A safety time-varying formation control method for nonlinear multi-unmanned aerial vehicle system

Abstract

The application discloses a kind of safety time-varying formation control methods of nonlinear multi-unmanned aerial vehicle system, it is related to the time-varying formation control field of multi-unmanned aerial vehicle system, including: constructing multi-unmanned aerial vehicle communication topology model, nonlinear unmanned aerial vehicle dynamics model, sensor fault measurement model and denial-of-service attack model;Robust three-step volume Kalman filter is designed, the state of unmanned aerial vehicle system and sensor fault are decoupled estimation, obtain state estimation value and fault estimation value without fault pollution;Based on state estimation value and fault estimation value, design distributed resilience formation control law, compensate the measurement distortion caused by communication interruption and sensor fault caused by denial-of-service attack;Dynamic surface sliding mode attitude stability control law is designed, to ensure that unmanned aerial vehicle attitude is stable, realize multi-unmanned aerial vehicle under denial-of-service attack and sensor fault concurrent time-varying formation tracking.The application can maintain time-varying formation under the condition that DoS attack and sensor fault exist simultaneously.

Description

Technical Field

[0001] This invention relates to the field of time-varying formation control for multi-UAV systems, and specifically to a safe time-varying formation control method for nonlinear multi-UAV systems. Background Technology

[0002] Over the past decade, the application of unmanned aerial vehicles (UAVs) in civilian monitoring, cargo transportation, and disaster relief has expanded rapidly. To perform tasks beyond the capabilities of a single platform, multiple UAVs can collaborate to complete large-scale surveillance and sensor fusion. However, multi-UAV collaboration itself faces challenges such as limited communication, limited onboard computing power, and the scaling up of the system. Existing research has extensively explored time-invariant formation control. However, for complex tasks requiring time-varying geometric configurations and trajectories, fixed formation patterns often fall short, driving the development of time-varying formation (TVF) research.

[0003] However, there are still few studies that consider both DoS attacks and sensor failures in TVF scenarios. The coupling between communication interruption and measurement distortion further increases the difficulty of resilient formation control. Summary of the Invention

[0004] To address the aforementioned shortcomings in the existing technology, this invention provides a secure time-varying formation control method for nonlinear multi-UAV systems, which can maintain time-varying formation even when DoS attacks and sensor failures coexist.

[0005] To achieve the above-mentioned objectives, the technical solution adopted by this invention is: a safe time-varying formation control method for a nonlinear multi-UAV system, comprising the following steps:

[0006] S1: Construct a multi-UAV communication topology model, a nonlinear UAV dynamics model, a sensor fault measurement model, and a denial-of-service attack model;

[0007] S2: Design a robust three-step capacitive Kalman filter to decouple the state of the UAV system from sensor faults and obtain fault-free state and fault estimates.

[0008] S3: Based on state estimates and fault estimates, design a distributed resilient formation control law to compensate for communication interruptions caused by denial-of-service attacks and measurement distortions caused by sensor failures.

[0009] S4: Design a dynamic surface sliding mode attitude stabilization control law to ensure the attitude stability of the UAV and realize time-varying formation tracking of multiple UAVs under concurrent denial-of-service attacks and sensor failures.

[0010] Furthermore, the nonlinear UAV dynamics model is as follows:

[0011]

[0012]

[0013]

[0014] in, For the first The quality of the drone For position vectors, The rotation matrix for projecting thrust from the engine system to the inertial frame. To be determined by roll angle Pitch angle and yaw angle Parameterized pose vector, The control input generated for the actuator, The gravity vector For time, The diagonal matrix of rotational inertia. This is the attitude control input vector. The matrix is ​​a coupling matrix for angle and rotation vectors, with superscript... Indicates time First derivative, superscript Indicates time The second derivative, for , for , for , for , for , for , It is the acceleration due to gravity. , , These are the moments of inertia.

[0015] Furthermore, the sensor fault measurement model is as follows:

[0016]

[0017] in, For the system output vector, These respectively represent the drones in Direction, superscript This is the transpose of the matrix. For state vectors, , , , and These represent the measurement matrix and the fault distribution matrix, respectively. For sensor fault items, Indicates that drones are in Fault items caused by direction, Indicates the drone's roll angle Pitch angle and yaw angle The resulting fault, It is Gaussian white noise.

