A multi-unmanned aerial vehicle distributed formation safety control method based on a dual network

Abstract

The present application relates to the technical field of unmanned aerial vehicle safety, especially to a kind of multi-unmanned aerial vehicle distributed formation safety control method based on dual network, the method, including establishing dynamic model, connectivity index and DoS attack sequence, and define formation tracking error and control target, fusion feature parameter constructs continuous comprehensive communication quality evaluation index, constructs the hysteresis adaptive mode switching rule with anti-jitter characteristics, set up adaptive shrink network controller based on recursive balance network, generate the distributed control law adapted to current mode;Based on shrink mapping theory and multiple Lyapunov function method, the exponential stability of switching system is analyzed, and the verification operation is carried out through simulation experiment, the adaptive shrink network controller is constructed using recursive balance network architecture, the real-time control capability of embedded platform is improved, and the conflict problem of calculation complexity and real-time demand is solved.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) security technology, and in particular to a multi-UAV distributed formation security control method based on dual networks. Background Technology

[0002] Distributed collaborative operations of multiple UAV swarms have been widely used in low-altitude operations, collaborative reconnaissance, and disaster relief due to their flexibility and efficiency. Their stable operation is highly dependent on wireless communication links. However, the open nature of communication links makes UAV swarms vulnerable to adversarial threats such as DoS attacks and signal interference. Especially in disputed airspace or complex electromagnetic environments, communication security has become the core bottleneck restricting mission reliability. Unlike the stable communication infrastructure of ground systems, UAV swarms need to cope with complex situations such as rapid changes in channel conditions, intermittent connection interruptions, and deliberate interference. Communication quality often exhibits a gradual degradation characteristic.

[0003] Existing control methods suffer from three core shortcomings: First, they lack continuous communication quality assessment and adaptive control mechanisms. Most existing formation control methods rely on binary fault detection logic to determine communication status, failing to reflect the gradual degradation of communication quality from excellent to poor. This results in a lack of precise quality basis for control strategy adjustments. Second, there is insufficient theoretical guarantee for the stability of the switching system. For potential mode switching mechanisms, existing technologies have not established a comprehensive stability analysis system. This leads to a lack of theoretical basis for designing the quality threshold for mode switching. The optimization of switching gain and Lyapunov function weight matrix lacks a systematic method, resulting in a significant gap between experimental results and theoretical analysis, and failing to ensure system stability during switching. Finally, there is a conflict between computational complexity and real-time requirements. In emergency scenarios with severe communication quality degradation, the computational resources of UAV embedded platforms are limited. It is necessary to reduce the computational overhead of control algorithms to ensure real-time performance. Traditional fully connected neural networks have high computational complexity, making it difficult to meet the real-time control requirements of embedded platforms. Even if some methods use recursive balanced networks to reduce complexity to some extent, the fixed network size still presents a computational bottleneck in emergency scenarios. At present, a multi-UAV distributed formation safety control method based on dual networks is needed. Summary of the Invention

[0004] To address the problems of unstable formation and low control accuracy in existing multi-UAV distributed formation control due to the lack of theoretical guarantees for the stability of the switching system and the difficulty in balancing computational complexity and real-time performance, this invention provides a multi-UAV distributed formation safety control method based on dual networks.

[0005] This invention provides a multi-UAV distributed formation security control method based on dual networks, which adopts the following technical solution:

[0006] A method for distributed formation security control of multiple unmanned aerial vehicles based on dual networks includes:

[0007] Collect multimodal data from multiple UAV clusters, establish dynamic models, connectivity indices, and DoS attack sequences based on the multimodal data, and define formation tracking errors and control objectives;

[0008] Extract physical layer channel feature parameters and network layer topology feature parameters, and fuse the feature parameters to construct a continuous comprehensive communication quality evaluation index;

[0009] Based on the real-time calculation results of the comprehensive communication quality assessment index, a hysteresis adaptive mode switching rule with anti-jitter characteristics is constructed to realize the dynamic switching between normal mode and emergency mode.

[0010] An adaptive shrinking network controller based on a recursive equilibrium network is established. Different network sizes are configured according to the needs of different control modes, and a distributed control law adapted to the current mode is generated.

[0011] Based on the contraction mapping theory and the multi-Lyapunov function method, combined with the dynamic model and controller parameters, the exponential stability of the switching system is analyzed, and the steady-state error bound is quantified.

[0012] Furthermore, the establishment of the dynamic model, connectivity index, and DoS attack sequence includes acquiring multimodal data composed of state data, communication link data, and external environment data of each UAV; establishing a continuous-time state-space equation for the i-th UAV based on the state data; the continuous-time state-space equation including the state vector, control input, and external disturbance; and, for the quadcopter UAV platform, establishing a dynamic model in the form of a second-order integrator. The system matrix of the dynamic model is constructed in a block matrix form, and the expression of the dynamic model is:

[0013] ,

[0014] in, This is a state vector containing the drone's position and velocity information. The thrust control input applied to the UAV is as follows: It is an external disturbance and satisfies boundedness constraints. A is the system matrix, and B is the input matrix. This is the upper bound of the boundedness constraint for external disturbances.

[0015] Furthermore, the establishment of the dynamic model, connectivity index, and DoS attack sequence also includes:

[0016] Based on communication link data, a directed graph is used. Construct a communication network topology between drones, where the node set The elements correspond to the drone numbers, edge sets The elements represent the connectivity state of the communication links between UAVs, and the adjacency matrix... The element quantizes the connection weights of the communication link;

[0017] Define degree matrix Furthermore, a Laplace matrix is ​​constructed by combining the adjacency matrix, and the second smallest eigenvalue of the Laplace matrix is ​​used as the algebraic connectivity index.

[0018] Establish a DoS attack sequence based on external environment data. And introduce frequency constraints. Duration constraints ;

[0019] in, Let N be the communication degree of the drone. Let k be the start time of the k-th DoS attack. This represents the end time of the k-th DoS attack. This is the attack frequency offset parameter. To define the upper bound parameter for the attack duty cycle, For attack duration elasticity parameters, To calculate the start time, This is the current statistical time.

[0020] Furthermore, the extraction of physical layer channel feature parameters and network layer topology feature parameters includes obtaining the signal-to-noise ratio (SNR), packet loss rate, and bit error rate of the communication link. Based on the dimensional differences and numerical range characteristics of the SNR, a typical communication threshold is used as the mapping center, and the Sigmoid function is employed to map it to the zero-to-one interval. The mapping sensitivity is controlled by adjusting the steepness coefficient. The normalized SNR quality index, the complementary amount of the packet loss rate, and the complementary amount of the bit error rate are weighted and fused to construct the physical layer channel quality index. The expression of the physical layer channel quality index is as follows:

[0021] ,

[0022] in, This is a normalized signal-to-noise ratio (SNR) quality metric. For packet loss rate, For bit error rate, , and These are the corresponding weighting coefficients.

[0023] Furthermore, the step of fusing the feature parameters to construct a continuous comprehensive communication quality assessment index includes: calculating the algebraic connectivity feature value of the current communication topology in real time based on the Laplace matrix; performing a ratio operation between the current algebraic connectivity feature value and the maximum algebraic connectivity feature value under nominal conditions to obtain the network layer topology quality index; and integrating the physical layer channel quality index and the network layer topology quality index into a comprehensive communication quality assessment index through a hierarchical weighted fusion mechanism. The expression for the network layer topology quality index is as follows:

[0024] ,

[0025] in, To maximize algebraic connectivity, It is the second smallest eigenvalue of the current Laplacian matrix.

[0026] Furthermore, the construction of the hysteresis adaptive mode switching rule with anti-jitter characteristics includes setting a recovery switching threshold. Emergency switching threshold Formation of hysteresis bandwidth Based on hysteresis bandwidth, a quantitative relationship is established between average dwell time, hysteresis bandwidth, and quality change rate. The recovery handover threshold characterizes the quality recovery level required to return from emergency mode to normal mode, while the emergency handover threshold characterizes the tolerable quality degradation limit when switching from normal mode to emergency mode. A segmented mode switching logic rule is constructed.

