matrix corresponding to nonlinear function is optional parameter, , , , is attack decay rate corresponding to attack model .

[0098] In this embodiment, estimator state evolution term is exactly identical to leader ideal model . Self-evolution law of leader state is simulated, nonlinear disturbance consistent with leader is introduced, for example, gust impact on leader and estimator is consistent. By replicating the basic dynamics of the leader, the evolution trend of is consistent with , which lays the foundation for subsequent attack bias compensation. On this basis, the estimator is provided with DoS attack compensation term , and FDI attack compensation term . is DoS attack gain, the more frequent the attack and the more link interruption, the greater is. is feedback gain matrix, the product of the two ensures that can amplify error signal and enhance compensation strength. is local estimation error, reflecting the deviation of current estimated value from the real desired position, and the negative sign indicates reverse compensation. When increases due to DoS attack, the compensation term output increases, pushing towards the real desired position, offsetting the impact of information loss caused by link interruption. For FDI attack, by setting nonlinear function , it is ensured that the compensation direction is accurate and along the direction of error reduction.

[0099] The formula defines the first part of the quantification of the estimated deviation between the followers, and the second part of the quantification of the deviation between the follower and the leader under attack state. The overall formula is a comprehensive quantification of the local information deviation, which provides an accurate attack impact signal for the compensation term and avoids blind compensation. On this basis, constraints are also performed on The core of the constraint is to ensure the stability of the estimator, and finally realize the convergence of the estimation error.

[0100] In specific implementation, the estimator is constructed in accordance with the three steps of parameter calibration, stability verification, and attack test. First, the and are determined according to the platform type, and then the and are determined through attack intensity test. Thereafter, the Lyapunov matrix constraint formula is substituted, and the satisfying the condition is solved and the stability is verified. Finally, the test is performed in the city confrontation simulation scene to ensure that the deviation meets the accuracy requirements of the cluster cooperation.

[0101] Step S400, based on the expected position of the follower, a distributed resilient safety controller with compensation mechanism is constructed, and the follower is controlled using the distributed resilient safety controller, so that the leader and the follower of the unmanned platform cluster are safely cooperated.

[0102] In this embodiment, the same as the distributed resilient safety estimator with compensation mechanism, the distributed resilient safety controller with compensation mechanism is constructed, and each follower only designs the control input based on the expected position estimated by itself, the actual state and the local information of the direct communication neighbor, without relying on the centralized control center, which is suitable for the scene of dispersed cluster nodes and easily interrupted communication links in the city confrontation. The leader and the follower of the unmanned platform cluster are safely cooperated, which is specifically manifested as state cooperation and dynamic stability. The state cooperation is expressed as the deviation of the state after control of all followers from the ideal state converging to a set value, and the dynamic stability is expressed as no overshoot or overshoot less than a set value when the attack is switched, which meets the safety requirements.

[0103] In one implementation mode, the distributed resilient safety controller with compensation mechanism is constructed based on the expected position of the follower, and the follower is controlled using the distributed resilient safety controller, so that the leader and the follower of the unmanned platform cluster are safely cooperated, which specifically includes the following steps: Step S410, the distributed resilient safety controller with compensation mechanism is constructed based on the expected position of the follower, which is expressed as:

[0104] Wherein, is the first a control input of the follower for controlling the follower, for estimating the tracking error, , , is a nonlinear function satisfying:

[0105] wherein, is a control gain constant, is a compensation gain constant, is a feedback gain matrix, wherein is a given symmetric positive definite matrix, is a Lyapunov matrix satisfying:

[0106] wherein, is a Lipschitz matrix corresponding to the nonlinear function is an optional parameter, , , is a damping rate.

[0107] In the embodiment, the constructed controller is provided with a basic dynamics compensation term which is used to offset the dynamics difference between the follower and the leader, ensure the basic movement trend of the follower consistent with the leader, and introduce a nonlinear disturbance consistent with the estimator and the leader, so as to ensure that the controller can adapt to non-ideal factors in the actual environment. , , There are differences between different types of followers, for example, the coefficients of the associated nonlinear disturbance and the state of the unmanned aerial vehicle follower are greatly affected by the wind, and the values are larger than those of the unmanned vehicle follower. The corresponding also needs to be adjusted to ensure that the controllers of different platforms can meet the stability constraints to meet the target of heterogeneous nonlinearity.

