Event-based intermittent control method, system, device and medium for uav formation

Abstract

The application discloses an event-based intermittent control method and system for a UAV formation, equipment and a medium, and relates to the technical field of UAV control.The application comprises: constructing a dynamic model of a UAV formation; constructing a state space model of a deception attack on the UAV formation based on graph theory; and constructing an intermittent control strategy based on an observer.The application uses the mathematical tools of graph theory to construct a dynamic model and a state space model of the UAV formation in detail, and on this basis, designs an efficient and economical intermittent control strategy based on an observer, which can detect and compensate external interference in real time by precisely defining the expected relative position and tracking error and by carefully designing a deception attack observer, so that the calculation amount and energy consumption are greatly reduced while the control performance is maintained, and in addition, the intermittent control strategy constructed further optimizes the energy efficiency of the UAV formation by intelligently adjusting the frequency of the control input.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) control technology, specifically to an event-based intermittent control method, system, device, and medium for UAV formations. Background Technology

[0002] Unmanned aerial vehicle (UAV) swarm systems face increasingly serious security challenges, particularly the threat of deception attacks. These attacks can be carried out through various means, including tampering with sensor data, sending false location information, and interfering with communication signals, all aimed at deceiving the system's control and decision-making processes. Once attacked, the UAV swarm may be misled into executing incorrect mission instructions, leading to mission failure or incomplete completion, and could even result in equipment damage, collisions, or the leakage of critical data. In military applications, such attacks could expose tactical intentions or disrupt strategic plans, posing a serious threat to national security.

[0003] Effective management and optimization of communication resources is one of the key issues in UAV swarm communication. Large-scale UAV swarms typically require the simultaneous transmission of massive amounts of real-time data, such as high-definition video, sensor information, and location data. This data volume is enormous and demands extremely high communication bandwidth. Furthermore, the limited spectrum resources restrict the improvement of communication capabilities, especially in dense communication environments or areas with congested spectrum. Communication latency is particularly sensitive in certain application scenarios, such as collaborative operations and emergency response; therefore, ensuring the real-time performance and reliability of communication is crucial. Simultaneously, with the increasing complexity of the electromagnetic environment, UAV swarms also face security risks from interference and malicious attacks, leading to reduced UAV control performance. To address these challenges, we propose an event-based intermittent control method, system, device, and medium for UAV swarms. Summary of the Invention

[0004] The purpose of this invention is to provide an event-based intermittent control method, system, device, and medium for unmanned aerial vehicle (UAV) formations to solve the problems mentioned in the background art.

[0005] According to a first aspect of the present invention, in order to achieve the above-mentioned objective, the present invention provides the following technical solution: an event-based intermittent control method for UAV formations, comprising the following steps:

[0006] Construct a dynamic model of the drone formation;

[0007] A state-space model of a drone formation under deception attack is constructed based on graph theory.

[0008] Constructing an observer-based intermittent control strategy specifically includes defining the desired relative position and tracking error, designing a deception attack observer, and constructing an intermittent control strategy based on the design of the deception attack observer.

[0009] Constructing an event triggering mechanism based on the averaging method specifically includes defining the state error and its average value, defining the trigger threshold function, defining the trigger condition, defining the trigger signal, defining the system state equation, and constructing the error system.

[0010] Perform stability analysis on the drone formation and evaluate the flight status of the drone formation based on the analysis results.

[0011] Furthermore, a dynamic model of the drone formation is constructed, as follows:

[0012] (1) Establish a drone swarm, which includes a virtual leader, labeled as drone number 0, and N There are 1, 2, ..., N followers;

[0013] The kinematic equations of the i-th fixed-wing UAV are expressed as follows:

[0014]

[0015] In the formula Let [i] represent the position of the i-th drone. T This represents the transpose of the matrix. Let x, y, and z represent the x, y, and z coordinates of the i-th drone at time t, respectively, and their specific definitions are as follows:

[0016]

[0017] In the formula θ i (t) represents the tilt angle of the flight path of the i-th UAV, λ i (t) represents the azimuth angle of the flight path of the i-th UAV, V i (t) represents the flight speed of the i-th drone;

[0018] (2) For the i-th follower drone, the following equation is satisfied:

[0019]

[0020] In the formula, g represents the acceleration due to gravity; λ xi (t), λ yi (t) and λ zi (t) represent the roll, pitch, and yaw accelerations of the UAV, respectively;

[0021] Based on steps (1) and (2), the actual control formula can be obtained:

[0022] q i (t)=[λ xi (t) λ yi (t) λ zi (t)]T (5)

[0023] Combining the above formulas, we can obtain the final formula:

[0024]

[0025] in,

[0026]

[0027] In the formula, Represents the acceleration vector of the UAV; θ i (t) represents the tilt angle of the flight path of the i-th UAV, λ i (t) represents the azimuth angle of the flight path of the i-th UAV.

[0028] Furthermore, a state-space model of a drone formation under deception attack is constructed, as follows:

[0029] For the i-th drone, under the condition of being deceived, its state equation is as follows:

[0030]

[0031] In the formula f i (t) represents an unknown deception attack signal, and E0 is a known constant matrix with appropriate dimensions. This is the location information of the i-th drone, v i (t) is the velocity vector of the i-th UAV.