[0027] ,

[0028] in, For mode signals, To switch to the previous mode state, Normal mode For emergency mode, It serves as a comprehensive communication quality assessment indicator.

[0029] Furthermore, the generation of a distributed control law adapted to the current mode includes constructing an adaptive shrinking network controller using a recursive balanced network architecture, defining an L-layer network structure, and the... The layers achieve forward propagation of information through weight matrices and activation functions. The input layer receives the UAV state deviation signal, and the output layer generates a nonlinear control mapping signal. Based on normal mode and emergency mode, differentiated network size parameters are configured. The normal mode uses the number of first neurons. To fully utilize neighbor collaborative information, the emergency mode employs a second neuron count. ,and To reduce computational overhead, a distributed control law adapted to the current mode is generated based on a recursive balancing network mapping function and mode-dependent control gain. This control law is constructed as a weighted sum of neighbor connection weights and network mapping outputs, expressed as:

[0030] ,

[0031] in, For mode-dependent control gain, For the neighborhood group, For connection weights, For recursive balanced network mapping functions, and These are the state vectors of the i-th and j-th drones, respectively.

[0032] Furthermore, the determination of the mode-dependent control gain includes analyzing the shrinkage characteristics of the recursive equilibrium network based on shrinkage mapping theory, determining the shrinkage factor of the network mapping, wherein the shrinkage factor is determined by the power form of the product of the Lipshitz constant of the activation function and the spectral norm of the weight matrix, constructing a Lyapunov function composed of the augmented system matrix, the graphical Laplace matrix, and the mode-dependent positive definite weight matrix, and determining the lower bound constraint of the control gain based on the Lyapunov function, wherein the control gain satisfies the following lower bound constraint conditions:

[0033] ,

[0034] in, For pattern Control gain below, To augment the system matrix, For pattern-dependent positive definite weight matrices, For pattern-dependent Laplace matrix, To augment the input matrix, It is the network shrinkage factor and satisfies , for The non-zero smallest eigenvalue, Similarly, it is the largest eigenvalue.

[0035] Furthermore, the analysis of the shrinkage characteristics of the recursive equilibrium network based on the shrinkage mapping theory includes constructing the recursive equilibrium network using an activation function that satisfies the Lipshitz continuity condition. The Lipshitz continuity condition is characterized by the fact that, for any input vector, the deviation of the activation function output is constrained by a linear function of the input deviation, where the coefficient of the linear function is the Lipshitz constant. An upper bound constraint on the spectral norm of the weight matrices of each layer of the recursive equilibrium network is set. Based on the Lipshitz constant and the upper bound of the spectral norm, the shrinkage factor of the recursive equilibrium network mapping is obtained. The recursive equilibrium network mapping satisfies the following shrinkage condition:

[0036] ,

[0037] in, For recursive balanced network mapping functions, Let Lipschitz constant be the activation function. The upper bound of the spectral norm of the weight matrix is ​​given by... For network layers, For any input vector of the recursive balancing network, Let be another arbitrary input vector for the recursive balancing network.

[0038] Furthermore, the exponential stability of the analysis switching system includes:

[0039] Based on normal mode and emergency mode, Lyapunov functions are constructed respectively. The Lyapunov functions are constructed in the form of quadratic matrix with the augmented formation error vector as the independent variable. The derivative of the Lyapunov function is calculated along the system trajectory. Combined with the constraint of control gain, sufficient conditions for the exponential decay of the Lyapunov function during the duration of each mode are established to determine the Lyapunov function jump ratio at the mode switching time to quantify the switching gain.

[0040] Based on the constraint of average residence time, a sufficient condition for the average residence time to be globally exponentially stable in the switching system is established, under the presence of bounded external disturbances. Under the given conditions, based on the Lyapunov function derivative constraint and contraction mapping property, the steady-state upper bound is analytically obtained.

[0041] In summary, the present invention has the following beneficial technical effects:

[0042] 1. This invention establishes a complete modeling system that includes dynamic models, connectivity indices, and DoS attack sequences by collecting multimodal data from multiple UAV clusters. Combined with the clear definition of formation tracking errors and control targets, it achieves a comprehensive and accurate characterization of UAV motion characteristics, communication network topology, and resistance to environmental interference. This provides solid data support and model foundation for the design of subsequent safety control strategies and effectively solves the problems of one-sided modeling and disconnection from actual scenarios in traditional methods.

[0043] 2. This invention extracts physical layer channel feature parameters and network layer topology feature parameters, uses the Sigmoid function to normalize the signal-to-noise ratio, and weights and fuses complementary quantities such as packet loss rate and bit error rate to construct a physical layer channel quality index. Combined with the network layer topology quality index obtained by algebraic connectivity ratio calculation, a continuous comprehensive communication quality evaluation index is further constructed through hierarchical weighted fusion. This invention breaks through the limitations of traditional binary communication state detection, realizes real-time and accurate perception of the gradual degradation process of communication quality, and provides a scientific decision basis for mode switching.

[0044] 3. Based on the real-time calculation results of comprehensive communication quality evaluation indicators, this invention constructs an adaptive mode switching rule with hysteresis bandwidth. By setting recovery switching threshold and emergency switching threshold, a quantitative relationship between average dwell time and hysteresis bandwidth and quality change rate is established, which effectively avoids system oscillation caused by frequent mode switching and realizes smooth dynamic switching between normal mode and emergency mode. When the communication quality is good, it makes full use of neighbor cooperative information to optimize performance, and relies on local state to maintain stability when the communication degrades, thus balancing control accuracy and system robustness.

[0045] 4. This invention uses a recursive balanced network architecture to construct an adaptive shrinking network controller. Different network sizes are configured for different control modes. In the normal mode, a larger number of neurons ensures the accuracy of collaborative control, while in the emergency mode, the number of neurons is reduced to reduce computational overhead. Combined with the mode-dependent distributed control law design, the computational complexity is reduced compared to traditional fully connected networks, which improves the real-time control capability of embedded platforms and solves the conflict between computational complexity and real-time requirements.

[0046] 5. This invention analyzes the shrinkage characteristics of recursive equilibrium networks based on shrinkage mapping theory, determines the network shrinkage factor, constructs a quadratic Lyapunov function by combining the multi-Lyapunov function method, and quantifies the steady-state error bound by deriving the lower bound constraint of the control gain and the average residence time condition for the global exponential stability of the switching system. This establishes a complete stability theory guarantee system, ensuring the stability and convergence of the system during mode switching, and avoiding the defects of traditional switching systems such as lack of theoretical support and performance fluctuations. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of the overall process of a multi-UAV distributed formation security control method based on dual networks according to an embodiment of the present invention.

[0048] Figure 2 This is a system architecture diagram of a multi-UAV distributed formation security control method based on dual networks according to an embodiment of the present invention.

[0049] Figure 3 This is a diagram illustrating the dynamic correlation between communication quality score and mode switching in a DoS attack scenario, as described in this embodiment of the invention.

[0050] Figure 4 This is a diagram of the triangular formation double-hole obstacle crossing trajectory according to an embodiment of the present invention.

[0051] Figure 5 This is a pentagonal formation 3D complex obstacle avoidance trajectory diagram according to an embodiment of the present invention. Detailed Implementation

[0052] The present invention will be further described in detail below with reference to the accompanying drawings.

[0053] Example 1: Refer to Figure 1 This embodiment of a multi-UAV distributed formation security control method based on dual networks includes:

[0054] S1. Collect multimodal data of multiple UAV clusters, establish dynamic models, connectivity indices and DoS attack sequences based on the multimodal data, and define formation tracking error and control objectives;

[0055] S2. Extract physical layer channel feature parameters and network layer topology feature parameters, and fuse the feature parameters to construct a continuous comprehensive communication quality evaluation index;

[0056] S3. Based on the real-time calculation results of the comprehensive communication quality evaluation index, construct a hysteresis adaptive mode switching rule with anti-jitter characteristics to realize dynamic switching between normal mode and emergency mode.

