CN114924588B - Unmanned aerial vehicle cluster elastic safety formation method - Google Patents
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Abstract
The invention relates to an unmanned aerial vehicle cluster elastic safety formation method, which relates to the field of unmanned aerial vehicle cluster control, and comprises the following steps: establishing a network attack model and a system fault model of the unmanned aerial vehicle cluster system; establishing a dynamic model of the unmanned aerial vehicle i according to the network attack model and the system fault model; constructing a neighbor state estimator of the unmanned aerial vehicle i according to the dynamics model; constructing a self state estimator of the unmanned aerial vehicle i according to the dynamics model; acquiring a time period of stable operation and a time period of unstable operation of an unmanned aerial vehicle cluster system when the unmanned aerial vehicle cluster system is attacked or fails; determining an overall stability analysis function of the unmanned aerial vehicle cluster system according to the time period of stable operation and the time period of unstable operation; and constructing a dynamical equation of the unmanned aerial vehicle cluster system comprising the distributed security protocol according to the dynamical model, the neighbor state estimator, the self state estimator and the overall stability analysis function. The invention can improve the reliability and the operation safety of unmanned aerial vehicle cluster formation.
Description
Technical Field
The invention relates to the field of unmanned aerial vehicle cluster control, in particular to an unmanned aerial vehicle cluster elastic safety formation method.
Background
With increasingly complex combat environments and combat demands, combat patterns of single unmanned aerial vehicles have become difficult to complete combat tasks, and multi-unmanned aerial vehicle collaborative combat technologies have become an important development direction of future weaponry. Meanwhile, the safety of space unmanned aerial vehicles is increasingly focused in various aerospace countries in the world, and in order to improve the risk resistance of the space unmanned aerial vehicles, a cluster fight is required to complete a fight task. The multi-unmanned aerial vehicle formation collaborative attack is an important combat mode suitable for future combat environments, the multi-space unmanned aerial vehicle cluster combat not only needs to reasonably distribute tasks for different unmanned aerial vehicles according to various constraint conditions, but also requires each unmanned aerial vehicle to cooperate with other unmanned aerial vehicles to combat targets accurately, so that the overall combat efficiency of the unmanned aerial vehicle is maximized.
Unmanned aerial vehicle cluster formation is based on unmanned aerial vehicle technology, and a plurality of unmanned aerial vehicles are utilized to cooperatively work to form a formation to fly, so that a better application effect than that of a single unmanned aerial vehicle is achieved, and a brand new solution idea and scheme are provided for future cluster cooperative tasks. The elastic safety formation refers to that when the unmanned aerial vehicle cluster encounters network attack or physical fault, the stability of the system can be maintained, an initial task is completed according to the original formation form, and the unmanned aerial vehicle cluster is higher-order fault-tolerant control.
The unmanned aerial vehicle cluster formation shows great application value and development prospect in the application level of realizing accurate positioning, three-dimensional imaging and the like, and typical application scenes such as 'star link plan' of SpaceX can form a space unmanned aerial vehicle-based space-earth integrated three-dimensional network, so that corresponding requirements of areas (offshore, south-north poles, deserts and the like) unsuitable for erecting ground base stations are met. According to the system, a plurality of spacecrafts with mutually independent physical structures are actually used for transmitting data information with other spacecrafts in a formation through spaceborne communication equipment according to the instruction of a certain spacecrafts task, and the spacecrafts keep a relatively close distance and a specific formation in space, so that cooperative work is realized, and an integral virtual platform is formed. However, due to the reasons of relatively low reliability, complex external environment, high difficulty in communication among unmanned aerial vehicles and the like, individual faults, communication faults among unmanned aerial vehicles and node faults of unmanned aerial vehicle cluster formation are easily caused, and the overall performance of unmanned aerial vehicle cluster formation is seriously affected. Therefore, a novel distributed formation control protocol with elasticity is designed aiming at the failure of the executor and the communication failure, and the reliability and the operation safety of unmanned aerial vehicle cluster formation are improved.
