A hybrid attack defense control method and system for a heterogeneous cluster in a city confrontation environment, a terminal device, and a medium

Abstract

The application discloses a kind of mixed attack defense control method, system, terminal equipment and medium of heterogeneous cluster under city confrontation environment, it is related to unmanned platform cluster control technical field, the method includes: constructing the ideal system model of unmanned platform cluster containing a leader and several followers, and constructing information physical hybrid attack model based on the model;Attack model is used to simulate the attack behavior of attacker to ideal system, and the attacked system model is obtained;Based on the attacked system model, a distributed resilient security estimator with compensation mechanism is constructed, and the expected position of each follower is estimated by compensating the attack influence;Based on the expected position of the follower, a distributed resilient security controller with compensation mechanism is constructed, and the follower is controlled.The application designs estimator and controller, offsets attack interference and generates control input, to ensure the safety of heterogeneous nonlinear unmanned cluster in information physical hybrid attack.

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:

[0008] 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:

[0009] 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 topological graph, and the communication between any two unmanned platforms has directionality;

[0010] 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 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;

[0011] 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 kinematic state and local estimation state information;

[0012] 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 are safely coordinated.

[0013] In an implementation manner, the constructing of the ideal system model of the cluster of unmanned platforms comprises:

[0014] constructing a system topological graph of the ideal system model:

[0015]

[0016] wherein the topological 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 th follower, The initial topology is the set of edges between nodes. It has a directed spanning tree with the leader as the root node;

[0017] Build system topology diagram The corresponding communication link matrix is ​​represented by a Laplace matrix:

[0018]

[0019] 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;

[0020] 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.

[0021] 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:

[0022] Build An ideal system model with one follower:

[0023]

[0024] 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;

[0025] Constructing an ideal system model for leaders:

[0026]

[0027] 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;

[0028] 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:

[0029]

[0030] in, It is a vector function The One portion, They are vectors The Each component.

[0031] 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:

[0032] For the aforementioned ideal system model, an asynchronous DoS attack model for the network layer is constructed:

[0033]

[0034] 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;

[0035] Construct the adjacency matrix of the attacked system model under the attack model

[0036]

[0037] where, is the channel communication weight under the current time attack model If the channel is attacked, i.e. , then If the channel is safe, i.e. , the link weight remains unchanged, i.e. , is the initial topology under the non-attack case channel communication weight; Construct the communication link matrix of the attacked system model under the attack model

[0038]

[0039]

[0040] where, represents the one-way communication from the leader to the follower under the attack model represents the communication link between the followers under the attack model The diagonal elements of the Laplacian matrix are , and the other elements are , ;

[0041] When constructing the asynchronous DoS attack model of the network layer, the attack duration is limited, and the expression is:

[0042]

[0043] where, represents the time starting point, represents the time parameter, is the set of time periods in which the edge is subjected to DoS attack, is a positive scalar describing the diversity of attackers, is the attack strength parameter; When constructing the asynchronous DoS attack model of the network layer, the attack frequency is limited, and the expression is:

[0044]

[0045] ​​​​​​

[0046] where, is the number of times the internal DoS attack occurs, is a parameter describing the attacker behavior, are the equivalent attenuation rates when the edge is subjected to DoS attack and normal communication, respectively, and is an optional parameter, is the maximum attack model switching rate, where , denotes the eigenvalue;

[0047] The follower's dynamics model under asynchronous DoS attack is constructed as follows:

[0048]

[0049] where, is the actual state of the th follower under network attack, is the actual state at the corresponding time , and is the control input dynamically adjusted with the attack model .

[0050] The leader's dynamics model under unknown FDI attack signal injection is constructed as follows:

[0051]

[0052] where, is the actual state of the leader under FDI attack, is the actual state at the corresponding time , and is an unknown bounded FDI injection signal satisfying .

[0053] In an implementation manner, based on the attacked system model, a distributed resilient safety estimator with a compensation mechanism is constructed, and for each follower in the cluster of unmanned platforms of the attacked system model, the attack influence is compensated and the expected position is estimated based on the distributed resilient safety estimator with the compensation mechanism, including:

[0054] Based on the attacked system model, a distributed resilient safety estimator with a compensation mechanism is constructed, denoted as:

[0055]

[0056]

[0057] wherein, is the estimation state of the th estimator, i.e., the estimated expected position, is the local estimation error, is a nonlinear function satisfying:

[0058]

[0059] wherein, and are the DoS attack compensation gain constant and the FDI attack compensation gain constant, respectively, is the feedback gain matrix, where is a given symmetric positive definite matrix, is a Lyapunov matrix satisfying:

[0060]

[0061] wherein, is a Lipschitz matrix corresponding to the nonlinear function is an optional parameter, , , , is an attack decay rate corresponding to the attack model .