[0057] S4. Establish an adaptive shrinking network controller based on a recursive equilibrium network, configure differentiated network sizes according to the needs of different control modes, and generate distributed control laws that adapt to the current mode.

[0058] S5. Based on the contraction mapping theory and the multi-Lyapunov function method, combined with the dynamic model and controller parameters, the exponential stability of the switching system is analyzed, and the steady-state error bound is quantified.

[0059] Specifically, a multi-UAV distributed formation security control method based on dual networks includes the following steps:

[0060] like Figure 1 As shown, S1 collects multimodal data of multiple UAV clusters, establishes dynamic models, connectivity indices and DoS attack sequences based on the multimodal data, and defines formation tracking error and control objectives;

[0061] First, multimodal data collection was conducted across a multi-UAV swarm. The inertial measurement units (IMUs) and global positioning systems (GPS) onboard the UAVs were used to collect real-time status data for each UAV, including its three-dimensional position coordinates. 3D velocity information In addition to acceleration data, communication link data is collected through the communication link monitoring module, covering signal-to-noise ratio (SNR), packet loss rate (PLR), bit error rate (BER), and the communication connection status between UAVs (i.e., whether there is a valid communication link). Finally, environmental perception sensors are used to collect external environmental data, including observations of external disturbances such as wind load and air resistance, as well as relevant parameters of DoS attacks, such as the start time, end time, and intensity of the attack, to ensure that multimodal data can comprehensively characterize the UAV's motion state, communication network characteristics, and external environmental interference.

[0062] Based on the collected UAV state data, a continuous-time state-space equation for the i-th UAV is established. Considering the flight characteristics of quadcopter UAVs, a dynamic model is constructed using a second-order integrator. This model accurately describes the coupling relationship between the UAV's position and velocity, as well as the influence of control inputs and external disturbances on its motion state. The expression for the dynamic model is as follows: ,in, The state vector contains the position and velocity information of the UAV, specifically represented as follows: , These represent the position information of the i-th drone along the x, y, and z axes, respectively. These are the velocity information in the corresponding axial directions. The three-dimensional thrust control input applied to the UAV is used for control purposes. For external perturbation, dimension and state vector Consistent, encompassing nondeterministic disturbance factors such as wind load, air resistance, and mechanical vibration, and satisfying boundedness constraints. A is the system matrix, and B is the input matrix. The upper limit of the bounded constraint on external disturbances is determined based on actual flight environment tests. In this embodiment, the value is taken as 0.5 m / s² to ensure that the disturbance is always within the tolerable range.

[0063] Both the system matrix A and the input matrix B are constructed using a block matrix approach. Considering the dynamic characteristics of the second-order integrator, A is... A 3D matrix, B is A 3D matrix, specifically expressed as:

[0064] ,

[0065] in, for zero-order matrix for The identity matrix of order 1 ensures that the control input directly affects the velocity change process, which conforms to the motion law of the quadcopter UAV.

[0066] Based on the connection state information in the collected communication link data, a directed graph is used. Construct a communication network topology for drones, node set Where N is the total number of drones in the swarm, and in this embodiment, N can be 3, 4, or 5, corresponding to triangle, square, and pentagon formations, respectively. Each positive integer element in the set corresponds to a drone number, which is a unique identifier for the drone in the communication network. Elements are represented by ordered pairs (i,j). If a valid communication link is detected between the i-th drone and the j-th drone, then... ,otherwise Adjacency matrix Given an N×N dimensional matrix, matrix elements Used to quantify the connection weights of communication links, if ,but Based on the SNR value of the communication link, specifically: The value ranges from (0, 0.1]. The higher the SNR, the better. The larger the value, the better the quality of the communication link. ,but .

[0067] Further define the degree matrix The matrix is A 3D diagonal matrix containing non-zero elements only on its diagonal, where the diagonal elements are... The communication degree of the Nth drone is the sum of the weights of the effective communication links established between this drone and other drones in the cluster. It is used to characterize the communication connectivity of a single drone. For the Nth drone, the calculation method for the communication degree with other drones is the same, combined with the adjacency matrix. Sum-degree matrix Constructing the Laplace matrix The construction method is This matrix can reflect the topological characteristics of the communication network, and its second smallest eigenvalue... As an algebraic connectivity metric, it is used to quantify the connectivity strength of communication networks. The larger the value, the stronger the network connectivity and the smoother the information exchange between drones. In actual calculations, the Laplacian matrix is ​​processed by the eigenvalue decomposition algorithm, and its second smallest eigenvalue is extracted as the quantification result of algebraic connectivity.

[0068] Based on the attack parameters in the collected external environment data, a DoS attack sequence is established. Where k represents the number of attacks. Let k be the start time of the k-th DoS attack. The interval is the end time of the k-th DoS attack. The duration of the k-th attack is represented by the attack mode, which can be any combination of bandwidth flooding (BF), selective interference (SJ), protocol interruption (PD), and coordinated attack (CA). To quantify the impact boundary of the attack on the communication network, frequency constraints and duration constraints are introduced, where the frequency constraint is as follows: In the formula Indicates the time interval Total number of DoS attacks that occurred within the period. To calculate the start time, For the current statistical time, This is the attack frequency offset parameter, which is set to 1 in this embodiment to correct for sudden attacks during the initial time period. To ensure the average attack interval is 10 seconds in this embodiment, the attack frequency is kept within a reasonable range; the duration constraint is... In the formula Time interval The sum of the durations of all DoS attacks within the region. The upper bound parameter for the attack duty cycle is set to 0.5 in this embodiment, which limits the maximum cumulative duration of the attack per unit time. The attack duration is set as an elastic parameter, which is set to 2 seconds in this embodiment to provide flexibility in constraining the attack duration.

[0069] Finally, the formation tracking error and control objective are defined, and the desired formation vector is set according to the actual mission requirements. Since the location information is three-dimensional, we take... , This represents the expected position offset of the i-th drone relative to the virtual leader. For example, in a triangular formation, if the virtual leader's position is... Then the desired formation vectors of the three drones can be set as follows: , This ensures that the formation forms an equilateral triangle with sides of 4 meters.

[0070] Formation tracking error Defined as This is used to quantify the deviation between the actual position of the drones and the desired formation position, where Let i be the actual position of the i-th drone. The virtual leader's position can be preset based on the task trajectory, such as a straight line trajectory. (This indicates uniform motion along the x-axis, with the y-axis position remaining constant, and a height of 5 meters). The control objective of this invention is to make the formation tracking error converge to a preset tolerable range over time, i.e., to satisfy... ,in To accommodate the formation error boundary, a value of 0.2 meters is used in this embodiment to ensure that the drone swarm can stably maintain the desired formation and accurately track the trajectory of the virtual leader.

[0071] S2. Extract physical layer channel feature parameters and network layer topology feature parameters, and fuse the feature parameters to construct a continuous comprehensive communication quality evaluation index;

[0072] Physical layer channel characteristic parameters are extracted and physical layer channel quality indicators are constructed. The communication link monitoring module collects three core characteristic parameters of each communication link in real time: signal-to-noise ratio (SNR), packet loss rate (PLR), and bit error rate (BER). Since SNR has different dimensions and significantly different numerical ranges than PLR and BER, direct fusion will lead to distorted evaluation results. Therefore, SNR needs to be normalized. In this embodiment, a typical communication threshold of 20dB is used as the mapping center (i.e.,...). The signal-to-noise ratio (SNR) is mapped to the [0,1] interval using the Sigmoid function. This function can achieve a nonlinear dimensionless transformation of the SNR, and the steepness coefficient can be adjusted. In this embodiment, the mapping sensitivity is controlled. The value is set to 5, so that the mapping function is... The signal-to-noise ratio (SNR) has suitable sensitivity, capable of distinguishing differences in channel quality without saturation due to extreme values. The expression for the normalized SNR is:

[0073] ,

[0074] in dB is the normalization center. Controlling the steepness, this function will reduce the SNR from Mapped to interval, when hour This achieves dimensionless quality indicators.

