A method and apparatus for attacking a drone flight control system

Abstract

The present invention discloses a method and device for attacking a UAV flight control system, and relates to the field of UAV countermeasures. It is used to solve the problem that the countermeasures in the field of UAV countermeasures are single and lack of pertinence, resulting in poor attack effects and inability to accurately interfere with target UAVs. It includes: according to the PBH rank criterion, combining the key row vectors and key column vectors of the candidate matrix to obtain a key matrix, and obtaining a tampered optimal attack matrix according to the key matrix; according to the tampered optimal attack matrix, a tampered input matrix, a tampered parameter of the input matrix, a tampered output matrix, and a tampered parameter of the output matrix are obtained, and according to the tampered parameter of the input matrix and the tampered parameter of the output matrix, the internal parameters of the target UAV flight control system are tampered.

Description

Technical Field

[0001] The present invention relates to the field of unmanned aerial vehicle (UAV) countermeasures, and more specifically to an attack method and device for an unmanned aerial vehicle (UAV) flight control system. Background Art

[0002] Unmanned aerial vehicles (UAVs) are unmanned aircraft that are controlled by radio remote control equipment and self-contained program control devices, or are operated completely or intermittently autonomously by on-board computers. Compared with manned aircraft, drones can be divided into military and civilian applications according to their application fields. In the military, drones are divided into reconnaissance aircraft and target aircraft; in the civilian field, the combination of drones and industry applications is the real rigid demand for drones; their applications in aerial photography, agriculture, plant protection, micro selfies, express delivery, disaster relief, wildlife observation, infectious disease monitoring, surveying and mapping, news reporting, power inspections, disaster relief, film and television shooting, and romance creation have greatly expanded the use of drones themselves. Developed countries are also actively expanding industry applications and developing drone technology. However, because drones can carry explosives, poisons and other dangerous items that endanger public safety and human life, drone flights are prohibited in specific airspaces. However, some people ignore this regulation and fly drones in these prohibited airspaces at will, which poses a hidden danger to public and personal safety.

[0003] Most existing researchers focus on the stability of UAV systems and have invested a lot of energy in stability analysis and optimization. However, there are relatively few studies on the controllability and observability of UAV systems. As important characteristics of the system, controllability and observability are crucial for in-depth understanding and control of the operating status and behavior of UAV systems. In practical applications, UAVs face complex and changing environments and potential attack threats. In-depth research on the controllability and observability of UAVs will help to better evaluate the safety and reliability of UAV flight control systems and provide new ideas and methods for improving the anti-attack capabilities of UAV flight control systems. Summary of the invention

[0004] The embodiment of the present invention provides a method and device for attacking a UAV flight control system, which is used to solve the problem that the countermeasures in the current UAV countermeasure field are single and lack of specificity, resulting in poor attack effects and inability to accurately interfere with the target UAV.

[0005] An embodiment of the present invention provides a method for attacking a UAV flight control system, comprising:

[0006] An attack instruction is received, internal parameters of a flight control system of a target UAV are obtained according to the attack instruction, and an initial system model of the flight control system of the target UAV is established according to the internal parameters, wherein the internal parameters include an initial system matrix, an initial input matrix, and an initial output matrix;

[0007] According to the initial system model and the initial system matrix subjected to Jordan standard modification, a system model in a new linear space including a Jordan block is obtained, and a candidate matrix is ​​constructed according to the system model in the new linear space, the system matrix in the new space, the input matrix in the new space, the output matrix in the new space and the Jordan block;

[0008] According to the PBH rank criterion, the key row vector and the key column vector of the candidate matrix are combined to obtain a key matrix, the norm of each row vector included in the key matrix is ​​determined, and the optimal attack matrix is ​​obtained by rearranging the vectors in ascending order according to the norms, and the first k rows of the optimal attack matrix are set to zero to obtain the tampered optimal attack matrix; wherein k represents a positive integer, and k is less than the number of rows of the optimal attack matrix;

[0009] Returning the tampered optimal attack matrix to the input matrix in the new space and the output matrix in the new space, obtaining the input matrix in the judgment space and the output matrix in the judgment space, wherein the input matrix in the judgment space is transformed to obtain the tampered input matrix, and the output matrix in the judgment space is transformed to obtain the tampered output matrix;

[0010] According to the relationship between the tampered input matrix and the initial input matrix, the tampered parameters of the input matrix are obtained; according to the relationship between the tampered output matrix and the initial output matrix, the tampered parameters of the output matrix are obtained; according to the tampered parameters of the input matrix and the tampered parameters of the output matrix, the internal parameters of the target UAV flight control system are tampered.

