Safety control method of multi-UAV system based on unknown input observer

Abstract

The present invention discloses a multi-UAV system safety control method based on an unknown input observer, including: improving the unknown input observer as a state observer based on measurement information and system nonlinear design, and performing state estimation on the current multi-UAV system; constructing a residual function through state estimation and measurement output and performing node attack detection; when it is determined that a node attack occurs, reconstructing and compensating the attack signal based on the improved unknown input observer to flexibly control the state estimation process of the multi-UAV system and obtain the safety state information of the system; using the current estimation result of the state observer as the safety state information of the system; and performing safety control on the multi-UAV system based on the safety state information. The method reduces the impact of sensor attacks on the performance of UAV state estimation, makes the system flexible to node sensor attacks, and improves the safety control effect; at the same time, it can realize on-demand control and save system communication resources.

Description

Technical Field

[0001] The present invention belongs to the field of security defense of unmanned cyber-physical systems, and specifically relates to a multi-unmanned aerial vehicle system security control method based on an unknown input observer. Background Art

[0002] Drones have the advantages of small size, light weight, easy operation, high flexibility, high adaptability, and high adjustability. They have important applications in various fields, such as surveying and mapping remote sensing, security reconnaissance, and environmental detection. As an information-physical system that integrates communication equipment, execution equipment, sensor equipment, and control modules, drones can build a closed-loop process of sensing data, exchanging information, making decisions, and executing tasks, and realize the close integration of computing elements and network processes with physical objects. They can be regarded as a type of information-physical system. Compared with a single-drone system, a multi-drone system has the advantages of short task execution time, fast information transmission, and high system fault tolerance. Multiple drones can cooperate to handle various complex problems, thereby improving the efficiency and success rate of task completion.

[0003] Due to the openness of the network environment, unmanned cyber-physical systems may be affected by potential hostile behaviors, namely, multi-node sensor FDI (False data injection) attacks. If the countermeasures to network attacks are ignored, the system performance will be greatly affected, and may even cause system instability, resulting in unpredictable economic and social losses. For a multi-UAV system composed of multiple individuals, attackers can attack different UAVs at different times, making network attacks coupled in time and space. At the same time, cyber-physical security introduces the dimension of physical dynamics on the basis of traditional network security, that is, the failure and fluctuation of the UAV system also affect the stability of the network system. Therefore, it is necessary to study the security defense strategy of the multi-UAV system to provide theoretical guidance and technical support for the multi-UAV system to move towards a wider and more complex application scenario.

[0004] At present, the existing technology mainly provides the following security control methods:

[0005] Reference [1] (Hota, Ashish Ranjan and Shreyas Sundaram. "Interdependent security games on networks under behavioral probability weighting." IEEE Transactions on Control of Network Systems 5 (2015): 262-273.) designed a resilient control architecture based on game theory to mitigate the impact of information injected by attackers on the performance of the intelligent agent.

[0006] Reference [2] (Jin, Xu and Wassim M. Haddad. "An adaptive control architecture for leader–follower multiagent systems with stochastic disturbances and sensor and actuator attacks." International Journal of Control 92 (2019): 2561-2570.) and reference [3] (Arabi, Ehsan et al. "Mitigating the effects of sensor uncertainties in networked multi-agent systems." Journal of Dynamic Systems Measurement and Control-transactions of The Asme 139 (2017): 041003.) apply adaptive resilience architectures to ensure that the attacked intelligent agent system can achieve consistent control goals with consistent ultimate boundedness under network attacks.

[0007] Reference [4] (Meng, Min et al. "Adaptive consensus for heterogeneous multi-agent systems under sensor and actuator attacks." Autom. 122 (2020): 109242.) studied the leader-follower resilient consensus problem for heterogeneous multi-agent systems under simultaneous sensor and actuator attacks.

[0008] Reference [5] (Modares, Hamidreza et al. "Static output-feedback synchronisation of multi-agent systems: a secure and unified approach." Iet Control Theory and Applications 12 (2018): 1095-1106.) proposed a unified static output feedback method to study the resilience consistency of multi-agent systems under sensor and actuator attacks.

