Detailed Description
The present invention will be described in further detail with reference to specific examples, but embodiments of the present invention are not limited thereto.
Example 1
First, it should be noted that the multi-unmanned aerial vehicle system contemplated by the present invention includes a sensor, a state observer, an event trigger, a controller, an actuator, and an attack detector. Wherein the sensors of each follower drone may be subject to persistent FDI attacks. Considering a multi-drone system with 1 leader drone and N follower drones, the system dynamics equation of the ith follower drone that is subject to sensor FDI attack can be expressed as:
Wherein, xi(t)∈Rn is the total number of the components,Respectively representing the state, control input and measurement output of the follower agent i, t representing time,Represents the differentiation of the state xi (t), ωi (t) is the process noise, Φ (xi(t))＝[φ1(xi(t)),…,φn(xi(t))]T is a nonlinear term, ai (t) is the sensor attack signal.
The leader's dynamic equation can be expressed as:
Wherein, x0(t)∈Rn is the total number of the components,Respectively representing the status and output of the leader agent i.Is the derivative of x0 (t), phi (x0 (t)) is a nonlinear term in the leader's dynamic equation.
Without loss of generality, the following assumptions can be made for the multi-drone system and sensor attacks in the present discussion:
(1) Communication mapA directed spanning tree exists and the leader is the root node of the directed spanning tree.
(2) (A, B) is stable and (A, C) is observable.
(3) For any x1(t),x2(t)∈Rn, the nonlinear function in the unmanned aerial vehicle dynamic equation, φ (xi), satisfies the Lipschitz condition.
(4) Sensor attack ai (t) and its derivativeAre bounded, but all upper bounds are unknown to the defender.
Accurate state estimation is the basis of methods such as attack detection, elasticity control, consistency control and the like. In order to correctly estimate the state of the unmanned aerial vehicle under the influence of process noise, the invention provides a method for improving an unknown input observer (advanced unknown input observer, AUIO) to realize attack detection and elastic control of a multi-unmanned aerial vehicle system.
Specifically, referring to fig. 1, fig. 1 is a flow chart of a multi-unmanned aerial vehicle system security control method based on an unknown input observer, which includes:
and step 1, improving an unknown input observer to serve as a state observer based on measurement information and system nonlinear design, and carrying out state estimation on the current multi-unmanned aerial vehicle system by utilizing the state observer.
Optionally, in this embodiment, an improved unknown input observer considering system nonlinearity is constructed based on local measurement information and neighbor measurement information, and is used as a state observer, so as to perform state estimation on the multi-unmanned aerial vehicle system, where the expression is as follows:
wherein,Representing the state estimation result of the follower agent i, t representing time, zi (t) being the unknown input observer state of the follower agent i,For the derivative of zi (t), ui (t) and yi (t) represent the control input and measurement output, respectively, of follower agent i,Is a generalized inverse matrix operation, t=i-HC, g=tb, f=ta-K1C,Ku＝K1+FH,A、B、C、Dω is a constant matrix, I is an identity matrix, K1、K2 is an observer matrix to be designed,AndRespectively representing the output estimation errors of the follower agent i,The output estimation errors of the leader agents are represented, aij and ai0 represent corresponding parameters of the adjacency matrix, wherein aij represents the connection condition of the follower i and the neighbor j thereof, if the information can be accepted, aij =1, otherwise aij＝0;ai0 represents the connection condition of the follower i and the leader, and the value standard is the same. Therefore, it is possible to use the adjacency matrixRepresenting the connection between nodes of algebraic graph and passing through adjacency matrixMatrix and metric matrixAnd defining a Laplace matrix L corresponding to the unmanned aerial vehicle communication topological graph.
It can be seen that AUIO has two matrices K1,K2 to be designed. If K2 is taken to be 0, then the state estimation error of the unknown input observer must converge as long as K1 is designed to ensure that the matrix F is Schur. However, since there are two matrices to be designed here, the design needs to be performed simultaneously. The specific design method is described later.