[0032] E0 and u i The specific form of (t) is as follows:

[0033]

[0034] u i (t)=j i (t)*q i (t)

[0035] To represent the state of the drone, the state vector x i (t) is defined as:

[0036]

[0037] Therefore, the state-space model of the system can be represented as:

[0038]

[0039] y i (t)=C1*x i (t)(11)

[0040] In the formula It is the state vector x i (t) derivative with respect to time, y i (t) is the output vector, and A, B, C1, and E are the system matrix, input matrix, attack matrix, and output matrix, respectively.

[0041] The specific forms of system matrix A, input matrix B, attack matrix E, and C1 are as follows:

[0042]

[0043] C1 = [I3 0]

[0044] In the formula, I3 refers to the 3×3 identity matrix.

[0045] Furthermore, an observer-based intermittent control strategy is constructed, specifically including defining the desired relative position and tracking error, designing a deception attack observer, and constructing the intermittent control strategy, as follows:

[0046] (1) Define the desired relative position and tracking error:

[0047] The directed communication topology F of the multi-UAV system has a directed spanning tree, with the root node being the virtual leader UAV. To obtain the trajectory of the i-th UAV, the relative position between the i-th UAV and the 0th UAV is described as follows:

[0048]

[0049] Where Δζ xi (t), Δζ yi (t), Δζ zi (t) are respectively:

[0050]

[0051] In the formula, θ0(t) represents the initial expected relative distance vector between two arbitrary adjacent UAVs, λ0 represents the parameter setting value under deception attack, and s i (t) represents the distance between the i-th drone and the 0th drone, χ i (t) is the acute angle between the connecting line (connecting the i-th UAV and the 0-th UAV) and the xy-plane, β i (t) is the distance s i (t) and relative velocity d vi (t) The angle between the projections on the xy plane, where λ0 represents the parameter setting value under specific conditions;

[0052] The desired position of the i-th drone can be represented as:

[0053]

[0054] in These are the coordinates of the 0th drone;

[0055] Finally, the tracking error of the i-th UAV is denoted as:

[0056]

[0057] in This is the location information of the i-th drone, v i (t) is the velocity vector of the i-th UAV;

[0058] (2) Design a deception attack observer:

[0059] To estimate and eliminate the impact of deception attacks on each UAV, the deception attack observer for the i-th UAV is designed as follows:

[0060]

[0061]

[0062] In the formula, ξ(t) is an intermediate variable used to assist in estimating the attack signal. Here, H is the estimated spoofing attack signal, C2 is the observer gain matrix that needs to be determined, C1 is the invertible parameter matrix with appropriate dimensions, and C2 is the output matrix. i (t) is the measurement output, A and B are the system matrices, and E is the observation matrix;

[0063] The H and C2 matrices are used to estimate the deception attack signal, and their specific design is as follows:

[0064] H = I6

[0065] C2 = [I3 0]

[0066] In the formula, I6 represents a sixth-order identity matrix, and I3 represents a third-order identity matrix;

[0067] (3) Based on the design of the deception attack observer, an intermittent control strategy is constructed, which is divided into control time and rest time:

[0068] Control time: [nT, nT+S)

[0069] Rest time: [nT+S, (n+1)T)

[0070] Where S∈(0,T] is the control duration within period T, and n is used to identify the index of the period;

[0071] Then, the following control strategy for the UAV formation system is proposed:

[0072]

[0073] in, It is a control signal that takes effect within the control time. It is a compensation for the estimated deception attack signal; It is the desired acceleration, used for trajectory tracking; B + Let be the pseudo-inverse of matrix B;

[0074] B + The specific design is as follows:

[0075]

[0076] The specific control signal is defined as follows:

[0077]

[0078] in,

[0079]

[0080] in, It is an event trigger signal; This is the latest transmission signal from UAV J; w ij These are weighting coefficients, reflecting the communication topology between drones; b i is the bias term; K is the controller gain matrix that needs to be determined.

[0081] Furthermore, an event triggering mechanism based on the averaging method is constructed, specifically including defining the state error and its average value, defining the trigger threshold function, defining the trigger condition, defining the trigger signal, defining the system state equation, and constructing the error system, as detailed below:

[0082] (1) Define the state error and the average state error as follows:

[0083] State error e yi (t) represents the state error of the i-th UAV at time t, defined as:

[0084]

[0085] In the formula It is a state estimate. These are the actual measured values, and C1 is the output matrix. At the most recent event trigger time At that time, the state vector of the i-th drone, It is the estimated value of the state vector;

[0086] average state error The specific definition is:

[0087]

[0088] In the formula w ij This represents the weight of the connection between drones i and j. This represents the state estimate of the i-th UAV at time t. Indicates the time of the most recent event trigger. At time, the average state of the i-th drone and its neighbors, This represents the weighted average of the neighbor states of the i-th drone at time t;

[0089] (2) Define the trigger threshold function as follows:

[0090] Trigger threshold function σ i (t) is a time-dependent function used to dynamically adjust the threshold of the trigger condition, defined as:

[0091]

[0092] In the formula σ mini and σ maxi These are the minimum and maximum trigger thresholds, respectively. It is the average value of the state error;

[0093] (3) Define the triggering conditions as follows:

[0094]

[0095] This indicates that if the state error e yi The weighted norm of (t) is less than the threshold σ. i (t) Mean state error The product of the weighted norms will not trigger an event;