[0018] Furthermore, the implementation steps of the robust three-step capacitive Kalman filter include:

[0019] Volume point calculation:

[0020]

[0021] in, For a moment With drones The relevant first One volume point, For state estimation, Let be the state dimension. The state estimation error covariance, To obtain the matrix of the first... Column operations, To obtain the matrix of the first... Column operations;

[0022] Updated in time:

[0023]

[0024]

[0025]

[0026] in, , , They respectively represent the use of to The first time measurement information obtained under the condition of time measurement Individual volume points, predicted state values, and state prediction error covariance. This is the state transition function. , The first and the Each sampling time, To apply control inputs to the system, For integration variables;

[0027] Measurement Update:

[0028]

[0029] in, For a moment The The transformed volume points, For a moment The The transformed volume points correspond to the predicted measurements. To predict the measurement mean, For cross covariance, To measure covariance, ;

[0030] Sensor fault estimation:

[0031]

[0032] in, For measurement information, For fault estimation error covariance, For fault estimation gain, Fault The estimated value, This is the output matrix after sensor measurement;

[0033] State estimation:

[0034]

[0035]

[0036]

[0037] in, Here is the Kalman gain matrix. The updated state prediction value, This is the updated state prediction error covariance matrix.

[0038] Furthermore, the design of the distributed resilient formation control law is as follows:

[0039]

[0040] in, This is a distributed resilient formation control law. , , For the gain matrix to be designed, For state estimation, For the first The desired reference state vector of the UAV, including the desired position. With expected speed , Indicates drone With drones Communication status, drones for neighbors State estimation, drones for neighbors The expected reference state vector, This is the compensation coefficient.

[0041] Furthermore, the dynamic surface sliding mode attitude stability control law is as follows:

[0042]

[0043] in, For drones The estimated attitude angular velocity, For virtual control laws, , It is a constant. For angular error, Let be the desired attitude angle vector. It is the integral variable.

[0044] The beneficial effects of this invention are:

[0045] (1) This invention proposes a resilient control framework for nonlinear multi-UAV systems, which can maintain time-varying formations under the simultaneous presence of DoS attacks and sensor failures. Compared with existing technologies that mainly address single problems, this framework explicitly handles both types of challenges in a unified manner. Simulation results show that the required formations can still be accurately maintained under combined adversarial conditions.

[0046] (2) This invention designs a robust three-step capacitive Kalman filter (RTS-CKF) for handling state measurements contaminated by sensor faults. Unlike the standard CKF, which can only perform state estimation, the proposed RTS-CKF estimates both the system state and sensor faults simultaneously through decoupling design, thus maintaining accurate state recovery capability. At the same time, this invention rigorously proves the bounded convergence of the estimation error based on Lyapunov stability analysis.

[0047] (3) Based on the state estimation provided by RTS-CKF, this invention proposes a distributed resilient control law that simultaneously compensates for DoS communication interruptions and sensor failures. Compared with traditional methods that can only handle single-type failure scenarios, this controller can concurrently cope with DoS attacks and sensor failures. Furthermore, this invention also introduces a dynamic surface sliding mode attitude stabilizer to ensure attitude stability and system robustness. Attached Figure Description

[0048] Figure 1 This is a flowchart of the safe time-varying formation control method for nonlinear multi-UAV systems of the present invention.

[0049] Figure 2 This is a diagram illustrating the safe time-varying formation control framework of the nonlinear multi-UAV system of the present invention.

[0050] Figure 3 This is a network topology diagram of drones.

[0051] Figure 4 This is a flight path diagram of a drone formation.

[0052] Figure 5 The diagram shows the fault estimation results for each UAV. Detailed Implementation

[0053] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0054] like Figure 1 As shown, a safe time-varying formation control method for a nonlinear multi-UAV system includes the following steps:

[0055] S1: Construct a multi-UAV communication topology model, a nonlinear UAV dynamics model, a sensor fault measurement model, and a denial-of-service attack model;

[0056] The communication topology between multiple drones can be modeled as an undirected connected graph. .in, Represents a set of nodes. Represents the set of communication edges. Adjacency matrix. Satisfy: If node With nodes There are edges between them ( ),but ;otherwise Each intelligent agent Gather with its neighbors To interact. The Laplace matrix is ​​defined as follows: ,in ,and .