[0108] In specific implementation, first, then adjust through the tracking error convergence speed requirement, and finally solve the Lyapunov matrix . Thereafter, the mixed attack is substituted to verify that the controller output and the tracking error meet the real-time and security requirements of urban confrontation.

[0109] In an implementation manner, the defense control method further includes the following steps: Step S510, for the distributed elastic security estimator, a Lyapunov function is constructed based on the estimation error, for evaluating the convergence of the estimation error of the distributed elastic security estimator, expressed as:

[0110] in, , Representing the Kronecker product, the distributed resilient security estimator can achieve the decay of the Lyapunov function, i.e. ; Among them, the decay rate of the Lyapunov function The following conditions must be met:

[0111]

[0112]

[0113] in, For attack strength parameters, and When the sides are respectively The equivalent attenuation rate during a DoS attack and during normal communication; Step S520: Based on the attenuation condition and attack behavior, obtain the convergence of the estimation error of the distributed resilient security estimator. ,Right now The estimation error asymptotically converges. Step S610: For the distributed resilient safety controller, construct a Lyapunov function based on the tracking error to evaluate the convergence of the tracking error of the distributed resilient safety controller, expressed as:

[0114] in, For the first Tracking error of a follower unmanned platform express In time transpose below; Step S620: Based on the control input, obtain the convergence of the tracking error of the distributed resilient safety controller. ,Right now The tracking error asymptotically converges, indicating the state of the unmanned platform follower. Able to track the leader's status .

[0115] In this embodiment, for the distributed resilient security estimator, a Lyapunov function is constructed based on the estimation error. First, the local estimation error set of all followers is defined. This set serves as a quantification of the global estimation error, avoiding the omission of global collaboration caused by analyzing only the error of a single follower. Subsequently, through... Cronbach's alpha, positive definite weight of single platform extended to global, ensure that each follower error is given the same positive definite weight, both maintain distributed characteristics, not dependent on centralized weight distribution, and ensure the positive definiteness of global function , consistent with the premise of Lyapunov stability analysis. Through the constraint condition of decay rate, ensure the sum of global communication link attenuation is negative, avoid too strong attenuation caused by attack, and clear that attack will lead to channel attenuation enhancement, in line with the actual scene of attack deteriorating communication quality in urban confrontation. The derivation of the convergence proves the theoretical effectiveness of the estimator. Under the above attack constraints of time length and frequency limit, the estimation error will gradually converge to 0, ensuring that the expected position estimate value can accurately approximate the real state of the leader, providing a reliable target benchmark for the subsequent controller, and avoiding control failure caused by estimation deviation.

[0116] Similarly, for the distributed resilient security controller, when constructing the Lyapunov function based on the tracking error, first define the follower tracking error , the error represents the final coordination error, directly reflecting whether the cluster achieves safe coordination. Due to the heterogeneous characteristics of the unmanned cluster, an independent for each follower needs to be designed, and specific constraints need to be met to ensure that the error of each follower can be attenuated, avoiding convergence failure caused by heterogeneous parameters for some followers. The derivation of the convergence proves the final coordination effect of the controller, that is, on the basis of accurate estimation by the estimator, the controller can further eliminate the estimation residual error and attack residual interference, so that the states of all followers are completely synchronized with the leader. For example, the spacing error between the unmanned aerial vehicle and the unmanned vehicle in urban defense converges to within the expected effect, meeting the requirements of coordination tasks.

[0117] In specific implementation, first, the Lyapunov function of the distributed resilient security estimator ensures the accuracy of the estimator output, providing a reliable target for the controller. Then, the Lyapunov function of the distributed resilient security controller ensures that the controller can make the follower track the estimated state of the leader and eventually approach the ideal state. Both of them together realize safe coordination under information-physical hybrid attack.