Disclosure of Invention
The invention aims to provide an unmanned aerial vehicle cluster elastic safety formation method which can improve reliability and operation safety of unmanned aerial vehicle cluster formation.
In order to achieve the above object, the present invention provides the following solutions:
An unmanned aerial vehicle cluster elastic safety formation method comprises the following steps:
Establishing a network attack model and a system fault model of the unmanned aerial vehicle cluster system;
establishing a dynamic model of the unmanned aerial vehicle i according to the network attack model and the system fault model;
Constructing a neighbor state estimator of the unmanned aerial vehicle i according to the dynamics model;
constructing a self state estimator of the unmanned aerial vehicle i according to the dynamics model;
Acquiring a time period of stable operation and a time period of unstable operation of an unmanned aerial vehicle cluster system when the unmanned aerial vehicle cluster system is attacked or fails;
Determining an overall stability analysis function of the unmanned aerial vehicle cluster system according to the stable operation time period and the unstable operation time period;
And constructing an unmanned aerial vehicle cluster system dynamics equation containing a distributed security protocol according to the dynamics model, the neighbor state estimator, the self state estimator and the overall stability analysis function, wherein the unmanned aerial vehicle cluster system dynamics equation containing the distributed security protocol is used for enabling the unmanned aerial vehicle cluster system to still complete a set formation flight task when network attack or system failure occurs.
Optionally, the network attack model is a switching function.
Optionally, the system fault model is:
ui(t)＝Liuci(t)+fai(t)
＝uci(t)+fmi(t)+fai(t)
Where u i (t) represents the input to unmanned aerial vehicle i, f ai (t) is an additive fault, L i＝diag{lik } is an indication matrix, L ik E [0,1] is the kth system input indication factor for unmanned aerial vehicle i, u ci (t) represents the controller output, and f mi(t)＝(Li-I)uci (t) is a virtual multiplicative fault.
Optionally, the dynamics model is:
yi(t)＝Cxi(t)
Wherein, For the dynamics model, x i (t) is the system state, u i (t) is the input of the unmanned aerial vehicle i, y i (t) is the system output, a is the system state matrix, B is the system input matrix, C is the system output matrix, D is the system interference matrix, D i (t) is the external disturbance, u ci (t) represents the controller output, f mi(t)＝(Li-I)uci (t) is the virtual multiplicative fault, and f ai (t) is the additive fault.
Optionally, the neighbor state estimator is:
Wherein, Is the state estimation value of unmanned plane i to neighbor unmanned plane j, j is N i (G),/>A is a system state matrix.
Optionally, the self state estimator is:
Where x oi (t) is the self-estimator state, Respectively representing estimated values of x ai(t),xi(t),fmi(t),fai (T), T representing a matrix transpose; m is an estimator state matrix, J u is an estimator input matrix, J y is an estimator output matrix, and W is an estimated value output matrix.
Optionally, the functional expression of the period of stable operation and the period of unstable operation is:
Wherein, As a function of the system in steady operation,/>As a function of the unstable operation of the system, W r＝[ηr+vr,ηr+1),Wr represents the r-th sleep period, τ represents the start of the period, Z r represents the r-th attack period, Z r＝[ηr,ηr+vr),{ηr and { v r } are two non-negative sequences, η -1＝v-1＝0,ηr represents the start of the DoS attack, and v r represents the duration of the DoS attack.
Optionally, the overall stability analysis function is:
where gamma m＝max{1/β1,1/β2},γm is the maximum value of the interference coefficients, beta 1 is the first interference coefficient, beta 2 is the second interference coefficient, Maximum value of infinite modulus of interference vector,/>Is the infinite modulus of the first interference vector, |d t||∞ is the infinite modulus of the second interference vector.