[0057] The time-varying topology consists of piecewise constant switching signals. Control, it is in the range ( From a finite set Selected image and its Laplace matrix All candidate graphs share the same vertex set. Thus, a joint graph is defined. Its edge set is It should be noted that within certain specific sub-intervals, It might be disconnected.

[0058] Definition 1. If in each interval ( On the above, the joint diagram If each of the given elements contains a spanning tree, then the switching topology is said to satisfy the joint connectivity property.

[0059] Lemma 1. Let... It is a constant, and It is a uniformly continuous nonnegative function. If it satisfies Then there is .

[0060] The nonlinear UAV dynamics model is as follows:

[0061] (1)

[0062]

[0063]

[0064] in, For the first The quality of the drone For position vectors, , The rotation matrix for projecting thrust from the engine system to the inertial frame. To be determined by roll angle Pitch angle and yaw angle Parameterized pose vector, The control input generated for the actuator, The gravity vector For time, The diagonal matrix of rotational inertia. This is the attitude control input vector. This represents the control input generated by the four actuators. The matrix is ​​a coupling matrix for angle and rotation vectors, with superscript... superscript , for , for , for , for , for , for , It is the acceleration due to gravity. , , These are the moments of inertia.

[0065] This invention employs a two-layer control structure, decoupling the outer loop position tracking from the inner loop attitude stabilization, thereby improving the system's resilience to DoS attacks and sensor failures. The position loop is responsible for achieving the target formation geometry, while the attitude loop is responsible for ensuring flight stability. Based on this, the translational mechanics in equation (1) can be written in the form of a dual integrator:

[0066] (2)

[0067] in, For velocity vectors, , For virtual control input matrix, respectively drones in Virtual control input.

[0068] Airborne sensor measurements may be affected by malfunctions; therefore, the sensor malfunction measurement model is as follows:

[0069] (3)

[0070] in, For the system output vector, These respectively represent the drones in Direction, superscript This is the transpose of the matrix. For state vectors, , , , and These represent the measurement matrix and the fault distribution matrix, respectively. For sensor fault items, Indicates that drones are in Fault items caused by direction, Indicates the drone's roll angle Pitch angle and yaw angle The resulting fault, It is Gaussian white noise.

[0071] Communication between multiple drones typically relies on open networks, making them vulnerable to malicious cyberattacks. Among numerous threats, DoS attacks cause congestion by injecting illegal traffic into communication links, thereby weakening formation control. This invention focuses on intermittent DoS attacks, where the attack alternates between active and dormant states due to the attacker's limited resources. The start time of this DoS attack is The attack duration is The relevant assumptions are given below.

[0072] Assumption 1: Let Representing an interval The total duration of the DoS attack, and If a constant exists and , making If the attack duration satisfies the boundedness constraint, then the attack duration is also bounded.

[0073] DoS attack status is toggled by a signal. Description, in which Indicates the attack activation phase. This indicates the attack is in a dormant phase.

[0074] Assumption 2: Initial Communication Diagram It contains a spanning tree. During a DoS attack, communication links may be blocked for extended periods, leaving the topology disconnected within the attack interval; however, between attacks, the network intermittently restores connectivity. Although the communication graph may be disconnected for certain periods due to the ongoing DoS attack, it remains connected in each cycle. Above, by sub-interval The joint graph formed by aggregation It always contains a spanning tree. Therefore, switching graph families... In each interval The above satisfies the joint connectivity property.

[0075] Consider a mountain search and rescue scenario. The complex environment presents challenges to communication and impacts perception quality. The drones need to track a designated formation trajectory under conditions of potential DoS attacks and internal sensor malfunctions. Let the... The desired reference trajectory of the drone is The TVF control objective is to ensure that each drone can accurately track its desired trajectory even under concurrent DoS attacks and sensor failures.

[0076] (4)

[0077] in, Indicates the formation reference center.