[0009] Reference [6] (Mustafa, Aquib and Hamidreza Modares. "Attack Analysis and Resilient Control Design for Discrete-Time Distributed Multi-Agent Systems." IEEE Robotics and Automation Letters 5 (2018): 369-376.) analyzes the adverse effects of cyber-physical attacks on discrete-time distributed multi-agent systems and proposes a mitigation method for attacks on sensors and actuators.

[0010] However, the above methods still have some defects. Among them, the method used in reference [1] makes assumptions about the statistical characteristics of the attacker and the system, and such assumptions may be difficult to meet simultaneously in the actual system; the methods in references [2-4] do not consider the influence of process noise in the UAV system, which makes the accuracy of attack detection depend on the statistical characteristics of noise, has a certain attack false alarm rate, and also reduces the suppression effect of elastic control on attacks; references [5-6] do not consider the influence of system nonlinearity on the design. In the actual process, there are certain requirements for the integrity of the intelligent system, and the actual control effect depends on the accuracy of the linearization model.

[0011] In summary, existing methods are unable to perform attack detection and compensation based on the precise system status when performing security control on multi-UAV systems, thus reducing the actual control effect. Summary of the invention

[0012] In order to solve the above problems existing in the prior art, the present invention provides a multi-UAV system safety control method based on an unknown input observer.

[0013] The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0014] A multi-UAV system safety control method based on unknown input observer, comprising:

[0015] Step 1: Based on the measurement information and system nonlinear design, the unknown input observer is improved as the state observer, and the state observer is used to estimate the state of the current multi-UAV system;

[0016] Step 2: Construct the residual function through state estimation and measurement output and perform node attack detection;

[0017] Step 3: When it is determined that a node attack occurs, the attack signal is reconstructed and compensated based on the improved unknown input observer to flexibly control the state estimation process of the multi-UAV system and obtain the security state information of the system;

[0018] Otherwise, the current estimation result of the state observer is used as the safety state information of the system;

[0019] Step 4: Perform safety control on the multi-UAV system based on the safety status information.

[0020] Beneficial effects of the present invention:

[0021] 1. The present invention takes into account the situation where the system contains nonlinear terms, introduces drone measurement and state estimation information to design an unknown input observer, eliminates the influence of drone process noise on state estimation performance, enables the system to perform attack detection based on accurate state estimation, and synchronously perform attack reconstruction and attack compensation elastic control after detecting the attack, reduces the influence of sensor attacks on drone state estimation performance, and improves the safety control effect;

[0022] 2. The attack reconstruction and attack compensation elastic control mechanism designed by the present invention based on the unknown input observer can reduce the impact of node sensor attacks on the state estimation of the UAV, ensure the effectiveness of the consistency control law based on state estimation, and have high application value; at the same time, the elastic control is triggered by attack detection, so that the elastic control mechanism will not affect the state estimation and system consistency under normal circumstances, that is, the UAV system is elastic to node sensor attacks;

[0023] 3. The present invention also designs an event-triggered control mechanism for consistency control. By constructing a Lyapunov function and deriving it, sufficient LMI conditions for solving each matrix to be solved are obtained. Thus, the required matrix to be solved can be obtained by selecting relevant parameters, so that the system can be controlled on demand, further saving communication resources of multi-UAV systems, which has great practical significance.

[0024] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a flowchart of a multi-UAV system safety control method based on an unknown input observer provided by an embodiment of the present invention;

[0026] Figure 2 is a flow chart of another multi-UAV system safety control method based on an unknown input observer provided by an embodiment of the present invention;

[0027] Figure 3 is the consistency error diagram of the follower UAV when there is no elastic control in the simulation experiment;

[0028] Figure 4 is the state estimation error diagram of the follower UAV when there is no elastic control in the simulation experiment;

[0029] Figure 5 It is the residual signal and residual threshold diagram when the system is attacked by the sensor in the simulation experiment;

[0030] Figure 6 is the consistency error graph of the follower UAV when the system is subjected to mixed attacks and uses elastic control in the simulation experiment;

[0031] Figure 7 This is the state estimation information diagram of the follower UAV when the system is subjected to mixed attacks and uses elastic control in the simulation experiment;