[0011] Preferably, combining the key row vector and the key column vector of the candidate matrix to obtain the key matrix according to the PBH rank criterion specifically includes:

[0012] According to the PBH rank criterion, determine the i-th Jordan block J i The last row in the table affects the controllability of the UAV flight control system. The i-th Jordan block J i The first column affects the observability of the UAV flight control system, and the i-th Jordan block J i The last row in is determined as the key row vector, and the i-th Jordan block J i The first column is determined as a key column vector, and the key row vector and the key column vector are combined to obtain a key matrix;

[0013] The key matrix is ​​as follows:

[0014]

[0015] Among them, represents the key matrix, represents the corresponding key row vector in represents the multiple row vectors corresponding to J i corresponding to Among them, represents the corresponding key column vector in represents the multiple column vectors corresponding to J i corresponding to Among them, J i represents the i-th Jordan block, represents the input matrix in the new space, represents the output matrix in the new space, represents the key row vector the l-th row vector in represents the key column vector the l-th column vector in, γ represents the dimension of J i l represents the number of Jordan blocks, 1 ≤ l < n, and n represents a positive integer.

[0016] Preferably, the PBH rank criterion is as follows:

[0017]

[0018]

[0019] Among them, K c represents the controllability matrix, K o represents the observability matrix, I represents the identity matrix, represents the system matrix in the judgment space, represents the input matrix in the judgment space, represents the output matrix in the judgment space, λ i represents the eigenvalue of the initial system matrix, 1 ≤ i ≤ l < n, and n represents a positive integer,

[0020] i represents the serial number of the Jordan block, s represents a complex variable, λ l represents the l-th eigenvalue of the initial system matrix, represents the input matrix in the judgment space the row vector composed of all elements in the n-th row of represents the output matrix in the judgment space The column vector composed of all elements in the nth column, where l represents the number of Jordan blocks.

[0021] Preferably, the system model under the new linear space including Jordan blocks is as follows:

[0022]

[0023] Wherein, represents the system state at time k under the new linear space, represents the system state at time k + 1 under the new linear space, y k represents the system measurement output at time k under the new linear space, represents the system matrix under the new space, represents the input matrix under the new space, represents the output matrix under the new space, u k represents the initial system control input at time k,

[0024] J i represents the ith Jordan block, where l represents the number of Jordan blocks, represents the multiple row vectors corresponding to J i corresponding to the multiple row vectors, represents the multiple column vectors corresponding to J i corresponding to the multiple column vectors, 1 ≤ i ≤ l < n, where n represents a positive integer.

[0025] Preferably, constructing the candidate matrix according to the system model under the new linear space, the system matrix under the new space, the input matrix under the new space, the output matrix under the new space, and the Jordan blocks includes:

[0026] Combining the multiple row vectors of the input matrix under the new space corresponding to the ith Jordan block J i and the multiple column vectors of the output matrix under the new space corresponding to the ith Jordan block J to obtain the candidate matrix, which is as follows: i to obtain the candidate matrix, which is as follows: to obtain the candidate matrix, which is as follows:

[0027]

[0028] Wherein, M represents the candidate matrix, represents the multiple row vectors corresponding to J i corresponding to the multiple row vectors, represents the multiple column vectors corresponding to J i corresponding to the multiple column vectors, J i represents the ith Jordan block, denote the γ-th row vector in denote the γ-th column vector in, where γ represents the dimension of J, l represents the number of Jordan blocks, 1 ≤ i ≤ l < n, and n represents a positive integer i and 1 ≤ i ≤ l < n, where n represents a positive integer denote the transpose of

[0029] Preferably, determining the norm of each row vector included in the key matrix, re - arranging according to the ascending order of the norms to obtain the optimal attack matrix, and setting the first k rows of the optimal attack matrix to zero to obtain the tampered optimal attack matrix specifically includes:

[0030] Determine the norm of each row vector included in the key matrix, and sort according to the magnitude of the norms in ascending order. The matrix obtained after sorting is the optimal attack matrix;

[0031] Set all the first k rows included in the optimal attack matrix to zero to obtain the tampered optimal attack matrix, where the number of rows and columns of the optimal attack matrix is equal to the number of rows and columns of the tampered optimal matrix respectively.

