Energy-limited hybrid control multi-uav cluster formation cooperative method with double-layer structure and anti-dos attack

Abstract

This invention relates to a two-layer structured multi-UAV swarm anti-DoS attack formation coordination method based on energy-constrained hybrid control. First, a two-layer UAV swarm architecture integrating physical and virtual layers is proposed, which can uniformly divide a large number of UAV nodes into groups and establish biomimetic communication between these nodes. Second, a hybrid control protocol based on energy constraints is designed by combining continuous-time control and pulse control mechanisms and introducing a saturation function. When applied to formation coordination, this protocol simultaneously solves the problems of control efficiency, operating cost, and system robustness. Finally, a novel DoS attack model is introduced, which integrates "multi-interval periods" and "recovery probabilities." These multi-interval periods include a buffer period during which the recovery probability of the attacked communication channel follows a Bernoulli distribution. This method effectively addresses the limitations of existing DoS attack models in practical applications.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology, and in particular to a two-layer structure multi-UAV swarm anti-DoS attack formation and coordination method with energy-constrained hybrid control. Background Technology

[0002] With the rapid development of the low-altitude economy and the gradual liberalization of airspace management policies in recent years, the formation and cooperative control technology of UAV swarms has shown great application prospects in fields such as logistics distribution, agricultural plant protection, and disaster reconnaissance. In fact, UAV swarms are essentially distributed multi-agent networks. To achieve formation and cooperation in UAV swarms, scholars typically conduct research based on the consensus theory of multi-agent networks, focusing on aspects such as UAV swarm networking, formation and cooperative control protocols, and communication security.

[0003] A drone swarm can be formally defined as a network system composed of multiple drone nodes, exhibiting distributed self-organizing characteristics and supporting cooperative communication. From the perspective of algebraic graph theory, it can be further divided into undirected networks, directed networks, fixed networks, weighted networks, and time-delay networks. Some scholars have used an improved artificial potential field method to study the formation and cooperative control of drone swarms, where the drone nodes form an undirected network, which has the advantage of simplicity. Other scholars have constructed the communication between drone nodes as a directed network, enabling directional information transmission between nodes. Still others have studied an adaptive formation tracking control scheme for multiple vertical take-off and landing drones based on pure azimuth measurement. The drone nodes form a fixed network, whose topology remains unchanged over time. To characterize the communication signal strength between different drone nodes, some scholars have used weighted networks to describe drone swarms, which shows good applicability in scenarios with uneven wireless signal coverage. A leaderless drone swarm was studied, using a time-delay network to simulate the communication delay between drone nodes, successfully achieving the preset formation cooperation. It is not difficult to find that most related research, especially the examples above, mainly focuses on single drone swarms with a small number of drone nodes. Furthermore, communication between these drone nodes almost universally relies on connectivity metrics from algebraic graph theory for simplification, lacking detailed strategies for constructing the communication network topology. In many practical applications, complex tasks often comprise multiple subtasks. To efficiently execute these subtasks, it is necessary to evenly divide a large number of drone nodes into multiple drone swarms and effectively construct the communication network topology for these drone sub-swarms.

[0004] Formation coordination control protocols provide the most direct support for the cooperative operation of UAV swarms. Among them, adaptive control protocols, strait control protocols, and fault-tolerant control protocols have been widely adopted. Some scholars have studied a class of quadrotor UAV swarms and developed an adaptive control protocol with anti-interference capabilities, achieving efficient formation coordination control. Other scholars have modeled UAV swarms as multi-agent networks and designed a pure azimuth finite-time strait control protocol, achieving formation coordination control within a finite time. To mitigate the impact of actuator failures on UAV swarms, some scholars have developed a fault-tolerant control protocol, enabling collision-free formation coordination control. However, the above-mentioned formation coordination control protocols all fall under the category of continuous-time control protocols, requiring uninterrupted control signal input. While this helps achieve high control efficiency, the continuous demand for control execution significantly increases operating costs and may even adversely affect the lifespan of the UAVs. To overcome this limitation, some scholars have attempted to introduce discrete-time control protocols into the field of UAV swarm coordination. Among them, pulse control protocols are widely used due to their advantages in low operating costs and high robustness. To enable UAV swarms to operate effectively in environments with communication delays, some researchers have designed pulse control protocols to achieve multi-formation tracking control resistant to communication delays. Other researchers have modeled UAV swarms as vector second-order Lipschitz nonlinear multi-agent systems and designed a pulse control protocol that only includes speed regulation, achieving low-cost formation cooperative control based on state consistency. It is worth noting that although the above pulse control protocols meet the requirements of low cost and high robustness, they are prone to causing unfriendly large state jumps in UAVs at the pulse moment. Furthermore, all of the above-mentioned studies have only used a single control mechanism, failing to integrate the advantages of multiple control mechanisms.

[0005] In the field of unmanned aerial vehicles (UAVs), communication security is paramount. Early research often assumed that the communication channels between UAV nodes were completely immune to network attacks to simplify analysis. While this idealized assumption significantly reduced model complexity, it neglected the problems caused by insecure communication. In recent years, more and more scholars have recognized that communication security issues such as DoS attacks not only severely impact the formation coordination performance of UAV swarms but can even directly lead to the complete failure of formation coordination. Therefore, UAV swarm formation coordination under DoS attacks has received widespread attention. Some researchers have studied a class of UAV swarms with communication delays, where the communication channels between UAV nodes are subject to denial-of-service attacks. Under an event-triggered control protocol, the formation coordination objective was successfully achieved. Other researchers have modeled UAV swarms as second-order nonlinear multi-agent networks and designed a control protocol resistant to asynchronous DoS attacks, thus achieving predefined formation coordination. Furthermore, some researchers have proposed a coordination method between heterogeneous UAV swarms and unmanned ground vehicles whose communication environments are vulnerable to DoS attacks. By designing a distributed model predictive control protocol, secure formation coordination of UAV swarms against DoS attacks was achieved. However, in the aforementioned and related studies, a common assumption for simplifying modeling and analysis is that the communication function of the attacked channel will recover immediately after the DoS attack ends. This assumption has certain limitations in practical applications, because in real-world scenarios, communication channels subjected to DoS attacks usually cannot recover immediately, but rather undergo a buffer period. Some severely damaged communication channels may even fail to recover after the buffer period ends. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide a two-layer structure multi-UAV swarm anti-DoS attack formation coordination method with energy-constrained hybrid control, which effectively solves the limitations of existing DoS attack models in practical applications.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: a two-layer structure multi-UAV swarm anti-DoS attack formation coordination method with energy-constrained hybrid control, comprising the following steps:

[0008] S1: A two-layer UAV swarm architecture integrating physical and virtual layers is proposed, which evenly groups a large number of UAV nodes and establishes biomimetic communication between these UAV nodes to promote practical deployment;

[0009] S2: Design an energy-constrained hybrid control protocol for UAV swarms that balances control efficiency, operating costs, and system robustness during formation coordination.

[0010] S3: Introduces a novel DoS attack model that combines multiple time intervals and recovery probability; this DoS attack model enhances the survivability of drone swarms in real-world DoS attack scenarios.

[0011] In a preferred embodiment, in step S1, a virtual layer is introduced, and the physical layer and the virtual layer are combined to construct a two-layer architecture for the drone swarm; based on the positional relationships between drone nodes, a large number of drone nodes are uniformly divided into multiple drone swarms, and bionic communication is efficiently established between them; a total of One drone node , of which Nodes In time Position and velocity are respectively expressed as and Set the initial time to and will Set the time at which the virtual layers to be introduced almost reach a consistent coordination; upon reaching Previously, it was assumed that all drone nodes Remain unchanged, that is ;Will The neighbor node is defined as Then the time hour and The average position offset of each UAV node is defined as

[0012] (1)

[0013] in, ,and , and Represented on the x-axis, y-axis and z-axis respectively The value; similarly. Written as .

[0014] In a preferred embodiment, The average position offset factor is defined as

[0015] (2)

[0016] definition The overall variance is

[0017] (3)

[0018] in, These represent the weights on the x-axis, y-axis, and z-axis, respectively; then, through... and definition The positional centrality factor is

[0019] (4)

[0020] Reflecting UAV nodes The average similarity in location between it and all its neighboring UAV nodes, and The smaller the value, the higher the average similarity. reflect and The degree of consistency between them, among which The smaller the value, the higher the degree of inconsistency; consider and This enables control over UAV nodes. An effective measurement of positional centrality; when drone nodes More centrally located compared to all other drone nodes;

[0021] use , The drone nodes are evenly divided into n drone clusters based on their location relationships. ;

[0022] get The drone swarm, the first The number of drone nodes contained in a drone cluster is denoted as , Established; System redistribution of all drone nodes: (The following is a partial translation of the original text, which is not possible without further context.) A drone swarm is denoted as , No. The positions and speeds of the drone nodes in this cluster are as follows: and Also known as physical position and physical velocity.

[0023] In a preferred embodiment, a virtual layer is introduced, which includes A virtual UAV node, represented as ;in, As the overall leader, and each As with the A local leader associated with each UAV cluster; in time hour, Position and velocity are respectively expressed as and ; In time Position and velocity are respectively expressed as and After the introduction of the virtual layer, the first UAV nodes in a UAV cluster It will be designed to communicate with other UAV nodes, including both virtual and physical nodes, using virtual information; the virtual information includes virtual location. and virtual speed ,in It is necessary to maintain and Position offset between them to achieve formation coordination; in order to enable local leaders Able to better express and lead A swarm of drones, whose positions and velocities are initialized based on the average concept. and Similarly, global facilitator The initial position and velocity were set to and ;

[0024] At the physical layer A swarm of drones establishes a biomimetic communication network topology; the first... The strategy for a drone swarm topology consists of three steps:

[0025] Step 1: Drone Node Form a complete graph, that is, any two distinct drone nodes and The adjacency value between them is ;exist In the middle, superscript The index representing the initial communication network topology is denoted as: Since this invention will subsequently consider denial-of-service attacks, various communication network topologies will emerge, which are indexed as follows: ;

[0026] Step 2: Calculate the values ​​for each UAV node separately. and Similarity of composite velocities between As shown below:

[0027] (5)

[0028] in, Middle and upper bids The meaning is the same as in step 1 above; and These represent the cosine similarity threshold and the Manhattan distance threshold, respectively, and their values ​​will be set according to actual needs; obviously, show and Their speeds are sufficiently similar; conversely, This indicates that their speeds are not similar enough; specifically, when ,set up ;

[0029] Step 3: For each drone node If their corresponding composite velocity similarity If the connection is broken, all communication edges are disconnected; otherwise, all communication edges remain unchanged. This is achieved by assigning each pair of drone nodes... and adjacency value reallocation value To achieve this process; all isolated drone nodes are individually connected. Information only from Flow direction .

[0030] In a preferred embodiment, in the virtual layer, The dynamics are defined by the following formula

[0031] (6)

[0032] For each local leader Its dynamics are defined as

[0033] (7)

[0034] in, and These are two virtual control protocols, also known as virtual control inputs;

[0035] At the physical layer, the dynamics of drone nodes Defined as

[0036] (8)

[0037] Virtual Control Protocol and A pulse control mechanism is employed to reduce computational costs; it is assumed that the virtual layer is immune to DoS attacks. and Defined respectively

[0038] (9)

[0039] (10)

[0040] in It involves two pulses controlling the intensity; It is the Dirac increment function used for simulating pulse input, which satisfies the condition that when... hour, This represents the instantaneous pulse in the virtual layer, and also satisfies... , ;set up and ,prove and It is right-continuous.