[0062] In one implementation, the follower-based expected position, 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, including:

[0063] The follower-based expected position, a distributed resilient safety controller with compensation mechanism is constructed, and is expressed as:

[0064]

[0065] wherein, is the control input of the th follower for controlling the follower, is the estimation tracking error, , , is a nonlinear function satisfying:

[0066]

[0067] wherein, is a control gain constant, is a compensation gain constant, is the feedback gain matrix, where is a given symmetric positive definite matrix, is a Lyapunov matrix satisfying:

[0068]

[0069] where, is a Lipschitz matrix corresponding to the nonlinear function , is an optional parameter, , is a decay rate.

[0070] In an implementation, the defense control method further comprises:

[0071] For the distributed resilient security estimator, a Lyapunov function is constructed based on the estimation error, for evaluating the convergence of the estimation error of the distributed resilient security estimator, denoted as:

[0072]

[0073] where, , denotes the Kronecker product, and the distributed resilient security estimator can realize the decay of the Lyapunov function, that is, ;

[0074] where, the decay rate of the Lyapunov function satisfies the following conditions:

[0075]

[0076]

[0077]

[0078] where, is an attack strength parameter, and are the equivalent decay rates when the edge suffers a DoS attack and normal communication, respectively;

[0079] Based on the decay condition and the attack behavior, the convergence of the estimation error of the distributed resilient security estimator , that is, , the estimation error asymptotically converges;

[0080] 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, denoted as:

[0081]

[0082] wherein, is the tracking error of the th follower unmanned platform, denotes the transpose at time ;

[0083] Based on the control input, the convergence of the tracking error of the distributed resilient safety controller is obtained , i.e. , the tracking error asymptotically converges, indicating that the state of the follower unmanned platform can track the leader state .

[0084] 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:

[0085] An ideal system model construction module is 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 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;

[0086] An information-physical hybrid attack model construction module is 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 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 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;

[0087] A resilient safety estimator construction module is configured to construct a distributed resilient safety estimator with a 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 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;

[0088] An elastic safety controller construction module is configured to construct a distributed elastic safety controller with a compensation mechanism based on a desired position of the follower, and control the follower using the distributed elastic safety controller, so that the leader and the follower of the unmanned platform cluster are safely coordinated.

[0089] 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, the 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.

[0090] 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 the processor executes the hybrid attack defense control program for the heterogeneous cluster in the city confrontation environment, the 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.

[0091] 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

[0092] 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.

[0093] 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.

[0094] Figure 3is the internal structure principle block diagram of the terminal device provided by the embodiment of the application. DETAILED DESCRIPTION

[0095] 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.

[0096] 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 be executed in the order described. For example, some operations or steps can also be decomposed, combined or partially merged, so the actual execution order may be changed according to the actual situation.

[0097] 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.

[0098] 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.

[0099] 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.

[0100] 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.

[0101] 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 collaborative 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.

[0102] Large-scale unmanned swarm is a typical information-physical system, and each platform achieves information sharing and collaborative decision-making through a distributed network. Although this interaction architecture improves the flexibility and scalability of the system, the open task execution environment in urban confrontation scenarios also makes the unmanned swarm system face double security threats at the network and physical layers. Therefore, while ensuring the efficiency of emergency response, 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 confrontation environments. At the physical layer, false data injection attack (FDI attack) is a typical security threat. Attackers damage the integrity of data by injecting malicious signals into each unmanned platform, thereby disrupting the normal operation of the system. At the network layer, the system is often affected by denial-of-service attacks (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 attack considers 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 the actual urban confrontation environment. 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 of composite attacks at the network and physical layers, accurately simulating the security threat situation faced by large-scale unmanned swarm systems in complex urban confrontation environments.

[0103] At the same time, most existing unmanned swarm collaborative control methods linearize the actual system dynamics of unmanned platforms. Through mathematical techniques such as Taylor expansion or small perturbation methods, an approximate dynamic model is obtained near the system equilibrium point, thereby simplifying the design of the controller. However, in complex urban confrontation environments, multiple external environmental disturbances such as electromagnetic noise, building obstructions, and dynamic obstacles may cause the system to deviate from equilibrium, thereby 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 the real external disturbance model, thereby depicting more realistic system operation rules and laying a theoretical foundation for unmanned swarm collaborative defense in complex urban confrontation environments.

[0104] 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 the urban confrontation scene, 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.

[0105] The hybrid attack defense control method for heterogeneous clusters in urban confrontation environment provided by the embodiment specifically comprises the following steps as shown in the figure: Figure 1 The steps are as follows:

[0106] Step S100, an ideal system model of the unmanned platform cluster is constructed, wherein the unmanned platform cluster includes a plurality of 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 topological graph, and the communication between any two unmanned platforms has directionality.

[0107] 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 generally has 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. This leader unmanned platform is the reference for 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.