[0032] Preferably, the input matrix in the judgment space is transformed to obtain the tampered input matrix, and the output matrix in the judgment space is transformed to obtain the tampered output matrix, specifically as follows:

[0033]

[0034] Obtaining the tampering parameter of the input matrix according to the relationship between the tampered input matrix and the initial input matrix, and obtaining the tampering parameter of the output matrix according to the relationship between the tampered output matrix and the initial output matrix, specifically as follows:

[0035]

[0036] where B′ represents the tampered input matrix, C′ represents the tampered output matrix, B represents the initial input matrix, C represents the initial output matrix, ΔB represents the tampering parameter of the input matrix, and ΔC represents the tampering parameter of the output matrix represents the input matrix in the judgment space represents the output matrix in the judgment space, Q represents the invertible transformation matrix of the initial system matrix, and Q -1 represents the inverse matrix of matrix Q

[0037] An embodiment of the present invention provides an attack device for an unmanned aerial vehicle flight control system, including:

[0038] An establishing unit, configured to receive an attack instruction, obtain internal parameters of a target UAV flight control system according to the attack instruction, and establish an initial system model of the target UAV flight control system according to the internal parameters, wherein the internal parameters include an initial system matrix, an initial input matrix, and an initial output matrix;

[0039] A construction unit is used to obtain a system model in a new linear space including a Jordan block according to the initial system model and the initial system matrix subjected to Jordan standard modification, and to construct a candidate matrix according to the system model in the new linear space, the system matrix in the new space, the input matrix in the new space, the output matrix in the new space and the Jordan block;

[0040] The first obtaining unit is used to combine the key row vector and the key column vector of the candidate matrix to obtain a key matrix according to the PBH rank criterion, determine the norm of each row vector included in the key matrix, rearrange the norms in ascending order to obtain an optimal attack matrix, set the first k rows of the optimal attack matrix to zero, and obtain the tampered optimal attack matrix; wherein k represents a positive integer, and k is less than the number of rows of the optimal attack matrix;

[0041] The second obtaining unit is used to return the tampered optimal attack matrix to the input matrix in the new space and the output matrix in the new space, to obtain the input matrix in the judgment space and the output matrix in the judgment space, wherein the input matrix in the judgment space is transformed to obtain the tampered input matrix, and the output matrix in the judgment space is transformed to obtain the tampered output matrix;

[0042] The tampering unit is used to obtain the tampering parameters of the input matrix according to the relationship between the tampered input matrix and the initial input matrix, obtain the tampering parameters of the output matrix according to the relationship between the tampered output matrix and the initial output matrix, and tamper with the internal parameters of the flight control system of the target UAV according to the tampering parameters of the input matrix and the tampering parameters of the output matrix.

[0043] An embodiment of the present invention provides a computer device, which includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes any one of the above-mentioned methods for attacking a drone flight control system.

[0044] An embodiment of the present invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the processor executes any one of the above-mentioned methods for attacking a drone flight control system.