[0041] In a preferred embodiment, the design ; Integrated continuous time control component and energy-limited pulse control component ,Right now Control components and Defined as:

[0042] (11)

[0043] (12)

[0044] in To control the intensity over continuous time, For pulse control intensity; Representing the The pulse instant of a drone swarm, it satisfies , ;set up ,Right now It is also right-continuous;

[0045] It is a saturation function, defined as follows:

[0046] .

[0047] In a preferred embodiment, the DoS attack model includes multiple cycles, each cycle being further divided into a normal period, an attack period, a buffer period, and a recovery period; For periodicity;

[0048] For general periods, the time range is: Apply continuous time control components to it , No. A drone swarm adopts The indexed biomimetic communication network topology, in particular, sets... .

[0049] In a preferred embodiment, the time range for the attack period is: During this period, the attackers executed a DoS attack at the physical layer, causing the compromised communication edges to be blocked and lose connection, subsequently resulting in changes to the communication network topology of the drone swarm; the indices of these altered communication network topologies during the attack period are denoted as... And the adjacency value and Defined as

[0050] (13)

[0051] (14)

[0052] in and It is an attack signal; if in the first In a communication network topology, drone nodes and If the communication edge between them is blocked by a DoS attack, then ;otherwise, Similarly, if drone nodes and If the communication edge between them is blocked by a DoS attack, then ;otherwise, During this period, because DoS attacks can easily have a significant negative impact on control inputs that last for a long time, the physical layer only uses the pulse control protocol. Therefore, we set Furthermore, assume that the number of pulse control inputs during this time period is... And their occurrence time is represented as .

[0053] In a preferred embodiment, the time range for the buffer period is [missing information]. This period is primarily used to simulate the communication delay between the end of a DoS attack and the restoration of communication functionality; the communication network topology during this period remains consistent with that during the attack period, i.e. Furthermore, during this period, and A value of 0 indicates that no control is applied.

[0054] In a preferred embodiment, the time range for the recovery period is: During this period, the new communication network topology was indexed as ; in the In a communication network topology, let Indicates drone node and The random events that restore communication between them after being blocked by a DoS attack, in which Within this interval and The value is defined as

[0055] (15)

[0056] (16)

[0057] In addition, a continuous time control component is applied during the recovery period. .

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] (1) This invention proposes a two-layer UAV swarm architecture that integrates the physical layer and the virtual layer. This architecture can evenly divide a large number of UAV nodes into multiple UAV swarms according to their positional relationships, and provides a biomimetic strategy to establish a communication network topology for these UAV swarms, thereby solving the limitations of the existing research.

[0060] (2) Design a hybrid control protocol with energy constraints for UAV swarms. The design integrates continuous-time and pulse control mechanisms and introduces a saturation function to constrain pulse amplitude jumps, aiming to achieve control efficiency, operating cost and system robustness in the formation coordination process.

[0061] (3) This invention introduces a novel DoS attack model that combines "multiple interval periods" and "recovery probability". These interval periods include a buffer period during which the recovery probability of the attacked communication channel follows a Bernoulli distribution. This method effectively addresses the limitations of existing DoS attack models in practical applications.

[0062] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0063] Figure 1 This is a schematic diagram of the physical layer;

[0064] Figure 2 This is a schematic diagram of the virtual layer;

[0065] Figure 3 This is a schematic diagram of a biomimetic communication network topology.

[0066] Figure 4 A schematic diagram illustrating the strategy for establishing the topology of the i-th UAV cluster;

[0067] Figure 5 This is a schematic diagram of a DoS attack model;

[0068] Figure 6 This refers to the communication network topology of the virtual layer.

[0069] Figure 7 The evolution of UAV position and velocity errors in the virtual layer;

[0070] Figure 8 This is the initial communication network topology for the first drone swarm;

[0071] Figure 9 This is the situation during the first cycle of a DOS attack;

[0072] Figure 10 The evolution of the position and velocity errors of the first drone swarm;

[0073] Figure 11 The movement trajectory and formation of the first drone swarm;

[0074] Figure 12 A top-down view of the first drone swarm;

[0075] Figure 13 This is the initial communication network topology for the second drone swarm.

[0076] Figure 14 The evolution of the position and velocity errors of the second drone swarm;

[0077] Figure 15 The movement trajectory and formation of the second drone swarm;

[0078] Figure 16 A top-down view of the second drone swarm;

[0079] Figure 17 This is the initial communication network topology for the third drone swarm.

[0080] Figure 18 The evolution of the position and velocity errors of the third drone swarm;

[0081] Figure 19 The movement trajectory and formation of the third drone swarm;

[0082] Figure 20 A top-down view of the third drone swarm;

[0083] Figure 21 The evolution of the position and velocity errors of the first UAV cluster when energy constraints are removed. Detailed Implementation

[0084] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0085] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0086] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations according to this application; as used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise; furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0087] A two-layer structured, energy-constrained hybrid control method for multi-UAV swarm anti-DoS attack formation coordination, referenced... Figure 1-21 Specifically, it includes the following steps:

[0088] A virtual layer is introduced, and the physical and virtual layers are combined to construct a two-layer architecture for drone swarms. This architecture aims to uniformly divide a large number of drone nodes into multiple drone swarms based on their positional relationships, and to efficiently establish bionic communication between them. Assume there are a total of... One drone node , of which Nodes In time Position and velocity are respectively expressed as and Set the initial time to and will The virtual layer is set to achieve near-consistent coordination within a short period of time. Previously, it was assumed that all drone nodes Remain unchanged, that is .Will The neighbor node is defined as Then the time hour and The average position offset of each UAV node is defined as

[0089] (1)

[0090] in, ,and , and Represented on the x-axis, y-axis and z-axis respectively The value of. Similarly. It can be written as .

[0091] Will The average position offset factor is defined as

[0092] (2)

[0093] definition The overall variance is

[0094] (3)

[0095] in, These represent the weights on the x, y, and z axes, respectively. Then, through... and The positional centrality factor of vi is defined as

[0096] (4)

[0097] Reflecting UAV nodes The average similarity in location between itself and all its neighboring UAV nodes, and smaller This indicates a high average similarity. Furthermore, It can reflect and The degree of consistency between them, among which The smaller the value, the higher the degree of inconsistency. Considered and This enables control over UAV nodes. An effective measurement of the positional centrality. When drone nodes It is more centrally located compared to all other drone nodes.