[0075] The normalized signal-to-noise ratio quality index Subsequently, considering that a higher packet loss rate (PLR) and bit error rate (BER) indicate a worse channel quality, their complementary values ​​(1-PLR) and (1-BER) are used as effective quality characterization parameters. Then, a weighted fusion mechanism is used to construct the physical layer channel quality index. Set weighting coefficients. , and These correspond to the weights of the normalized signal-to-noise ratio (SNR) quality index, the packet loss rate complement, and the bit error rate complement, respectively. The values ​​of the weight coefficients are determined based on the degree of influence of each parameter on channel quality in the actual communication scenario. In this embodiment, considering the actual needs of multi-UAV swarm communication, the following settings are used: , , This approach emphasizes both the core impact of signal-to-noise ratio (SNR) and the roles of packet loss rate and bit error rate. Physical layer channel quality indicators. The expression is: ,in, This is a normalized signal-to-noise ratio (SNR) quality metric. For packet loss rate, For bit error rate, , and The corresponding weighting coefficient is [0,1]. The value of this index is between [0,1]. The larger the value, the better the physical layer channel quality.

[0076] Next, network layer topology feature parameters are extracted and network layer topology quality indicators are constructed, based on the Laplace matrix corresponding to the communication network topology structure constructed in step S1. The second smallest eigenvalue of the matrix is ​​calculated in real time using an eigenvalue decomposition algorithm. This characteristic value is the algebraic connectivity of the communication network, which is a core indicator for measuring the strength of network topological connectivity. This indicates network connectivity, with larger values ​​signifying stronger network connectivity, smoother information exchange between drones, and stronger anti-interference capabilities. Simultaneously, the second smallest eigenvalue of the Laplace matrix of the communication network under nominal communication conditions (i.e., an ideal communication environment without DoS attacks or interference) is obtained through offline simulation or experimental testing. This value serves as a benchmark for network topology quality, quantifying the degree of degradation in the current topology. Network Layer Topology Quality Indicators It is obtained by calculating the ratio of the current algebraic connectivity eigenvalue to the maximum algebraic connectivity eigenvalue, and the expression is: ,in, To maximize algebraic connectivity, This is the second smallest eigenvalue of the current Laplacian matrix. Its value ranges between [0,1]. When the value approaches 1, it indicates that the current network topology is almost complete and the connectivity is close to ideal; when... When the value approaches 0, it indicates that the network topology has severely degraded, is on the verge of disconnection, and cannot achieve effective information exchange.

[0077] Finally, a continuous comprehensive communication quality evaluation index Q(t) is constructed through a hierarchical weighted fusion mechanism. This mechanism is achieved by setting weight coefficients. and Adjust the physical layer channel quality indicators separately and network layer topology quality indicators The influence weight, and satisfying Considering the communication characteristics of multi-UAV formations in adversarial environments, the physical layer channel quality directly affects the effectiveness of data transmission, while the network layer topology quality affects the scope and efficiency of information exchange. Therefore, this embodiment sets... , This emphasizes the dominant role of physical layer channel quality while also considering the impact of network layer topology quality. A comprehensive communication quality assessment index is proposed. The expression is: This indicator, with a value range of [0,1], can continuously and comprehensively depict the gradual degradation process of communication quality from excellent to poor. It overcomes the limitation of traditional binary detection, which can only determine "valid" or "invalid," providing a precise and continuous decision-making basis for the subsequent construction of hysteresis adaptive mode switching rules. In actual calculations, the comprehensive communication quality evaluation index... The update frequency is consistent with the data acquisition frequency, which is 100Hz, to ensure that the dynamic changes in communication quality can be reflected in real time.

[0078] S3. Based on the real-time calculation results of the comprehensive communication quality evaluation index, construct a hysteresis adaptive mode switching rule with anti-jitter characteristics to realize dynamic switching between normal mode and emergency mode.

[0079] Based on the comprehensive communication quality evaluation index obtained in step S2 Based on real-time calculation results, a hysteresis adaptive mode switching rule with anti-jitter characteristics is formed by setting a hysteresis threshold, establishing an average dwell time constraint, and constructing a segmented switching logic. First, the hysteresis threshold and hysteresis bandwidth are set. According to the actual needs of multi-UAV formation communication and the communication quality degradation law in adversarial environments, the recovery switching threshold is set through offline simulation testing and engineering experience value calibration. Emergency switching threshold Among them, the recovery switching threshold This threshold represents the level of communication quality recovery required to return from emergency mode to normal mode. The system is only allowed to switch back to normal mode when the comprehensive communication quality assessment index Q(t) remains consistently above this threshold, ensuring that communication quality has been stably restored and avoiding ineffective switching due to a temporary rebound in quality. Emergency switching threshold. This threshold represents the tolerance limit for communication quality degradation when switching from normal mode to emergency mode. When the comprehensive communication quality assessment index Q(t) remains below this threshold, the system triggers a switch from normal mode to emergency mode to quickly respond to communication quality deterioration and ensure basic formation stability. The hysteresis bandwidth is defined by the difference between the recovery switch threshold and the emergency switch threshold. The hysteresis bandwidth is the core of achieving anti-jitter characteristics. By setting a reasonable bandwidth range, frequent mode switching caused by small fluctuations in the comprehensive communication quality evaluation index Q(t) around a single threshold can be avoided, thereby reducing the impact of switching transients on system control performance.

[0080] Next, a quantitative relationship is established between average dwell time, hysteresis bandwidth, and quality change rate based on hysteresis bandwidth to further constrain mode switching behavior and ensure the stability and controllability of switching. The change rate of the comprehensive communication quality assessment index Q(t) is affected by factors such as the dynamic characteristics of the communication link and changes in the intensity of DoS attacks. Qmax is defined as the maximum change rate of the comprehensive communication quality assessment index, which is determined by real-time monitoring of the absolute value of the time derivative of Q(t) and taking its statistical maximum value. In this embodiment... The value is 0.1 (unit: 1 / second). According to the anti-jitter principle of the hysteresis handover rule, when the system switches from one mode to another, to achieve another handover, the comprehensive communication quality evaluation index Q(t) must traverse the entire hysteresis bandwidth. Therefore, minimum switching interval satisfy: Substituting the threshold and maximum rate of change parameters in this embodiment, we can obtain The minimum time interval between any two mode switches is no less than 3 seconds, effectively avoiding system oscillations caused by high-frequency switching. Furthermore, based on the minimum switching interval, a lower bound for the average dwell time is derived. Defined as the average time the system continuously operates in any mode, considering the worst-case scenario where the comprehensive communication quality evaluation index Q(t) oscillates between two thresholds, with each oscillation requiring two crossings of the hysteresis bandwidth, the lower bound of the actual average dwell time satisfies: Substituting the parameters, we can obtain the following calculation: The second constraint sets an upper limit on the frequency of mode switching, ensuring that the system has enough time to operate stably in each mode and avoiding problems such as insufficient execution of control commands and increased formation errors caused by excessive switching.

[0081] Subsequently, a segmented mode switching logic rule was constructed to clarify the mode switching decision within the range of different comprehensive communication quality assessment indicators Q(t), and the mode signal. Used to identify the current operating mode of the system, This indicates the normal mode, in which the system makes full use of neighboring cooperative information among UAVs and adopts a more complex network scale and control strategy to achieve high-precision formation tracking control; This indicates the emergency mode. In this mode, the system relies solely on the drone's own status and virtual leader information, employing a simplified network scale and control strategy. This sacrifices some control precision to ensure basic formation stability even when communication quality severely degrades. The specific expression for the switching logic rule is:

[0082] ,

[0083] in, For mode signals, To switch to the previous mode state, Normal mode For emergency mode, It serves as a comprehensive communication quality assessment indicator.