[0108] In the ideal system model of the unmanned platform cluster constructed in this embodiment, a directed topological graph is used to simulate the communication between unmanned platforms. The topology is a directed topological 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.

[0109] 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 according to the maximum speed, load capacity and other hardware parameters, and finally the directed topological 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.

[0110] In one implementation, the ideal system model of the unmanned platform cluster is constructed, specifically including the following steps:

[0111] Step S110, constructing a system topology graph of the ideal system model:

[0112]

[0113] 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;

[0114] Step S120, constructing a system topology graph corresponding to the communication link matrix, which is represented by a Laplacian matrix:

[0115]

[0116] wherein, denotes the leader's own loop-free communication, denotes the follower-to-leader communication, denotes the leader-to-follower one-way communication, denotes the communication link between followers, denotes the real set, and the communication link matrix satisfies and denotes that the communication between any two unmanned platforms has directionality, denotes the transpose processing;

[0117] Step S130, based on the system topology graph of the ideal system model and the corresponding communication link matrix, the ideal system model of the follower and the ideal system model of the leader in the secure network environment are constructed.

[0118] In this embodiment, the directed topology graph is used to depict the communication relationship between unmanned platforms. Unlike the undirected graph of two-way communication, the edge of the directed topology graph has a clear direction. For example, in the urban confrontation environment, the unmanned aerial vehicle can send signals to the unmanned ground vehicle due to the height advantage, but the unmanned ground vehicle cannot feedback to the unmanned aerial vehicle due to the building obstruction. This one-way communication relationship needs to be mathematically expressed by a directed edge. In one implementation, in the node set of the constructed system topology graph, each node uniquely corresponds to one unmanned platform, is a leader node, which can be a command unmanned aerial vehicle with global positioning capability, is a follower node, which can be an unmanned vehicle or a reconnaissance unmanned aerial vehicle performing patrol tasks, and the total number of nodes is determined according to the urban confrontation task requirements. In addition, the edge in the edge set of the system topology graph represents that the information sender node can transmit data to the information receiver node. Whether the edge exists or not depends on the communication distance, signal obstruction, electromagnetic interference and other urban environmental factors. 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 initially constructed. The directed spanning tree in the initial topology means that there is at least one directed path from the leader node to cover the follower node, which is the connectivity condition of the ideal system, used to ensure that the basic instructions of the leader can be transmitted to the cluster, avoiding that part of the followers become information islands in the initial state.

[0119] In the constructed system topology graph, the block structure of the Laplacian matrix is used to express the communication link. Specifically, in the communication link matrix, the upper left block on the diagonal line represents that the leader node has no self-loop communication, i.e., the leader does not need to send data to itself, and the state instruction of the leader is generated by the self-determination system without internal circulation transmission. The first row of the remaining blocks is a zero vector, indicating that in an ideal system, the follower cannot send a communication signal to the leader and only receives the control signal of the leader to complete the control of the follower and the leader communication block represents the strength of the one-way communication from the leader to the follower, wherein, represents the leader, represents the follower. The leader and the follower can be represented by , which represents the th follower receiving the control signal data sent by the leader, and represents 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 inter-follower communication block is used to quantify the one-way communication relationship between the followers, for example represents that the th follower can transmit information to the th follower, represents that the th follower can transmit information to the th follower, and represents 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.

[0120] After the overall system topology graph is constructed, based on the node relationship in the system topology graph, a dynamic model for expressing the state change of the leader and the follower in a safe network environment is further constructed, which is an ideal system model of the follower and an ideal system model of the leader.

[0121] 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 safe network environment, and the specific steps include the following steps:

[0122] Step S131, constructing an ideal system model of the follower:

[0123]

[0124] wherein, 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;

[0125] Step S132: Construct an ideal system model for the leader:

[0126]

[0127] 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;

[0128] 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:

[0129]

[0130] in, It is a vector function The One portion, They are vectors The Each component.

[0131] 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. The state dimension, for example, for unmanned vehicles, can be 3, which can express two-dimensional coordinates and running speed, and for unmanned aerial vehicles, the state dimension can be 6, which expresses three-dimensional coordinates, running speed, roll angle, pitch angle, and the like. These state components directly reflect the running state of the follower, and are the basis for subsequent state comparison under attack. The control input refers to the instruction signal for driving the motion of the follower in the safe environment, for example, the throttle opening of the unmanned vehicle, the steering angle, the motor speed of the unmanned aerial vehicle, and only in the ideal model, there is a pure input without attack interference, and the subsequent attacked model will adjust the input to offset the attack. The system state matrix expresses the dynamic characteristics of the follower itself, for example, the speed attenuation of the unmanned vehicle due to ground friction, and then can be used to express the attenuation coefficient. Different types of followers differ, for example, the air resistance coefficient of the unmanned aerial vehicle is different from the ground resistance coefficient of the unmanned vehicle, which reflects the heterogeneous characteristics of the unmanned platform cluster in the embodiment. Another matrix associates the control input and the state change, for example, using the elements to represent that the state component is affected by the control input, the coefficient of the speed state row of the unmanned vehicle corresponding to the throttle input is non-zero, and the like. Among them, is a nonlinear function output dimension, together with constitutes the basic dynamics framework of the follower.