[0032] Figure 8 It is the triggering moment of the event triggering control mechanism of each follower drone under the hybrid FDI attack in the simulation experiment. DETAILED DESCRIPTION

[0033] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0034] Embodiment 1

[0035] First of all, it should be noted that the multi-UAV system considered in the present invention includes sensors, state observers, event triggers, controllers, actuators, and attack detectors. The sensors of each follower UAV may be subjected to continuous FDI attacks. Consider a multi-UAV system with 1 leader UAV and N follower UAVs. The system dynamic equation of the i-th follower UAV subjected to sensor FDI attack can be expressed as:

[0036]

[0037] Among them, x i (t)∈R n , They represent the state, control input and measurement output of follower agent i respectively, t represents time, Represents state x i The differential of (t), ω i (t) is the process noise, φ(x i (t))=[φ1(x i (t)),…,φ n (x i (t))] T is a nonlinear term, a i (t) is the sensor attack signal. In addition, A, B, C, D ω is a constant matrix of appropriate dimension.

[0038] The dynamic equation for leaders can be expressed as:

[0039]

[0040] Where x0(t)∈R n , Represent the state and output of leader agent i respectively. is the differential of x0(t), and φ(x0(t)) is the nonlinear term in the leader dynamic equation.

[0041] Without loss of generality, the following assumptions can be made for multi-UAV systems and sensor attacks in the discussion of this invention:

[0042] (1) Connectivity Graph There exists a directed spanning tree in , and the leader is the root node of the directed spanning tree.

[0043] (2) (A,B) is stable and (A,C) is observable.

[0044] (3) For any x1(t),x2(t)∈R n , the nonlinear function φ(x i ) satisfies the Lipschitz condition.

[0045] (4) Sensor attack a i (t) and its derivative are all bounded, but all upper bounds are unknown to the defender.

[0046] Accurate state estimation is the basis of attack detection, resilience control, consistency control and other methods. In order to correctly estimate the state of UAVs under the influence of process noise, this paper proposes a method of improving the advanced unknown input observer (AUIO) to achieve attack detection and resilience control of multi-UAV systems.

[0047] For details, see Figure 1, Figure 1 1 is a flow chart of a multi-UAV system safety control method based on an unknown input observer provided by an embodiment of the present invention, which includes:

[0048] Step 1: Based on the measurement information and system nonlinear design, the unknown input observer is improved as the state observer, and the state observer is used to estimate the state of the current multi-UAV system.

[0049] Optionally, this embodiment constructs an improved unknown input observer taking into account the nonlinearity of the system as a state observer based on local measurement information and neighbor measurement information, and estimates the state of the multi-UAV system accordingly, and its expression is:

[0050]

[0051] in, represents the state estimation result of follower agent i, t represents time, z i (t) is the unknown input observer state of follower agent i, For z i The derivative of (t), u i (t) and y i (t) represent the control input and measurement output of follower agent i, It is a generalized inverse matrix operation, T = I-HC, G = TB, F = TA-K1C, K u =K1+FH,A,B,C,D ω is a constant matrix, I is the unit matrix, K1 and K2 are the observer matrices to be designed, and They represent the output estimation error of follower agent i, represents the output estimation error of the leader agent, a ij and a i0 Represents the corresponding parameters of the adjacency matrix, where a ij Indicates the connection between follower i and its neighbor j. If it can receive information, then a ij =1, otherwise a ij =0; a i0 represents the connection between follower i and the leader, and the value standard is the same as above. Therefore, we can use the adjacency matrix Represents the connection between nodes in the algebraic graph, and uses the adjacency matrix Matrix and Metric Matrix Define the Laplace matrix L corresponding to the UAV communication topology graph.

[0052] It can be seen that AUIO has two matrices K1 and K2 to be designed. If K2 is taken as 0, as long as K1 is designed to ensure that the matrix F is Schur, the state estimation error of the unknown input observer will converge. However, since there are two matrices to be designed here, they need to be designed at the same time. The specific design method is described later.

[0053] In addition, H can be further S is an arbitrary matrix to increase the freedom of observer design.

