CN116540665A - Multi-unmanned aerial vehicle system safety control method based on unknown input observer - Google Patents

Multi-unmanned aerial vehicle system safety control method based on unknown input observer Download PDF

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CN116540665A
CN116540665A CN202310441206.7A CN202310441206A CN116540665A CN 116540665 A CN116540665 A CN 116540665A CN 202310441206 A CN202310441206 A CN 202310441206A CN 116540665 A CN116540665 A CN 116540665A
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unmanned aerial
aerial vehicle
matrix
attack
observer
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杨飞生
吴正田
潘泉
弓镇宇
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Northwestern Polytechnical University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B23/00—Testing or monitoring of control systems or parts thereof
    • G05B23/02—Electric testing or monitoring
    • G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
    • G05B23/0218—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults
    • G05B23/0243—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults model based detection method, e.g. first-principles knowledge model
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/20—Pc systems
    • G05B2219/24—Pc safety
    • G05B2219/24065—Real time diagnostics
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/10—Internal combustion engine [ICE] based vehicles
    • Y02T10/40—Engine management systems

Abstract

The invention discloses a multi-unmanned aerial vehicle system safety control method based on an unknown input observer, which comprises the following steps: based on measurement information and system nonlinear design, an unknown input observer is improved to serve as a state observer, and state estimation is carried out on the current multi-unmanned aerial vehicle system; constructing a residual function through state estimation and measurement output and performing node attack detection; when judging that node attack occurs, carrying out attack signal reconstruction and compensation based on an improved unknown input observer so as to carry out elastic control on the state estimation process of the multi-unmanned aerial vehicle system and obtain the safety state information of the system; taking the current estimation result of the state observer as the safety state information of the system; and safety control is carried out on the multi-unmanned aerial vehicle system based on the safety state information. The method reduces the influence of sensor attack on the state estimation performance of the unmanned aerial vehicle, so that the system has elasticity on node sensor attack, and the safety control effect is improved; meanwhile, the control according to the need can be realized, and the communication resources of the system are saved.

Description

Multi-unmanned aerial vehicle system safety control method based on unknown input observer
Technical Field
The invention belongs to the field of security defense of unmanned information physical systems, and particularly relates to a multi-unmanned-plane system security control method based on an unknown input observer.
Background
The unmanned aerial vehicle has advantages such as little volume, light weight, easy operation, high flexibility, high adaptability, high adjustability, has important application in various fields such as survey remote sensing, security investigation, environmental detection. The unmanned aerial vehicle is used as an information physical system integrating communication equipment, execution equipment, sensing equipment and a control module, can construct a closed loop process of sensing data, interacting information, making decisions and executing tasks, realizes the tight combination of a computing element and a network process with a physical object, and can be regarded as an information physical system. Compared with a single unmanned aerial vehicle system, the multi-unmanned aerial vehicle system has the advantages of short task execution time, fast information transmission, high system fault tolerance and the like. The cooperation of multiple unmanned aerial vehicles can solve various complex problems, so that the efficiency and success rate of task completion are improved.
Because of the openness of the network environment, unmanned information physical systems may suffer from potential hostile behavior, i.e., multi-node sensor FDI (False data injection, hidden false data intrusion) attacks, which if neglected would result in greater impact on system performance and possibly even system instability, leading to unpredictable economic and social losses. For a multi-drone system consisting of multiple individuals, an attacker can attack different drones at different times, thus making the network attack coupled in both time and space. Meanwhile, the physical security of information introduces the dimension of physical dynamics on the basis of the traditional network security, namely the faults and fluctuation of the unmanned aerial vehicle system also influence the stability of the network system. Therefore, a security defense strategy of the multi-unmanned aerial vehicle system needs to be researched, and theoretical guidance and technical support are provided for application scenes with wider and more complex trend of the multi-unmanned aerial vehicle system.
Currently, the prior art mainly provides the following safety control methods:
document [1] (Hota, ashish Ranjan and Shreyas Sundaram. "Interdependent security games on networks under behavioral probability weighting." IEEE Transactions on Control of Network Systems (2015): 262-273.) designs a game theory-based resilient control architecture to mitigate the impact of attacker-injected information on agent performance.