[0132] Further, the nonlinear function is used to quantify non-ideal factors such as electromagnetic interference, gust resistance, and load fluctuation in the actual environment, and the Lipschitz continuity is used for constraint. Specifically, the non-negative constant limits the nonlinearity, avoids divergence of the model due to too strong nonlinearity, and ensures the designability of the subsequent attack model and defense strategy, which is consistent with the actual scene in urban confrontation. In one implementation, when constructing the ideal model of the follower, the platforms can be first grouped according to the platform type, for example, the unmanned aerial vehicle group and the unmanned vehicle group, the parameters of the platforms in the same group are similar, and the calculation amount is reduced, and then the parameters are calibrated according to the measured data of a single platform, for example, the speed attenuation rate of the unmanned vehicle on the flat road, and finally the Lipschitz condition is verified to ensure that the model can reflect the true motion law of the follower without attack.

[0133] Similarly, in the ideal system model of the leader constructed, there is no control input corresponding to the control input in the follower model, because the leader is the target benchmark of the cluster, and the state such as the task area coordinate and the cruise path is generated by the self decision system, and does not need external control instruction, so only the state self-evolution item and the nonlinear disturbance item , expresses the leader to provide global target and follower to track the architecture logic. In addition, the ideal state is the desired tracking target of all followers, such as the real-time position of the leader, that is, the rendezvous point of the follower, the dimension of which is consistent with the follower, ensuring that the state can be compared. And in the leader model, the nonlinear function shares the same set of Lipschitz matrices with the follower, ensuring consistent quantification standards for nonlinear disturbances in the cluster, avoiding tracking deviations due to differences in disturbance models between leaders and followers, and laying the foundation for unified compensation under subsequent attacks.

[0134] In specific implementation, the parameter calibration of the ideal leader model can adopt the strategy of prioritizing stability, and the rationality of the state is verified through field testing, and finally an ideal cooperative basis is formed that the leader can stably output the target and the follower can track.

[0135] Step S200, 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 an attacked system model corresponding to the unmanned platform cluster, wherein the attack behavior includes 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 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.

[0136] 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. Among them, the network layer affects information interaction by blocking communication, and the physical layer destroys dynamic stability by tampering with device state, and the superposition of the two is more in line with the actual scene of multi-dimensional destruction of the attacker in the 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, causing the cluster to be in chaos.

[0137] 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.

[0138] Unknown FDI attack signal injection refers to the injection of a fake signal by an attacker whose specific waveform and amplitude are unknown, similar to the inability to predict the details of an attack signal in a real attack. The target of this FDI attack signal is the leader, because the leader is the target benchmark of the cluster, and altering its state will cause all followers to deviate from their tracking.

[0139] 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.

[0140] 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:

[0141] Step S210: For the ideal system model, construct an asynchronous DoS attack model at the network layer:

[0142]

[0143] 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;

[0144] Build an attack model The adjacency matrix of the attacked system model:

[0145]

[0146] 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 for non-attack case Channel communication weight

[0147] Step S220, construct attack model The communication link matrix of the attacked system model under the attack model is represented by the Laplacian matrix:

[0148]

[0149] Wherein, represents the one-way communication from leader to follower under the attack model represents the communication link between followers under the attack model The diagonal elements of the Laplacian matrix are , and the other elements are , , ;

[0150] Step S230, when constructing the asynchronous DoS attack model of the network layer, limit the attack duration, and the expression is:

[0151]

[0152] Wherein, represents the starting point of time, represents the time parameter, is the edge set of time periods suffered from DoS attack within , is a positive scalar describing the diversity of attackers, is an attack intensity parameter; Step S240, when constructing the asynchronous DoS attack model of the network layer, limit the attack frequency, and the expression is:

[0153]

[0154]

[0155] Wherein, is the number of DoS attacks within , is a parameter describing the behavior of the attacker, are the equivalent attenuation rates when the edge suffered from DoS attack and normal communication respectively, and are optional parameters, is the maximum attack model switching rate, , wherein , represents the eigenvalue; ​​

[0156] Step S250: Construct a dynamic model of followers under asynchronous DoS attacks:

[0157]

[0158] in, For the first time under a network attack The actual state of a follower For the corresponding time The actual state under the following conditions As attack models Dynamically adjustable control input;

[0159] Step S260: Construct a dynamic model of the leader under unknown FDI attack signal injection:

[0160]

[0161] 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 .