[0084] The specific execution process of this segmented logic rule is as follows: If the system is currently in normal mode, when the real-time calculated Q(t) is continuously lower than... When this happens, the system triggers a switch, updating the mode signal to... Enter emergency mode; if the system is currently in emergency mode, when the real-time calculated Q(t) is consistently higher than... When this happens, the system triggers a switch, updating the mode signal to... If Q(t) fluctuates between 0.4 and 0.7, the mode remains unchanged regardless of the current mode, effectively avoiding frequent switching caused by boundary jitter.

[0085] During actual system operation, the comprehensive communication quality evaluation index Q(t) is calculated in real time according to the 100Hz update frequency set in step S2, and the mode switching rules are executed synchronously in real time. Each time it is executed, the Q(t) value at the current moment and the mode state at the previous moment are obtained first. Then, based on the above segmented logic rules, it is determined whether a mode switch is needed. To ensure the accuracy of the "continuously below" or "continuously above" threshold judgment, a time judgment window is set to 0.5 seconds, that is, when Q(t) is lower than... Furthermore, the emergency mode switching condition is only met when the duration reaches 0.5 seconds; when Q(t) is higher than... Furthermore, the switching condition is only considered met when the duration reaches 0.5 seconds, further enhancing the anti-jitter performance of the switching rules and avoiding false switching caused by instantaneous quality fluctuations. After generation, it is transmitted to the adaptive shrinking network controller in real time, providing a mode identifier for the controller to configure differentiated network size according to the current mode and generate adaptive control laws, thereby realizing dynamic matching between control mode and communication quality status.

[0086] S4. Establish an adaptive shrinking network controller based on a recursive equilibrium network, configure differentiated network sizes according to the needs of different control modes, and generate distributed control laws that adapt to the current mode.

[0087] By constructing an Adaptive Shrinking Network (ASCN) controller based on a recursive balanced network, differentiated network sizes are configured for normal and emergency modes. Combined with the quantization design of mode-dependent control gain, a distributed control law adapted to the current communication quality state is generated. This resolves the conflict between computational complexity and real-time performance while ensuring control accuracy. First, the architecture of the adaptive shrinking network controller is designed, employing a recursive balanced network structure with a non-cyclic forward propagation to achieve low-complexity nonlinear control mapping. The total number of network layers is defined as L (L=3 in this embodiment, balancing control accuracy and computational efficiency). Each layer completes the forward propagation of information through a weight matrix and activation function. The input layer receives the UAV state deviation signal, the hidden layer performs feature extraction and nonlinear mapping, and the output layer generates the nonlinear control mapping signal. The output expression for layer (l=1,2,…,L) is:

[0088] ,

[0089] in, For the activation function, this embodiment uses the improved form of the ReLU function, LeakyReLU, to avoid the gradient vanishing problem of the ReLU function in the negative region. For the first The weight matrix of the layer, The output signal of the output layer, i.e., the mapping function of the recursive balanced network. The output satisfies ,in addition, The input signal is represented as the state deviation between the i-th UAV and its neighboring UAV j in normal mode. In emergency mode, the state deviation between the i-th drone and the virtual leader is... The computational complexity of this recursive balanced network is . Compared to traditional fully connected networks This significantly reduces costs and provides a foundation for real-time operation of embedded platforms.

[0090] Based on the two control modes determined in step S3, differentiated network size parameters are configured to achieve a dynamic balance between control accuracy and computational overhead. In normal mode, communication quality is good, inter-UAV neighbor collaboration information is effective, and a larger number of first neurons is used. (In this embodiment) ), fully utilizing neighbor information to improve formation tracking accuracy, at which point the network computational complexity is O(n). In emergency mode, communication quality degrades, so priority must be given to ensuring real-time control, and a smaller number of second neurons should be used. And satisfy (In this embodiment) By reducing the network width, the computational overhead is reduced, and the network computational complexity is now O(n). The rate of reduction in computational complexity between the two modes Defined as:

[0091] ,

[0092] Substituting the parameters into this embodiment yields... This means that the computational complexity is reduced by 75% in emergency mode, effectively meeting the real-time requirements in communication-constrained scenarios. After configuring the network size parameters, the initial values ​​of the weight matrix and bias vector of each layer are determined through offline training. The training process aims to minimize the formation tracking error, and the gradient descent algorithm is used to iteratively update the parameters until the network converges.

[0093] Next, the mode-dependent control gain is determined. Based on the shrinkage mapping theory, the shrinkage characteristics of the recursive equilibrium network are analyzed to provide quantization constraints for the control gain. First, the Lipshitz continuity condition of the activation function is verified. For the selected LeakyReLU activation function, its Lipshitz constant is... Theoretical derivation shows that the activation function satisfies the following conditions within its domain: Set an upper bound on the spectral norm of the weight matrices of each layer in the recursive balanced network. To ensure the stability of the weight matrix and avoid gradient explosion during network training, this is based on the Lipschitz constant. upper bound of spectral norm Calculate the shrinkage factor of the network mapping. Its expression is: satisfy This indicates the recursive balanced network mapping function. The shrinking mapping can continuously compress input state deviations and promote formation error convergence.

[0094] To ensure the stability of the closed-loop system, a Lyapunov function is constructed, consisting of an augmented system matrix, a graphical Laplace matrix, and a mode-dependent positive definite weight matrix. The augmented system matrix... ,in, It is an N-order identity matrix. (This is the Kronecker product, where A is the single UAV system matrix defined in step S1), augmented input matrix. (B is the single UAV input matrix defined in step S1), mode-dependent Laplace matrix Let Laplace be the Laplace matrix of the communication network in the corresponding mode, and let the mode-dependent positive definite weight matrix be the weight matrix. A positive definite matrix with dimensions consistent with the augmented system matrix (determined in this embodiment by solving the Riccati equation). and (Specific values ​​to be taken). Based on Lyapunov stability theory, the lower bound constraint condition of the control gain is derived to ensure that the derivative of the Lyapunov function along the system trajectory satisfies the negative definite requirement, and the control gain... , Must meet:

[0095] ,

[0096] in, For pattern Control gain below, To augment the system matrix, For pattern-dependent positive definite weight matrices, For pattern-dependent Laplace matrix, To augment the input matrix, It is the network shrinkage factor and satisfies , To represent the pattern The smallest non-zero eigenvalue of the lower Laplacian matrix (i.e., algebraic connectivity) quantifies the network connectivity strength. Similarly, the largest eigenvalue actually takes the following values: , This satisfies both the lower bound constraint and ensures the smoothness of the control input. For matrix The largest eigenvalue, the inherent instability of the quantization augmented system. The effective coefficients for the network's shrinkage characteristics reflect the network's ability to compress input biases. In this embodiment, the eigenvalues ​​of each matrix and the shrinkage factor are substituted. The normal mode control gain was calculated. Emergency mode control gain The actual values ​​are respectively This satisfies the lower bound constraint while ensuring the smoothness of the control input.

[0097] Finally, a distributed control law adapted to the current mode is generated, which is combined with the recursive balancing network mapping function fθ and the mode-dependent control gain. The control law is constructed using a weighted summation of neighbor connection weights and network mapping outputs, expressed as: ,

[0098] in, For mode-dependent control gain, The neighbor set of the i-th drone is determined by the communication network topology in step S1, that is, the set of drones that have a valid communication link with the i-th drone. For connection weights, For recursive balanced network mapping functions, For recursive balancing networks to address state deviations The nonlinear mapping output, and Let i and j be the state vectors of the i-th and j-th UAVs, respectively. During actual system operation, the controller receives the current mode signal in real time. UAV state vector xi and neighbor state vectors Calculated through a recursive balanced network Then substitute the above control law formula to generate the control input. This enables distributed collaborative control, ensuring that the drone swarm can stably maintain the desired formation under different communication quality conditions.

[0099] S5. Based on the contraction mapping theory and the multi-Lyapunov function method, combined with the dynamic model and controller parameters, the exponential stability of the switching system is analyzed, and the steady-state error bound is quantified.