Optionally, the unmanned aerial vehicle cluster system dynamics equation including the distributed security protocol is:
yi(t)＝Cxi(t)
Where v i (t) is the formation compensation value, G ei is the error gain, G mi is the multiplicative gain, and G ai is the additive gain.
Optionally, G mi＝-I,Gai＝-I,Gei＝ωeR-1BTP-1, where I is an identity matrix, R is an optimization matrix, and P is a Li Kadi matrix.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
The invention designs a novel elastic distributed formation control protocol aiming at the failure of the executor and the communication failure, and improves the reliability and the operation safety of unmanned aerial vehicle cluster formation.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of an elastic safety formation method of a unmanned aerial vehicle cluster;
FIG. 2 is a three-dimensional position diagram of an initial drone of the present invention;
FIG. 3 is a three-dimensional position diagram of a unmanned aerial vehicle successfully formed into a specified formation in accordance with the present invention;
FIG. 4 is a three-dimensional position diagram of an unmanned aerial vehicle when network attack and failure occur in the invention;
FIG. 5 is a three-dimensional position diagram of a first unmanned aerial vehicle successfully formed into a designated formation using an elastic algorithm in accordance with the present invention;
FIG. 6 is a three-dimensional position diagram of a second unmanned aerial vehicle successfully formed into a designated formation using an elastic algorithm in accordance with the present invention;
FIG. 7 is a three-dimensional position diagram of a third unmanned aerial vehicle successfully formed into a specified formation using an elastic algorithm in accordance with the present invention;
FIG. 8 is a schematic diagram of the time period of a DoS attack according to the present invention;
fig. 9 is a schematic diagram of a communication trigger time point of each unmanned aerial vehicle according to the present invention;
FIG. 10 is a schematic diagram of a formation error of the system of the present invention;
Fig. 11 is a schematic diagram of a control output of the attacked unmanned aerial vehicle 1 according to the present invention;
fig. 12 is a schematic diagram of the output rate of the attacked unmanned aerial vehicle 1 according to the present invention;
fig. 13 is a schematic diagram of a control output of the attacked unmanned aerial vehicle 2 according to the present invention;
Fig. 14 is a schematic diagram of the output rate of the attacked drone 2 according to the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide an unmanned aerial vehicle cluster elastic safety formation method which can improve reliability and operation safety of unmanned aerial vehicle cluster formation.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
Fig. 1 is a flowchart of an elastic safety formation method of an unmanned aerial vehicle cluster, as shown in fig. 1, specifically including the following steps:
step 1: and establishing a network attack model and a system fault model.
Due to the vulnerability of the unmanned aerial vehicle cluster system network, malicious attacks can be blindly injected into the system through the network layer. And because the cluster unmanned aerial vehicle is mostly low in reliability and low in cost, system faults are easy to occur. Therefore, network attacks and system failures are modeled first when security of formation is considered.
(1) DoS attack modeling: in an unmanned aerial vehicle cluster system, doS attack influences a measurement channel to enable space unmanned aerial vehicles to be incapable of exchanging information, and stability of the system is damaged. Data cannot be exchanged, but the drone still has communication capability, which is the biggest difference between DoS attacks and sensor failures. DoS attacks include an active period and a dormant period, the nature of the model being a switching function (active period + dormant period), the ith drone being unable to receive status information of other drones when DoS occurs. Order theRepresents the slave/>A time series of DoS attacks is initiated. /(I)Represents the mth DoS period, length is/>Definitions Θ a (τ, t) and Θ s (τ, t) represent DoS active and sleep periods, respectively, i.e
Θs(τ,t)＝[τ,t]\Θa(τ,t) (2)
Define the number of DoS activations on [ tau, t ] as
Wherein n 0 is more than or equal to 0,Let/>Representing the attack frequency on [ tau, t ].
The total DoS attack duration on definition [ τ, t ] is expressed as:
wherein mu 0 is more than or equal to 0, and T is more than 1.
Specifically, equations (1) - (4) calculate the number and duration of DoS triggers over a period of time.