[0078] Considering the system's vulnerability to both sensor malfunctions and DoS attacks, achieving reliable multi-UAV swarm tracking is no easy task. The framework proposed in this invention can guarantee swarm tracking accuracy and flight stability under conditions of fault measurement and communication interruption. Figure 2As shown, the architecture consists of an outer formation tracking subsystem and an inner attitude stabilization subsystem. The outer loop generates virtual acceleration commands that meet the formation tracking requirements and further provides the desired attitude angles that the inner loop needs to track; the inner loop is responsible for attitude tracking to maintain flight stability. An FDD module is embedded in the framework for real-time estimation of sensor faults, enabling the control law to adaptively compensate for contaminated measurements and maintain formation performance.

[0079] S2: Design a robust three-step capacitive Kalman filter to decouple the state of the UAV system from sensor faults and obtain fault-free state and fault estimates.

[0080] This invention constructs a real-time sensor fault detection and diagnosis scheme based on RTS-CKF to simultaneously acquire state estimation and fault estimation. The proposed RTS-CKF is an extension based on the classic CKF. Since RTS-CKF requires a discrete-time model, equations (1) and (3) are discretized as follows:

[0081] (5)

[0082] in, Represents the state transition function. For the first The drone in The system state vector at the sampling time. For the first The drone in The system output vector at the sampling time. For the first The drone in The system state vector at the sampling time. For the first The drone in The system input applied at the sampling time, and These are zero-mean Gaussian white noise, used to characterize system disturbances and measurement disturbances.

[0083] The implementation steps of the robust three-step capacitive Kalman filter include:

[0084] Volume point calculation:

[0085] (6)

[0086] in, For a moment With drones The relevant first One volume point, For state estimation, Let be the state dimension. The state estimation error covariance, To obtain the matrix of the first... Column operations, To obtain the matrix of the first... Column operations;

[0087] Updated in time:

[0088] (7)

[0089] (8)

[0090] (9)

[0091] in, , , They respectively represent the use of to The first time measurement information obtained under the condition of time measurement Individual volume points, predicted state values, and state prediction error covariance. This is the state transition function. , The first and the Each sampling time, To apply control inputs to the system, For integration variables;

[0092] Measurement Update:

[0093]

[0094]

[0095] (10)

[0096] (11)

[0097] (12)

[0098] (13)

[0099] in, For a moment The The transformed volume points, For a moment The The transformed volume points correspond to the predicted measurements. To predict the measurement mean, For cross covariance, To measure covariance, The measurement noise covariance matrix;

[0100] Sensor fault estimation:

[0101] (14)

[0102] (15)

[0103] (16)

[0104] (17)

[0105] in, For measurement information, For fault estimation error covariance, For fault estimation gain, Fault The estimated value, This is the output matrix after sensor measurement;

[0106] State estimation:

[0107] (18)

[0108] (19)

[0109] (20)

[0110] in, Here is the Kalman gain matrix. The updated state prediction value, This is the updated state prediction error covariance matrix.

[0111] The estimation error and prediction error are defined as follows:

[0112] (twenty one)

[0113] For ease of analysis, the error expression can be approximated as:

[0114] (twenty two)

[0115] in:

[0116]

[0117] in, State transition function Regarding the status The Jacobian matrix is ​​used to approximate the propagation of nonlinear prediction errors into a linear form. This is a combined term of first-order linearization truncation error and process noise. For the first The drone in The control input at time is substituted as a known quantity for the Jacobian matrix calculation.

[0118] By introducing an unknown diagonal matrix To uniformly characterize the first-order linearization error and noise term The above formula can be rewritten in its precise form:

[0119] (twenty three)

[0120] Theorem 1. Consider a nonlinear system using the RTS-CKF estimator. If the uncertainty term satisfies and For any given positive scalar ,definition If a positive definite matrix exists... and Make the following linear matrix inequalities hold:

[0121] (twenty four)

[0122] (25)

[0123] (26)

[0124] Then the state estimate of RTS-CKF will asymptotically converge to the true system state. For sensor fault estimation error, This is the bounded upper bound of the fault estimation error. For the first The measurement noise vector at time step, To measure the bounded upper bound of noise, For the corresponding dimension, , , These are the measurement noise matrix, fault propagation matrix, and state error propagation matrix, respectively.