[0100] This step, based on the contraction mapping theory and the multi-Lyapunov function method, combined with the dynamic model established in step S1 and the controller parameters determined in step S4, first clarifies the core assumptions of the stability analysis, laying the foundation for subsequent derivations: Assumption 1: The communication topology satisfies joint connectivity, that is, the sum of the Laplace matrices of each mode within any time window is a positive definite matrix, ensuring the continuity of information interaction within the cluster; Assumption 2: The activation function selected in step S4 satisfies the Lipshitz continuity condition, that is... ,in, Let be the Lipschitz constant, and let the spectral norm of the weight matrix satisfy . This makes the shrinkage factor of the network mapping... (L is the number of network layers), ensuring the shrinkage characteristic of the recursive balanced network; Assumption 3, mode switching satisfies the average dwell time constraint, that is, in any time interval... Number of switching within satisfy ,in, For jump parameters, To average dwell time and avoid system instability caused by excessive switching.

[0101] Based on the above assumptions, Lyapunov functions are constructed for both normal and emergency modes. These functions, using the augmented formation error vector as the independent variable and constructed in quadratic matrix form, effectively characterize system energy changes. First, the augmented formation error is defined. ,in Let be the formation tracking error of the i-th UAV. The actual location of the drone. For the virtual leader position, For the desired formation vector, the augmented error dimension is consistent with the overall cluster state dimension. For the pattern... The Lyapunov function is constructed as follows: ,in, For pattern The Laplace matrix of the communication network, For Kronecker product, The mode-dependent positive definite weight matrix (determined by solving the Riccati equation, in this embodiment) is used. and (All are symmetric positive definite matrices). The positive definiteness of this quadratic form function is determined by... joint connectivity and The positive definiteness is guaranteed, and there exists a constant. , making ,in , , and Let represent the minimum and maximum eigenvalues ​​of the matrix, respectively.

[0102] Next, the derivative of the Lyapunov function is calculated along the system trajectory, combined with the dynamic model from step S1. and the distributed control law in step S4 To derive the error dynamics equation, we first substitute the control law into the dynamic model and, combined with the definition of augmented error, obtain the augmented error dynamics: in, ( (where A is an N-order identity matrix and A is the matrix of a single UAV system). (B is the input matrix for a single UAV). To augment the external perturbation vector, satisfying ( (Upper limit for disturbance of a single drone). Mapping function for recursive balanced networks An augmented form.

[0103] Differentiating the Lyapunov function along the error dynamics trajectory, we obtain: Combining the shrinkage characteristics of network mapping in step S4 And Young's inequality, scaling the derivative terms. The lower bound constraint satisfied by the control gain is:

[0104] ,

[0105] Substituting into the derivation, sufficient conditions for the exponential decay of the Lyapunov function during the duration of each mode can be established: in, The minimum shrinkage rate of the system is given by eigenvalues ​​and The positive definiteness is determined. As a normal number related to the disturbance, this condition indicates that the system energy decays exponentially over time during the duration of each mode, ensuring stability within the mode.

[0106] Subsequently, the Lyapunov function transition ratio at the mode switching moment was determined to quantize the switching gain. Defined as the maximum jump ratio of the Lyapunov function under different modes. At the switching time... The system from the mode Switch to At this point, the Lyapunov function satisfies: in, , For two modes The maximum value, For two modes The minimum value is used to ensure that the system energy jump is within a controllable range at the time of switching, and to avoid instability caused by excessive jump.

[0107] Based on the constraint of average residence time, establish sufficient conditions for the global exponential stability of the switching system. Average residence time Defined as the average switching interval of the system over any time interval, i.e. ,in Time interval Number of switching times within, This is a jitter limit for the number of handovers, used to allow the system a limited number of rapid handovers at the initial moment. At the initial moment, This refers to the current moment.

[0108] Combining the exponential decay characteristic of the Lyapunov function and the switching gain The sufficient condition for the mean residence time to be globally exponentially stable is derived as follows: ,in, This represents the lower bound of the average dwell time. The maximum shrinkage rate of the system. It is the natural logarithm function.

[0109] Finally, there exists a bounded external perturbation. Under the condition of Lyapunov function derivative constraints and contraction mapping properties, the steady-state error bound is quantified, and the inequalities of Lyapunov function derivatives are applied. In the time interval Inner integral, combined with jump constraints at the switching moment and average length of stay conditions The error evolution inequality is derived recursively.

[0110] The specific derivation process is as follows: During the mode duration interval Inside, to Applying the comparison principle of ordinary differential equations, we obtain:

[0111] ,

[0112] At the switching time Combined with jump constraints For time intervals Internal occurrence Applying the above inequality recursively to each switch, we obtain:

[0113] ,

[0114] Using the average length of stay condition , and select ,(in It can be proven that as t→∞, the exponential decay term... The exponent approaches 0, and the series terms converge. Therefore, as t→∞, the exponent term approaches 0, combined with... and Equivalence relation The steady-state error bound is obtained. Further combined with contractile factors The effect of this is ultimately expressed as: in, The minimum of the non-zero smallest eigenvalues ​​of the Laplacian matrix under both modes. The network mapping shrinkage factor. The upper limit of external disturbances for a single UAV was set, verifying the accuracy guarantee capability of the control method.

[0115] Example 2: The difference between this example and Example 1 is that this example provides a verification operation for a simulation experiment;

[0116] Configure the system's core parameters and various attack scenarios, and verify the operation through simulation experiments, such as... Figure 2 As shown, the overall architecture of the information quality perception adaptive distributed control system is illustrated. First, the core system parameters are configured. Based on the requirements of multi-UAV swarm operations and the characteristics of the hardware platform, the values ​​of various key parameters are clarified and a standardized configuration table is formed (see Table 1) to ensure parameter consistency and reproducibility. The UAV swarm supports 3-UAV (triangular), 4-UAV (square), and 5-UAV (pentagonal) swarm configurations. All swarms perform a crossing mission from x=−5m to x=5m, passing through a circular obstacle (safe passage radius r=2m). The quadcopter UAVs adopt a second-order integrator dynamic model. The system matrix A and input matrix B are configured in a block matrix form, with an upper limit for external disturbances. The weighting coefficient for communication quality assessment is set to... Sigmoid function normalization center Steepness coefficient α=5; Mode switching threshold Average length of stay In the adaptive shrinking network controller parameters, the number of neurons in the normal mode is... Control gain Emergency mode neuron count Control gain The network has L=3 layers, uses LeakyReLU as the activation function, and has an upper bound on the spectral norm of the weight matrix. This ensures that all parameters are deeply adapted to the system's dynamic characteristics, communication quality assessment mechanisms, and mode switching rules.

[0117] Table 1. System Core Parameter Configuration Table;

[0118]

[0119] Next, various DoS attack scenarios were constructed to comprehensively simulate the degradation of communication quality under adversarial conditions: the attack modes covered four categories: bandwidth flooding (BF), selective interference (SJ), protocol interruption (PD), and coordinated attack (CA), with varying attack strengths. According to mild (0.3≤ <0.5), moderate (0.5≤ <0.7), severe (0.7≤ Attacks ≤0.85 are classified into three levels, with attack duration Δt ∈ [20, 40] steps; the impact of the attack on communication performance is characterized by a quantification formula, and the channel quality degradation formula is: The formula for delaying the increase is: The formula for increasing packet loss rate is: Simultaneously, three types of composite attack scenarios were designed, including a DoS attack intensity gradient scenario (link blocking rate 30%–90%), a bandwidth flooding attack gradient scenario (channel quality 50%–5%), and a hybrid attack scenario (50% link blocking + 30% channel quality degradation), to comprehensively test the system's adaptability under complex interference.