[0096] In the formula It is the state error vector e yi The transpose of (t); matrix φ i It is a weight matrix used to adjust the importance of different state error components; It is the mean state error The transpose of the matrix;

[0097] (4) Define the trigger signal as follows:

[0098] Event trigger signal It can be represented as:

[0099]

[0100] Where e yi (t) represents the state error of the i-th UAV at time t;

[0101] The estimation error is expressed as Using the Kronecker product, we can obtain:

[0102]

[0103] in,

[0104]

[0105] C1 = [I3 0];

[0106] C2 = [I3 0];

[0107]

[0108] Among them, f i (t) represents the actual deception attack signal of the i-th drone; This represents the estimated deception attack signal for the i-th drone;

[0109] (5) Define the system state equations as follows:

[0110] The system state equations for the control period and the rest period are expressed as follows:

[0111]

[0112] in,

[0113] [nT, nT+S) is the control time; [nT+S, (n+1)T) is the rest time; S∈(0,T] is the control duration within period T, and n is used to identify the index of the period;

[0114] B0 = diag{b1,b2,…,b N}; It is the estimated value of the state vector; It is the state error vector e N The transpose of (t);

[0115] (6) Construct the error system as follows:

[0116] definition:

[0117]

[0118] The error system is defined as follows:

[0119]

[0120] Among them, A 1 =A1;A 2 =A2;B 1 =B; B 2 =0; ε 1 =ε 2 =ε; z(t) is the output of the multi-UAV system;

[0121] Where, l, A 1 The specific definitions of A2,B,ε,G,D are as follows:

[0122]

[0123] G = [I 6N 0 6N×3N ]

[0124] D = [2 2 3 3 2 2].

[0125] Furthermore, stability analysis of the drone formation is conducted using the following method:

[0126] If it exists v＞0 The attenuation rate ω makes the error system exponentially stable for the UAV formation system control strategy, then for all t＞0 :

[0127] ||η(t)||≤ve -ωt ||η0|| (29)

[0128] Where η0 = η(0);

[0129] If a matrix exists φ i If >0 (i∈g), then the exponent of the error system is stable, and:

[0130]

[0131] κ=ρ1s-ρ2(TS)>0

[0132] in:

[0133]

[0134]

[0135] φ = diag{φ1,φ2,…,φ N}

[0136] γ = 3.61

[0137] Where S∈(0,T] is the control duration within the undetermined period T; ρ ι (ι={1,2}) are all undetermined parameters, K is the control gain matrix and H is the observation gain matrix;

[0138] When a drone formation meets the above conditions, it is considered that the drone formation can carry out stable flight.

[0139] According to a second aspect of the present invention, the present invention provides an event-based intermittent control system for unmanned aerial vehicle (UAV) formations, for implementing the above-described event-based intermittent control method for UAV formations, comprising:

[0140] The first building module is used to construct the dynamic model of the drone formation;

[0141] The second building module is used to construct a state-space model of a drone formation under deception attack based on graph theory.

[0142] The third building module is used to build an observer-based intermittent control strategy, which specifically includes defining the desired relative position and tracking error, designing a deception attack observer, and building the intermittent control strategy.

[0143] The fourth module is used to build an event triggering mechanism based on the averaging method. Specifically, it includes defining the state error and the average value of the state error, defining the trigger threshold function, defining the trigger condition, defining the trigger signal, defining the system state equation, and building the error system.

[0144] The analysis module is used to perform stability analysis on drone formations and evaluate the flight status of drone formations based on the analysis results.

[0145] According to a third aspect of the present invention, the present invention provides a terminal device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The memory stores the computer program capable of running on the processor, and when the processor loads and executes the computer program, it employs the above-described event-based intermittent control method for UAV formations.

[0146] According to a fourth aspect of the present invention, the present invention provides a storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform the above-described event-based intermittent control method for unmanned aerial vehicle formations.

[0147] According to a fifth aspect of the present invention, the present invention provides a computer program product comprising a computer program, which, when executed by a processor, is used to load and execute the above-described event-based intermittent control method for unmanned aerial vehicle formations.

[0148] The present invention has at least the following beneficial effects:

[0149] 1. This invention utilizes graph theory to meticulously construct the dynamic and state-space models of UAV formations. Based on this, an efficient and economical observer-based intermittent control strategy is designed. By precisely defining the desired relative position and tracking error, and employing a carefully designed deception attack observer, external disturbances can be detected and compensated in real time. This significantly reduces computational load and energy consumption while maintaining control performance. Furthermore, the constructed intermittent control strategy further optimizes the energy efficiency of the UAV formation by intelligently adjusting the frequency of control inputs.

[0150] 2. This invention introduces an event triggering mechanism based on an averaging method. By defining the state error, the average value of the state error, the trigger threshold function, and the triggering conditions, it ensures the stability and response speed of the control system when subjected to deception attacks. The design of the trigger signal ensures that the system only performs control updates when necessary, thereby avoiding unnecessary computation and energy waste.