(2) Fault modeling: establishing an unmanned aerial vehicle cluster system executor stuck fault (LIP) u i(t)＝fai (t) and an efficiency reduction fault (LOE) u i(t)＝Liuci (t), wherein u i (t) represents the input of the unmanned aerial vehicle i, f ai (t) is an additive fault, L i＝diag{lik is an indication matrix, L ik epsilon [0,1] is the kth system input indication factor of the unmanned aerial vehicle i, and u ci (t) represents the controller output.
The generalized control input (fault model) of the drone can thus be expressed as:
where f mi(t)＝(Li-I)uci (t) is a virtual multiplicative fault, used to design a security control protocol.
Defining additive faults f ai (t) and external disturbances d i (t) are both unknown but bounded, i.e Is an additive fault boundary,/>Is an interference boundary.
Step 2: and establishing an unmanned aerial vehicle cluster model.
Substituting the attack model and the fault model established in the step 1 into a dynamic equation of the whole cluster system, and establishing a dynamic model of the unmanned aerial vehicle i as follows:
yi(t)＝Cxi(t)(6b)
Wherein the method comprises the steps of Is the derivative of the system state x i (t), representing the dynamics model, x i (t) is the system state, y i (t) is the system output, a system state matrix, B system input matrix, C system output matrix, D system interference matrix.
The control input of the cluster system needs to update the input signal according to a certain trigger strategy, and definesA sequence of trigger events (no matter what trigger logic is generated) for drone i, where/>If the system internal sampling time/>The method meets the following conditions:
Where Δ > 0 represents the lower bound of the internal sampling rate, then it is called With limited sample rate properties. Note that in equation (3)/>Also satisfy/>Consider/>And DoS time series/>, in step 1And (3) making:
Representing an integer whose trigger time is just within the DoS.
Further, h i (t) and θ (t) are defined as the desired time-varying formation vector and formation reference function. If the status of unmanned plane i satisfies:
where h i (t) is segmented, continuous, and can be made small, then the drone cluster system can be said to be capable of completing the desired formation.
Step 3: the neighbor state estimator is designed.
The purpose of the neighbor state estimator is to enable the unmanned aerial vehicle i to estimate the state variable of the neighbor in the time of communication interruption with the neighbor, thereby increasing the allowed communication interval time of the whole system.
If an intruder attacks the communication network of the unmanned aerial vehicle cluster system, the unmanned aerial vehicle cannot exchange information with the neighbor unmanned aerial vehicle. Therefore, according to the unmanned aerial vehicle cluster model in the step 2, the state estimator of the unmanned aerial vehicle i is designed to be:
Wherein the method comprises the steps of Is the state estimation value of unmanned plane i to neighbor unmanned plane j, j is N i (G),/>
The local formation neighbor estimation error of the unmanned aerial vehicle i (the local formation neighbor estimation error is used in a control protocol) is designed as follows:
Step 4: the self state estimator is designed.
The purpose of the self state estimator is to accurately estimate the self state information and attack/fault information through the input and output signals of the unmanned aerial vehicle i, and is used for designing a distributed security formation control protocol.
The unmanned aerial vehicle cluster model of the expansion step 2 is as follows:
yi(t)＝Caxai(t)(12b)
wherein, define Ca＝[In 0 0],Da＝diag{D,Ip,Ip}。
The fault estimator of the unmanned aerial vehicle i is designed according to the expansion system formulas (12 a) and (12 b) as follows:
Where x oi (t) is the estimator state, Respectively representing estimated values of x ai(t),xi(t),fmi(t),fai (T), T representing a matrix transpose; m is an estimator state matrix, J u is an estimator input matrix, J y is an estimator output matrix, and W is an estimated value output matrix. M, J u、Jy, W denote the estimator matrix that needs to be designed.