[0054] Step 2: Construct the residual function through state estimation and measurement output and perform node attack detection.

[0055] 21) Construct the residual function r when the drone is not attacked by the sensor i * (t), and based on this, calculate the residual function r when the drone is attacked by the sensor i (t).

[0056] Specifically, consider the case where the drone is attacked by sensors and take the residual function Assume r i * (t) is the residual function when the UAV system is not attacked by sensors, then

[0057]

[0058] where z i (t)e i (t) represents the state estimation error of UAV i, φ(x i (t)) and Both represent nonlinear terms.

[0059] When the drone is attacked by sensors, combining equation (3) and equation (4) we can get:

[0060]

[0061] a i (t) represents sensor attack, for a i The derivative of (t).

[0062] 22) For the residual function r i (t) Perform Euclidean norm detection. If the norm of the residual function J is determined i (t) is greater than a preset threshold, the drone is determined to be under sensor attack; otherwise, the drone is determined not to be under sensor attack.

[0063] It is understandable that, under the correct design, the state estimation error of AUIO satisfies the UUB (Uniformly Ultimately Bounded) condition, so the sensor attack can be detected by the Euclidean norm of the residual, that is,

[0064]

[0065] The corresponding threshold J th,i It can be selected according to the following formula:

[0066] J th,i = sup{r i * (t)} (7)

[0067] Then the detection criteria for node sensor attacks in a multi-UAV system can be defined as:

[0068]

[0069] Step 3: When it is determined that a node attack occurs, the attack signal is reconstructed and compensated based on the improved unknown input observer to flexibly control the state estimation process of the multi-UAV system and obtain the true state information of the system; otherwise, the current estimation result of the state observer is used as the true state information of the system.

[0070] Specifically, when it is determined that a node attack occurs, it is necessary to reconstruct and compensate the attack signal based on the improved unknown input observer, and its expression is as follows:

[0071]

[0072] in, is the estimation of the sensor FDI attack signal, and M is the attack reconstruction matrix to be sought.

[0073] This embodiment can reduce the impact of sensor attacks on state estimation performance by reconstructing attack signals and performing compensation in state estimation.

[0074] Furthermore, the observer matrices K1, K2 and the attack reconstruction matrix M can be calculated by the following sufficient conditions:

[0075] For a given positive definite scalar ε1 and positive definite matrix R, if there exist symmetric positive definite matrices Q1, Q2 that satisfy the LMI (Linear matrix inequality LMI) condition shown in formula (10), and at the same time take the observer gain matrix The state observer based on attack reconstruction and compensation can ensure that the state estimation error and attack reconstruction error are UUB under process noise, communication channel interference and node sensor FDI attacks.

[0076]

[0077] Among them, λ0 is the parameter corresponding to the Laplace matrix L1 of the follower UAV communication topology, λ max (Θ) is the maximum eigenvalue of the positive definite matrix Θ. The specific method of obtaining the value is to take the matrix Θ so that it satisfies λ0 is a matrix The minimum eigenvalue of i (t)) corresponds to the Lipschitz parameter matrix, T represents the transpose, I N Represents the identity matrix of dimension N.

[0078] Through the above conditions, the observer matrices K1, K2, and M to be designed can be obtained.

[0079] It should be noted that since the UAV model is not affected by measurement noise, the designed observer matrix can be directly used for attack detection. However, the elastic control based on attack reconstruction and compensation still needs to be initiated after the sensor attack is detected, otherwise it will affect the performance of the UAV under normal circumstances.

[0080] The elastic control mechanism for attack reconstruction and attack compensation based on unknown input observer designed in the present invention can reduce the impact of node sensor attacks on UAV state estimation, ensure the effectiveness of the consistency control law based on state estimation, and have high application value; at the same time, the elastic control is triggered by attack detection, so that the elastic control mechanism will not affect the state estimation and system consistency under normal circumstances, that is, the UAV system is elastic to node sensor attacks.

[0081] Step 4: Safely control the multi-UAV system based on real status information.