[0162] 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 channel communication weight, which reflects the blocking effect of DoS attack on communication. The communication link matrix of the constructed attacked system model is consistent with the form of the communication connection matrix of the ideal system model, but the element values change due to the attack.

[0163] After constructing 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 key link, such as the link between the leader and the core follower, causing the system to fail to recover communication. This constraint ensures that the attack has a gap and the defense has a time window, which is consistent with the actual situation that the attacker's resources are limited and cannot attack continuously in urban 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. High frequency will cause control lag.

[0164] Based on the asynchronous DoS attack model, the dynamic model of the follower under attack is constructed. The control input of the follower changes 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 information interaction to be interrupted, and deviation will occur 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.

[0165] For unknown FDI attack signal injection, the leader's dynamic 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, and tampering with the state of the leader will cause tracking errors of all followers, the attack influence range is the largest, which is consistent with the attacker's goal of maximizing destruction with the least cost.

[0166] ​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 the local estimation state information.

[0167] In the embodiment, a distributed resilient security estimator with compensation mechanism is specifically constructed. The resilient security estimator is different from the centralized estimation relying on the central node calculation. Each follower completes the expected position estimation based on the kinematic state and the information of the direct communication neighbor node, without global information interaction, which meets the requirement that the link interruption does not affect the whole in the urban confrontation when part of the nodes fail. Because, if the central node is attacked, the centralized estimation will completely fail, and the use of the distributed can avoid this problem. In addition, the resilient estimator can dynamically adapt to the attack changes, for example, when the DoS attack link is switched, the compensation strategy can be quickly adjusted, and the security is compensated by the built-in compensation mechanism to offset the attack influence, rather than passively bearing the attack. The goal is to make the estimation result after the attack still close to the real expected position of the leader, so as to provide a reliable target benchmark for the subsequent controller. The compensation mechanism of the resilient security estimator is the defense core of the estimator, and a hierarchical compensation logic is designed for the double threat of information-physical hybrid attack. Specifically, for the network layer asynchronous DoS attack, that is, the information is missing due to the link interruption, the compensation is achieved by adjusting the communication weight and the neighbor information fusion ratio. And for the unknown FDI attack at the physical layer, that is, the leader state is tampered, the compensation is achieved by attack signal boundary estimation. The two compensations are effective in parallel, which ensures that effective estimation can be achieved under single attack or composite attack, and avoids estimation failure due to missing attack type.

[0168] Further, the estimated expected position refers to the leader attack-free state that the follower needs to track, but the actual state of the leader has been tampered by the FDI attack due to the attack influence. Therefore, the core task of the estimator is to reconstruct the approximate value of the leader attack-free state from the tampered leader state and the interrupted local estimation state information, which directly determines the control accuracy of the subsequent controller. If the estimation deviation is too large, the follower will track the wrong target, resulting in failure of the cluster cooperation.

[0169] In an implementation manner, the distributed resilient security estimator with compensation mechanism is constructed based on the attacked system model, 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, and the specific steps include the following steps:

[0170] Step S310, based on the attacked system model, a distributed resilient security estimator with compensation mechanism is constructed, which is represented as:

[0171]

[0172]

[0173] wherein, is the estimation state of the th estimator, i.e. the estimated expected position, is the local estimation error, is a nonlinear function satisfying:

[0174]

[0175] wherein, and are the DoS attack compensation gain constant and the FDI attack compensation gain constant, respectively, is the feedback gain matrix, wherein is a given symmetric positive definite matrix, is a Lyapunov matrix satisfying:

[0176]

[0177] wherein, is the Lipschitz matrix corresponding to the nonlinear function is an optional parameter, , , , is the attack decay rate corresponding to the attack model .

[0178] In the present embodiment, the estimator state evolution term is exactly identical to the leader ideal model . The self-evolution law of the leader state is simulated, a nonlinear disturbance identical to the leader is introduced, e.g. the effect of a gust on the leader and the estimator is identical. By replicating the underlying dynamics of the leader, the evolution trend of is identical to , laying the foundation for subsequent compensation of attack bias. On this basis, the estimator is provided with a DoS attack compensation term , and is provided with an FDI attack compensation term . is the DoS attack gain, the more frequent the attack and the more link interruption, the greater needs to be. is the feedback gain matrix, the product of the two ensures that is the local estimation error, reflecting the current estimation value deviation from the real expected position, the negative sign represents the reverse compensation. When the compensation term output increases, pushing the real expected position, offsetting the impact of information loss caused by link interruption. For FDI attacks, by setting a nonlinear function , ensure the compensation direction is accurate, along the direction of error reduction.

[0179] For the formula definition of , the first part quantifies the estimation deviation between followers, and the second part quantifies the deviation between followers and leader under attack state. The overall formula is a comprehensive quantification of local information deviation, providing an accurate attack impact signal for the compensation term, avoiding blind compensation. On this basis, the constraint is also made, the core of which is to ensure the stability of the estimator, and finally realize the convergence of the estimation error.