[0151] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0152] Figure 1 This is a flowchart illustrating the method described in this invention. Detailed Implementation

[0153] The technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this disclosure, and not all embodiments. Based on the embodiments of this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0154] Please see Figure 1 This invention provides a technical solution: an event-based intermittent control method for UAV formations, comprising the following steps:

[0155] S1. Construct a dynamic model of the drone formation, as follows:

[0156] (S11) Establish a drone swarm, which includes a virtual leader, labeled as drone number 0, and N There are 1, 2, ..., N followers;

[0157] The kinematic equations of the i-th fixed-wing UAV are expressed as follows:

[0158]

[0159] In the formula Let [i] represent the position of the i-th drone. T This represents the transpose of the matrix. Let x, y, and z represent the x, y, and z coordinates of the i-th drone at time t, respectively, and their specific definitions are as follows:

[0160]

[0161] In the formula θ i (t) represents the tilt angle of the flight path of the i-th UAV, λ i (t) represents the azimuth angle of the flight path of the i-th UAV, V i (t) represents the flight speed of the i-th drone;

[0162] (S12) For the i-th follower drone, the following equation is satisfied:

[0163]

[0164] In the formula, g represents the acceleration due to gravity; λ xi (t), λ yi (t) and λ zi (t) represent the roll, pitch, and yaw accelerations of the UAV, respectively;

[0165] The actual control formula can be obtained from steps (S11) and (S12):

[0166] q i (t)=[λ xi (t) λ yi (t) λ zi (t)] T (34)

[0167] Combining the above formulas, we can obtain the final formula:

[0168]

[0169] in,

[0170]

[0171] In the formula, Represents the acceleration vector of the UAV; θ i (t) represents the tilt angle of the flight path of the i-th UAV, λ i (t) represents the azimuth angle of the flight path of the i-th UAV;

[0172] S2. A state-space model of a drone formation subjected to deception attacks is constructed based on graph theory, as follows:

[0173] For the i-th drone, under the condition of being deceived, its state equation is as follows:

[0174]

[0175] In the formula f i (t) represents an unknown deception attack signal, and E0 is a known constant matrix with appropriate dimensions. This is the location information of the i-th drone, v i (t) is the velocity vector of the i-th UAV.

[0176] E0 and u i The specific form of (t) is as follows:

[0177]

[0178] u i (t)=j i (t)*q i (t)

[0179] To represent the state of the drone, the state vector x i (t) is defined as:

[0180]

[0181] Therefore, the state-space model of the system can be represented as:

[0182]

[0183] y i (t)=C1*x i (t)(40)

[0184] In the formula It is the state vector x i (t) derivative with respect to time, y i (t) is the output vector, and A, B, C1, and E are the system matrix, input matrix, attack matrix, and output matrix, respectively.

[0185] The specific forms of system matrix A, input matrix B, attack matrix E, and C1 are as follows:

[0186]

[0187] C1 = [I3 0]

[0188] In the formula, I3 refers to the 3×3 identity matrix;

[0189] S3. Construct an observer-based intermittent control strategy, specifically including defining the desired relative position and tracking error, designing a deception attack observer, and constructing an intermittent control strategy based on the designed deception attack observer, as detailed below:

[0190] (S31) Define the desired relative position and tracking error:

[0191] The directed communication topology F of the multi-UAV system has a directed spanning tree, with the root node being the virtual leader UAV. To obtain the trajectory of the i-th UAV, the relative position between the i-th UAV and the 0th UAV is described as follows:

[0192]

[0193] Where Δζ xi (t), Δζ yi (t), Δζ zi (t) are respectively:

[0194]

[0195]

[0196] In the formula, θ0(t) represents the initial expected relative distance vector between two arbitrary adjacent UAVs, λ0 represents the parameter setting value under deception attack, and s i (t) represents the distance between the i-th drone and the 0th drone, χ i (t) is the acute angle between the connecting line (connecting the i-th UAV and the 0-th UAV) and the xy-plane, β i (t) is the distance s i (t) and relative velocity d vi (t) The angle between the projections on the xy plane, where λ0 represents the parameter setting value under specific conditions;

[0197] The desired position of the i-th drone can be represented as:

[0198]

[0199] in These are the coordinates of the 0th drone;

[0200] Finally, the tracking error of the i-th UAV is denoted as:

[0201]

[0202] in This is the location information of the i-th drone, v i (t) is the velocity vector of the i-th UAV;

[0203] (S32) Construct an intermittent control strategy based on the design of a deception attack observer:

[0204] To estimate and eliminate the impact of deception attacks on each UAV, the deception attack observer for the i-th UAV is designed as follows:

[0205]

[0206] In the formula, ξ(t) is an intermediate variable used to assist in estimating the attack signal. Here, H is the estimated spoofing attack signal, C2 is the observer gain matrix that needs to be determined, C1 is the invertible parameter matrix with appropriate dimensions, and C2 is the output matrix. i (t) is the measurement output, A and B are the system matrices, and E is the observation matrix;

[0207] The H and C2 matrices are used to estimate the deception attack signal, and their specific design is as follows:

[0208] H = I6

[0209] C2 = [I3 0]

[0210] In the formula, I6 represents a sixth-order identity matrix, and I3 represents a third-order identity matrix;

[0211] (S33) To reduce the computational and energy consumption of multi-UAV systems, a periodic intermittent control strategy was constructed, which is divided into control time and rest time:

[0212] Control time: [nT, nT+S)

[0213] Rest time: [nT+S, (n+1)T)

[0214] Where S∈(0,T] is the control duration within period T, and n is used to identify the index of the period;