In addition, H can be further takenS is an arbitrary matrix to increase the degree of freedom of observer design.
And 2, constructing a residual function through state estimation and measurement output and detecting node attack.
21 Constructing a residual function ri* (t) when the unmanned aerial vehicle is not attacked by the sensor, and calculating a residual function ri (t) when the unmanned aerial vehicle is attacked by the sensor according to the residual function ri* (t).
Specifically, taking a residual error function into consideration when the unmanned aerial vehicle is attacked by a sensorLet ri* (t) be the residual function of the unmanned aerial vehicle system when it is not under sensor attack, then there are
Where zi(t)ei (t) represents the state estimation error, phi (xi (t)) and of the drone iAll represent nonlinear terms.
When the unmanned aerial vehicle is subjected to sensor attack, the combination of the formula (3) and the formula (4) can be obtained:
ai (t) represents a sensor attack,Is the derivative of ai (t).
22 Detecting a Euclidean norm of the residual function ri (t), if the norm Ji (t) of the residual function is larger than a preset threshold, judging that the unmanned aerial vehicle is attacked by the sensor, otherwise, judging that the unmanned aerial vehicle is not attacked by the sensor.
It will be appreciated that under proper design, AUIO's state estimation error is satisfied by UUVB (Uniformly ultimately Bounded, ultimately consistent with the constraints), so that sensor attacks can be detected by the Euclidean norm of the residual, i.e., taken
The corresponding threshold Jth,i may be selected according to the following equation:
Jth,i＝sup{ri*(t)} (7)
The detection criteria for node sensor attacks in a multi-drone system may be defined as:
And 3, when judging that node attack occurs, carrying out attack signal reconstruction and compensation based on the improved unknown input observer so as to carry out elastic control on the state estimation process of the multi-unmanned aerial vehicle system to obtain the real state information of the system, otherwise, taking the current estimation result of the state observer as the real state information of the system.
Specifically, when it is determined that a node attack occurs, an attack signal reconstruction and compensation needs to be performed based on an improved unknown input observer, and the expression is as follows:
wherein,Is an estimate of the sensor FDI attack signal, M is the attack reconstruction matrix to be solved.
The embodiment can reduce the influence of sensor attack on state estimation performance by reconstructing the attack signal and compensating in state estimation.
Further, the reconstruction matrix M for the observer matrix K1、K2 and the attack can be calculated by the following sufficiency conditions:
For a given positive scaling quantityEpsilon1 and positive definite matrix R, if there is a symmetric positive definite matrix Q1,Q2 that satisfies the LMI (Linear matrix inequality LMI linear matrix inequality) condition shown in equation (10), taking the observer gain matrix at the same timeThe state observer based on attack reconstruction and compensation can ensure that the state estimation error and the attack reconstruction error are UUB under the process noise, the communication channel interference and the node sensor FDI attack.
Wherein lambda0 is a parameter corresponding to Laplace matrix L1 of communication topology of the follower unmanned aerial vehicle, lambdamax (Θ) is a maximum eigenvalue of positive definite matrix Θ, and a specific value method is to take matrix Θ to enable the matrix Θ to meet the requirementLambda0 is matrixΛ represents the Lipschitz parameter matrix corresponding to the nonlinear term phi (xi (T)), T represents the transpose, and IN represents the identity matrix of dimension N.
By the above conditions, observer matrices K1、K2, M to be designed can be determined.
It should be noted that, since the unmanned plane model is not affected by the measurement noise, the designed observer matrix can be directly used for attack detection. But the elastic control based on attack reconstruction and compensation still needs to be initiated after the sensor attack generation is detected, otherwise the performance of the unmanned aerial vehicle under normal conditions is affected.