[0082] In order to reduce the network burden caused by the increase in agent information transmission, this embodiment adopts an event-triggered consistency strategy to reduce the frequent operation of the controller, so as to save communication resources.

[0083] Specifically, first, let Represents the event triggering time sequence of the i-th drone, and sets the following event triggering mechanism:

[0084]

[0085]

[0086] Among them,∈2, h i and η1 is a given positive definite scalar, Measure the error for the event trigger mechanism.

[0087] Then, calculate the consistency control matrix K c .

[0088] Specifically, the consistency control matrix K c And the design method of the parameters related to the event trigger mechanism can be given by the following sufficient conditions:

[0089] Consider a multi-UAV system under an event-triggered controller. If there exists a symmetric positive definite matrix P1 and a positive definite scalar ε2, So that the linear matrix inequalities (13)-(14) hold, the consistency control gain is taken as When the system can achieve H ∞ Asymptotically stable consistency under performance indicator σ1, and no Zeno phenomenon occurs.

[0090]

[0091]

[0092] in,

[0093]

[0094]

[0095] represents the maximum number of neighbors in the system, L1 represents the Laplace matrix corresponding to the follower drone communication topology, and λ min (·) and λ max (·) represent the maximum and minimum eigenvalues ​​of the matrix, N represents the total number of follower drones, and h i It is the parameter in the event triggering mechanism;

[0096] In this embodiment, H ∞ The asymptotically stable consistency under the performance index σ1 can be expressed as:

[0097]

[0098] in, is the mathematical expectation, δ(t)=col{x i (t)-x0(t)} is the consistency error, ρ(t)=col{e x (t),ω(t)} is the composite perturbation, and V2(t) is the Lyapunov function of δ(t).

[0099] Finally, based on the event trigger mechanism and the consistency control matrix K c An event-triggered consistency control strategy is formulated to perform consistency control on the multi-UAV system. The formula is expressed as:

[0100]

[0101] Among them, u i (t) represents the control input of agent i, ξ i (·) represents the local area error, and its calculation formula is:

[0102] in, and denote the state estimates of follower agents i and j respectively, Represents the state estimate of the leader agent.

[0103] At this point, based on the safety status information of the UAV system obtained in step 3, consistency control based on the event trigger mechanism is realized.

[0104] The present invention designs an event-triggered control mechanism for consistency control, and obtains sufficient LMI conditions for solving each matrix by constructing a Lyapunov function and deriving it. Thus, the required matrix can be obtained by selecting relevant parameters, so that the system can be controlled on demand, further saving communication resources of multi-UAV systems, which has great practical significance.

[0105] It is understandable that, based on step 3, a conventional consistency control strategy can also be used to perform system security control, and the detailed process will not be introduced here.

[0106] In summary, the overall solution of the present invention can be described as follows:

[0107] like Figure 2 As shown in the figure, firstly, an improved unknown input observer considering the nonlinearity of the system is constructed by combining local measurement information and neighbor measurement information as a state observer, and the state estimation value is obtained. In the absence of attack, each UAV can use the state estimation for event-triggered consistency control. In the case of attack, each UAV needs to first perform node attack detection to determine whether it is attacked by node sensors, so as to decide whether to enable the elastic control mechanism. If it is judged that it is not attacked, it will run normally without enabling elastic control; if it is judged that it is attacked, the elastic control mechanism will be enabled, and the node sensor attack signal will be reconstructed through the corresponding attack reconstruction algorithm, and elastic control of attack compensation will be performed based on the reconstructed attack signal, thereby reducing the impact of sensor attack on the state estimation value, obtaining a safe state estimation, and performing event-triggered consistency control based on the safe state estimation.

[0108] The multi-UAV system safety control method based on unknown input observer provided by the present invention takes into account the situation that the system contains nonlinear terms, introduces UAV measurement and state estimation information to design an unknown input observer, eliminates the influence of UAV process noise on state estimation performance, and enables the system to perform attack detection based on accurate state estimation, and synchronously perform attack reconstruction and attack compensation elastic control after detecting the attack, thereby reducing the influence of sensor attacks on UAV state estimation performance and improving the safety control effect.