[0120] Subsequently, a multi-UAV distributed formation control simulation platform was built based on MATLAB / Simulink. The simulation step size was set to 0.01s, and the total duration of a single scenario was 15s. Four types of core verification experiments were conducted: First, adaptive switching behavior verification: a pentagonal formation (5 UAVs) was selected, and a moderate DoS coordinated attack was initiated at t=50 steps and stopped at t=100 steps. The comprehensive communication quality evaluation index Q(t) and the mode switching time of each UAV were recorded in real time to analyze the switching frequency and anti-shake effect; Second, multi-formation obstacle avoidance and trajectory tracking verification: the task completion rate, formation deviation, and collision situation of three formations were tested in four obstacle scenarios: single-hole, double-hole, vertical, and 3D complex obstacles, verifying multi-scenario adaptability; Third, [the text abruptly ends here, likely due to an incomplete sentence or missing information]. Technical comparison and verification were conducted. A dual-aperture formation (4 UAVs) was selected under a moderate DoS attack (50% link blocking rate, attack period t∈[15,25]s). The proposed ASCN method was compared with fixed normal mode, fixed emergency mode, traditional PID control, and model predictive control (MPC). The evaluation indicators covered formation accuracy (maximum error, average error, steady-state error), convergence speed, computational overhead (single-step computation time), energy consumption (average amplitude of control input), and switching stability (see Table 2). Fourth, robustness boundary verification was conducted. By adjusting the attack intensity of the system, the maximum tolerable link blocking rate, minimum channel quality, and recovery time under mixed attacks for each method were determined, and the improvement of robustness boundary was quantified.

[0121] Under a moderate DoS attack (50% link disruption rate, attack period t∈[15,25]), the performance of five control methods was compared using a dual-aperture formation (4 agents). The comparison methods included: fixed normal-only mode, fixed emergency-only mode, traditional PID control, model predictive control (MPC), and the proposed ASCN method. Evaluation metrics covered four dimensions: formation accuracy, control efficiency, computational overhead, and robustness.

[0122] Table 2. Performance comparison with baseline methods;

[0123]

[0124] Note: "Instability" indicates that the formation has diverged; N / A indicates that it is not applicable.

[0125] (1) Outstanding formation accuracy across the board: The ASCN method in this paper is the best in all three accuracy indicators: maximum error, average error, and steady-state error. Compared with the fixed normal mode, it reduces the accuracy of formation accuracy by 10% and 10% respectively. , and Compared to the suboptimal MPC method, it also reduces , and In a normally operating mode, a DoS attack causes communication disruption, leading to controller failure and formation divergence (with a maximum error of [missing information]). This verifies the necessity of mode switching; although the fixed emergency mode remains stable, its performance is significantly worse than the adaptive method due to the lack of neighbor cooperation information (higher average error). ).

[0126] (2) Convergence speed and energy consumption balance: ASCN convergence time For the fastest speed, faster than emergency mode Speed ​​improvement compared to PID ; Control input average amplitude While maintaining high precision, it has moderate energy consumption and is more energy-efficient than PID controllers. Slightly higher than emergency mode This demonstrates the good balance between performance and energy consumption achieved by adaptive switching—normal mode utilizes collaboration to improve accuracy, while emergency mode reduces communication and lowers energy consumption.

[0127] (3) Significantly improved computational efficiency: ASCN single-step calculation MPC only )of To meet real-time control requirements ( Recursive balancing networks reduce complexity from... Down to The emergency mode further achieves this by halving the number of neurons. Complexity reduction rate:

[0128] ,

[0129] (4) Stable and controllable switching behavior: ASCN average switching Secondly, a small standard deviation indicates stable and controllable switching, with switching concentrated at the attack initiation / exit points, demonstrating clear and reasonable logic. The hysteresis threshold strategy effectively avoids frequent boundary fluctuations.

[0130] like Figure 3 As shown, Figure 3 The figure above illustrates the dynamic correlation between communication quality score and mode switching in a pentagonal formation (5 agents) under a DoS attack scenario. Comprehensive communication quality score within each time step Real-time changes, including Independent scoring curves for each agent (solid colored line), average quality curve (thick black line), recovery threshold (dashed green line), ) and emergency threshold (orange dashed line, The diagram below shows the mode switching times of each agent in the form of a state matrix. The red upward arrow indicates switching to emergency mode, and the green downward arrow indicates returning to normal mode. The background color distinguishes between normal mode (light green) and emergency mode (light red).

[0131] Three-stage dynamic characteristics:

[0132] (1) Normal communication phase ( Step 1): The communication quality of all agents stabilizes at... The system is running in normal mode (light green background), making full use of neighbor collaboration information to optimize formation performance.

[0133] (2) Attack duration ( step): After the DoS attack is initiated, the communication quality drops sharply, with the average quality at [missing information]. Step falls below emergency threshold This triggers the first centralized mode switch (highlighted by dense red arrows). Communication quality during the attack was... The switching frequency fluctuates dramatically between different topological locations. Agents make independent decisions based on their local communication quality scores, exhibiting asynchronous switching characteristics. Some agents (such as Agent 3, Agent 4, and Agent 5) switch at significantly higher frequencies, reflecting the differences in the impact of attacks on different topological locations.

[0134] (3) Recovery phase step): After the attack ended, communication quality quickly recovered. Above, all intelligent agents are in The system gradually returns to normal mode within the step interval (green arrows appear), and the system smoothly transitions to normal operation.

[0135] Switching frequency characteristics: Throughout the simulation process, The total number of switching operations per agent is approximately Times, average frequency (equivalent to each) Step switching (times), no frequent oscillations were observed. Hysteresis bandwidth This effectively avoids fluctuations in quality indicators around the threshold, and the minimum switching interval meets the following requirements:

[0136] ;

[0137] The effectiveness of the hysteresis handover rule was verified. Based on the verification of the effectiveness of the adaptive handover mechanism, the obstacle avoidance and formation maintenance capabilities of different formation sizes in complex obstacle environments were further tested. Figure 4 , Figure 5As shown, the obstacle avoidance trajectories of the triangular formation (3 agents) and the pentagonal formation (5 agents) are displayed in the dual-hole obstacle and 3D complex obstacle scenarios, respectively.

[0138] like Figure 4 As shown, Figure 4 This demonstrates the obstacle avoidance process of a triangular formation navigating a double-hole obstacle, with two cylindrical holes (red dashed line x=-3.0, blue dashed line x=3.0). Three drones start from the starting point (hollow circle), each choosing a suitable hole to traverse, and finally reach the destination (pentagram marker). The XY and XZ plane projections on the right clearly show the relationship between the movement trajectories of each agent and the hole positions, verifying the system's distributed collaborative decision-making capability in a multi-hole obstacle scenario.

[0139] like Figure 5 As shown, Figure 5 This demonstration showcases the obstacle avoidance process of a pentagonal formation in a complex 3D obstacle scenario. Five drones faced multiple cylindrical obstacles, autonomously planning their trajectories to bypass the obstacle area after starting from the starting point. The trajectories exhibited a smooth, spiraling upward characteristic, ultimately reaching the destination precisely while maintaining the predetermined formation (top left sub-image). Throughout the entire process, the agents maintained a safe distance, and no collisions occurred.

[0140] Statistical data shows that the maximum formation deviation was less than 0.3m and the average deviation was less than 0.15m in all test scenarios, with zero collisions and a 100% task completion rate. This verifies the robustness and adaptability of the ASCN method under different formation sizes and obstacle complexities, ensuring obstacle avoidance safety while maintaining formation accuracy and stability.