Definition of the definitionFor estimator error, the first derivative of e ai (t) is calculated as:
where J y＝Jy1+Jy2, it is therefore necessary to design M, J u、Jy, W such that M is a Hulvitz matrix ,Aa-WCaAa-Jy1Ca＝M,MW-Jy2＝0,Ba-WCaBa-Ju＝0,(I-WCa)Da＝0,, the fault values can be accurately estimated, and the fault estimates are given in equation (13 b).
Step 5: a distributed security control protocol is designed.
The purpose of designing a distributed safety control protocol is to enable the unmanned aerial vehicle cluster in the step 2 to still complete a given formation flight task under the influence of network attack and system fault, and refer to a formula (9) in the step 2.
Therefore, in combination with step 2, step 3 and step 4, the unmanned aerial vehicle i is designed to be in a time periodThe safety fault-tolerant control protocol of (1) is:
Where v i (t) is the formation compensation value and G ei、Gmi、Gai represents the designed controller gain.
Defining neighbor errors (the errors are communication triggering conditions, when the errors reach a certain size, the communication is triggered, and the control protocol is updated once) of each unmanned aerial vehicle as follows:
bringing the neighbor error into the original system-available ε i (t) is an external perturbation term, so ε i (t) should be designed as small as possible while satisfying:
Wherein 0 < alpha i < 1, and the triggering condition of the protocol (15) can be defined as
Substituting the distributed security control protocol into the unmanned aerial vehicle cluster system equation of the step 2 to obtain the following steps:
yi(t)＝Cxi(t)(18b)
Where v i (t) is the formation compensation value, G ei is the error gain, G mi is the multiplicative gain, and G ai is the additive gain.
The compact form of the drone cluster system may further be written as:
Wherein the method comprises the steps of Ge＝diag{Ge1,...,GeN},Gm＝diag{Gm1,...,GmN},Ga＝diag{Ga1,...,GaN}.
Let z i(t)＝xi(t)-hi (t), equation (18) can be written as:
define xi i(t)＝zi (t) -theta (t), Then:
Wherein the method comprises the steps of Further, L aMa＝MaLa＝La,/>Definition v i (t) satisfies formation feasibility condition/>This feasibility condition ensures that the desired formation h i (t) is completed, then equation (21) can be written as:
The controller gain G ei、Gmi、Gai design process will be given in step 7.
Step 6: the stable and unstable intervals when the cluster system operates are divided.
In order to design the control gain in step 5, we need to find out the time period of stable operation and unstable operation of the unmanned aerial vehicle cluster system under the attack/fault condition.
First two time periods are definedAnd/>The method comprises the following steps:
Further defining the mth period affected by the attack as:
the trigger condition is not necessarily satisfied during this period. Note that Including T m plus the corresponding DoS induced actuator delay, and/>
Due toAnd/>May overlap (/ >)Belonging to/>When) defining an auxiliary sequence { eta r } instead of the original DoS sequence/>
The design flow of { η r } is:
Wherein the method comprises the steps of Definition:
Wherein the method comprises the steps of Indicating that all elements belong to/>But not belong to/>Is a set of (3).
Finally, defineAnd/>Make the trigger condition be satisfied and not necessarily satisfied, system stable interval/>And system instability interval/>The expression of (2) is:
where W r＝[ηr+vr,ηr+1),Wr represents the r sleep period, τ represents the start of the period, Z r represents the r attack period, Z r＝[ηr,ηr+vr),{ηr and { v r } are two non-negative sequences, η -1＝v-1＝0,ηr represents the start of the DoS attack, and v r represents the duration of the DoS attack.
Step 7: the distributed security control protocol gain is designed.
The purpose of this step is to give a design range of control gains by analyzing the stability. Stabilizing zone divided according to step 6The design stability analysis function is:
Where ζ (t) is given in step 5, P is the solution of a TP+PA-PBR-1BT p+q=0, P and Q are both positive definite matrices. The first derivative of V (t) (a function established to demonstrate stability) is expressed as:
Wherein the method comprises the steps of
The control protocol gain in step 5 can be designed according to equation (31) as: g m＝-I,Ga＝-I,Gei＝ωeR- 1BTP-1, wherein I is an identity matrix, R is an optimization matrix, and P is a Li Kadi matrix.Lambda 2 represents the smallest non-zero feature root of L a for the cluster topology and lambda N represents the largest non-zero feature root of L a for the cluster topology.