[0215] Then, the following control strategy for the UAV formation system is proposed:

[0216]

[0217] in, It is a control signal that takes effect within the control time. It is a compensation for the estimated deception attack signal; It is the desired acceleration, used for trajectory tracking; B + Let be the pseudo-inverse of matrix B;

[0218] B + The specific design is as follows:

[0219]

[0220] The specific control signal is defined as follows:

[0221]

[0222] in,

[0223]

[0224] in, It is an event trigger signal; This is the latest transmission signal from UAV J; w ij These are weighting coefficients, reflecting the communication topology between drones; b i It is the bias term; K is the controller gain matrix that needs to be determined;

[0225] This strategy uses an event-triggered mechanism for control, performing control calculations only when a significant state change is detected, thereby reducing the computational burden. At the same time, the intermittent control strategy further reduces the energy consumption of the controller through periodic rest periods.

[0226] S4. Construct an event triggering mechanism based on the averaging method, specifically including defining the state error and its average value, defining the trigger threshold function, defining the trigger condition, defining the trigger signal, defining the system state equation, and constructing the error system, as detailed below:

[0227] (S41) Define the state error and the average state error as follows:

[0228] State error e yi (t) represents the state error of the i-th UAV at time t, defined as:

[0229]

[0230] In the formula It is a state estimate. These are the actual measured values, and C1 is the output matrix. At the most recent event trigger time At that time, the state vector of the i-th drone, It is the estimated value of the state vector;

[0231] average state error The specific definition is:

[0232]

[0233] In the formula w ij This represents the weight of the connection between drones i and j. This represents the state estimate of the i-th UAV at time t. Indicates the time of the most recent event trigger. At time, the average state of the i-th drone and its neighbors, This represents the weighted average of the neighbor states of the i-th drone at time t;

[0234] (S42) Define the trigger threshold function as follows:

[0235] Trigger threshold function σ i (t) is a time-dependent function used to dynamically adjust the threshold of the trigger condition, defined as:

[0236]

[0237] In the formula σ mini and σ maxi These are the minimum and maximum trigger thresholds, respectively. It is the average value of the state error;

[0238] (S43) Define the triggering condition as follows:

[0239]

[0240] This indicates that if the state error e yi The weighted norm of (t) is less than the threshold σ. i (t) Mean state error The product of the weighted norms will not trigger an event;

[0241] In the formula It is the state error vector e yi The transpose of (t); matrix φ i It is a weight matrix used to adjust the importance of different state error components; It is the mean state error The transpose of the matrix;

[0242] (S44) Define the trigger signal as follows:

[0243] Event trigger signal It can be represented as:

[0244]

[0245] Where e yi (t) represents the state error of the i-th UAV at time t;

[0246] The estimation error is expressed as Using the Kronecker product, we can obtain:

[0247]

[0248] in,

[0249]

[0250] C1 = [I3 0];

[0251] C2 = [I3 0];

[0252]

[0253]

[0254] Among them, f i (t) represents the actual deception attack signal of the i-th drone; This represents the estimated deception attack signal for the i-th drone;

[0255] (S45) Define the system state equations as follows:

[0256] The system state equations for the control period and the rest period are expressed as follows:

[0257]

[0258] in,

[0259] [nT, nT+S) is the control time; [nT+S, (n+1)T) is the rest time; S∈(0,T] is the control duration within period T, and n is used to identify the index of the period;

[0260] B0 = diag{b1,b2,…,b N}; It is the estimated value of the state vector; It is the state error vector e N The transpose of (t);

[0261] (S46) Construct the error system as follows:

[0262] definition:

[0263]

[0264] The error system is defined as follows:

[0265]

[0266] Among them, A 1 =A1;A 2 =A2;B1 =B; B 2 =0; ε 1 =ε 2 =ε; z(t) is the output of the multi-UAV system;

[0267] Where, l, A 1 The specific definitions of A2,B,ε,G,D are as follows:

[0268]

[0269]

[0270] G = [I 6N 0 6N×3N ]

[0271] D = [2 2 3 3 2 2];

[0272] S5. Perform stability analysis on the drone formation and evaluate the flight status of the drone formation based on the analysis results, as follows:

[0273] If it exists v＞0 The attenuation rate ω makes the error system exponentially stable for the UAV formation system control strategy, then for all t＞0 :

[0274] ||η(t)||≤ve -ωt ||η0|| (58)

[0275] Where η0 = η(0);

[0276] If a matrix exists φ i If >0 (i∈g), then the exponent of the error system is stable, and:

[0277]

[0278] κ=ρ1s-ρ2(TS)>0

[0279] in:

[0280]

[0281] φ = diag{φ1,φ2,…,φ N}

[0282] γ = 3.61

[0283] Where S∈(0,T] is the control duration within the undetermined period T; ρ ι(ι={1,2}) are all undetermined parameters, K is the control gain matrix and H is the observation gain matrix;

[0284] When a drone formation meets the above conditions, it is considered that the drone formation can carry out stable flight.

[0285] In summary, the technical solution of this embodiment provides a strong guarantee for the safe operation of the UAV system. This embodiment first uses the mathematical tools of graph theory to meticulously construct the dynamic model and state space model of the UAV formation. On this basis, an efficient and economical observer-based intermittent control strategy is designed. By accurately defining the desired relative position and tracking error, and using a carefully designed deception attack observer, external interference can be detected and compensated in real time, thereby significantly reducing the amount of computation and energy consumption while maintaining control performance. In addition, the constructed intermittent control strategy further optimizes the energy efficiency of the UAV formation by intelligently adjusting the frequency of control input.