Document [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 (2019): 2561-2570.)) and document [3] (Arabic, 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): 04003.)) employ adaptive elastic architectures to ensure that an attacked agent system is able to achieve consistent control objectives with consistent final boundaries under network attacks.
Document [4] (Meng, min et al, "Adaptive consensus for heterogeneous multi-agent systems under sensor and actuator assays," Autom.122 (2020): 109242.) studied the lead-following elasticity consistency problem of heterogeneous multi-agent systems that were simultaneously challenged by sensors and actuators.
Document [5] (Modares, hamidreza et al, "Static output-feedback synchronisation of multi-agent systems: a secure and unified application," Iet Control Theory and Applications (2018): 1095-1106.) proposes a unified Static output feedback method to study the elastic consistency of multi-agent systems under sensor and actuator attacks.
Document [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 sensor and actuator attacks.
However, the above-described method still has some drawbacks. Wherein the method used in document [1] makes assumptions about the statistical properties of the attacker and the system, which assumptions may be difficult to satisfy simultaneously, particularly in an actual system; the method of the document [2-4] does not consider the influence of process noise in the unmanned aerial vehicle system, so that the accuracy of attack detection depends on the statistical characteristics of the noise, has a certain attack false alarm rate, and simultaneously reduces the inhibition effect of elastic control on the attack; the documents [5-6] do not consider the influence of system nonlinearity on the design, there is a certain requirement on the integrity of the intelligent agent system in the actual process, and the actual control effect depends on the accuracy of the linearization model.
In summary, in the existing method, when the security control is performed on the multi-unmanned aerial vehicle system, attack detection and compensation cannot be performed based on the accurate system state, so that the actual control effect is reduced.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a multi-unmanned aerial vehicle system safety control method based on an unknown input observer.
The technical problems to be solved by the invention are realized by the following technical scheme:
a multi-unmanned aerial vehicle system safety control method based on an unknown input observer comprises the following steps:
step 1: an unknown input observer is improved to be used as a state observer based on measurement information and system nonlinear design, and the state observer is utilized to perform state estimation on the current multi-unmanned aerial vehicle system;
step 2: constructing a residual function through state estimation and measurement output and performing node attack detection;
step 3: when judging that node attack occurs, carrying out attack signal reconstruction and compensation based on an improved unknown input observer so as to carry out elastic control on the state estimation process of the multi-unmanned aerial vehicle system and obtain the safety state information of the system;
otherwise, taking the current estimation result of the state observer as the safety state information of the system;
step 4: and carrying out safety control on the multi-unmanned aerial vehicle system based on the safety state information.
The invention has the beneficial effects that:
1. according to the invention, the situation that the system comprises a nonlinear item is considered, the unmanned aerial vehicle measurement and state estimation information is introduced to design an unknown input observer, so that 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, and after attack generation is detected, attack reconstruction and attack compensation elastic control are synchronously performed, the influence of sensor attack on unmanned aerial vehicle state estimation performance is reduced, and the safety control effect is improved;
2. the elastic control mechanism for attack reconstruction and attack compensation based on the unknown input observer can reduce the influence of node sensor attack on unmanned aerial vehicle state estimation, ensure the effectiveness of a consistency control law based on state estimation, and has higher application value; meanwhile, the elastic control is triggered by attack detection, so that an elastic control mechanism does not influence the state estimation and system consistency under the general condition, namely, the multi-unmanned-plane system has elasticity to node sensor attack;
3. the invention also designs an event trigger control mechanism for consistency control, and a method for constructing Lyapunov functions and deriving the same is used for obtaining the sufficient LMI condition for solving each matrix to be solved, so that the required matrix to be solved can be obtained by a method for selecting 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.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
Fig. 1 is a schematic flow chart of a multi-unmanned aerial vehicle system security control method based on an unknown input observer according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of another method for controlling security of a multi-unmanned aerial vehicle system based on an unknown input observer according to an embodiment of the present invention;
FIG. 3 is a graph of the compliance error of the follower drone with inelastic control in simulation experiments;
FIG. 4 is a graph of the state estimation error of the follower drone when there is no elastic control in the simulation test;
FIG. 5 is a graph of residual signal and residual threshold when the system is under sensor attack in a simulation experiment;
FIG. 6 is a graph of the consistency error of the follower drone when the system is subject to a hybrid attack and uses elastic control in a simulation experiment;
FIG. 7 is a graph of state estimation information of a follower unmanned aerial vehicle when the system is subject to hybrid attack and elastic control is used in a simulation test;
fig. 8 is a trigger time of the event trigger control mechanism of each follower unmanned aerial vehicle under the mixed FDI attack in the simulation test.