Step 8: the extent to which a computing cluster system can tolerate attacks/faults.
For further decomposition of equation (31) of step 7, the stability analysis function for the available stability interval satisfies:
the function is a function demonstrating stability, with the aim of demonstrating that the first derivative of the established lyapunov function is less than zero.
Consider the unstable interval in step 6The triggering condition formula (17) is not necessarily satisfied, and the stability analysis function of the unstable interval can be obtained to satisfy the following conditions:
Wherein, γ0＝λmin(QP-2),γ1＝||P-1BGe||,γ2＝||P-1D||,γ3＝||P-1B||,/>Alpha max＝max{ai},ai defines equation (17) at step3. /(I)The design is free for external interference items.
Summarizing equation (32) and equation (33), the overall stability analysis function can be obtained to satisfy:
Wherein, gamma m＝max{1/β1,1/β2 },
Consider Θ a (τ, t) and in step 6Equation (34) may be rewritten as:
where gamma m＝max{1/β1,1/β2},γm is the maximum value of the interference coefficients, beta 1 is the first interference coefficient, beta 2 is the second interference coefficient, Maximum value of infinite modulus of interference vector,/>Is the infinite modulus of the first interference vector, |d t||∞ is the infinite modulus of the second interference vector.
The number and duration of attacks that a clustered system can tolerate over the entire run-time period therefore needs to be sufficientWherein Delta * is a non-negative constant representing the upper bound of actuator delay and sampling frequency while meeting
In particular, according to the solution of the present invention, a specific embodiment is given:
DoS time periods were designed (fig. 8 original parameters, meaning that the system was subject to DoS attacks over these time periods):
[1,2)∪[4,5)∪[7,7.5)∪[14,14.5)∪[17,17.5)∪[21,21.5)∪[26,26.5)∪[33,34.5)∪[44,45)
Fig. 2 shows initial state values for 6 drones, here random values are used. When there is no fault, the cluster system can complete the system to the desired formation for about 15s using the given fault tolerant formation control protocol. When the fault is injected for 20 seconds, the original formation is destroyed, and the formation can be restored in about 30 seconds because the fault condition is considered when the formation protocol is designed. Fig. 8, 9 and 10 show DoS occurrence time, trigger time of control law and system formation error. An error of about 15 seconds can be seen to be zero, i.e. formation is completed. When a fault is injected, the error suddenly increases and then returns to zero. The abrupt change in formation error caused by the reduced efficiency fault is less pronounced than the stuck fault. Fig. 11, 12 and 13, 14 show the output of the actuators when the drone 1 and the drone 2 are subjected to DoS attacks and to failure of the actuators.
The invention also discloses the following technical effects:
Compared with the existing elastic distributed formation method, the method considers the influence of external interference on the system, uses more strict input-state stable computing system to tolerate attack information, and uses event triggering technology to reduce communication resources.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (10)
1. An unmanned aerial vehicle cluster elastic safety formation method is characterized by comprising the following steps:
Establishing a network attack model and a system fault model of the unmanned aerial vehicle cluster system;
establishing a dynamic model of the unmanned aerial vehicle i according to the network attack model and the system fault model;
Constructing a neighbor state estimator of the unmanned aerial vehicle i according to the dynamics model;
constructing a self state estimator of the unmanned aerial vehicle i according to the dynamics model;
Acquiring a time period of stable operation and a time period of unstable operation of an unmanned aerial vehicle cluster system when the unmanned aerial vehicle cluster system is attacked or fails;
Determining an overall stability analysis function of the unmanned aerial vehicle cluster system according to the stable operation time period and the unstable operation time period;
And constructing an unmanned aerial vehicle cluster system dynamics equation containing a distributed security protocol according to the dynamics model, the neighbor state estimator, the self state estimator and the overall stability analysis function, wherein the unmanned aerial vehicle cluster system dynamics equation containing the distributed security protocol is used for enabling the unmanned aerial vehicle cluster system to still complete a set formation flight task when network attack or system failure occurs.