[0125] Proof: Take the Lyapunov function:

[0126] (27)

[0127] The difference between the system output and its estimate can be written as:

[0128] (28)

[0129] Substituting equation (19) into equation (21), we get:

[0130] (29)

[0131] Combining equation (28) yields:

[0132] (30)

[0133] in,

[0134] and .

[0135] From the Lyapunov function, we can further obtain:

[0136] (31)

[0137] Therefore, the difference form is:

[0138] (32)

[0139] Using Young's inequality, we can scale the cross terms to obtain:

[0140] (33)

[0141] If equations (24)-(26) hold, then the above difference is not positive, therefore Monotonically non-increasing. Therefore, we obtain... .

[0142] Therefore, under the conditions of equations (24)-(26), the proposed FDD scheme can guarantee that the error between the estimated state and the true state asymptotically converges to zero.

[0143] S3: Based on state estimates and fault estimates, design a distributed resilient formation control law to compensate for communication interruptions caused by denial-of-service attacks and measurement distortions caused by sensor failures.

[0144] To compensate for sensor failures, the controller bases its response on the estimated state. Design is performed. Based on equation (2), the estimated state dynamics are written as:

[0145] (34)

[0146] in, , .

[0147] The distributed resilient formation control law is designed as follows:

[0148] (35)

[0149] in, , This is a distributed resilient formation control law. , , For the gain matrix to be designed, For state estimation, For the first The desired reference state vector of the UAV, including the desired position. With expected speed , Indicates drone With drones Communication status, drones for neighbors State estimation, drones for neighbors The expected reference state vector, This is the compensation coefficient.

[0150] make:

[0151]

[0152] Then, under equation (35), equation (34) becomes:

[0153] (36)

[0154] in, To compensate for the diagonal matrix, for An identity matrix of dimension 1 For the desired state, Let be the expectation matrix. It refers to Kronecker.

[0155] make ,and Then equation (36) can be written as:

[0156] (37)

[0157] Under a DoS attack, the communication graph changes over time, therefore the system is further written as follows:

[0158] (38)

[0159] in, For time The compensation diagonal matrix at that time.

[0160] Theorem 2. For a given matrix If there exists a symmetric positive definite matrix Makes the following linear matrix inequality hold:

[0161] (39)

[0162] (40)

[0163] in, Under the action of equation (35), equation (38) can achieve the desired TVF when DoS attack and sensor failure are present.

[0164] Proof: Consider the Lyapunov function

[0165] (41)

[0166] Differentiating along the trajectory of equation (38), we have

[0167] (42)

[0168] According to equation (40), we have .therefore, It is monotonically non-increasing and has a bounded lower bound. According to the Cauchy criterion, for any... ,exist , making when hour,

[0169] (43)

[0170] in, Let be any given positive number, used to characterize the upper bound of the difference. For the index of the time interval, The set of natural numbers, For the first Each topology switching moment For the first Topology switching moments.

[0171] The above formula can be rewritten as:

[0172] (44)

[0173] Dividing the integration interval into an unattacked phase and an attacked phase can be written as:

[0174] (45)

[0175] in, For the first The start time of each time interval, The switching time between attack and non-attack states. For the first The end time of each time interval, in each interval The communication topology can be divided into non-attack states. and attack state Therefore, we have:

[0176] (46)

[0177] in, For interval Inner The termination time of each sub-interval For interval Inner The start time of each sub-interval For switching signals The Laplace matrix of the communication graph below, For switching signals The compensation coefficient matrix is ​​shown below.

[0178] Finally, according to Lemma 1, we have

[0179] (47)

[0180] in, , The comprehensive matrix at the moment of activation of the DoS attack. This is a comprehensive matrix showing the state of sleep during a DoS attack. , for .

[0181] because Therefore, ,thereby It remains bounded over the entire time interval. Combined with system dynamics, we know that the scalar function...

[0182]

[0183] It is consistent and continuous. If the communication network in each cycle If the matrix remains jointly connected, then the matrix It is always positive definite. Therefore, the unique solution that satisfies the above equation is:

[0184] (48)

[0185] That is, the estimation error of all UAVs asymptotically converges to zero.