[0098] use , The drone nodes can be evenly divided according to their positional relationships. The drone swarm is divided into several groups. For details on the specific partitioning scheme, please refer to Algorithm 1.

[0099]

[0100] get The drone swarm, the first The number of drone nodes contained in a drone cluster is denoted as ,therefore, Established. This invention systematically redistributes all UAV nodes: the first... A drone swarm is denoted as , No. The positions and speeds of the drone nodes in this cluster are as follows: and Also known as physical position and physical velocity, these drone swarms serve as the physical layer, such as Figure 1 As shown.

[0101] For the virtual layer, it includes A virtual UAV node, represented as .in, As the overall leader, and each As with the A local leader associated with each UAV cluster. In time... hour, Position and velocity are respectively expressed as and . In time Position and velocity are respectively expressed as and After the introduction of the virtual layer, the first UAV nodes in a UAV cluster It will be designed to communicate with other UAV nodes, including both virtual and physical nodes, using virtual information. The virtual information includes virtual location. and virtual speed ,in It is necessary to maintain and Position offsets between them to achieve formation coordination. To enable local leaders... Able to better express and lead A swarm of drones, whose positions and velocities are initialized according to the "average idea" are... and Similarly, global facilitator The initial position and velocity were set to and The node organization of the virtual layer is as follows Figure 2 As shown.

[0102] After the nodes in the physical and virtual layers are organized, bionic communication is established between them. Figure 3This displays the communication network topology of the entire system. At the top layer, a global leader is responsible for transmitting overall task instructions or reference information to all sub-clusters. The middle layer (virtual layer) has multiple local leaders (virtual UAV nodes), each responsible for a cluster. They receive instructions from the global leader and manage communication and coordination with their own sub-clusters. At the bottom layer (physical layer), multiple drone clusters exist. Since virtual UAV nodes are typically unaffected by network attacks, therefore… The communication network topology between them is directly established as a connected graph to conform to the industry's "Keep It Simple and Straightforward" (KISS) principle, thus omitting complex operations. The edges of this connected graph are undirected. and The adjacency value between them is denoted as .in addition, and Information transmission between them is directional; the arrow indicates the direction of transmission, and the adjacency value between them is denoted as... .

[0103] Inspired by the natural phenomenon of individuals with similar speeds forming clusters to facilitate communication and cooperation, this invention provides a physical layer... A swarm of drones established a biomimetic communication network topology. The strategy for a drone swarm topology consists of three steps, such as... Figure 4 As shown.

[0104] Step 1: Drone Node Forming a complete graph means that any two distinct drone nodes and The adjacency value between them is .exist In the middle, superscript The index representing the initial communication network topology is denoted as: Since this invention will subsequently consider denial-of-service attacks, various communication network topologies will emerge, which are indexed as follows: .

[0105] Step 2: Calculate the values ​​for each UAV node separately. and Similarity of composite velocities between As shown below:

[0106] (5)

[0107] in, Middle and upper bids The meaning is the same as in step 1 above. and These represent the cosine similarity threshold and the Manhattan distance threshold, respectively, and their values ​​will be set according to actual needs. Clearly, show and Their speeds are sufficiently similar. Conversely, This indicates that their speeds are not similar enough. Specifically, when ,set up .

[0108] Step 3: For each drone node If their corresponding composite velocity similarity If the connection is broken, all communication edges are disconnected; otherwise, all communication edges remain unchanged. This is achieved by defining each pair of drone nodes... and adjacency value reallocation value To achieve this process, some drone nodes and clusters may become isolated. For a cluster, ensure it contains at least one drone node connected to a local leader. Furthermore, to prevent the emergence of "information silos," all isolated drone nodes are individually connected to... Information only from Flow direction Therefore, each drone node is assigned as specified in Table 1. and Initial adjacency values ​​between In Table 1, . superscript The meaning is consistent with step one. Furthermore, in the event of a DoS attack, and They were converted respectively and Their values ​​will be defined in detail in the subsequent DoS attack model section.

[0109] For the dynamic characteristics of all drone nodes, including both the virtual and physical layers, typically, a global leader acts as a specific type of agent. Typically, a constant speed is maintained during the collaborative process to facilitate analysis. Therefore, in the virtual layer, The dynamics are defined by the following formula

[0110] (6)

[0111] For each local leader Its dynamics are defined as

[0112] (7)

[0113] in, and These are two virtual control protocols, also known as virtual control inputs. Normally, direct control inputs cannot be applied to the location of a UAV node. However, due to... Residing in the virtual layer rather than the physical drone node, any value that satisfies the computational rules is acceptable. Therefore, the control input... Apply to its location It is feasible.

[0114] At the physical layer, the dynamics of drone nodes Defined as

[0115] (8)

[0116] Since the virtual layer runs first, the virtual control protocol... and A pulse control mechanism is employed to reduce computational costs. Assuming the virtual layer is immune to DoS attacks, then... and Defined respectively

[0117] (9)

[0118] (10)

[0119] in The intensity is controlled by two pulses. It is the Dirac increment function used for simulating pulse input, which satisfies the condition that when... hour, Represents the instantaneous pulse in the virtual layer, which satisfies , .set up and This proves and It is right-continuous.

[0120] Integrated continuous time control component and energy-limited pulse control component ,Right now Control components and Defined as:

[0121] (11)

[0122] (12)

[0123] in To control the intensity over continuous time, This refers to the pulse control intensity. Representing the The pulse instant of a drone swarm, it satisfies , .set up ,Right now It is also right-continuous. It is a saturation function, defined as follows:

[0124]

[0125] Consider a DoS attack at the physical layer, where a compromised communication edge is blocked and loses connection. To be realistic, assume the attacker's energy is finite; after one attack, they need to store energy for the next. A DoS attack model includes multiple phases, each further divided into a normal phase, an attack phase, a buffer phase, and a recovery phase. For a period, such as Figure 5 As shown.