[0045] An embodiment of the present invention provides a method and device for attacking a drone flight control system, the method comprising: receiving an attack instruction, obtaining internal parameters of a target drone flight control system according to the attack instruction, establishing an initial system model of the target drone flight control system according to the internal parameters, wherein the internal parameters include an initial system matrix, an initial input matrix, and an initial output matrix; obtaining a system model in a new linear space including a Jordan block according to the initial system model and the initial system matrix subjected to Jordan standard modification, and constructing a candidate matrix according to the system model in the new linear space, the system matrix in the new space, the input matrix in the new space, the output matrix in the new space, and the Jordan block; combining key row vectors and key column vectors of the candidate matrix according to the PBH rank criterion to obtain a key matrix, determining the norm of each row vector included in the key matrix, and rearranging the norms in ascending order to obtain the optimal matrix. An optimal attack matrix is ​​obtained, and the first k rows of the optimal attack matrix are set to zero to obtain the tampered optimal attack matrix; wherein k represents a positive integer, and k is less than the number of rows of the optimal attack matrix; the tampered optimal attack matrix is ​​returned to the input matrix in the new space and the output matrix in the new space to obtain the input matrix in the judgment space and the output matrix in the judgment space, and the input matrix in the judgment space is transformed to obtain the tampered input matrix, and the output matrix in the judgment space is transformed to obtain the tampered output matrix; according to the relationship between the tampered input matrix and the initial input matrix, the tampered parameters of the input matrix are obtained, and according to the relationship between the tampered output matrix and the initial output matrix, the tampered parameters of the output matrix are obtained, and according to the tampered parameters of the input matrix and the tampered parameters of the output matrix, the internal parameters of the flight control system of the target UAV are tampered. This method is completely independent of specific models and can be more widely applied to real-world scenarios of various control systems, improving the flexibility and versatility of attackers' system attacks. Furthermore, this method will basically not produce unnecessary tampering of input and output matrices. Since the generated attack matrix is ​​less different from the original matrix, the attack intention is more difficult to detect, thereby greatly improving the success rate of the attack. Finally, this method can help strengthen the defense strategy of the target UAV flight control system, provide additional protection and monitoring for the key positions of the UAV flight control system, and prevent attackers from causing various accidents. This method solves the problem that the current countermeasures in the field of UAV countermeasures are single and lack of specificity, resulting in poor attack effects and inability to accurately interfere with the target UAV. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0047] Figure 1 A schematic diagram of a flow chart of a method for attacking a UAV flight control system provided by an embodiment of the present invention;

[0048] Figure 2 A schematic diagram of the structure of an attack device of a UAV flight control system provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0049] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0050] Terms used in this manual:

[0051] 1) Controlled object: refers to the physical entity or process whose behavior and state are affected by the control in the control system. For example, in a temperature control system, the heating furnace that needs to control the temperature is the controlled object; in an automated production line, the machinery and equipment, product components, etc. operated and monitored by automated equipment are also controlled objects. Its characteristics include observability and controllability.

[0052] 2) Random discrete LTI (Linear Time-Invariant System) system: A discrete system is a system whose input and output signals are discrete in time. This discreteness is usually obtained by sampling a continuous signal.

[0053] 3) Identity Matrix is ​​a special square matrix. For an n*n square matrix, if all elements on its main diagonal are 1 and all other elements are 0, then this matrix is ​​the identity matrix.

[0054] 4) The PBH rank criterion (Popov-Belevitch-Hautus Rank Criterion) is an important tool in modern control theory for judging the controllability and observability of LTI systems. Controllability refers to whether the control input of the system can transfer the state of the system from any initial state to any desired state within a finite time; observability refers to whether the state of the system can be determined by observing the output of the system.

[0055] Figure 1 A schematic diagram of a method for attacking a UAV flight control system provided by an embodiment of the present invention is shown below. Figure 1 Taking this as an example, a method for attacking a UAV flight control system provided by an embodiment of the present invention is introduced.

[0056] like Figure 1 As shown, the method comprises the following steps:

[0057] Step 101, receiving an attack instruction, obtaining internal parameters of a target UAV flight control system according to the attack instruction, and establishing an initial system model of the target UAV flight control system according to the internal parameters, wherein the internal parameters include an initial system matrix, an initial input matrix, and an initial output matrix;

[0058] Step 102, based on the initial system model and the initial system matrix subjected to Jordan standard modification, obtain the system model in the new linear space including the Jordan block, and construct a candidate matrix based on the system model in the new linear space, the system matrix in the new space, the input matrix in the new space, the output matrix in the new space and the Jordan block.

[0059] Step 103, according to the PBH rank criterion, the key row vector and the key column vector of the candidate matrix are combined to obtain a key matrix, the norm of each row vector included in the key matrix is ​​determined, and the optimal attack matrix is ​​obtained by rearranging the vectors in ascending order according to the norm, and the first k rows of the optimal attack matrix are set to zero to obtain the tampered optimal attack matrix; wherein k represents a positive integer, and k is less than the number of rows of the optimal attack matrix;

[0060] Step 104, returning the tampered optimal attack matrix to the input matrix in the new space and the output matrix in the new space, obtaining the input matrix in the judgment space and the output matrix in the judgment space, wherein the input matrix in the judgment space is transformed to obtain the tampered input matrix, and the output matrix in the judgment space is transformed to obtain the tampered output matrix;

[0061] Step 105, obtaining the tampered parameters of the input matrix according to the relationship between the tampered input matrix and the initial input matrix, obtaining the tampered parameters of the output matrix according to the relationship between the tampered output matrix and the initial output matrix, and tampering the internal parameters of the flight control system of the target UAV according to the tampered parameters of the input matrix and the tampered parameters of the output matrix.