[0186] S4: Design a dynamic surface sliding mode attitude stabilization control law to ensure the attitude stability of the UAV and realize time-varying formation tracking of multiple UAVs under concurrent denial-of-service attacks and sensor failures.

[0187] The position loop control input can be obtained from equation (35). For ease of analysis, for all set up . No. The desired roll angle and pitch angle of the individual agent , The definition is as follows:

[0188] (49)

[0189] make , Based on the rotational dynamics given by equation (1), the following attitude stability control law is designed.

[0190] (50)

[0191] in, For drones The estimated attitude angular velocity, For virtual control laws, , It is a constant. For angular error, The desired attitude angle vector is obtained by inverse solving of the outer loop position controller. It is the integral variable.

[0192] Theorem 3. Let , , , , as well as It is a constant and satisfies

[0193] (51)

[0194] (52)

[0195] (53)

[0196] (54)

[0197] Then, under the action of equation (50), the first The actual attitude state of the drone will asymptotically converge to the corresponding desired set value.

[0198] Proof: To analyze the stability of the attitude loop, construct Lyapunov candidate functions.

[0199] (55)

[0200] Then there is

[0201] (56)

[0202] in, , This is the output of a first-order low-pass filter, and satisfy

[0203] (57)

[0204] remember , and These represent angle error, virtual control input, and filtering error, respectively. Construct a new Lyapunov function:

[0205] (58)

[0206] Known ,remember ,but

[0207] (59)

[0208] Further by

[0209] (60)

[0210] It can be seen that, yes , , and The function. Assume ,in That is, the initial state of the system is bounded. When When it is bounded, It also has boundaries, denoted as Therefore, equation (59) can be transformed into:

[0211] (61)

[0212] According to equation (54), we can obtain:

[0213] (62)

[0214] when When the above equation holds, then for any expression satisfying this equation, the following holds true. and The initial values ​​of all have This indicates the system state. , and Consistency is eventually bounded. By appropriately increasing... This can reduce attitude tracking error It converges to any small neighborhood near zero.

[0215] In one embodiment of the present invention, the effectiveness of the proposed framework, including the RTS-CKF estimator, formation control law, and attitude control law, is verified through simulation. The simulation subjects are four UAVs, achieving TVF under the combined effects of DoS attacks and sensor failures. UAV model parameters are shown in Table 1, initial UAV states are shown in Table 2, and the communication topology for information exchange is as follows: Figure 3 As shown, (a) represents normal communication, and (b) represents communication during a DoS attack.

[0216] Table 1 Model parameters of the four UAVs

[0217]

[0218] Table 2 Initial values ​​for each UAV

[0219]

[0220] Formation reference trajectory of four drones ( Set as:

[0221]

[0222] The drone formation control parameters are set as follows. The position loop control gain is selected as:

[0223]

[0224] The compensation matrix is:

[0225]

[0226] The parameters of the attitude control subsystem are selected as follows: , and .

[0227] Figure 4 The tracking trajectories of a four-UAV formation in a three-dimensional environment are presented. Even with DoS attacks hindering inter-UAV communication and sensor failures affecting individual state measurements, the proposed control framework successfully maintains the target TVF configuration, with each UAV accurately tracking its own target position while preserving its time-varying formation shape. The results demonstrate that the combination of RTS-CKF and distributed control facilitates robust cooperation under complex disturbances.

[0228] Figure 5 The fault estimation capability of the proposed RTS-CKF was verified. By decoupling sensor faults from measurement data, RTS-CKF can achieve high-precision fault reconstruction. The estimated fault values ​​are in high agreement with the actual injected faults. This invention designs the fault signal as different piecewise functions to simulate multiple types of fault characteristics and injects them stepwise at different time periods on multiple sensor channels, thereby more comprehensively evaluating the real sensor fault situation. The accurate tracking of the fault estimation curve to the actual fault signal shows that the proposed method can effectively complete the joint estimation of state and fault under the conditions considered in this invention.

[0229] This invention proposes a resilient time-varying formation control method for nonlinear networked multi-UAV systems facing sensor failures and network-induced DoS attacks. The framework integrates a distributed formation controller for TVF tracking, a dynamic surface sliding mode attitude stabilizer to ensure flight stability, and an RTS-CKF scheme for accurately estimating system state and sensor failures under adverse conditions. Lyapunov analysis proves the system's boundedness and convergence, while simulation results with four UAVs show that the proposed method has significant advantages in robustness and tracking performance compared to existing methods.