[0126] For general periods, the time range is: Apply continuous time control components to it , No. A drone swarm adopts The biomimetic communication network topology of the index, such as Figure 4 As shown, specifically, the settings .

[0127] For the attack period, the time range is: During this period, the attackers executed a DoS attack at the physical layer, causing the compromised communication edges to be blocked and lose connectivity, subsequently altering the communication network topology of the drone swarm. The indices of these altered communication network topologies during the attack period are denoted as... And the adjacency value and Defined as

[0128] (13)

[0129] (14)

[0130] in and This is an attack signal. If in the... In a communication network topology, drone nodes and If the communication edge between them is blocked by a DoS attack, then ;otherwise, Similarly, if the drone node and If the communication edge between them is blocked by a DoS attack, then ;otherwise, During this period, because DoS attacks can easily have a significant negative impact on control inputs that last for extended periods, the physical layer only uses the pulse control protocol. Therefore, we set Furthermore, assume that the number of pulse control inputs during this time period is... And their occurrence time is represented as .

[0131] For the buffer period, the time range is This period is primarily used to simulate the communication delay between the end of a DoS attack and the restoration of communication functionality. The network topology during this period remains consistent with that during the attack period. Furthermore, during this period, and Both are equal to 0, indicating that no control was applied.

[0132] For the recovery period, the time range is as follows: During this period, communication channels subjected to DoS attacks may recover their communication functionality with a certain probability, leading to the indexing of new communication network topologies. In the first In a communication network topology, let Indicates drone node and The random events that restore communication between them after being blocked by a DoS attack, in which Within this interval and The value is defined as

[0133] (15)

[0134] (16)

[0135] In addition, a continuous time control component is applied during the recovery period. .

[0136] Furthermore, based on the consensus theory of multi-agent networks, the formation and coordination problem of UAV swarms is analyzed. Due to virtual location... The position offset is already included. Therefore, the control objective simplifies to ensuring through effective control. A consensus was reached. The discussion will then proceed to divide the discussion into virtual and physical layers.

[0137] The case of virtual layers: Let's assume and These are virtual drone nodes and The position and velocity errors between them. Then, by combining the dynamics (6) and (7) with the virtual control protocols (9) and (10), we can obtain

[0138] (17)

[0139] in, It is the first Laplace matrix corresponding to the topology of the communication network formed by all local leaders. row and number The elements in the column. Further, let... and Then we get

[0140] (18)

[0141] in, , It is a Laplace matrix. and They are respectively

[0142]

[0143] In the virtual layer, the control cycle is defined as and set .

[0144] The situation at the physical layer: From Figure 5 It can be seen that when At that moment, the pulse instants are respectively In order to match The instantaneous form of the pulse is uniformly represented as Furthermore, for ease of analysis, let Indicates during the attack period and This indicates the recovery period.

[0145] set up and For drone nodes and The position and velocity errors between them. It should be noted that when... At this time, the virtual layer achieves almost uniform coordination, so the impact of impulse control on this layer is negligible. This means that when hour, and Can be regarded as Then, by combining the DoS attack model, dynamics (8), and control components (11) and (12), we can obtain...

[0146] (19)

[0147] in It corresponds to the first In a drone cluster, at the drone node The first Laplace matrix of the complete graph formed between them row and number Elements in the column. and The meaning is similar to The only difference is that they correspond to and Communication network topology. When the... UAV nodes of a drone swarm and Located in the th In a communication network topology, their adjacency values ​​are... and It is an indicator function and satisfies

[0148] (20)

[0149] Furthermore, set and Then we get

[0150] (twenty one)

[0151] in, , Laplace matrix , and . , and .parameter Defined as:

[0152]

[0153] Lemma 1: Let vector , , It is a group A 3D diagonal matrix, where all diagonal elements are or For example, when Sometimes,

[0154]

[0155] Will Each element in is represented as ,Then Furthermore, let's assume... Obviously, Too One of the elements. If ,but Established.

[0156] According to Lemma 1, when , It is from Some elements and from The set consisting of the remaining elements. Similarly, given two matrices... , It is from Some elements and from The set consisting of the remaining elements. Therefore, if , Established. Furthermore, if it exists... And satisfy ,but .

[0157] Based on the above, let Then, when , and At that time, it can be deduced that

[0158]

[0159] set up Then formula (21) can be rewritten as:

[0160] (twenty two)

[0161] Formulas (18) and (22) above are collectively referred to as the formation coordination system, and the formation coordination objective is expressed as: Because each The position offset is already included. When all Once consensus is reached, the formation coordination goal is achieved. Therefore, the formal definition of formation coordination is as follows:

[0162] Definition 1: In a two-layer drone swarm architecture with a DoS attack, if there exists a sufficiently small normal quantity... and a sufficiently large normal quantity , making

[0163] (twenty three)

[0164] (twenty four)

[0165] in and This achieves the goal of formation coordination.

[0166] Definition 2: Given a function The upper right Dini derivative is defined as

[0167]

[0168] Note: yes The abbreviation of .

[0169] Definition 3: Let Represent a given matrix The measure of is defined as follows:

[0170]

[0171] Furthermore, the following contains two theorems that together provide sufficient conditions for achieving the formation coordination goal in Definition 1. More specifically, Theorem 1 provides sufficient conditions for the validity of Equation (23), which ensures consistency in the virtual layer. Based on this, Theorem 2 provides sufficient conditions for the validity of Equation (24), thereby guaranteeing formation coordination in the physical layer.

[0172] Theorem 1 If there exists a positive scalar constant , , and a sufficiently small positive number and a sufficiently large positive number And it satisfies the following inequalities:

[0173] 1)

[0174] 2)

[0175] Then, equation (23) and This ensures that the aforementioned consistent collaboration is achieved within the virtual layer. The proof is as follows:

[0176] In Theorem 1, it is easy to find a sufficiently small... satisfy ,thereby Established.