[0062] It should be noted that the executor of the embodiment of the present invention is an attacker, and the attacker may be another drone (task drone) relative to the target drone, or a robot, and the specific type of the attacker is not limited here.

[0063] In step 101, since each attacker performing a task exchanges signals with the control center, in this embodiment, when the attacker receives a control instruction sent by the control center, the attacker can obtain the internal parameters of the target UAV flight control system according to the control instruction. Here, there is no limitation on how the attacker obtains the internal parameters of the target UAV flight control system.

[0064] Furthermore, considering that the controlled object is a random discrete LTI system, the initial system model of the target UAV flight control system can be established according to the initial system matrix, initial input matrix and initial output matrix included in the internal parameters, as shown below:

[0065]

[0066] Among them, x k represents the initial system state at time k, u k represents the initial system control input at time k, y k represents the system measurement output at time k, A represents the initial system matrix, B represents the initial input matrix, C represents the initial output matrix, and x k+1 represents the initial system state at time k+1, x k ∈R n ,u k ∈R p ,y k ∈R q , R n represents n-dimensional real vector space, R p represents a p-dimensional real vector space, R q represents a q-dimensional real vector space.

[0067] In practical applications, if the flight control system of the target UAV is attacked, the attack model of the flight control system of the target UAV can be obtained according to the system state after the attack and the control input after the attack as shown below:

[0068]

[0069] Among them, x ′ k represents the system state after being attacked at time k, x ′ k represents the control input after being attacked at time k, y ′ k+1 represents the measured output after being attacked at time k+1, x ′ k+1 represents the system state after being attacked at time k+1, B ′ represents the tampered input matrix, C ′ represents the tampered output matrix, u ′ k Represents the system control input after being attacked at time k.

[0070] It should be noted that in actual applications, for the control execution module of the target UAV flight control system, B represents the structure and parameters of the actuator network; for the state observation module of the target UAV flight control system, C represents the structure and parameters of the sensor network; when the target UAV flight control system is damaged, the attacker may invade the actuator network to manipulate the controllability of the system, turning the controllable state into an uncontrollable state, and at the same time invade the sensor network to manipulate the observability of the system, turning the above uncontrollable but observable state into an unobservable state. In actual applications, the attacker's attack is an attack in the physical domain, which is a physical attack directly on the actuator network and sensor network of the target UAV, which can be expressed by the following formula:

[0071]

[0072] Where B represents the structure and parameters of the actuator network, C represents the structure and parameters of the sensor network, ΔB represents the perturbation matrix designed for the actuator network, ΔC represents the perturbation matrix designed for the sensor network, and B ′ represents the tampered input matrix, C ′ Represents the tampered output matrix. However, for the method provided in the embodiment of the present invention, the parameters B and C in formula (2) are respectively expressed as the initial input matrix and the initial output matrix. Accordingly, ΔB represents the tampered parameter of the input matrix, and ΔC represents the tampered parameter of the output matrix. When formula (2) is respectively for theoretical and practical applications, the expression forms of its parameters B and C are inconsistent. Accordingly, the expression forms of parameters ΔB and ΔC are also inconsistent. In the embodiment of the present invention, the expression forms of parameters B, C, ΔB and ΔC in formula (2) are not specifically limited. The expressions of parameters B, C, ΔB and ΔC can be determined according to the specific application scenario.

[0073] In step 102, the initial system matrix is ​​first subjected to Jordan standard transformation. The initial system matrix is ​​subjected to Jordan standard transformation by the following formula:

[0074]

[0075] Wherein, Q represents the reversible transformation matrix of the initial system matrix. In the embodiment of the present invention, formula (3) is combined with formula (1-1), and Q is multiplied on the left. -1 , Q -1 Representing the inverse matrix of matrix Q, we can get the following formula:

[0076]

[0077] Further, let Formula (4) can be transformed to obtain the system model in the new linear space as shown below:

[0078]

[0079] In the above formula, represents the system matrix in the new space, represents the input matrix in the new space, represents the output matrix in the new space. Specifically, the system matrix in the new space The input matrix in the new space And the output matrix in the new space As shown below:

[0080]

[0081] In the embodiment of the present invention, after formula (5), formula (6-1), formula (6-2) and formula (6-3) are sorted out, a system model in a new linear space including the Jordan block is obtained, which is specifically as follows:

[0082]

[0083] in, represents the system state at time k in the new linear space, represents the system state at time k+1 in the new linear space, y k represents the system measurement output at time k in the new linear space, represents the system matrix in the new space, represents the input matrix in the new space, represents the output matrix in the new space, l represents the number of Jordan blocks, J i represents the i-th Jordan block, Indicates that J i Corresponding A plurality of row vectors, representing those corresponding to J i corresponding a plurality of column vectors, 1 ≤ i ≤ l < n, where n represents a positive integer.

[0084] In step 103, based on the input matrix in the new linear space and the output matrix in the new linear space, the expression of the Jordan block, the expressions of a plurality of row vectors of the input matrix in the new space corresponding to the Jordan block, and the expressions of a plurality of column vectors of the output matrix in the new space corresponding to the Jordan block can be obtained from two formulas.

[0085] Among them, the i-th Jordan block J i can be expressed by the following formula:

[0086]

[0087] Among them, the plurality of row vectors of the input matrix in the new space corresponding to the i-th Jordan block J i can also be referred to as the plurality of row vectors corresponding to J corresponding i corresponding and are expressed by the following formula:

[0088]

[0089] Among them, the plurality of column vectors of the output matrix in the new space corresponding to the i-th Jordan block J i can also be referred to as the plurality of row vectors corresponding to J corresponding i corresponding and are expressed by the following formula:

[0090]

[0091] In the above formulas, represents the γ-th row vector in represents the γ-th column vector in i where γ represents the dimension of J.

[0092] It should be noted that in the embodiments of the present invention, the plurality of row vectors of the input matrix in the new space corresponding to the i-th Jordan block J i and the plurality of column vectors of the output matrix in the new space corresponding to the i-th Jordan block J are combined to obtain a candidate matrix, which can be expressed as: i corresponding and is:

[0093]

[0094] Among them, M represents the candidate matrix, denotes the γ-th row vector in denotes the γ-th column vector in denotes the multiple row vectors corresponding to J i corresponding thereof, denotes the multiple column vectors corresponding to J i corresponding thereof, denotes the transpose of denotes the input matrix in the new space, denotes the output matrix in the new space, γ represents the dimension of J i thereof.

[0095] In practical applications, the necessary and sufficient condition for a linear time-invariant continuous system to be completely controllable and completely observable is that all the eigenvalues λ i of the initial system matrix need to satisfy the following formula:

[0096] K c = rank[λ i I - A B] = n (11)

[0097]

[0098] Among them, K c represents the controllability matrix, K o represents the observability matrix, I represents the identity matrix, n represents the n-dimensional real vector space, referring to the dimension of the original system space, λ i represents the eigenvalue of the initial system matrix, 1 ≤ i ≤ l < n, n represents a positive integer.

[0099] In the embodiment of the present invention, a PBH rank criterion in the judgment space is established. Assume that the system matrix in the judgment space is the input matrix in the judgment space is the output matrix in the judgment space is which are respectively shown as follows:

[0100]

[0101] Furthermore, based on the system matrix the input matrix the output matrix in the judgment space, formula (11) and formula (12), the PBH rank criterion in the judgment space can be obtained, which are respectively:

[0102]

[0103]

[0104] In the embodiment of the present invention, when the linear steady-state continuous system is fully controllable and fully observable, all eigenvalues ​​λ of the initial system matrix i It needs to comply with the above formula (14) and formula (15), that is, according to the PBH rank criterion, the i-th Jordan block J i The last row in the table can affect the controllability of the system. The i-th Jordan block J i The first column can affect the observability of the system. In the embodiment of the present invention, the i-th Jordan block J i The last line in The last row in is determined as the key row vector, and the i-th Jordan block J i The first column is The first column in is determined as the key column vector, and then The last line and By combining the first column in , we can get the key matrix as shown below:

[0105]

[0106] in, represents the key matrix, express The corresponding key row vector in is, express The corresponding key column vector in . In practical applications, The last line in Can affect the controllability of the system, The first column corresponds to Can affect the observability of the system.