[0180] In specific implementation, the estimator is constructed in accordance with the three steps of parameter calibration, stability verification, and attack test. First, according to the platform type, determine and , and then determine and through attack intensity test. Thereafter, substitute into the Lyapunov matrix constraint formula, solve that meet the conditions and verify the stability. Finally, test in the city confrontation simulation scene to ensure that the deviation meets the accuracy requirements of cluster cooperation.

[0181] Step S400, based on the expected position of the follower, construct a distributed resilient security controller with compensation mechanism, and use the distributed resilient security controller to control the follower, so that the leader and follower of the unmanned platform cluster are safe and cooperative.

[0182] In this embodiment, the same as the distributed resilient security estimator with compensation mechanism, the distributed resilient security controller with compensation mechanism is constructed, and each follower only designs control input based on its own estimated expected position, actual state and local information of direct communication neighbors, without relying on centralized control center, suitable for the scene of dispersed cluster nodes and easy interruption of communication link in city confrontation. The leader and follower of the unmanned platform cluster are safe and cooperative, which is specifically manifested as state cooperation and dynamic stability. State cooperation is expressed as the deviation of the state of all followers after control from the ideal state converging to a set value, and dynamic stability is expressed as no overshoot or overshoot less than a set value when the attack switches, meeting the safety requirements.

[0183] In one implementation, the step of constructing a distributed resilient safety controller with a compensation mechanism based on the desired position of the followers, and using the distributed resilient safety controller to control the followers, enabling the leader and followers of the unmanned platform cluster to cooperate safely, specifically includes the following steps:

[0184] Step S410: The distributed resilient security controller with a compensation mechanism, based on the expected position of the followers, is constructed as follows:

[0185]

[0186] in, It is the first The control input for each follower is used to control the follower. To estimate the tracking error, , , It is a nonlinear function that satisfies:

[0187]

[0188] in, The control gain constant, To compensate for the gain constant, Here is the feedback gain matrix, where Given a symmetric positive definite matrix, Let Lyapunov be the matrix that satisfies:

[0189]

[0190] in, It corresponds to a nonlinear function The Lipschitz matrix, This is an optional parameter. , This represents the attenuation rate.

[0191] In this embodiment, the constructed controller includes a basic dynamic compensation term. This compensation term is used to offset the dynamic differences between followers and leaders, ensuring that the basic movement trends of followers are consistent with those of the leader. It also introduces nonlinear disturbances consistent with the estimator and the leader, ensuring that the controller can adapt to non-ideal factors in the real environment. Different types of followers... , , There are differences. For example, the coefficients of nonlinear disturbances and states associated with drone followers are greatly affected by gusts and therefore have larger values ​​than those of drone followers. The adjustment is also needed to ensure that the controllers of different platforms can meet the stability constraints to meet the target of heterogeneous nonlinearity.

[0192] In implementation, first, the , then the tracking error convergence speed requirement is adjusted , and finally the Lyapunov matrix is solved . Subsequently, the hybrid attack is substituted, and the controller output and tracking error are verified to meet the real-time and security requirements of urban confrontation.

[0193] In an implementation, the defense control method further includes the following steps:

[0194] Step S510, for the distributed resilient security estimator, a Lyapunov function is constructed based on the estimation error, which is used to evaluate the convergence of the estimation error of the distributed resilient security estimator, and is expressed as:

[0195]

[0196] wherein, , denotes the Kronecker product, and the distributed resilient security estimator can realize the decay of the Lyapunov function, that is, ;

[0197] wherein, the decay rate of the Lyapunov function satisfies the following condition:

[0198]

[0199]

[0200]

[0201] wherein, is an attack strength parameter, and are the equivalent decay rates when the edge suffers a DoS attack and when it communicates normally, respectively;

[0202] Step S520, based on the decay 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;

[0203] Step S610, for the distributed resilient security controller, a Lyapunov function is constructed based on the tracking error, which is used to evaluate the convergence of the tracking error of the distributed resilient security controller, and is expressed as:

[0204]

[0205] wherein, is the tracking error of the th follower unmanned platform, denotes the transpose at time ;

[0206] Step S620, based on the control input, obtaining the convergence of the tracking error of the distributed resilient safety controller , i.e. , the tracking error asymptotically converges, indicating that the state of the follower unmanned platform can track the leader state .