[0286] An event triggering mechanism based on the averaging method was introduced. By defining the state error, the average value of the state error, the trigger threshold function, and the triggering conditions, the stability and response speed of the control system when subjected to deception attacks were ensured. The design of the trigger signal ensures that the system only updates the control when necessary, thereby avoiding unnecessary computation and energy waste. Finally, the stability analysis of UAV formation flight was carried out to ensure the stability of the UAVs during flight.

[0287] Example 2:

[0288] This invention provides an event-based intermittent control system for UAV formations, used to implement the event-based intermittent control method for UAV formations described in Embodiment 1, comprising:

[0289] The first building module is used to construct the dynamic model of the drone formation;

[0290] The second building module is used to construct a state-space model of a drone formation under deception attack based on graph theory.

[0291] The third building module is used to build an observer-based intermittent control strategy, which specifically includes defining the desired relative position and tracking error, designing a deception attack observer, and building the intermittent control strategy.

[0292] The fourth module is used to build an event triggering mechanism based on the averaging method. Specifically, it includes defining the state error and the average value of the state error, defining the trigger threshold function, defining the trigger condition, defining the trigger signal, defining the system state equation, and building the error system.

[0293] The analysis module is used to perform stability analysis on drone formations and evaluate the flight status of drone formations based on the analysis results.

[0294] Specifically, the first, second, third, and analysis modules can be embedded in a computer processing system. The computer, based on the event-based intermittent control method for UAV formations provided above, calls each of the above modules to complete the task of controlling the UAV formation. The first, second, third, and analysis modules can perform operations according to the specific steps given by the event-based intermittent control method for UAV formations.

[0295] It should be noted that the division of the various modules in the above system is merely a division of logical functions. In actual implementation, they can be fully or partially integrated into a single physical entity, or they can be physically separated. These modules can be implemented entirely in software through processing element calls; they can be fully implemented in hardware; or some modules can be implemented by processing element calls to software, while others are implemented in hardware. For example, the analysis module can be a separate processing element, or it can be integrated into a chip in the aforementioned device. Alternatively, it can be stored as program code in the memory of the aforementioned device, and its signal processing module function can be called and executed by a processing element of the device. The implementation of other modules is similar. Furthermore, these modules can be fully or partially integrated together, or they can be implemented independently. The processing element mentioned here can be an integrated circuit with signal processing capabilities. In the implementation process, each step of the above method or each of the above modules can be completed through the integrated logic circuits in the hardware of the processor element or through software instructions.

[0296] For example, these modules can be one or more integrated circuits configured to implement the above methods, such as one or more Application Specific Integrated Circuits (ASICs), one or more Digital Signal Processors (DSPs), or one or more Field Programmable Gate Arrays (FPGAs). As another example, when a module is implemented using processing element scheduler code, the processing element can be a general-purpose processor, such as a Central Processing Unit (CPU) or other processor capable of calling program code. Furthermore, these modules can be integrated together to form a system-on-a-chip (SOC).

[0297] Example 3:

[0298] The present invention provides a terminal device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The memory stores the computer program capable of running on the processor. When the processor loads and executes the computer program, it employs the above-mentioned event-based intermittent control method for UAV formation.

[0299] It should be noted that the terminal device can be a computer device such as a desktop computer, a laptop computer, or a cloud server, and the terminal device includes, but is not limited to, a processor and a memory. For example, the terminal device may also include input / output devices, network access devices, and buses.

[0300] Furthermore, the processor can be a central processing unit (CPU). Of course, depending on the actual use, other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), off-the-shelf programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. can also be used. The general-purpose processor can be a microprocessor or any conventional processor, etc., and this application does not limit it in this regard.

[0301] Example 4:

[0302] The present invention provides a storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform the above-described event-based intermittent control method for UAV formations.

[0303] The computer program can be stored in a computer-readable medium. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or certain middleware. The computer-readable medium includes any entity or device capable of carrying computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the computer-readable medium includes, but is not limited to, the above-mentioned components.

[0304] Example 5:

[0305] The present invention provides a computer program product, which includes a computer program. When the computer program is executed by a processor, it is used to load and execute the above-described event-based intermittent control method for UAV formation.

[0306] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0307] For those skilled in the art, the specific meaning of the above terms in this invention can be understood according to the specific circumstances. When an element is referred to as being "assembled on," "mounted on," "fixed to," or "set on" another element, it may be directly on the other element or there may be an intermediate element present. When an element is considered to be "connected to" another element, it may be directly connected to the other element or there may be an intermediate element present. The terms "vertical," "horizontal," "upper," "lower," "left," "right," and similar expressions used herein are for illustrative purposes only and do not represent the only possible embodiments.