[0118] In summary, under the technical solutions of the above embodiments, an information-physical hybrid attack model is constructed to simulate the composite security threat situation faced by the network layer and the physical layer, and a layered compensation mechanism is designed to resist denial of service attacks and false data injection attacks for a heterogeneous nonlinear large-scale unmanned cluster system model, a distributed resilient security estimation method and a security cooperative control framework based on estimation compensation are proposed, which effectively compensates for the security threats caused by network layer and physical layer cooperative attacks, accurately reconstructs the leader's information and realizes safe cooperative tracking in the presence of multiple source external environmental disturbances and information-physical hybrid attacks. At the same time, the equivalent channel attenuation rate is introduced, and the attenuation condition is analyzed under the condition that each communication link is attacked independently, which effectively deals with the complexity and diversity of network attacks in actual situations.

[0119] As shown in Figure 2 The embodiment of the present application provides a hybrid attack defense control system for heterogeneous clusters in urban confrontation environment, which comprises: an ideal system model construction module 10, an information-physical hybrid attack model construction module 20, an elastic security estimator construction module 30, and an elastic security controller construction module 40.

[0120] Specifically, the ideal system model construction module 10 is configured to construct an ideal system model of a UAV cluster, wherein the UAV cluster includes several different types of UAVs, one of which is a leader and the rest are followers, the dynamic state of the UAVs changes nonlinearly, the UAVs communicate through a topological graph, and the communication between any two UAVs is directional; the information-physical hybrid attack model construction module 20 is configured to construct an information-physical hybrid attack model based on the ideal system model, simulate the attack behavior of an attacker on the ideal system using the information-physical hybrid attack model, and obtain a corresponding attacked system model of the UAV cluster, wherein the attack behavior includes an asynchronous DoS attack at the network layer and an unknown FDI attack signal injection at the physical layer, the asynchronous DoS attack is an independent attack by the attacker on different communication links of the UAV cluster at different time periods, and the unknown FDI attack signal injection is an unknown FDI attack signal injected by the attacker into the leader; the distributed resilient security estimator construction module 30 is configured to construct a distributed resilient security estimator with a compensation mechanism based on the attacked system model, and for each follower in the UAV cluster of the attacked system model, compensate for the attack effect and estimate the desired position based on the distributed resilient security estimator, wherein the follower completes the calculation of the desired position based on its own kinematic state and local estimation state information; and the distributed resilient security controller construction module 40 is configured to construct a distributed resilient security controller with a compensation mechanism based on the desired position of the follower, and control the follower using the distributed resilient security controller, so that the leader and the follower of the UAV cluster are safely coordinated.

[0121] Based on the above embodiment, the application further provides a terminal device, and a principle block diagram thereof can be as shown in the figure. Figure 3 The terminal device includes a processor, a memory, a network interface, a display screen, and a temperature sensor connected through a system bus. The processor of the terminal device is configured to provide computing and control capabilities. The memory of the terminal device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operating system and the computer program in the non-volatile storage medium to run. The network interface of the terminal device is configured to communicate with external terminals through network connection. The computer program is executed by the processor to implement a hybrid attack defense control method for a heterogeneous cluster in a city confrontation environment. The display screen of the terminal device can be a liquid crystal display screen or an electronic ink display screen. The temperature sensor of the terminal device is pre-set in the terminal device and is configured to detect the running temperature of the internal device.

[0122] Those skilled in the art can understand that, Figure 3The principle block diagram shown in the figure is only a block diagram of part of the structure related to the present application, and does not constitute a limitation on the terminal device to which the present application is applied. The specific terminal device can include more or fewer components than those shown in the figure, or combine certain components, or have a different component arrangement.

[0123] In one embodiment, a terminal device is provided, comprising a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by one or more processors, the one or more programs comprising instructions for: calculating prediction uncertainty of all unknown points based on geographical optimal similarity between sample points and unknown points; constructing a double-objective function, the double-objective function comprising a first sub-objective function, a second sub-objective function, and a weight parameter, wherein the first sub-objective function is used to reduce unknown points with high prediction uncertainty, the second sub-objective function is used to reduce prediction uncertainty of the overall region, the prediction uncertainty of the overall region is composed of prediction uncertainty of all unknown points, and the weight parameter is used to regulate priority of the first sub-objective function and the second sub-objective function; selecting unknown points with prediction uncertainty higher than a prediction uncertainty threshold for supplementary sampling, aiming at minimizing the double-objective function; in the process of supplementary sampling, adaptively adjusting the weight parameter of the double-objective function and the prediction uncertainty threshold, wherein the prediction uncertainty threshold is lowered as the prediction uncertainty of the overall region decreases, and the priority of the first sub-objective function is lowered as the proportion of the number of unknown points with high prediction uncertainty decreases.