2. The unmanned aerial vehicle cluster elastic security formation method of claim 1, wherein the network attack model is a switching function.
3. The unmanned aerial vehicle cluster elastic safety formation method of claim 1, wherein the system fault model is:
ui(t)＝Liuci(t)+fai(t)
＝uci(t)+fmi(t)+fai(t)
Where u i (t) represents the input to unmanned aerial vehicle i, f ai (t) is an additive fault, L i＝diag{lik } is an indication matrix, L ik E [0,1] is the kth system input indication factor for unmanned aerial vehicle i, u ci (t) represents the controller output, and f mi(t)＝(Li-I)uci (t) is a virtual multiplicative fault.
4. The unmanned aerial vehicle cluster elastic safety formation method of claim 1, wherein the dynamics model is:
yi(t)＝Cxi(t)
Wherein, For the dynamics model, x i (t) is the system state, u i (t) is the input of the unmanned aerial vehicle i, y i (t) is the system output, a is the system state matrix, B is the system input matrix, C is the system output matrix, D is the system interference matrix, D i (t) is the external disturbance, u ci (t) represents the controller output, f mi(t)＝(Li-I)uci (t) is the virtual multiplicative fault, and f ai (t) is the additive fault.
5. The unmanned aerial vehicle cluster elastic security formation method of claim 1, wherein the neighbor state estimator is:
Wherein, Is the state estimation value of unmanned plane i to neighbor unmanned plane j, j is N i (G),/>A is a system state matrix.
6. The unmanned aerial vehicle cluster elastic security formation method of claim 1, wherein the self state estimator is:
Where x oi (t) is the self-estimator state, Respectively representing estimated values of x ai(t),xi(t),fmi(t),fai (T), T representing a matrix transpose; m is an estimator state matrix, J u is an estimator input matrix, J y is an estimator output matrix, and W is an estimated value output matrix.
7. The unmanned aerial vehicle cluster elastic safety formation method of claim 1, wherein the functional expression of the period of stable operation and the period of unstable operation is:
Wherein, As a function of the system in steady operation,/>As a function of the unstable operation of the system, W r＝[ηr+vr,ηr+1),Wr represents the r-th sleep period, τ represents the start of the period, Z r represents the r-th attack period, Z r＝[ηr,ηr+vr),{ηr and { v r } are two non-negative sequences, η -1＝v-1＝0,ηr represents the start of the DoS attack, and v r represents the duration of the DoS attack.
8. The unmanned aerial vehicle cluster elastic safety formation method of claim 1, wherein the overall stability analysis function is:
where gamma m＝max{1/β1,1/β2},γm is the maximum value of the interference coefficients, beta 1 is the first interference coefficient, beta 2 is the second interference coefficient, Maximum value of infinite modulus of interference vector,/>Is the infinite modulus of the first interference vector, |d t||∞ is the infinite modulus of the second interference vector.
9. The unmanned aerial vehicle cluster elastic security formation method according to claim 1, wherein the unmanned aerial vehicle cluster system dynamics equation including the distributed security protocol is:
yi(t)＝Cxi(t)
Where v i (t) is the formation compensation value, G ei is the error gain, G mi is the multiplicative gain, and G ai is the additive gain.
10. The unmanned aerial vehicle cluster elastic safety formation method of claim 9, wherein G mi＝-I,Gai＝-I,Gei＝ωeR-1BTP-1, wherein I is an identity matrix, R is an optimization matrix, and P is a Li Kadi matrix.
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