[0308] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

[0309] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

Claims

1. An event-based intermittent control method for UAV formation, characterized in that, The method comprises the following steps: constructing a dynamic model of the UAV formation; constructing a state space model of the UAV formation under deception attack based on graph theory; constructing an intermittent control strategy based on an observer, specifically including defining a desired relative position and a tracking error, designing a deception attack observer, and constructing an intermittent control strategy based on the designed deception attack observer; constructing an event-triggered mechanism based on an averaging method, specifically including defining a state error and an average of the state error, defining a triggering threshold function, defining a triggering condition, defining a triggering signal, defining a system state equation, and constructing an error system; performing stability analysis on the UAV formation, and evaluating the flight state of the UAV formation according to the analysis result; constructing a dynamic model of the UAV formation, specifically as follows: (1) establishing a UAV formation, which comprises a virtual leader, marked as the 0th UAV, and N followers, marked as 1, 2,..., N; the kinematic equation of the ith fixed-wing UAV is expressed as: wherein represents the position of the i-th drone, T represents the transpose of the matrix, respectively represent the x, y, z axis position coordinates of the i-th drone at time t, which are defined as follows: where θ i (t) represents the inclination angle of the flight path of the i-th unmanned aerial vehicle, λ i (t) represents the azimuth angle of the flight path of the i-th unmanned aerial vehicle, V i (t) represents the flight speed of the i-th unmanned aerial vehicle; (2) for the ith follower UAV, the following equation is satisfied: where g represents the acceleration of gravity; λ xi (t), λ yi (t) and λ zi (t) represent the accelerations of roll, pitch and yaw of the UAV, respectively According to steps (1) and (2), the actual control formula can be obtained as follows: q i (t) = [λ xi (t)λ yi (t)λ zi (t)] T (5) Combining the above formula, the final formula can be obtained as follows: wherein, wherein represents the acceleration vector of the UAV; θ i (t) represents the tilt angle of the flight path of the i-th UAV, λ i (t) represents the azimuth angle of the flight path of the i-th UAV. 2.The event-based intermittent control method for UAV formation according to claim 1, wherein, constructing a state space model of the UAV formation under deception attack, specifically as follows: for the ith UAV, in the case of deception attack, the state equation is as follows: where f i (t) represents unknown spoofing attack signals, E0is a known constant matrix with appropriate dimensions, is the position information of the ith UAV, v i (t) is the velocity vector of the ith UAV, E0 and u i A specific form of (t) is as follows: u i (t) = j i (t) * q i (t) To represent the state of the UAV, a state vector x i (t) is defined as: Accordingly, the state space model of the system can be expressed as: y i (t) = C1 * x i (t) (11) wherein is a state vector x i (t) is a derivative with respect to time, y i (t) is an output vector, A, B, C1, E are system matrix, input matrix, attack matrix and output matrix, respectively; The specific forms of the system matrix A, the input matrix B, the attack matrix E, and C1 are as follows: C1 = [I3 0] In the formula, I3 refers to a 3*3 unit matrix. 3.The event-based intermittent control method for UAV formation according to claim 2, wherein, constructing an intermittent control strategy based on an observer, specifically including defining a desired relative position and a tracking error, designing a deception attack observer, and constructing an intermittent control strategy, specifically as follows: (1) defining a desired relative position and a tracking error: The directed communication topology F of the multi-UAV system has a directed spanning tree, and the root node is the virtual leader UAV; in order to obtain the trajectory of the ith UAV, the relative position between the ith UAV and the 0th UAV is described as follows: where Δζ xi (t), Δζ yi (t), Δζ zi (t) are respectively: In the formula, θ0(t) represents the initial expected relative distance vector between two arbitrary adjacent UAVs, λ0 represents the parameter setting value under deception attack, and s i (t) represents the distance between the i-th drone and the 0th drone, χ i (t) is the acute angle between the connecting line (connecting the i-th UAV and the 0-th UAV) and the xy-plane, β i (t) is the distance s i (t) and relative velocity d vi (t) The angle between the projections on the xy plane, where λ0 represents the parameter setting value under specific conditions; The desired position of the ith UAV can be expressed as: wherein is the coordinates of the 0th drone; Finally, the tracking error of the ith UAV is denoted as: wherein is position information of the i-th UAV, v i (t) is a velocity vector of the i-th UAV; (2) designing a deception attack observer: In order to estimate and eliminate the influence of deception attack on each UAV, the deception attack observer of the ith UAV is designed as follows: where ξ(t) is an intermediate variable used to assist in estimating the attack signal, is the estimated spoofing attack signal, H is the observer gain matrix to be determined, C2is a reversible parameter matrix of appropriate dimension, C1is the output matrix, y i (t) is the measurement output, A, B are system matrices, E is the observation matrix; The H and C2 matrices are used to estimate the deception attack signal, and the specific design forms are as follows: H = I6 C2 = [I3 0] In the formula, I6 represents a six-order unit matrix, and I3 represents a three-order unit matrix; (3) constructing an intermittent control strategy based on the designed deception attack observer, which is divided into a control time and a rest time: Control time: [nT, nT + S) Rest time: [nT + S, (n + 1)T) Wherein, S ∈ (0, T] is the control time length within a period T, and n is used to identify the index of the period; Then the following UAV formation system control strategy is proposed: wherein is a control signal, effective for a control time; is a compensation of the estimated spoofing attack signal; is a desired acceleration, for trajectory tracking; B + is a pseudo-inverse of the matrix B; B + The specific design form of the above-mentioned is as follows: The specific control signal is defined as: wherein, wherein, is an event-triggered signal; is the latest transmission signal from the jth UAV; w ij is a weight coefficient, reflecting the communication topology among UAVs; b i is a bias term; K is the controller gain matrix to be determined. 4.The event-based intermittent control method for UAV formation according to claim 3, wherein, The event-triggered mechanism based on the average method is constructed, and specifically includes the following steps of defining a state error and an average value of the state error, defining a triggering threshold function, defining a triggering condition, defining a triggering signal, defining a system state equation, and constructing an error system. (1) Defining a state error and an average value of the state error, the method is as follows: State error e yi (t) denotes the state error of the i-th UAV at time t, defined as: In the formula is a state estimation value, is an actual measurement value, C1 is an output matrix, is the state vector of the ith UAV at the time of the last event trigger is the state vector of the ith UAV at the time of the last event trigger is a state vector estimation value; average value of the state error is defined as: where w ij denotes the weight of the connection between drones i and j, denotes the state estimate of the i-th drone at time t, denotes the average state of the i-th drone and its neighbors at the time of the last event trigger, denotes the average state of the i-th drone and its neighbors at the time of the last event trigger, denotes the weighted average of the neighbors' states of the i-th drone at time t; (2) Defining a triggering threshold function, the method is as follows: Trigger threshold function σ i (t) is a time-dependent function that dynamically adjusts the threshold of the trigger condition, defined as: where σ mini and σ maxi are the minimum and maximum triggering thresholds, respectively, is the average value of the state error; (3) Defining a triggering condition, the method is as follows: represents if the weighted norm of the state error e yi (t) is less than a threshold σ i (t) average state error the product of the weighted norm of the state error e where is the state error vector e yi is the transpose of the matrix φ i is a weight matrix that adjusts the importance of different state error components; is the average state error is the transpose of the matrix (4) Defining a triggering signal, the method is as follows: Event trigger signal may be expressed as: where e yi (t) denotes the state error of the i-th drone at time t; The estimation error is represented as Using the Kronecker product, we have Wherein, C1=[I3 0]; C2=[I3 0]; wherein f i (t) denotes the actual spoofing attack signal of the i-th drone; denotes the estimated spoofing attack signal of the i-th drone; (5) Defining a system state equation, the method is as follows: The system state equation is represented as follows in the control time period and the rest time period: wherein [nT,nT+S) is the control time; [nT+S,(n+1)T) is the rest time; S is the control duration in the period T, and n is used to identify the index of the period; B0= diag{b1, b2,..., b N} ; is the state vector estimate; is the state error vector e N (t) transpose matrix; (6) Constructing an error system, the method is as follows: Definition: The error system is defined as follows: where A 1 = A1; A 2 = A2; B 1 = B; B 2 = 0; ε 1 = ε 2 = ε; z(t) is the output of the multi-UAV system; wherein, l, A 1 The specific definitions of A2, B, ε, G, and D are as follows: G = [I 6N 0 6N×3N ] D＝[2 2 3 3 2 2]。 5.The event-based intermittent control method for UAV formation according to claim 4, wherein, The stability of the unmanned aerial vehicle formation is analyzed, and the method is as follows: If there is v>0 and a decay rate ω such that the error system of the unmanned aerial vehicle formation system control strategy is exponentially stable, then for all t>0: ||η(t)|| < v e -ωt ||η0|| (29) Wherein η0=η(0); If there exists a matrix φ i > 0 (i = 1, 2, 3,..., N), then the error system is exponentially stable and: κ=ρ1s-ρ2(T-S)>0 Wherein: φ = diag{φ1, φ2,..., φN} N} γ=3.61 where S e (0, T] is the control duration within the pending period T; p ι , i = {1, 2} are pending parameters, K is a control gain matrix and H is an observation gain matrix; When the unmanned aerial vehicle formation satisfies the above conditions, it is considered that the unmanned aerial vehicle formation can fly stably.