[0141] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for distributed formation safety control of multiple unmanned aerial vehicles based on dual networks, characterized in that, include: Collect multimodal data from multiple UAV clusters, establish dynamic models, connectivity indices, and DoS attack sequences based on the multimodal data, and define formation tracking errors and control objectives; Extract physical layer channel feature parameters and network layer topology feature parameters, and fuse the feature parameters to construct a continuous comprehensive communication quality evaluation index; Based on the real-time calculation results of the comprehensive communication quality assessment index, a hysteresis adaptive mode switching rule with anti-jitter characteristics is constructed to realize the dynamic switching between normal mode and emergency mode. The construction of the hysteresis adaptive mode switching rule with anti-jitter characteristics includes setting a recovery switching threshold and an emergency switching threshold forming a hysteresis bandwidth , based on the hysteresis bandwidth, establishing a quantitative relationship between the average residence time and the hysteresis bandwidth and the quality change rate, wherein the recovery switching threshold represents the required quality recovery level for returning from the emergency mode to the normal mode, and the emergency switching threshold represents the limit of the quality degradation tolerated for switching from the normal mode to the emergency mode, and constructing a segmented mode switching logic rule: ， in, For mode signals, To switch to the previous mode state, Normal mode For emergency mode, As a comprehensive communication quality assessment indicator; An adaptive shrinking network controller based on a recursive equilibrium network is established. Different network sizes are configured according to the needs of different control modes, and a distributed control law adapted to the current mode is generated. The generation of distributed control laws adapted to the current mode includes constructing an adaptive shrinking network controller using a recursive balanced network architecture, defining an L-layer network structure, and the... The layers achieve forward propagation of information through weight matrices and activation functions. The input layer receives the UAV state deviation signal, and the output layer generates a nonlinear control mapping signal. Based on normal mode and emergency mode, differentiated network size parameters are configured. The normal mode uses the number of first neurons. To fully utilize neighbor collaborative information, the emergency mode employs a second neuron count. ,and To reduce computational overhead, a distributed control law adapted to the current mode is generated based on a recursive balancing network mapping function and mode-dependent control gain. This control law is constructed as a weighted sum of neighbor connection weights and network mapping outputs, expressed as: ， in, For mode-dependent control gain, For the neighborhood group, For connection weights, For recursive balanced network mapping functions, and These are the state vectors of the i-th and j-th drones, respectively; Based on the contraction mapping theory and the multi-Lyapunov function method, combined with the dynamic model and controller parameters, the exponential stability of the switching system is analyzed, and the steady-state error bound is quantified.

2. The multi-UAV distributed formation security control method based on dual networks according to claim 1, characterized in that, The establishment of the dynamic model, connectivity index, and DoS attack sequence includes acquiring multimodal data composed of state data, communication link data, and external environment data of each UAV; establishing a continuous-time state-space equation for the i-th UAV based on the state data; the continuous-time state-space equation including the state vector, control input, and external disturbance; and, for the quadcopter UAV platform, establishing a dynamic model in the form of a second-order integrator. The system matrix of the dynamic model is constructed in the form of a block matrix, and the expression of the dynamic model is as follows: ， in, This is a state vector containing the drone's position and velocity information. The thrust control input applied to the UAV is as follows: It is an external disturbance and satisfies boundedness constraints. A is the system matrix, and B is the input matrix. This is the upper bound of the boundedness constraint for external disturbances.

3. The multi-UAV distributed formation security control method based on dual networks according to claim 2, characterized in that, The establishment of the dynamic model, connectivity index, and DoS attack sequence also includes: Based on communication link data, a directed graph is used. Construct a communication network topology between drones, where the node set The elements correspond to the drone numbers, edge sets The elements represent the connectivity state of the communication links between UAVs, and the adjacency matrix... The element quantizes the connection weights of the communication link; Define degree matrix Furthermore, a Laplace matrix is ​​constructed by combining the adjacency matrix, and the second smallest eigenvalue of the Laplace matrix is ​​used as the algebraic connectivity index. Establish a DoS attack sequence based on external environment data. And introduce frequency constraints. Duration constraints ; in, Let N be the communication degree of the drone. Let k be the start time of the k-th DoS attack. This represents the end time of the k-th DoS attack. This is the attack frequency offset parameter. To define the upper bound parameter for the attack duty cycle, For attack duration elasticity parameters, To calculate the start time, For the current statistical time, This represents the average attack interval.

4. The multi-UAV distributed formation security control method based on dual networks according to claim 1, characterized in that, The extraction of physical layer channel feature parameters and network layer topology feature parameters includes obtaining the signal-to-noise ratio (SNR), packet loss rate, and bit error rate of the communication link. Based on the dimensional differences and numerical range characteristics of the SNR, a typical communication threshold is used as the mapping center, and the Sigmoid function is used to map it to the zero-to-one interval. The mapping sensitivity is controlled by adjusting the steepness coefficient. The normalized SNR quality index, the complementary amount of the packet loss rate, and the complementary amount of the bit error rate are weighted and fused to construct the physical layer channel quality index. The expression of the physical layer channel quality index is as follows: ， in, This is a normalized signal-to-noise ratio (SNR) quality metric. For packet loss rate, For bit error rate, , and These are the corresponding weighting coefficients.

5. The multi-UAV distributed formation security control method based on dual networks according to claim 1, characterized in that, The process of constructing a continuous comprehensive communication quality assessment index by fusing the aforementioned feature parameters includes: calculating the algebraic connectivity feature value of the current communication topology in real time based on the Laplace matrix; performing a ratio calculation between the current algebraic connectivity feature value and the maximum algebraic connectivity feature value under nominal conditions to obtain the network layer topology quality index; and integrating the physical layer channel quality index and the network layer topology quality index into a comprehensive communication quality assessment index through a hierarchical weighted fusion mechanism. The expression for the network layer topology quality index is as follows: , in, To maximize algebraic connectivity, It is the second smallest eigenvalue of the current Laplacian matrix.

6. The multi-UAV distributed formation security control method based on dual networks according to claim 1, characterized in that, The determination of the mode-dependent control gain includes analyzing the shrinkage characteristics of the recursive equilibrium network based on shrinkage mapping theory, determining the shrinkage factor of the network mapping, which is determined by the power form of the product of the activation function Lipshitz constant and the spectral norm of the weight matrix, constructing a Lyapunov function composed of the augmented system matrix, the graphical Laplace matrix, and the mode-dependent positive definite weight matrix, and determining the lower bound constraint of the control gain based on the Lyapunov function. The control gain satisfies the following lower bound constraint conditions: ， in, For pattern Control gain below, To augment the system matrix, For pattern-dependent positive definite weight matrices, For pattern-dependent Laplace matrix, To augment the input matrix, It is the network shrinkage factor and satisfies , for The non-zero smallest eigenvalue, Similarly, it is the largest eigenvalue.

7. A multi-UAV distributed formation security control method based on dual networks according to claim 6, characterized in that, The analysis of the shrinkage characteristics of the recursive equilibrium network based on the shrinkage mapping theory includes constructing the recursive equilibrium network using an activation function that satisfies the Lipshitz continuity condition. The Lipshitz continuity condition is characterized by the fact that, for any input vector, the deviation of the activation function output is constrained by a linear function of the input deviation, where the coefficient of the linear function is the Lipshitz constant. An upper bound constraint on the spectral norm of the weight matrices of each layer of the recursive equilibrium network is set. Based on the Lipshitz constant and the upper bound of the spectral norm, the shrinkage factor of the recursive equilibrium network mapping is obtained. The recursive equilibrium network mapping satisfies the following shrinkage conditions: ， in, For recursive balanced network mapping functions, Let Lipschitz constant be the activation function. The upper bound of the spectral norm of the weight matrix is ​​given by... For network layers, For any input vector of the recursive balancing network, Let be another arbitrary input vector for the recursive balancing network.

8. A multi-UAV distributed formation security control method based on dual networks according to claim 7, characterized in that, The analysis of the exponential stability of the switching system includes: Based on normal mode and emergency mode, Lyapunov functions are constructed respectively. The Lyapunov functions are constructed in the form of quadratic matrix with the augmented formation error vector as the independent variable. The derivative of the Lyapunov function is calculated along the system trajectory. Combined with the constraint of control gain, sufficient conditions for the exponential decay of the Lyapunov function during the duration of each mode are established to determine the Lyapunov function jump ratio at the mode switching time to quantify the switching gain. Based on the constraint of average residence time, a sufficient condition for the average residence time to be globally exponentially stable in the switching system is established, under the presence of bounded external disturbances. Under the given conditions, based on the Lyapunov function derivative constraint and contraction mapping property, the steady-state upper bound is analytically obtained.

Images