[0107] Furthermore, in the key matrix shown in formula (16), the key row vector and the key column vector As shown below:

[0108]

[0109] in, Represents the key row vector The lth row vector in Represents the key column vector The lth column vector in .

[0110] In practical applications, the attack can be carried out by simply tampering with the key row vectors and key column vectors included in the candidate matrix to obtain the optimal attack matrix.

[0111] Specifically, the l2 norm of each row vector included in the key matrix is ​​determined, and the row vectors of the key matrix are reordered from small to large according to the norm. The reordered matrix obtained is the optimal attack matrix Furthermore, to achieve controllable and observable attacks, we only need to transform the optimal attack matrix The first k rows of are set to zero. In practical applications, the size of k depends on the strength of the required attack, that is, the degree of controllability and observability of the tampered data. Therefore, the optimal attack matrix is The matrix obtained after setting the first k rows to zero is called the optimal attack matrix after tampering

[0112] It should be noted that, in practical applications, the structural size of the optimal attack matrix and the tampered optimal attack matrix is ​​consistent with the structural size of the key matrix.

[0113] In the embodiment of the present invention, the input matrix in the new space shown in formula (6-2) is Included in Represents the i-th Jordan block J i The corresponding input matrix in the new space Multiple row vectors of The expression is formula (9-1); further, the formula (9-1) is related to the i-th Jordan block J i The corresponding input matrix in the new space Multiple row vectors of Included in express Further, extract all the γth row vectors in formula (6-2) The last line of Construct the key matrix, that is, obtain the key row vector in the key matrix shown in formula (17-1) Represents the key row vector The lth row vector in . Accordingly, the output matrix in the new space shown in formula (6-3) is Included in Represents the i-th Jordan block J i The output matrix corresponding to the new space Multiple column vectors of The expression is formula (9-2); further, the formula (9-2) is related to the i-th Jordan block J i The output matrix corresponding to the new space Multiple column vectors of Included in express Further, extract all the γth column vectors in formula (6-3) The first column Construct the key matrix, that is, obtain the key column vector in the key matrix shown in formula (17-2) Represents the key column vector The lth column vector in .

[0114] In the embodiment of the present invention, since the structure size of the optimal attack matrix after tampering is consistent with the structure size of the key matrix, the candidate matrix includes The last line and The key matrix is ​​obtained by combining the first column in . Therefore, after obtaining the tampered optimal matrix, the tampered optimal matrix can be returned to the input matrix in the new space shown in formula (6-2) and formula (6-3) And the output matrix in the new space Since the size of the modified optimal matrix is ​​the same as the size of the key matrix, the row vector corresponding to the modified optimal matrix is ​​returned to the input matrix in the new space When , the corresponding row vector position is all the The last line of The input matrix in the new space The contents of the other rows of remain unchanged; the column vector corresponding to the modified optimal attack matrix is ​​returned to the output matrix in the new space When , the corresponding column vector position is all the The first column The output matrix in the new space The contents of the other columns remain unchanged.

[0115] Furthermore, the input matrix in the new space modified by the tampered optimal attack matrix and the output matrix in the new space execute the above process again, that is, formula (6-2) and formula (6-3) are reconstructed into the candidate matrix shown in formula (10) after formula (7). The candidate matrix is ​​obtained according to the PBH rank criterion, and the input matrix in the judgment space shown in formula (13-2) and formula (13-3) is obtained. And the output matrix in the judgment space

[0116] In practical applications, considering that the controllability and observability of the system remain unchanged under linear transformation, the input matrix in the judgment space And the output matrix in the judgment space The tampered input matrix and the tampered output matrix are obtained by Q transformation and Q inverse transformation respectively, as shown below:

[0117]

[0118]

[0119] Among them, B ′ represents the tampered input matrix, C ′ represents the tampered output matrix, B represents the initial input matrix, and C represents the initial output matrix.

[0120] In the embodiment of the present invention, according to formula (2), if the tampered input matrix B′, the tampered output matrix C′, the initial input matrix B and the initial output matrix C are known, the tampering parameter ΔB of the input matrix and the tampering parameter ΔC of the output matrix can be obtained.

[0121] Furthermore, according to the determined tampering parameter ΔB of the input matrix and the tampering parameter ΔC of the output matrix, the internal parameters of the flight control system of the target UAV can be tampered with, thereby obtaining an uncontrollable and unobservable system.