[0207] In this embodiment, for the distributed resilient safety estimator, a Lyapunov function is constructed based on the estimation error. First, a local estimation error set of all followers is defined , which is a quantitative carrier of the global estimation error, avoiding global coordination omission caused by analyzing only a single follower error. Thereafter, by Kronecker product, the positive definite weight of a single platform is extended to the global, ensuring that the error of each follower is given the same positive definite weight, maintaining the distributed characteristics, not relying on centralized weight allocation, and ensuring the positive definiteness of the global function , meeting the premise of Lyapunov stability analysis. Through the constraint condition of the decay rate, it is ensured that the sum of the decay of the global communication link is negative, avoiding too strong decay caused by attacks, and explicitly stating that attacks will lead to an increase in channel decay, which fits the actual scenario of attacks deteriorating communication quality in urban confrontation. The derivation of this convergence proves the theoretical effectiveness of the estimator. Under the attack constraints of the time and frequency limits set above, the estimation error will gradually converge to 0, ensuring that the expected position estimate can accurately approximate the leader's true state, providing a reliable target benchmark for the subsequent controller, and avoiding control failure caused by estimation bias.

[0208] Similarly, for the distributed resilient safety controller, when constructing a Lyapunov function based on the tracking error, first define the follower tracking error , which expresses the final coordination error and directly reflects whether the swarm has achieved safe coordination. Due to the heterogeneous nature of the unmanned swarm, an independent , and needs to meet the constraint specific constraint, ensures that each follower error can be attenuated, avoid due to isomerism parameter causes part of the follower convergence failure. The derivation of the convergence, prove the final effect of the controller, that is, on the basis of accurate estimation of the estimator, the controller can further eliminate the estimation residual error and attack residual interference, so that the state of all followers is completely synchronized with the leader, for example, the spacing error between the unmanned aerial vehicle and the unmanned vehicle in the city defense converges to the expected effect, meets the requirements of cooperative tasks.

[0209] In specific implementation, first, the Lyapunov function of the distributed elastic security estimator is used to ensure the accuracy of the estimator output, and then the Lyapunov function of the distributed elastic security controller is used to ensure that the controller can make the follower track the estimated state of the leader, and finally approach the ideal state, both of which realize the secure cooperation under the information-physical hybrid attack.

[0210] In summary, under the technical scheme of the above embodiment, 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 the heterogeneous nonlinear large-scale unmanned cluster system model. A distributed elastic security estimation method and a secure 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 secure cooperative tracking in the presence of multiple external environmental disturbances and information-physical hybrid attacks. At the same time, the equivalent attenuation rate of the channel is introduced, and the attenuation condition is analyzed in the case of independent attack on each communication link, which effectively deals with the complexity and diversity of network attacks in actual situations.

[0211] As shown in Figure 2 The embodiment of the present application provides a hybrid attack defense control system for heterogeneous clusters in urban counter-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.

[0212] 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.

[0213] 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.

[0214] 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.

[0215] 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:

[0216] Based on the geographical optimal similarity between the sample points and the unknown points, the prediction uncertainty of all unknown points is calculated;

[0217] A double-objective function is constructed, 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 the unknown points with high prediction uncertainty, the second sub-objective function is used to reduce the prediction uncertainty of the overall region, the prediction uncertainty of the overall region is composed of the prediction uncertainty of all unknown points, and the weight parameter is used to regulate the priority of the first sub-objective function and the second sub-objective function;

[0218] The unknown points with prediction uncertainty higher than a prediction uncertainty threshold are selected for supplementary sampling, aiming to minimize the double-objective function;

[0219] During the supplementary sampling process, the weight parameter of the double-objective function and the prediction uncertainty threshold are adaptively adjusted, 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.

[0220] 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 embodiment 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).

[0221] Any combination of the technical features of the above embodiments can be made. In order to make the description simple, all possible combinations of the technical features in the above embodiments are not described, however, as long as the combination of the technical features does not exist, it should be considered as the scope of the present application.

[0222] 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 unmanned platform cluster, wherein the unmanned platform cluster comprises several unmanned platforms of different types, one of which is a leader and the others are followers, the dynamic state of the unmanned platform changes nonlinearly, the unmanned platforms communicate through a topological graph, and the communication between any two unmanned platforms has directionality; based on the ideal system model, an information-physical hybrid attack model is constructed, and the attack behavior of an attacker 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 comprises 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 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; based on the attacked system model, a distributed resilient security estimator with a 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; based on the expected position of the follower, a distributed resilient security controller with a compensation mechanism is constructed, and the follower is controlled using the distributed resilient security controller to enable the leader and the follower of the unmanned platform cluster to safely cooperate, wherein each follower designs a control input based only on the estimated expected position, the actual state and the local information of the direct communication neighbor; the ideal system model of the follower and the ideal system model of the leader in a safe network environment are constructed based on the system topological graph and the corresponding communication link matrix of the ideal system model, comprising: Construction An ideal system model for a follower: wherein, with respectively a state of a th follower and a control input in a secure network environment, denotes a state of a th follower denotes a dimension of a state of a th follower, denotes a time variable, denotes a derivative of a state of a th follower, used to describe a change rule of a state of the unmanned platform over time, denotes a state matrix of a follower with a dimension of and denotes a state matrix of a follower with a dimension of denotes a Lipschitz continuous nonlinear function, is an 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 respectively. 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​​ based on the attacked system model, a distributed resilient security estimator with a 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, comprising: based on the attacked system model, a distributed resilient security estimator with a 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, comprising: where, is the estimate of the state of the th estimator, i.e. the estimated expected position, is the actual state of the leader under FDI attack, 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, where 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 ; based on the expected position of the follower, a distributed resilient security controller with a compensation mechanism is constructed, and the follower is controlled using the distributed resilient security controller to enable the leader and the follower of the unmanned platform cluster to safely cooperate, comprising: based on the expected position of the follower, a distributed resilient security controller with a compensation mechanism is constructed, and the follower is controlled using the distributed resilient security controller to enable the leader and the follower of the unmanned platform cluster to safely cooperate, comprising: wherein is the control input of the th follower for controlling the follower, is the estimated tracking error, is the actual state of the th follower under cyber attack, , , 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.