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)∈R n ，Respectively representing the state, control input and measurement output of the follower agent i, t representing time,/->Representing state x i Differentiation of (t), ω i (t) is the process noise, φ (x) i (t))＝[φ 1 (x i (t)),…,φ n (x i (t))] T Nonlinear term, a i And (t) is a sensor attack signal. In addition to A, B, C, D ω Is a constant matrix of appropriate dimensions.
The leader's dynamic equation can be expressed as:
wherein ,x0 (t)∈R n ，Respectively representing the status and output of the leader agent i. />Is x 0 Differentiation of (t), φ (x) 0 (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 x 1 (t)，x 2 (t)∈R n Nonlinear function phi (x in unmanned aerial vehicle dynamic equation i ) The Lipschitz condition is satisfied.
(4) Sensor attack a i (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:
step 1: and (3) improving an unknown input observer to serve as a state observer based on the measurement information and the nonlinear design of the system, and performing 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 represents time, z i (t) is the unknown input observer state of follower agent i, +.>Is z i Derivative of (t), u i(t) and yi (t) control input and measurement output of follower agent i, respectively, < -> Is a generalized inverse matrix operation, t=i-HC, g=tb, f=ta-K 1 C，K u ＝K 1 +FH，A、B、C、D ω Is a constant matrix, I is a unit matrix, K 1 、K 2 For the observer matrix to be designed, < >>Andoutput estimation errors of follower agent i are represented respectively,/->Representing the output estimation error of the leader agent, a ij and ai0 Representing corresponding parameters of the adjacency matrix, wherein a ij Indicating the connection of follower i to its neighbor j, if the information can be accepted, a ij =1, otherwise a ij ＝0；a i0 The connection condition of the follower i and the leader is indicated, and the value standard is the same as the value standard. Therefore, it is possible to use the adjacency matrix +.>Representing the connection between nodes of algebraic graph and passing through adjacency matrixMatrix and metric matrix->And defining a Laplace matrix L corresponding to the unmanned aerial vehicle communication topological graph.
It can be seen that AUIO has two matrices K to be designed 1 ，K 2 . If take K 2 0, provided K is designed 1 To ensure that the matrix F is Schur, the state estimation error of the unknown input observer must converge. 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.
Step 2: and constructing a residual function through state estimation and measurement output and detecting node attack.
21 No unmanned aerial vehicle is constructedResidual function r when subject to sensor attack i * (t) and calculating therefrom the residual function r of the unmanned aerial vehicle when it is subjected to a sensor attack i (t)。
Specifically, taking a residual error function into consideration when the unmanned aerial vehicle is attacked by a sensorLet r be i * (t) is a residual function of the unmanned aerial vehicle system when the unmanned aerial vehicle system is not attacked by the sensor, then there are
wherein zi (t)e i (t) represents the state estimation error of the unmanned plane i, φ (x) i(t)) and All 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:
a i (t) represents a sensor attack,is a as i (t) derivative.
22 For residual function r) i (t) performing Euclidean norm detection if the norm J of the residual function is determined i (t) if the value is larger than a preset threshold value, 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, the state estimation error of AUIO is such that UUB (Uniformly ultimately Bounded, ultimately consistent with the constraint) conditions are met, so that sensor attacks can be detected by the Euclidean norm of the residual, i.e., taken
Corresponding threshold J th,i Can be selected according to the following formula:
J th,i ＝sup{r i * (t)} (7)
the detection criteria for node sensor attacks in a multi-drone system may be defined as:
step 3: when judging that node attack occurs, carrying out attack signal reconstruction and compensation based on an improved unknown input observer so as to carry out elastic control on the state estimation process of the multi-unmanned aerial vehicle system and obtain the real state information of the system; otherwise, the current estimation result of the state observer is used 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, for observer matrix K 1 、K 2 And the attack reconstruction matrix M can be calculated by the following sufficiency conditions:
for a given positive scaling quantityε 1 And a positive definite matrix R, if there is a symmetrical positive definite matrix Q 1 ，Q 2 Satisfying the LMI (Linear matrix inequality LMI linear matrix inequality) condition shown in equation (10) while taking the observer gain matrix +.>The 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 ,λ0 Laplace matrix L for communication topology of follower unmanned aerial vehicle 1 Corresponding parameter lambda max (Θ) is the maximum eigenvalue of positive definite matrix Θ, and the specific value-taking method is to take matrix Θ to make it meetλ 0 Is a matrixIs a minimum feature value of (2); Λ represents the nonlinear term φ (x i (T)) corresponding Lipschitz parameter matrix, T representing the transpose, I N Representing an identity matrix of dimension N.