[0124] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer readable storage medium, and when the computer program is executed, the processes of the above-mentioned embodiments of the methods can be included. Any reference to memory, storage, database or other medium used in the embodiments provided by the present application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration but not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0125] The technical features of the above embodiments can be combined in any way. In order to make the description simple, all possible combinations of the technical features in the above embodiments are not described, but as long as the combination of the technical features does not exist, it should be considered as the scope of the present application.

[0126] The above embodiments only express several implementation manners of the present application, and the description is more specific and detailed, but it should not be understood as a limitation on the scope of the patent of the present application. It should be pointed out that for ordinary skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are all within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the appended claims.

Claims

1. A method for hybrid attack defense control of a heterogeneous cluster in a city-oriented adversarial environment, characterized in that, The method comprises: constructing an ideal system model of a UAV cluster, wherein the UAV cluster comprises UAVs of different types, one of which is a leader and the others are followers, the dynamic state of the UAVs changes nonlinearly, the UAVs communicate through a topological graph, and the communication between any two UAVs is directional; based on the ideal system model, constructing an information-physical hybrid attack model, and using the information-physical hybrid attack model to simulate the attack behavior of an attacker on the ideal system to obtain an attacked system model corresponding to the UAV cluster, wherein the attack behavior comprises an asynchronous DoS attack on the network layer and unknown FDI attack signal injection on the physical layer, the asynchronous DoS attack is an independent attack by the attacker on different communication links of the UAV cluster in different time periods, and the unknown FDI attack signal injection is the injection of an unknown FDI attack signal into the leader by the attacker; based on the attacked system model, constructing a distributed resilient safety estimator with a compensation mechanism, and for each follower in the UAV cluster of the attacked system model, compensating for the attack effect and estimating the expected position based on the distributed resilient safety estimator, wherein the follower completes the calculation of the expected position based on the kinematic state and the local estimation state information of the follower; based on the expected position of the follower, constructing a distributed resilient safety controller with a compensation mechanism, and using the distributed resilient safety controller to control the follower, so that the leader and the follower of the UAV cluster are safely coordinated.

2. The hybrid attack defense control method for the heterogeneous cluster in the urban confrontation environment according to claim 1, characterized in that, The method comprises: constructing a system topological graph of the ideal system model; Wherein, the topological graph is a directed graph, is a node set composed of unmanned platforms, is a node representing a leader, when , is a node representing the th follower, is an edge set between nodes, and the initial topological has a directed spanning tree with the leader as a root node; Constructing system topology The corresponding communication link matrix, expressed in terms of the Laplacian matrix: wherein, denotes leader-to-leader communication without self-loop, denotes follower-to-leader communication, denotes leader-to-follower unidirectional communication, denotes communication links between followers, denotes the set of real numbers, the communication links matrix satisfies and denotes that the communication between any two unmanned platforms has directionality, denotes the transpose operation; based on the system topological graph and the corresponding communication link matrix of the ideal system model, constructing the ideal system model of the follower and the ideal system model of the leader in a secure network environment.