[0177] when This means Then, through the formation coordination system (18), we have:

[0178]

[0179] Therefore, we can obtain .

[0180] when At that time, this means Furthermore:

[0181]

[0182] The mathematical induction used is as follows: Case 1: When ,Right now ,get ,so

[0183] (25)

[0184] Scenario 2: When ,Right now At that time, Combining with formula (25), we can obtain

[0185] (26)

[0186] According to formula (26), we can also obtain

[0187] (27)

[0188] Note that for and We can further obtain from formula (27)

[0189] (28)

[0190] As can be seen from the formula (28) above, with The gradual increase It will gradually decrease and approach [the value]. .set up ,Then

[0191] (29)

[0192] Clearly, formula (29) proves that formula (23) is true, thus completing the proof.

[0193] Theorem 2 If there exists a positive scalar constant , , and Then the following conditions are met.

[0194] 1)

[0195] 2)

[0196] 3)

[0197] 4)

[0198] in, Then, equation (24) holds, thus guaranteeing formation coordination in the physical layer. The proof is as follows:

[0199] For the formation cooperative system (22), consider the following Lyapunov function.

[0200] (30)

[0201] when When combining formulas (22) and (30), we have

[0202]

[0203] Therefore, we can obtain:

[0204] (31)

[0205] when ,have

[0206]

[0207] Therefore, we can obtain

[0208] (32)

[0209] Note: In the interval Inside, there is Pulse input. This time period is divided into... Each sub-interval has An initial time, such as Figure 5 As shown. In equation (32), these initial times are collectively referred to as In the subsequent analysis, Will be obtained in order An initial time.

[0210] when At that time, we can obtain:

[0211] (33)

[0212] when Similar to In this case, it follows

[0213]

[0214] Then, we can get

[0215] (34)

[0216] when You can get

[0217]

[0218] Therefore, we can obtain

[0219] (35)

[0220] From formulas (31) to (35), the following conclusions can be drawn through mathematical induction:

[0221] Scenario 1: The drone swarm is in its first cycle.

[0222] (1.1) When Combining formula (31) and considering At that time, one can obtain

[0223] (36)

[0224] (1.2) When When, combining formulas (32) and (36), we can obtain

[0225] (37)

[0226] (1.3) When When, combining formulas (33) and (37), we can obtain

[0227] (38)

[0228] (1.4) When Combining formulas (32) and (38), we can obtain

[0229] (39)

[0230] (1.5) When When, combining formulas (33) and (39), we can obtain

[0231] (40)

[0232] (1.6) When At that time, one can obtain

[0233] (41)

[0234] (1.7) When Combining formulas (32) and (41), we can obtain

[0235] (42)

[0236] (1.8) When Combining formulas (34) and (42), we can obtain

[0237] (43)

[0238] (1.9) When Combining formulas (35) and (43), we can obtain

[0239] (44)

[0240] This completes the first cycle.

[0241] Scenario 2: For the drone swarm in the second cycle, the following results can be obtained through a process similar to that in Scenario 1.

[0242] (45)

[0243] Scenario 3: Correspondingly, for The drone swarm during this period can be used to deduce

[0244] (46) when Sometimes, .because Bounded and ,get

[0245] (47)

[0246] Obviously, formula (47) proves that formula (24) is true, thus completing the proof.

[0247] This invention provides a two-layer structure multi-UAV swarm anti-DoS attack formation coordination method with energy-constrained hybrid control, combined with the attached... Figures 6-21 The following is an explanation in conjunction with Tables 2 through 5:

[0248] set up That is, there are 13 drone nodes. Their initial positions and velocity information are shown in Table 2. We set... According to Algorithm 1, three drone clusters can be obtained.

[0249]

[0250]

[0251]

[0252] For the first drone cluster The physical position and physical velocity are Further adjust the position offset: , , , , This indicates that the goal of the first drone swarm is to form a pentagonal formation.

[0253] For the second drone cluster The physical position and physical velocity are respectively The position offset was further set: , , , This indicates that the goal of the second drone swarm is to form a quadrilateral formation.

[0254] For the third drone cluster The physical position and physical velocity are respectively The position offset was further set: , , , This indicates that the goal of the third drone swarm is to form a linear formation. Then, three local leaders can be identified. and global leader The initial position and velocity values ​​are as follows:

[0255]

[0256]

[0257]

[0258]

[0259] according to Figure 3 This invention constructs a communication network topology for a virtual layer, such as... Figure 6 As shown.

[0260] according to Figure 6 Theorem 1 and the main idea of ​​this invention are to set the pulse control intensity. and Then, the evolution process of the virtual layer was simulated using MATLAB, with the step size set to 0.0015 and the control period... Set to 5 steps. With the initial values, communication network topology, and parameters configured above, a local leader can be obtained. , and Compared to the global leader The evolution of position and velocity errors, such as Figure 7 As shown.

[0261] In addition, settings You can get This means that the virtual layer has achieved the proposed collaboration. Subsequently, this invention simulated the evolution of three drone swarms at the physical layer.

[0262] The first drone swarm: Based on the simulation of the virtual layer above, we obtain... Local Leaders at All Times The position and velocity are respectively and Set a cosine similarity threshold. and Manhattan distance threshold Based on formula (5), we can obtain

[0263]

[0264] Then, according to Figure 4 The strategy shown yielded the initial communication network topology for the first drone swarm, as follows: Figure 8 As shown. Combined with Figure 5 The DoS attack model shown provides the time interval distribution of each cluster in each control cycle, the timing of the impulse control input, and the related communication network topology. Figure 9 The text details the situation of the first cycle.

[0265] Figure 9 attack signals in Corresponding to the communication edge under DoS attack, and This indicates a communication edge that will have its communication function restored during the recovery period. Clearly, Figure 9 It contains all the information from the first phase. According to... Figure 9 Table 3 provides detailed information from the second to the eighth control cycle.