2. The hybrid attack defense control method for the heterogeneous cluster in the urban confrontation environment according to claim 1, characterized in that, the ideal system model of the unmanned platform cluster is constructed, comprising: constructing a system topological graph of the ideal system model: wherein the topological graph is a directed graph, is composed of a node set consisting of nodes representing leaders, when , nodes representing the first followers, is an edge set between the nodes, the initial topological has a directed spanning tree with the leader as the 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 link between followers, denotes the set of real numbers, the communication link matrix satisfies and denotes that the communication between any two unmanned platforms has directionality, denotes transpose operation; based on the system topological graph and the corresponding communication link matrix of the ideal system model, the ideal system model of the follower and the ideal system model of the leader in a safe network environment are constructed.

3. The hybrid attack defense control method for the heterogeneous cluster in the city-oriented adversarial environment according to claim 2, characterized in that, constructing an information-physical hybrid attack model based on the ideal system model, and simulating 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 unmanned platform cluster, including: constructing an asynchronous DoS attack model of a network layer for the ideal system model: wherein, is the time-varying attack model corresponding to the time instant, 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 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; 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 of the network layer, limiting attack duration, 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 of the network layer, limiting attack frequency, 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 follower dynamics model under asynchronous DoS attack: wherein, the actual state of the nth follower under cyber attack, the actual state of the nth follower at the corresponding time, the control input adjusted dynamically with the attack model . constructing a leader dynamics model under unknown FDI attack signal injection: where is the actual state of the leader under FDI attack, is the actual state of the corresponding time under FDI attack, is an unknown bounded FDI injection signal satisfying .

4. The hybrid attack defense control method for the heterogeneous cluster in the city-oriented adversarial environment according to claim 3, characterized in that, the defense control method further includes: for the distributed resilient security estimator, constructing a Lyapunov function based on the estimation error for evaluating the convergence of the estimation error of the distributed resilient security 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 under 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 for the distributed resilient security controller, constructing a Lyapunov function based on the tracking error for evaluating the convergence of the tracking error of the distributed resilient security controller, denoted as: wherein, is the tracking error for the nth follower unmanned platform, is the tracking error for the nth follower unmanned platform, denotes the transpose 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 can track the leader state Can track the leader state .

5. A hybrid attack defense control system for a heterogeneous cluster in a city-oriented adversarial environment, characterized in that, application to implement the steps of the hybrid attack defense control method for the heterogeneous cluster in the urban confrontation environment as claimed in any one of claims 1-4, the system includes: an ideal system model construction module for constructing an ideal system model of an 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 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 for constructing an information-physical hybrid attack model based on the ideal system model, and simulating 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 unmanned platform cluster, wherein the attack behaviors include asynchronous DoS attack of a network layer and unknown FDI attack signal injection of a physical layer, the asynchronous DoS attack is independent attack of the attacker on different communication links of the unmanned platform cluster at different time periods, and the unknown FDI attack signal injection is injection of unknown FDI attack signals by the attacker to the leader; an elastic security estimator construction module for constructing a distributed resilient security estimator with a compensation mechanism based on the attacked system model, and for each follower in the unmanned platform cluster of the attacked system model, compensating for attack effects and estimating a desired position based on the distributed resilient security estimator, wherein the follower completes the calculation of the desired position based on its kinematic state and local estimation state information; an elastic security controller construction module for constructing a distributed resilient security controller with a compensation mechanism based on the desired position of the follower, and using the distributed resilient security controller to control the follower, so that the leader and the follower of the unmanned platform cluster are safe and cooperative.

6. A terminal device, characterized by comprising: The terminal device 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 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 according to any one of claims 1-4 are implemented.

7. 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. 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 according to any one of claims 1-4 are implemented.

Images