The elastic control mechanism based on the unknown input observer for attack reconstruction and attack compensation can reduce the influence of node sensor attack on unmanned aerial vehicle state estimation, ensure the effectiveness of a consistency control law based on the state estimation, and has higher application value, and meanwhile, the elastic control is triggered by attack detection, so that the elastic control mechanism can not influence the state estimation and system consistency under the general condition, and even if a plurality of unmanned aerial vehicle systems have elasticity on the node sensor attack.
And 4, carrying out safety control on the multi-unmanned aerial vehicle system based on the real state information.
In order to reduce network burden caused by increased transmission of agent information, the embodiment adopts an event trigger consistency policy to reduce frequent operation of the controller so as to achieve the purpose of saving communication resources.
Specifically, first, let theThe event triggering time sequence of the ith unmanned aerial vehicle is represented, and the following event triggering mechanism is set:
wherein, E2,Hi and η1 are given positive scalar quantities,Errors are measured for the event trigger mechanism.
Then, a consistency control matrix Kc is calculated.
Specifically, the design method of the consistency control matrix Kc and the related parameters of the event triggering mechanism can be given by the following sufficient conditions:
Considering that the multiple drone system is under event-triggered condition driven controllers, if there is a symmetric positive scaling matrix P1 and positive scaling quantity epsilon2,So that the linear matrix inequalities (13) - (14) are established, then taking the consistency control gainIn this case, the system can achieve progressive stability consistency under the performance index sigma1 of H∞, and Zeno phenomenon does not occur.
Wherein,
The method comprises the steps that the maximum neighbor number of a system is represented, L1 represents a Laplace matrix corresponding to the communication topology of the follower unmanned aerial vehicle, lambdamin (·) and lambdamax (·) respectively represent the maximum and minimum characteristic values of the matrix, N represents the total number of the follower unmanned aerial vehicle, and hi is a parameter in an event triggering mechanism;
In this embodiment, the progressive stability consistency under the H∞ performance index σ1 can be expressed as:
wherein,For mathematical expectations, δ (t) =col { xi(t)-x0 (t) } is a consistency error, ρ (t) =col { ex (t), ω (t) } is a complex perturbation, and V2 (t) is a Lyapunov function of δ (t).
Finally, an event trigger consistency control strategy is formulated based on an event trigger mechanism and a consistency control matrix Kc so as to carry out consistency control on the multi-unmanned aerial vehicle system, wherein the formula is as follows:
Wherein ui (t) represents the control input of the follower agent i, and ζi (DEG) represents the local area error, and the calculation formula is as follows
Wherein,AndRepresenting the state estimates of follower agents i and j respectively,Representing a state estimate of the leader agent.
So far, on the basis of obtaining the safety state information of the unmanned aerial vehicle system in the step 3, the consistency control based on the event triggering mechanism is realized.
The invention designs an event trigger control mechanism to carry out consistency control, and obtains the sufficient LMI condition for solving each matrix to be solved by constructing the Lyapunov function and deriving the function, so that the required matrix to be solved can be obtained by selecting the related parameters, the system can realize on-demand control, the communication resources of a multi-unmanned-plane system are further saved, and the method has great practical significance.
It will be appreciated that, based on step 3, a conventional consistency control strategy may also be used to perform system security control, and detailed procedures are not described herein.
In summary, the overall scheme of the present invention can be described as follows:
As shown in fig. 2, an improved unknown input observer taking system nonlinearity into consideration is first constructed by combining local measurement information with neighbor measurement information as a state observer, and a state estimation value is obtained. In the absence of an attack, each drone may use the state estimate for event-triggered consistency control. Under the condition of attack, each unmanned aerial vehicle needs to firstly carry out node attack detection to judge whether the unmanned aerial vehicle is attacked by a node sensor or not so as to determine whether to start an elastic control mechanism or not. If the node sensor attack signal is judged to be attacked, the node sensor attack signal is reconstructed through a corresponding attack reconstruction algorithm, and the elastic control of attack compensation is carried out based on the reconstructed attack signal, so that the influence of the sensor attack on a state estimation value is reduced, the safety state estimation is obtained, and the event triggering consistency control is carried out based on the safety state estimation.