[0109] Embodiment 2

[0110] On the basis of the above-mentioned first embodiment, this embodiment takes a specific application scenario as an example and combines simulation experiments to verify and illustrate the beneficial effects of the present invention.

[0111] Specifically, this embodiment takes the longitudinal consistency control of Aerosonde small UAV cluster assembly and standby process as the research background, and the matrices of the UAV dynamic equation are set as follows:

[0112]

[0113]

[0114]

[0115] Since the UAV may be disturbed by the external wind speed when in motion, and the nonlinear term of the longitudinal motion equation is mainly related to the pitch angle, we assume that the process noise is Gaussian noise and ||ω i (t)||≤5, assuming that the process noise matrix and nonlinear terms are:

[0116] D ω =[1.2,1.1,-0.1,-0.5] T

[0117] φ(x i )=[0.01sin(x i4(t) ),0,0,0] T

[0118] It is known that the process noise satisfies the bounded condition, and the nonlinear term of the UAV state equation satisfies the Lipschitz condition, so Λ=diag{0.01,…,0.01}.

[0119] Consider a multi-UAV system consisting of 1 leader UAV and 3 follower UAVs, then the Laplace matrix corresponding to the UAV communication topology is:

[0120]

[0121] The initial value of each drone is set to:

[0122] x0(0)=[1 9.8 0 -0.5] T

[0123] x1(0)=[-2.3 9.7 -0.3 0.3] T

[0124] x2(0)=[4.5 8.9 -0.2 -0.1] T

[0125] x3(0) = [7.1 -7.0 0.3 0.2] T

[0126] Based on the above conditions, the AUIO matrix to be calculated and the attack reconstruction matrix to be calculated are calculated according to the method provided in the first embodiment.

[0127] Specifically, we choose the parameter β Π1 =10,β Π2 =0.08, β Π3 =0.1,β Π4 =1,ε1=100,R=I 3×3 , according to the sufficient conditions for attack signal reconstruction and compensation in step 3 above, it can be calculated as follows:

[0128]

[0129]

[0130]

[0131] Next, the consistency control matrix is ​​calculated according to the sufficient conditions of the event triggering mechanism in step 4 above.

[0132] Specifically, we choose the parameter β π1 =1,β π2 =50,β π3 =10,ε2=0.3, η1=0.0001, we can get:

[0133] K c =[0.0010 0.0028 -0.0266 -0.0026]

[0134] Finally, let the process noise be Gaussian and ||ω i (t)||≤3.5. Assume that the upper bound of interference energy in the communication channel is The attacker launches a sensor attack on the three follower drones at the same time at t=20s. The sensor attack signal is:

[0135] a1(t)=[0.1·(t-20)+0.2·sin(0.5t),-0.1·(t-20)+0.2·sin(0.5t),0] T

[0136] a2(t)=[-0.15·(t-20)+0.2·sin(0.5t),0.1·(t-20)+0.2·sin(0.5t),0] T

[0137] a3(t)=[0,0,0.02·(t-20)+0.1·sin(0.5t)] T

[0138] In the above scenario, relevant modules are built and simulated in the Matlab / Simulink environment. The simulation time is 50 seconds, and the corresponding simulation results are obtained.

[0139] See also Figure 3-4 , Figure 3 and Figure 4 They are the consistency error and state estimation error of the follower UAV under inelastic control, that is, the consistency error and state estimation error of the UAV system when it is simultaneously subjected to random interference of the communication channel and FDI attack of the node sensor. Figure 3 and Figure 4 It can be seen that the node FDI sensor attack injected by the attacker greatly affects the performance of the system. By inducing the drone control center to misestimate the drone status and issue wrong control instructions to the drone, the follower drones cannot coordinate with the leader drone, thus causing the multi-drone system to lose consistency.

[0140] For further information, see Figure 5 , Figure 5 This is the residual signal and residual threshold diagram when the system is attacked by sensors in the simulation experiment. It can be seen that the attack detection mechanism correctly detects the local sensor attack. Since each state of the system is affected differently by the sensor attack, the accumulation of residual values ​​is also different, so each intelligent agent warns of the sensor attack at different times.