3. The hybrid attack defense control method for the heterogeneous cluster in the urban confrontation environment according to claim 2, characterized in that, The method comprises: Constructing An ideal system model of a follower: wherein, and respectively represent the state and control input of the i-th follower in a secure network environment, represents the dimension of the i-th follower state represents a time variable, represents the derivative of the i-th follower state, used to describe the change rule of the state of the unmanned platform over time, and respectively represent the follower system state matrix with dimensions and represents a Lipschitz continuous nonlinear function, is the output dimension of the Lipschitz continuous nonlinear function;​​​​​ constructing the ideal system model of the leader; wherein, is the ideal state of the leader, i.e. the desired state that the follower needs to track, denotes the leader state is the dimension of the leader state; denotes the derivative of the leader state, and denote the leader system state matrix of dimension and is the dimension of the leader state. wherein the non-linear function satisfies the Lipchitz condition, i.e. there exists a non-negative constant wherein such that for any vector satisfies: wherein is the i-th component of the vector function is the i-th component of the vector is the i-th component of the vector is the i-th component of the vector is the i-th component of the vector is the i-th component of the vector 4. The hybrid attack defense control method for the heterogeneous cluster in the city-oriented adversarial environment according to claim 3, characterized in that, based on the ideal system model, constructing an information-physical hybrid attack model, and using the information-physical hybrid attack model to simulate the attack behavior of an attacker on the ideal system to obtain an attacked system model corresponding to the UAV cluster, wherein the attack behavior comprises an asynchronous DoS attack on the network layer and unknown FDI attack signal injection on the physical layer, the asynchronous DoS attack is an independent attack by the attacker on different communication links of the UAV cluster in different time periods, and the unknown FDI attack signal injection is the injection of an unknown FDI attack signal into the leader by the attacker; constructing an asynchronous DoS attack model on the network layer for the ideal system model; wherein, is the time-varying attack model corresponding to the time instant t, satisfies , is the set of all attack models, is the total number of attack models, is the edge the set of time instants within suffering a DoS attack. Constructing an attack model adjacency matrix of the attacked system model under wherein, is the channel communication weight under the current time attack model if the channel is under attack, i.e. , if the channel is safe, i.e. the link weight remains unchanged, i.e. , is the initial topology under no attack channel communication weight;​​​​​ Constructing attack model The communication link matrix of the attacked system model under the attack model is represented by a Laplacian matrix: wherein, represents the leader-to-follower one-way communication under the attack model , represents the communication link between followers under the attack model , , other elements , ; when constructing the asynchronous DoS attack model on the network layer, the attack duration is limited, and the expression is: wherein, is an edge In a set of time periods during which the node is subject to DoS attacks, is a positive scalar describing the diversity of the attackers, is an attack strength parameter; when constructing the asynchronous DoS attack model on the network layer, the attack frequency is limited, and the expression is: wherein, denotes a time start point, denotes a time parameter, is the number of times an internal DoS attack occurs, is a parameter describing the behavior of the attacker, are the equivalent attenuation rates when the edge is subjected to a DoS attack and when it is communicating normally, respectively, and is an optional parameter, is the maximum attack model switching rate, wherein , denotes an eigenvalue; constructing a dynamic model of the follower under the asynchronous DoS attack; wherein, is the actual state of the th follower under cyber attack, is the actual state of the th follower at the corresponding time, is the control input adjusted dynamically with the attack model, ​ constructing a dynamic model of the leader under the unknown FDI attack signal injection; where is the actual state of the leader under FDI attack, is the actual state of the corresponding time is the actual state of the corresponding time is an unknown bounded FDI injection signal satisfying .

5. The hybrid attack defense control method for the heterogeneous cluster in the city-oriented adversarial environment according to claim 4, characterized in that, the method comprises: constructing a distributed resilient safety estimator with compensation mechanism based on the attacked system model, denoted as: where is the estimate of the state of the th estimator, i.e. the estimated expected position, is the local estimation error, is a nonlinear function satisfying: wherein and are a DoS attack compensation gain constant and a FDI attack compensation gain constant, respectively, is a feedback gain matrix, wherein is a given symmetric positive definite matrix, is a Lyapunov matrix satisfying: wherein, is a Lipschitz matrix corresponding to a non-linear function , is an optional parameter, , , is an attack decay rate corresponding to an attack model .