By the above conditions, the observer matrix K to be designed can be obtained 1 、K 2 、M。
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 for attack reconstruction and attack compensation based on the unknown input observer can reduce the influence of node sensor attack on unmanned aerial vehicle state estimation, ensure the effectiveness of a consistency control law based on state estimation, and has higher application value; meanwhile, the elastic control is triggered by attack detection, so that the state estimation and system consistency under the general condition cannot be influenced by an elastic control mechanism, namely, the multi-unmanned-plane system has elasticity to node sensor attacks.
Step 4: and safety control is carried out 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 ,∈2 ,h i And eta 1 Is a given positive scalar, ++>Errors are measured for the event trigger mechanism.
Then, a consistency control matrix K is calculated c 。
Specifically, the consistency control matrix K c Design party of event trigger mechanism related parametersThe method can be given by the following sufficient conditions:
consider that a multiple unmanned aerial vehicle system under an event-triggered condition driven controller, if there is a symmetric positive definite matrix P 1 And positive scaling amount epsilon 2 ，So that the linear matrix inequalities (13) - (14) are established, then the consistency control gain is taken +.>When the system can achieve H ∞ Performance index sigma 1 The consistency is stabilized gradually, and the Zeno phenomenon can not occur.
wherein ,
representing the maximum number of neighbors of the system, L 1 Laplace matrix lambda corresponding to communication topology of follower unmanned aerial vehicle min(·) and λmax (. Cndot.) represents the maximum and minimum eigenvalues of the matrix respectively, N represents the total number of follower unmanned aerial vehicles, h i Is a parameter in the event trigger mechanism;
in the present embodiment, H ∞ Performance index sigma 1 Lower part (C)Progressive stability consistency can be expressed as:
wherein ,for mathematical expectation, δ (t) =col { x } i (t)-x 0 (t) } is a consistency error, ρ (t) =col { e x (t), ω (t) } is a complex disturbance, V 2 (t) is the Lyapunov function of δ (t).
Finally, based on event trigger mechanism and consistency control matrix K c An event triggering consistency control strategy is formulated to carry out consistency control on the multi-unmanned aerial vehicle system, and the formula is expressed as follows:
wherein ,ui (t) represents the control input, ζ, of the follower agent i i (. Cndot.) represents local domain errors, whose formula is
wherein , and />State estimates representing 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 self is judged not to be attacked, the normal operation is carried out, and the elastic control is not started; if the sensor attack signal is judged to be under attack, an elastic control mechanism is started, the node sensor attack signal is reconstructed through a corresponding attack reconstruction algorithm, and the elastic control of attack compensation is performed based on the reconstructed attack signal, so that the influence of the sensor attack on the state estimation value is reduced, the safety state estimation is obtained, and the event triggering consistency control is performed 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 cluster aggregation standby process of aeroconde 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. Thus let the process noise be gaussian noise and ω i And (t) is less than or equal to 5, and the process noise matrix and the nonlinear term are respectively as follows:
D ω ＝[1.2,1.1,-0.1,-0.5] T
φ(x i )＝[0.01sin(x i4(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:
x 0 (0)＝[1 9.8 0 -0.5] T
x 1 (0)＝[-2.3 9.7 -0.3 0.3] T
x 2 (0)＝[4.5 8.9 -0.2 -0.1] T
x 3 (0)＝[7.1 -7.0 0.3 0.2] T
based on the above conditions, according to the method provided in the first embodiment, the calculation of the AUIO to-be-solved matrix and the attack reconstruction to-be-solved matrix is performed.