[0141] Furthermore, elastic control is applied to multi-UAV systems subjected to mixed attacks, and the consistency error and state estimation information are as follows: Figure 6 , Figure 7 As shown in Figure 2, it can be seen that the elastic control law reduces the impact of sensor attacks on the consistency performance and state estimation performance.

[0142] In addition, from Figure 3It can be seen from the figure that the sensor attack mainly affects the airspeed of the drone. Since the drone state is less affected by the oscillation mode in the time interval t∈[40,43], the mean value of the consistency error and the mean value of the estimation error of each follower drone in this interval are used as the analysis reference value. When there is no elastic control under mixed attack and the elastic control method based on AUIO proposed by the present invention is adopted, the consistency error and estimation error of each follower drone in the multi-drone system are shown in Table 1. One column represents the mean square value of the consensus error and the mean square value of the estimation error of all follower drones.

[0143] Table 1. Consistency error and state estimation error of follower drones in different scenarios

[0144]

[0145]

[0146] Combination Figures 3 to 6 As can be seen from Table 1, the AUIO-based elastic time-triggered control method proposed in the present invention effectively suppresses the impact of FDI attacks on drone node sensors. In particular, for the state variable components that are most severely affected by the attack, such as the x-axis airspeed and the z-axis airspeed, the AUIO elastic control method greatly reduces the changes in the consistency error and the estimation error relative to the node-free attack situation, effectively ensuring the consistency of the multi-drone system and the accuracy of state estimation. For the state variable components that are less affected by the attack, the consistency error and the estimation error under the AUIO elastic control method have a smaller change relative to the node-free attack situation, and considering the randomness of the communication channel interference, the change is within the allowable error range. Finally, the mean square value of the consistency error and state error of each drone under the AUIO elastic control method is smaller than the mean square value under the inelastic control situation, which further proves the effectiveness of the AUIO elastic control method.

[0147] In addition, the experiment also simulated the triggering moment of each follower drone event triggering control mechanism under the hybrid FDI attack, and the results are as follows: Figure 8 As shown. Figure 8 It can be seen that after combining with the elastic control method based on AUIO, the event-triggered control mechanism still achieves on-demand control well. Each follower UAV basically completes the elastic event-triggered control target in about 32 seconds, making the event triggering time of the elastic event-triggered control mechanism under hybrid attack have similar distribution characteristics to the event triggering time of the event-triggered control mechanism under channel interference.

[0148] In summary, the AUIO-based elastic control method designed in the present invention ensures the state estimation accuracy of the multi-UAV system while alleviating node FDI attacks, thereby making the event-triggered control mechanism resilient to attacks and further saving communication resources through the event-triggered control mechanism.

[0149] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A multi-UAV system safety control method based on unknown input observer, characterized in that: include: Step 1: Based on the measurement information and system nonlinear design, the unknown input observer is improved as the state observer, and the state observer is used to estimate the state of the current multi-UAV system; Step 2: Construct the residual function through state estimation and measurement output and perform node attack detection; Step 3: When it is determined that a node attack occurs, the attack signal is reconstructed and compensated based on the improved unknown input observer to flexibly control the state estimation process of the multi-UAV system and obtain the security state information of the system; Otherwise, the current estimation result of the state observer is used as the safety state information of the system; Step 4: Perform safety control on the multi-UAV system based on the safety status information.

2. The multi-UAV system safety control method based on unknown input observer according to claim 1 is characterized in that: Step 1 includes: Based on the local measurement information and neighbor measurement information, an improved unknown input observer considering the nonlinearity of the system is constructed as a state observer, and the state of the multi-UAV system is estimated accordingly. The expression is: in, represents the state estimation result of follower agent i, t represents time, z i (t) is the unknown input observer state of follower agent i, For z i The derivative of (t), and y i (t) represent the control input and measurement output of follower agent i, It is a generalized inverse matrix operation, T = I-HC, G = TB, F = TA-K1C, K u =K1+FH,A,B,C,D ω is a constant matrix, I is the unit matrix, K1 is the observer matrix to be designed, and denote the output estimation errors of follower agent i and its neighbor j, respectively. represents the output estimation error of the leader agent, a ij represents the connection between follower i and its neighbor j, a i0 Indicates the connection status of follower i with the leader.