[0266] According to Theorem 2, let... , , , Based on this, the evolution of the first UAV swarm was simulated using MATLAB, with a step size of 0.047. Under the above parameter configuration, the evolution of the position and velocity errors of the first UAV swarm was obtained, as follows: Figure 10 As shown. Figure 10 The illustration shows that at the moment the pulse occurs, the jump amplitude of any curve is less than or equal to 1, confirming that the hybrid control protocol proposed in this invention is energy-constrained.

[0267] also, Figure 10 The evolution of both position and velocity errors converged to 0, indicating that the first drone swarm had successfully achieved the predetermined pentagonal formation. This was achieved through methods such as... Figure 11 The following demonstrates the simulation of the motion trajectories of these drone nodes in MATLAB to verify this. Figure 12 A top-down view of the corresponding formation is displayed.

[0268] The second drone swarm: Through simulation of the virtual layer, in time... At that time, local leaders The position and velocity are respectively and Let cosine similarity threshold be used. and Manhattan distance threshold Combining the formula, we can obtain...

[0269]

[0270] Then, according to Figure 4 The strategy shown yielded the initial communication network topology for the second UAV swarm, as follows: Figure 13 As shown.

[0271] Similar to the first drone swarm, Table 4 provides details of the control cycle for the second drone swarm.

[0272] According to Theorem 2, let... , , , Then, the evolution of the second UAV swarm was simulated using MATLAB, with a step size of 0.047. Under the above parameter configuration, the evolution of the position and velocity errors of the second UAV swarm was obtained, as follows: Figure 14 As shown.

[0273] Obviously, Figure 14 The evolution of both position and velocity errors converges to 0, indicating that the second drone swarm has successfully achieved the pre-defined quadrilateral formation. Figure 15 This is demonstrated by simulating the motion trajectories of these drone nodes in MATLAB. Figure 16A top-down view of the corresponding formation is displayed.

[0274] The third drone swarm: Through simulation of the virtual layer, in time... At that time, local leaders The position and velocity are respectively and Set a cosine similarity threshold. and Manhattan distance threshold According to formula (5), we can obtain

[0275]

[0276] Then, according to Figure 4 The strategy shown yielded the initial communication network topology for the third drone cluster, as follows: Figure 17 As shown.

[0277] Similarly, Table 5 provides detailed information about the third drone swarm control cycle.

[0278] According to Theorem 2, let... , , , Based on this, the evolution of the third UAV swarm was simulated using MATLAB, with a step size of 0.047. Under the above parameter configuration, the evolution of the position and velocity errors of the third UAV swarm was obtained, as follows: Figure 18 As shown.

[0279] Obviously, Figure 18 The evolution of both position and velocity errors converged to 0, indicating that the third drone swarm had successfully achieved the predetermined linear formation. Figure 19 This is demonstrated by simulating the motion trajectories of these drone nodes in MATLAB. Figure 20 A top-down view of the corresponding formation is displayed.

[0280] Energy consumption is a key performance indicator of a control system. Figure 21 This paper illustrates the evolution of the position and velocity errors of the first UAV swarm when the energy constraint is removed from the proposed hybrid control protocol, while keeping other parameters constant. The results show that, without improvement in convergence time, excessively large impulse jumps occur, leading to significantly higher energy consumption. In contrast, the proposed hybrid control protocol effectively reduces overall energy consumption. Furthermore, due to the complexity of real-world environments, the inclusion of more realistic factors in this invention directly enhances the application potential of the proposed formation cooperation theory.

[0281] Table 1 shows... Assignment

[0282]

[0283] Table 2 shows the initial position and velocity information of the UAV nodes.

[0284]

[0285] Table 3 provides detailed information for the second to eighth control cycles of the first drone swarm.

[0286]

[0287] Table 4 provides detailed information for the second drone swarm control cycle.

[0288]

[0289] Table 5 provides detailed information for the third drone swarm control cycle.

[0290]

Claims

1. A two-layer structure multi-UAV swarm anti-DoS attack formation and cooperative method with energy-constrained hybrid control, characterized in that, Includes the following steps: S1: A two-layer UAV swarm architecture integrating physical and virtual layers is proposed, which evenly groups a large number of UAV nodes and establishes biomimetic communication between these UAV nodes to promote practical deployment; S2: Design an energy-constrained hybrid control protocol for UAV swarms that balances control efficiency, operating costs, and system robustness during formation coordination. S3: Introduces a novel DoS attack model that combines multiple time intervals and recovery probability; this DoS attack model enhances the survivability of drone swarms in real-world DoS attack scenarios.

2. The energy-constrained hybrid control method for dual-layer multi-UAV swarm anti-DoS attack formation coordination according to claim 1, characterized in that, In step S1, a virtual layer is introduced, and the physical layer and virtual layer are combined to construct a two-layer architecture for the UAV swarm; based on the positional relationships between UAV nodes, a large number of UAV nodes are uniformly divided into multiple UAV swarms, and bionic communication is efficiently established between them; a total of One drone node , of which Nodes In time Position and velocity are respectively expressed as and ; Set the initial time to and will Set the time at which the virtual layers to be introduced almost reach a consistent coordination; Upon reaching Previously, it was assumed that all drone nodes Remain unchanged, that is ;Will The neighbor node is defined as Then the time hour and The average position offset of each UAV node is defined as (1) in, ,and , and Represented on the x-axis, y-axis and z-axis respectively The value; similarly. Written as .