Specifically, the parameter beta is selected Π1 ＝10，β Π2 ＝0.08，β Π3 ＝0.1，β Π4 ＝1，ε 1 ＝100，R＝I 3×3 The following conditions for attack signal reconstruction and compensation in step 3 can be calculated:
then, the consistency control matrix calculation is performed according to the sufficient conditions of the event trigger mechanism in the step 4.
Specifically, the parameter beta is selected π1 ＝1，β π2 ＝50，β π3 ＝10，ε 2 ＝0.3，η 1 =0.0001, the following can be found:
K c ＝[0.0010 0.0028 -0.0266 -0.0026]
finally, let the process noise be Gaussian noise and ω i (t) is less than or equal to 3.5. Is provided withInterference energy upper bound 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:
a 1 (t)＝[0.1·(t-20)+0.2·sin(0.5t),-0.1·(t-20)+0.2·sin(0.5t),0] T
a 2 (t)＝[-0.15·(t-20)+0.2·sin(0.5t),0.1·(t-20)+0.2·sin(0.5t),0] T
a 3 (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. Due to t E [40,43]The unmanned plane state in the time interval is less affected by the oscillation mode, so that 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 AUIO-based elastic control method provided by the invention is adopted in inelastic control under hybrid attack, the consistency error and the estimation error of each follower unmanned plane in a multi-unmanned plane system are shown in a 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 inhibits the impact of the node sensor FDI attack 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-aerial-vehicle 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 relative to the node-free attack situation is small, and the variation is in the allowable error range in consideration of the randomness of the communication channel interference. 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 AUIO-based elastic control method ensures the state estimation accuracy of the multi-unmanned aerial vehicle system under the condition of relieving node FDI attack, so that an event trigger control mechanism has elasticity to attack, and communication resources are further saved 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.

Claims (9)

1. The multi-unmanned aerial vehicle system safety control method based on the unknown input observer is characterized by comprising the following steps:
step 1: an unknown input observer is improved to be used as a state observer based on measurement information and system nonlinear design, and the state observer is utilized to perform state estimation on the current multi-unmanned aerial vehicle system;
step 2: constructing a residual function through state estimation and measurement output and performing node attack detection;
step 3: when judging that node attack occurs, carrying out attack signal reconstruction and compensation based on an improved unknown input observer so as to carry out elastic control on the state estimation process of the multi-unmanned aerial vehicle system and obtain the safety state information of the system;
otherwise, taking the current estimation result of the state observer as the safety state information of the system;
step 4: and carrying out safety control on the multi-unmanned aerial vehicle system based on the safety state information.
2. The method for controlling the safety of a multi-unmanned aerial vehicle system based on an unknown input observer according to claim 1, wherein step 1 comprises:
an improved unknown input observer taking system nonlinearity into consideration is constructed based on local measurement information and neighbor measurement information to serve as a state observer, and state estimation is carried out on the multi-unmanned aerial vehicle system according to the state observer, wherein the expression is as follows:
wherein ,representing the state estimation result of the follower agent i, t represents time, z i (t) is the unknown input observer state of follower agent i, +.>Is z i (t) derivative, and y i (t) control input and measurement output of follower agent i, respectively, < -> Is a generalized inverse matrix operation, t=i-HC, g=tb, f=ta-K 1 C，K u ＝K 1 +FH，A、B、C、D ω Is a constant matrix, I is a unit matrix, K 1 For the observer matrix to be designed, +.> and />Output estimation errors respectively representing follower agent i and its neighbors j, < >>Representing the output estimation error of the leader agent, a ij Representing the connection of follower i with its neighbor j, a i0 Indicating the connection of follower i to the leader.
3. The method for controlling the safety of a multi-unmanned aerial vehicle system based on an unknown input observer according to claim 2, wherein step 2 comprises:
21 Constructing a residual function r when the unmanned aerial vehicle is not attacked by the sensor i * (t) and calculating therefrom the residual function r of the unmanned aerial vehicle when it is subjected to a sensor attack i (t)；
22 For the residual function r) i (t) performing Euclidean norm detection if the norm J of the residual function is determined i (t) if the value is larger than a preset threshold value, judging that the unmanned aerial vehicle is attacked by the sensor; otherwise, judging that the unmanned aerial vehicle is not attacked by the sensor.