According to the multi-unmanned aerial vehicle system safety control method based on the unknown input observer, the situation that the system comprises nonlinear items is considered, the unknown input observer is designed by introducing unmanned aerial vehicle measurement and state estimation information, the influence of unmanned aerial vehicle process noise on state estimation performance is eliminated, the system can perform attack detection based on accurate state estimation, attack reconstruction and attack compensation elastic control can be synchronously performed after attack generation is detected, the influence of sensor attack on unmanned aerial vehicle state estimation performance is reduced, and the safety control effect is improved.
Example two
On the basis of the first embodiment, the embodiment takes a specific application scenario as an example, and the beneficial effects of the invention are verified and explained by combining simulation tests.
Specifically, in this embodiment, longitudinal consistency control in the process of cluster aggregation and standby of Aerosonde small unmanned aerial vehicles is used as a research background, and each matrix of unmanned aerial vehicle dynamic equations is set as follows:
since the unmanned aerial vehicle can be disturbed by the external wind speed when moving, and the nonlinear term of the longitudinal movement equation is mainly related to the pitch angle. Therefore, the process noise is Gaussian noise and the I omegai (t) I is less than or equal to 5, and the process noise matrix and the nonlinear term are respectively:
Dω＝[1.2,1.1,-0.1,-0.5]T
φ(xi)＝[0.01sin(xi4(t)),0,0,0]T
process noise is known to satisfy a bounded condition, while the unmanned state equation nonlinear term satisfies the Lipschitz condition, so there is Λ=diag {0.01,..0.01 }.
Considering a multi-unmanned aerial vehicle system consisting of 1 leader unmanned aerial vehicle and 3 follower unmanned aerial vehicles, the Laplace matrix corresponding to the unmanned aerial vehicle communication topology is:
the initial value of each unmanned aerial vehicle is set as:
x0(0)＝[1 9.8 0 -0.5]T
x1(0)＝[-2.3 9.7 -0.3 0.3]T
x2(0)＝[4.5 8.9 -0.2 -0.1]T
x3(0)＝[7.1 -7.0 0.3 0.2]T
Based on the above conditions, according to the method provided in the first embodiment, AUIO the calculation of the matrix to be solved and the attack reconstruction matrix to be solved are performed.
Specifically, the selection parameter βΠ1＝10,βΠ2＝0.08,βΠ3＝0.1,βΠ4＝1,ε1＝100,R＝I3×3 may be calculated according to the sufficient conditions for attack signal reconstruction and compensation in the above step 3:
then, the consistency control matrix calculation is performed according to the sufficient conditions of the event trigger mechanism in the step 4.
Specifically, the selection parameter betaπ1＝1,βπ2＝50,βπ3＝10,ε2 =0.3,Η1 =0.0001, can be found:
Kc=[0.0010 0.0028 -0.0266 -0.0026]
finally, the process noise is Gaussian noise and the I omegai (t) I is less than or equal to 3.5. Setting an upper boundary of interference energy in a communication channelAn attacker simultaneously launches sensor attacks on three follower unmanned aerial vehicles when t=20s, and the sensor attack signals are as follows:
a1(t)＝[0.1·(t-20)+0.2·sin(0.5t),-0.1·(t-20)+0.2·sin(0.5t),0]T
a2(t)＝[-0.15·(t-20)+0.2·sin(0.5t),0.1·(t-20)+0.2·sin(0.5t),0]T
a3(t)＝[0,0,0.02·(t-20)+0.1·sin(0.5t)]T
In the scene, building a related module in a Matlab/Simulink environment, and carrying out simulation, wherein the simulation time is 50s, so as to obtain a corresponding simulation result.