[0230] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of the invention.

Claims

1. A safe time-varying formation control method for a nonlinear multi-UAV system, characterized in that, Includes the following steps: S1: Construct a multi-UAV communication topology model, a nonlinear UAV dynamics model, a sensor fault measurement model, and a denial-of-service attack model; S2: Design a robust three-step capacitive Kalman filter to decouple the state of the UAV system from sensor faults and obtain fault-free state and fault estimates. S3: Based on state estimates and fault estimates, design a distributed resilient formation control law to compensate for communication interruptions caused by denial-of-service attacks and measurement distortions caused by sensor failures. S4: Design a dynamic surface sliding mode attitude stabilization control law to ensure the attitude stability of the UAV and realize time-varying formation tracking of multiple UAVs under concurrent denial-of-service attacks and sensor failures.

2. The safe time-varying formation control method for a nonlinear multi-UAV system according to claim 1, characterized in that, The nonlinear UAV dynamics model is as follows: ； ； ； in, For the first The quality of the drone For position vectors, The rotation matrix for projecting thrust from the engine system to the inertial frame. To be determined by roll angle Pitch angle and yaw angle Parameterized pose vector, The control input generated for the actuator, The gravity vector For time, The diagonal matrix of rotational inertia. This is the attitude control input vector. The matrix is ​​a coupling matrix for angle and rotation vectors, with superscript... Indicates time First derivative, superscript Indicates time The second derivative, for , for , for , for , for , for , It is the acceleration due to gravity. , , These are the moments of inertia.

3. The safe time-varying formation control method for a nonlinear multi-UAV system according to claim 2, characterized in that, The sensor fault measurement model is as follows: ； in, For the system output vector, These respectively represent the drones in Direction, superscript This is the transpose of the matrix. For state vectors, , , , and These represent the measurement matrix and the fault distribution matrix, respectively. For sensor fault items, Indicates that drones are in Fault items caused by direction, Indicates the drone's roll angle Pitch angle and yaw angle The resulting fault, It is Gaussian white noise.

4. The safe time-varying formation control method for a nonlinear multi-UAV system according to claim 3, characterized in that, The implementation steps of the robust three-step capacitive Kalman filter include: Volume point calculation: ； in, For a moment With drones The relevant first One volume point, For state estimation, Let be the state dimension. The state estimation error covariance, To obtain the matrix of the first... Column operations, To obtain the matrix of the first... Column operations; Updated in time: ； ； ； in, , , They respectively represent the use of to The first time measurement information obtained under the condition of time measurement Individual volume points, predicted state values, and state prediction error covariance. This is the state transition function. , The first and the Each sampling time, To apply control inputs to the system, For integration variables; Measurement Update: ； in, For a moment The The transformed volume points, For a moment The The transformed volume points correspond to the predicted measurements. To predict the measurement mean, For cross covariance, To measure covariance, The measurement noise covariance matrix; Sensor fault estimation: ； in, For measurement information, For fault estimation error covariance, For fault estimation gain, For fault The estimated value, This is the output matrix after sensor measurement; State estimation: ； ； ； in, Here is the Kalman gain matrix. The updated state prediction value, This is the updated state prediction error covariance matrix.

5. The safe time-varying formation control method for a nonlinear multi-UAV system according to claim 4, characterized in that, The designed distributed resilient formation control law is as follows: ； in, This is a distributed resilient formation control law. , , For the gain matrix to be designed, For state estimation, For the first The desired reference state vector of the UAV, including the desired position. With expected speed , Indicates drone With drones Communication status, drones for neighbors State estimation, drones for neighbors The expected reference state vector, This is the compensation coefficient.

6. The safe time-varying formation control method for a nonlinear multi-UAV system according to claim 5, characterized in that, The dynamic surface sliding mode attitude stability control law is as follows: ； in, For drones The estimated attitude angular velocity, For virtual control laws, , It is a constant. For angular error, Let be the desired attitude angle vector. It is the integral variable.

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