4. A multi-unmanned aerial vehicle system security control method based on an unknown input observer according to claim 3, wherein in step 21) the residual function r when the unmanned aerial vehicle is subject to a sensor attack i The expression of (t) is:
wherein ,
a i (t) represents a sensor attack,is a as i Derivative of (t), e i (t) represents a state estimation error, φ (x) i(t)) and All represent nonlinear terms.
5. The method for controlling the security of a multi-unmanned aerial vehicle system based on an unknown input observer according to claim 4, wherein in step 3, when a node attack occurs, an attack signal reconstruction and compensation are performed based on an improved unknown input observer to elastically control a state estimation process of the multi-unmanned aerial vehicle system, comprising:
calculating observer matrix K 1 、K 2 And an attack reconstruction matrix M, and performing elastic control on the state estimation process of the multi-unmanned aerial vehicle system by using the following formula;
wherein ,is an estimate of the sensor FDI attack signal,/->Is->Is a derivative of (a).
6. The method for controlling the safety of a multi-unmanned aerial vehicle system based on an unknown input observer according to claim 5, wherein the observer matrix K 1 、K 2 And the attack reconstruction matrix M is calculated by the following sufficiency conditions:
for a given positive scaling amountε 1 And positive definite matrix R, let symmetrical positive definite matrix Q 1 ，Q 2 The following LMI conditions are satisfied:
the gain matrix of the state observer
wherein λ0 Laplace matrix L for communication topology of follower unmanned aerial vehicle 1 Corresponding parameter lambda max (Θ) is a positive definite matrix Θ=diag { θ } 1 ,…,θ N Maximum eigenvalue of }, Λ represents the nonlinear term phi (x i (T)) corresponding Lipschitz parameter matrix, T representing the transpose, I N Representing an identity matrix of dimension N.
7. The method for controlling safety of a multiple unmanned aerial vehicle system based on an unknown input observer according to claim 6, wherein the step 4 comprises:
setting an event-triggered consistency control strategy to perform consistency control on the multi-unmanned aerial vehicle system.
8. The method of claim 7, wherein setting an event-triggered coherency control policy for coherency control of a multi-unmanned aerial vehicle system comprises:
order theThe event triggering time sequence of the ith unmanned aerial vehicle is represented, and the following event triggering mechanism is set:
wherein ,∈2 、h i 、η 1 Are all given positive scalar, +.>Measuring errors for an event triggering mechanism, wherein e is a natural base number;
calculating a consistency control matrix K c ；
Based on event trigger mechanism and said consistency control matrix K c And carrying out consistency control on the multi-unmanned aerial vehicle system, wherein the formula is as follows:
wherein ,ui (t) represents the control input, ζ, of the follower agent i i (. Cndot.) represents a local area error, and its calculation formula is:
wherein , and />Representing the state estimation results of follower agents i and j, respectively,/->Representing the results of the state estimation of the leader agent.
9. The method for controlling the safety of a multi-unmanned aerial vehicle system based on an unknown input observer according to claim 8, wherein the consistency control matrix K c Calculated according to the following sufficient conditions:
for a given positive scaling amount epsilon 2 、And positive definite matrix P 1 Let it satisfy the following linear matrix inequality:
wherein ,
representing the maximum number of neighbors of the system, L 1 Laplace matrix lambda corresponding to communication topology of follower unmanned aerial vehicle min(·) and λmax (. Cndot.) represents the maximum and minimum eigenvalues of the matrix respectively, N represents the total number of follower unmanned aerial vehicles, h i Is a parameter in the event trigger mechanism;
then take K c ＝ε 2 B T P 1 -1 To enable the system to achieve H ∞ Performance index sigma 1 The gradual stability consistency is lower, and the Zeno phenomenon can not occur; wherein,
H ∞ performance index sigma 1 The following progressive stability consistency can be expressed as:
wherein δ (t) =col { x } i (t)-x 0 (t) } is a consistency error, ρ (t) =col { e x (t), ω (t) } is a complex disturbance, V 2 (t) is the Lyapunov function of δ (t).
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117034020A (en) * 2023-10-09 2023-11-10 贵州大学 Unmanned aerial vehicle sensor zero sample fault detection method based on CVAE-GAN model
CN117034020B (en) * 2023-10-09 2024-01-09 贵州大学 Unmanned aerial vehicle sensor zero sample fault detection method based on CVAE-GAN model

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