3. The multi-UAV system safety control method based on unknown input observer according to claim 2 is characterized in that: Step 2 includes: 21) Construct the residual function r when the drone is not attacked by the sensor i * (t), and based on this, calculate the residual function r when the drone is attacked by the sensor i (t); 22) For the residual function r i (t) Perform Euclidean norm detection. If the norm of the residual function J is determined i (t) is greater than a preset threshold, the drone is determined to be under sensor attack; otherwise, the drone is determined not to be under sensor attack.

4. The multi-UAV system safety control method based on unknown input observer according to claim 3 is characterized in that: In step 21), the residual function r when the drone is attacked by the sensor i The expression of (t) is: in, a i (t) represents sensor attack, for a i The derivative of (t), e i (t) represents the state estimation error, φ(x i (t)) and Both represent nonlinear terms.

5. The multi-UAV system safety control method based on unknown input observer according to claim 4 is characterized in that: In step 3, when a node attack occurs, the attack signal is reconstructed and compensated based on the improved unknown input observer to elastically control the state estimation process of the multi-UAV system, including: Calculate the observer matrix K1, K2 and the attack reconstruction matrix M, and use the following formula to perform elastic control on the state estimation process of the multi-UAV system; in, is an estimate of the sensor FDI attack signal, for The differential of .

6. The multi-UAV system safety control method based on unknown input observer according to claim 5 is characterized in that: The observer matrices K1, K2 and the attack reconstruction matrix M are calculated by the following sufficient conditions: For a given positive definite scalar ε1 and positive definite matrix R, let the symmetric positive definite matrices Q1 and Q2 satisfy the following LMI conditions: Then the gain matrix of the state observer is Where λ0 is the parameter corresponding to the Laplace matrix L1 of the follower UAV communication topology, λ max (Θ) is a positive definite matrix Θ = diag{θ1,…,θ N }, Λ represents the nonlinear term φ(x i (t)) corresponds to the Lipschitz parameter matrix, T represents the transpose, I N Represents the identity matrix of dimension N.

7. The multi-UAV system safety control method based on unknown input observer according to claim 6 is characterized in that: The step 4 comprises: Set up event-triggered consistency control strategy to perform consistency control on multi-UAV systems.

8. The multi-UAV system safety control method based on unknown input observer according to claim 7 is characterized in that: Set event-triggered consistency control strategies to perform consistency control on multi-UAV systems, including: make Represents the event triggering time sequence of the i-th drone, and sets the following event triggering mechanism: Among them,∈2, h i , η1 are given positive scalars, is the measurement error of the event trigger mechanism, and e is the natural base; Calculate the consistency control matrix K c ; Based on the event trigger mechanism and the consistency control matrix K c The consistency control of the multi-UAV system is expressed as: Among them, u i (t) represents the control input of agent i, ξ i (·) represents the local area error, and its calculation formula is: in, and Respectively represent the state estimation results of follower agents i and j, Represents the state estimation result of the leader agent.

9. The multi-UAV system safety control method based on unknown input observer according to claim 8 is characterized in that: The consistency control matrix K c Calculate according to the following sufficient conditions: For a given positive definite scalar ε2, And the positive definite matrix P1, let it satisfy the following linear matrix inequality: in, represents the maximum number of neighbors in the system, L1 represents the Laplace matrix corresponding to the follower drone communication topology, and λ min (·) and λ max (·) represent the maximum and minimum eigenvalues ​​of the matrix, N represents the total number of follower drones, and h i It is the parameter in the event triggering mechanism; Then take K c =ε2B T P1 -1 , so that the system can achieve H ∞ Asymptotically stable consistency under performance indicator σ1, and no Zeno phenomenon occurs; among them, H ∞ The asymptotically stable consistency under the performance index σ1 can be expressed as: Where, δ(t)=col{x i (t)-x0(t)} is the consistency error, ρ(t)=col{e x (t),ω(t)} is the composite perturbation, and V2(t) is the Lyapunov function of δ(t).

Images