Referring to fig. 3-4, fig. 3 and fig. 4 are graphs of a consistency error and a state estimation error of the follower unmanned aerial vehicle in inelastic control, that is, a consistency error and a state estimation error of the unmanned aerial vehicle system in random interference of a communication channel and attack of a node sensor FDI, respectively. It can be seen from fig. 3 and fig. 4 that the node FDI sensor attack injected by an attacker greatly affects the performance of the system, and by inducing the unmanned aerial vehicle control center to erroneously estimate the unmanned aerial vehicle state, an erroneous control instruction is given to the unmanned aerial vehicle, so that each follower unmanned aerial vehicle cannot cooperate with the leader unmanned aerial vehicle, and the multi-unmanned aerial vehicle system loses consistency.
Further, referring to fig. 5, fig. 5 is a graph of residual signal and residual threshold when the system is under sensor attack in a simulation test. It can be seen that the attack detection mechanism correctly detects local sensor attacks. Because the states of the system are affected by sensor attacks differently, the accumulation of residual values is also different, so that each intelligent agent alerts about the sensor attacks at different times.
Further, the system of multiple unmanned aerial vehicles under hybrid attack uses elastic control, and consistency errors and state estimation information are shown in fig. 6 and 7. It can be seen that the elastic control law reduces the impact of sensor attacks on the consistency performance and the state estimation performance.
Furthermore, as can be seen from fig. 3, the sensor attack mainly affects the airspeed of the drone. Since the unmanned plane state in the time interval t E [40,43] is less affected by the vibration mode, the consistency error mean value and the estimation error mean value of each follower unmanned plane in the interval are taken as analysis reference values, and when the elastic control method based on AUIO provided by the invention is adopted under the inelastic control under the mixed attack, the consistency error and the estimation error of each follower unmanned plane in the multi-unmanned plane system are shown in the table 1, wherein the table 1 shows thatA column represents the mean square of the uniformity error and the mean square of the estimated error for all follower drones.
TABLE 1 consistency error and State estimation error for follower unmanned aerial vehicle in different scenarios
As can be seen from fig. 3 to fig. 6 and table 1, the elastic time trigger control method based on AUIO provided by the invention effectively suppresses the FDI attack influence of the node sensor of the unmanned aerial vehicle. Particularly, for the state variable components most seriously affected by attack, such as x-axis airspeed and z-axis airspeed, the AUIO elastic control method greatly reduces the variation of the consistency error and the estimation error relative to the node-free attack situation, and effectively ensures the consistency of the multi-unmanned-plane system and the accuracy of state estimation. For the state variable component less affected by the attack, the variation of the consistency error and the estimation error under the AUIO elastic control method is smaller than that of the node-free attack, and the variation is in the allowable error range in consideration of the randomness of the interference of the communication channel. Finally, the mean square value of the consistency error and the state error of each unmanned aerial vehicle under the AUIO elastic control method is smaller than that under the inelastic control condition, and the effectiveness of the AUIO elastic control method is further proved.
In addition, the trigger time of the event trigger control mechanism of each follower unmanned aerial vehicle under the mixed FDI attack is also simulated in the test, and the result is shown in fig. 8. As can be seen from fig. 8, the event-triggered control mechanism still better accomplishes on-demand control in combination with the AUIO-based elastic control method. The follower unmanned aerial vehicle basically completes the elastic event trigger control target at about 32s, so that the event trigger time of the elastic event trigger control mechanism under the hybrid attack and the event trigger time of the event trigger control mechanism under the channel interference have similar distribution characteristics.
In summary, the elastic control method based on AUIO designed by the invention ensures the state estimation accuracy of the multi-unmanned aerial vehicle system under the condition of relieving node FDI attack, thereby enabling an event trigger control mechanism to have elasticity on attack and further saving communication resources through the event trigger control mechanism.
The foregoing is a further detailed description of the invention in connection with the preferred embodiments, and it is not intended that the invention be limited to the specific embodiments described. It will be apparent to those skilled in the art that several simple deductions or substitutions may be made without departing from the spirit of the invention, and these should be considered to be within the scope of the invention.