3. The energy-constrained hybrid control method for dual-layer multi-UAV swarm anti-DoS attack formation coordination according to claim 2, characterized in that, Will The average position offset factor is defined as (2) definition The overall variance is (3) in, These represent the weights on the x-axis, y-axis, and z-axis, respectively; then, through... and definition The positional centrality factor is (4) Reflecting UAV nodes The average similarity in location between it and all its neighboring UAV nodes, and The smaller the value, the higher the average similarity. reflect and The degree of consistency between them, among which The smaller the value, the higher the degree of inconsistency; consider and This enables control of UAV nodes. An effective measurement of positional centrality; when drone nodes More centrally located compared to all other drone nodes; use , The drone nodes are evenly divided into n drone clusters based on their location relationships. ; get The drone swarm, the first The number of drone nodes contained in a drone cluster is denoted as , Established; System redistribution of all drone nodes: (The following is a partial translation of the original text, which is not possible without further context.) A drone swarm is denoted as , No. The positions and speeds of the drone nodes in this cluster are as follows: and Also known as physical position and physical velocity.

4. The energy-constrained hybrid control method for dual-layer multi-UAV swarm anti-DoS attack formation coordination according to claim 3, characterized in that, Introducing a virtual layer, which contains A virtual UAV node, represented as ;in, As the overall leader, and each As with the A local leader associated with each UAV cluster; in time hour, Position and velocity are respectively expressed as and ; In time Position and velocity are respectively expressed as and After the introduction of the virtual layer, the first UAV nodes in a UAV cluster It will be designed to communicate with other UAV nodes, including both virtual and physical nodes, using virtual information; the virtual information includes virtual location. and virtual speed ,in It is necessary to maintain and Position offset between them to achieve formation coordination; in order to enable local leaders Able to better express and lead A swarm of drones, whose positions and velocities are initialized based on the average concept. and Similarly, global facilitator The initial position and velocity were set to and ; At the physical layer A swarm of drones establishes a biomimetic communication network topology; the first... The strategy for a drone swarm topology consists of three steps: Step 1: Drone Node Form a complete graph, that is, any two distinct drone nodes and The adjacency value between them is ;exist In the middle, superscript The index representing the initial communication network topology is denoted as: Since this invention will subsequently consider denial-of-service attacks, various communication network topologies will emerge, which are indexed as follows: ; Step 2: Calculate the values ​​for each UAV node separately. and Similarity of composite velocities between As shown below: (5) in, Middle and upper bids The meaning is the same as in step 1 above; and These represent the cosine similarity threshold and the Manhattan distance threshold, respectively, and their values ​​will be set according to actual needs; obviously, show and Their speeds are sufficiently similar; conversely, This indicates that their speeds are not similar enough; specifically, when ,set up ; Step 3: For each drone node If their corresponding composite velocity similarity If the connection is broken, all communication edges are disconnected; otherwise, all communication edges remain unchanged. This is achieved by assigning each pair of drone nodes... and adjacency value reallocation value To achieve this process; all isolated drone nodes are individually connected. Information only from Flow direction .

5. The energy-constrained hybrid control method for dual-layer multi-UAV swarm anti-DoS attack formation coordination according to claim 1, characterized in that, In the virtual layer, The dynamics are defined by the following formula (6) For each local leader Its dynamics are defined as (7) in, and These are two virtual control protocols, also known as virtual control inputs; At the physical layer, the dynamics of drone nodes Defined as (8) Virtual Control Protocol and A pulse control mechanism is employed to reduce computational costs; it is assumed that the virtual layer is immune to DoS attacks. and Defined respectively (9) (10) in It involves two pulses controlling the intensity; It is the Dirac increment function used for simulating pulse input, which satisfies the condition that when... hour, This represents the instantaneous pulse in the virtual layer, and also satisfies... , ;set up and ,prove and It is right-continuous.

6. The energy-constrained hybrid control method for dual-layer multi-UAV swarm anti-DoS attack formation coordination according to claim 5, characterized in that, design ; Integrated continuous time control component and energy-limited pulse control component ,Right now Control components and Defined as: (11) (12) in To control the intensity over continuous time, For pulse control intensity; Representing the The pulse instant of a drone swarm, it satisfies , ;set up ,Right now It is also right-continuous; It is a saturation function, defined as follows: 。 7. The energy-constrained hybrid control method for dual-layer multi-UAV swarm anti-DoS attack formation coordination according to claim 1, characterized in that, A DoS attack model consists of multiple cycles, each of which is further divided into a normal period, an attack period, a buffer period, and a recovery period; For periodicity; For general periods, the time range is: Apply continuous time control components to it , No. A drone swarm adopts The indexed biomimetic communication network topology, in particular, sets... .

8. The energy-constrained hybrid control method for dual-layer multi-UAV swarm anti-DoS attack formation coordination according to claim 7, characterized in that, For the attack period, the time range is: During this period, the attackers carried out a DoS attack at the physical layer, causing the damaged communication edges to be blocked and lose connection, which in turn caused changes in the communication network topology of the drone swarm. The indices of these communication network topologies that changed during the attack period are represented as follows: And the adjacency value and Defined as (13) (14) in and It is an attack signal; if in the first In a communication network topology, drone nodes and If the communication edge between them is blocked by a DoS attack, then ; otherwise, ; Similarly, if drone nodes and If the communication edge between them is blocked by a DoS attack, then ;otherwise, During this period, because DoS attacks can easily have a significant negative impact on control inputs that last for a long time, the physical layer only uses the pulse control protocol. Therefore, we set ; Furthermore, assuming the number of pulse control inputs during this time period is And their occurrence time is represented as .

9. The energy-constrained hybrid control method for dual-layer multi-UAV swarm anti-DoS attack formation coordination according to claim 8, characterized in that, For the buffer period, the time range is This period is primarily used to simulate the communication delay between the end of a DoS attack and the restoration of communication functionality; the communication network topology during this period remains consistent with that during the attack period, i.e. ; In addition, during this period, and A value of 0 indicates that no control is applied.

10. The energy-constrained hybrid control method for dual-layer multi-UAV swarm anti-DoS attack formation coordination according to claim 8, characterized in that, For the recovery period, the time range is as follows: During this period, the new communication network topology was indexed as ; in the In a communication network topology, let Indicates drone node and The random events that restore communication between them after being blocked by a DoS attack, in which Within this interval and The value is defined as (15) (16) In addition, a continuous time control component is applied during the recovery period. .

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