6. The hybrid attack defense control method for the heterogeneous cluster in the city-oriented adversarial environment according to claim 5, characterized in that, constructing a distributed resilient safety controller with compensation mechanism based on the expected position of the follower, and using the distributed resilient safety controller to control the follower, so that the leader and the follower of the unmanned platform cluster are safely coordinated, including: constructing a distributed resilient safety controller with compensation mechanism based on the expected position of the follower, denoted as: wherein is the control input of the th follower for controlling the follower, is an estimate of the tracking error, , , is a nonlinear function satisfying: wherein is a control gain constant, is a compensation gain constant, is a feedback gain matrix, wherein is a given symmetric positive definite matrix, is a Lyapunov matrix, satisfying: wherein, is a Lipschitz matrix corresponding to a non-linear function , is an optional parameter, , is a decay rate.

7. The method of claim 6, wherein the method further comprises: The defense control method further includes: constructing a Lyapunov function based on the estimation error for the distributed resilient safety estimator, for evaluating the convergence of the estimation error of the distributed resilient safety estimator, denoted as: wherein, , denotes the Kronecker product, the distributed resilient safety estimator can achieve a Lyapunov function decay, i.e. ; where the decay rate of the Lyapunov function satisfies the following condition: wherein, is an attack strength parameter, and are the equivalent attenuation rates when the edge is subjected to a DoS attack and when communicating normally, respectively. Based on the attenuation condition and the attack behavior, convergence of an estimation error of the distributed resilient security estimator is obtained That is , the estimation error asymptotically converges constructing a Lyapunov function based on the tracking error for the distributed resilient safety controller, for evaluating the convergence of the tracking error of the distributed resilient safety controller, denoted as: wherein, is the tracking error for the nth follower unmanned platform, represents the transpose of a matrix at time t.​ Based on the control input, convergence of tracking error of the distributed elastic safety controller is obtained That is Tracking error asymptotically converges, indicating that the state of the follower of the unmanned platform follows the leader Can track the leader state .

8. A hybrid attack defense control system for a heterogeneous cluster in a city-oriented adversarial environment, characterized in that, The system includes: an ideal system model construction module, configured to construct an ideal system model of an unmanned platform cluster, wherein the unmanned platform cluster includes several unmanned platforms of different types, one of which is a leader and the rest are followers, the dynamic state change of the unmanned platforms is nonlinear, the unmanned platforms communicate through a topology graph, and the communication between any two unmanned platforms has directionality; an information-physical hybrid attack model construction module, configured to construct an information-physical hybrid attack model based on the ideal system model, and simulate the attack behavior of an attacker on the ideal system using the information-physical hybrid attack model to obtain an attacked system model corresponding to the unmanned platform cluster, wherein the attack behavior includes asynchronous DoS attack at the network layer and unknown FDI attack signal injection at the physical layer, the asynchronous DoS attack is an independent attack by the attacker on different communication links of the unmanned platform cluster at different time periods, and the unknown FDI attack signal injection is an unknown FDI attack signal injected by the attacker into the leader; a resilient safety estimator construction module, configured to construct a distributed resilient safety estimator with compensation mechanism based on the attacked system model, and for each follower in the unmanned platform cluster of the attacked system model, to compensate for the attack effect and estimate the expected position based on the distributed resilient safety estimator, wherein the follower completes the calculation of the expected position based on its kinematic state and local estimation state information; a resilient safety controller construction module, configured to construct a distributed resilient safety controller with compensation mechanism based on the expected position of the follower, and to use the distributed resilient safety controller to control the follower, so that the leader and the follower of the unmanned platform cluster are safely coordinated.

9. A terminal device, comprising: The terminal device includes a memory, a processor, and a hybrid attack defense control program for a heterogeneous cluster in a city confrontation environment stored in the memory and executable on the processor. When the processor executes the hybrid attack defense control program for a heterogeneous cluster in a city confrontation environment, the steps of the hybrid attack defense control method for a heterogeneous cluster in a city confrontation environment as claimed in any one of claims 1-7 are implemented.

10. A computer-readable storage medium, characterized in that, The computer readable storage medium stores a hybrid attack defense control program for a heterogeneous cluster in a city confrontation environment, and the hybrid attack defense control program for the heterogeneous cluster in the city confrontation environment is executed by the processor to implement the steps of the hybrid attack defense control method for the heterogeneous cluster in the city confrontation environment according to any one of claims 1-7.

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