6. An event-based intermittent control system for UAV formation, for implementing the event-based intermittent control method for UAV formation according to any one of claims 1 to 5, characterized in that, It includes: A first construction module for constructing a dynamic model of the unmanned aerial vehicle formation; A second construction module for constructing a state space model of the unmanned aerial vehicle formation under deception attack based on graph theory; A third construction module for constructing an intermittent control strategy based on an observer, specifically including defining an expected relative position and tracking error, designing a deception attack observer, and constructing an intermittent control strategy; A fourth construction module for constructing an event-triggered mechanism based on the average method, specifically including defining a state error and an average value of the state error, defining a triggering threshold function, defining a triggering condition, defining a triggering signal, defining a system state equation, and constructing an error system; An analysis module for analyzing the stability of the unmanned aerial vehicle formation and evaluating the flight state of the unmanned aerial vehicle formation according to the analysis result.

7. A terminal device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, The memory stores a computer program capable of running on the processor, and the processor loads and executes the computer program, adopts the event-based intermittent control method of the unmanned aerial vehicle formation in any one of claims 1 to 5.

8. A storage medium containing computer-executable instructions, wherein: The computer executable instructions are used to execute the event-based intermittent control method of the unmanned aerial vehicle formation in any one of claims 1 to 5 when executed by the computer processor.

9. A computer program product, characterised in that, The computer program product includes a computer program, which is executed by the processor to load and execute the event-based intermittent control method of the unmanned aerial vehicle formation in any one of claims 1 to 5.

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