[0122] In order to more clearly introduce the drone flight control system attack method provided by the embodiment of the present invention, the method is introduced below with a specific embodiment.

[0123] Specifically, the embodiment includes the following steps:

[0124] Step 201, according to the attack instruction, the internal parameters of the target UAV flight control system are obtained, and the initial system model of the target UAV flight control system is established according to the internal parameters, wherein the initial system matrix, initial input matrix and initial output matrix included in the initial system model are as follows:

[0125]

[0126] Among them, A represents the initial system matrix, B represents the initial input matrix, and C represents the initial output matrix.

[0127] Step 202: Further, the initial system matrix A is subjected to Jordan standard transformation to obtain the system matrix and Jordan variation matrix in the new space, as shown below:

[0128]

[0129]

[0130] Among them, Q represents the reversible transformation matrix of the initial system matrix A, represents the system matrix in the new space.

[0131] Further, combine formula (3) with formula (1-1) and multiply Q by-1 , Q -1 Representing the inverse matrix of matrix Q, we can get formula (4).

[0132] Step 203, change the Q of the whole system, and make The following expression can be obtained:

[0133]

[0134] in, represents the input matrix in the new space, represents the output matrix in the new space, B represents the initial input matrix, and C represents the initial output matrix.

[0135] Furthermore, another expression of the system model in the new linear space including the Jordan block can be obtained, which is shown in formula (7).

[0136] Furthermore, according to the input matrix in the new space And the output matrix in the new space The expression of the Jordan block as described in formula (8) and the input matrix in the new space corresponding to the Jordan block as shown in formula (9-1) can be obtained: Multiple row vector expressions of And the output matrix in the new space corresponding to the Jordan block as described in formula (9-2) Multiple column vector expressions of

[0137] Furthermore, the i-th Jordan block J i The corresponding input matrix in the new space Multiple row vector expressions The i-th Jordan block J i The output matrix corresponding to the new space Multiple column vector expressions of Combine them and get the candidate matrix as shown below:

[0138]

[0139] Furthermore, according to the PBH rank criterion in the judgment space, the i-th Jordan block J i The last row in the table can affect the controllability of the system. The i-th Jordan block J i The first column can affect the observability of the system. i The last line in The last row in is determined as the key row vector, and the i-th Jordan block J i The first column is The first column in is determined as the key column vector, and then The last line and By combining the first column in , we can get the key matrix, that is,

[0140] Step 204, consider the attack requirements, reduce the controllability and observability of the original system, and calculate the key matrix The l2 norm of each row vector in and the key matrix By reordering the row vectors of according to the norm from small to large, we can get the optimal attack matrix as shown below:

[0141]

[0142] In practical applications, let the optimal attack matrix The first row of is set to 0, which can realize controllable and observable attack, that is, the optimal attack matrix after tampering is obtained The details are as follows:

[0143]

[0144] Will Returns the input matrix in the new space And the output matrix in the new space The input matrix in the new space and the output matrix in the new space can be obtained according to the method provided in the above embodiment, and the input matrix in the judgment space is as follows: And the output matrix in the judgment space is

[0145]

[0146]

[0147] Step 205: The input matrix in the judgment space is And the output matrix in the judgment space is After the inverse change of Q change, the tampered input matrix B' and the tampered output matrix C' are obtained, as shown below:

[0148]

[0149] Where A represents the initial system matrix, represents the input matrix in the judgment space, The output matrix in the judgment space is: B′ represents the tampered input matrix, C′ represents the tampered output matrix, Q represents the reversible transformation matrix of the initial system matrix A, Q -1 Represents the inverse matrix of matrix Q.

[0150] Furthermore, after obtaining the tampered input matrix and the tampered output matrix, the tampered parameters of the input matrix and the tampered parameters of the output matrix can be obtained according to the above formula (2), as shown below:

[0151]

[0152] In this embodiment, after obtaining the tampered parameters of the input matrix and the tampered parameters of the output matrix, the attacker's final attack method is determined. The attacker tampered with the internal parameters of the target UAV flight control system according to the tampered parameters of the input matrix and the tampered parameters of the output matrix, thereby obtaining an uncontrollable and unobservable system.

[0153] In summary, the embodiment of the present invention provides a method and device for attacking a UAV flight control system. The method is completely independent of a specific model and can be more widely applied to real-life scenarios of various control systems, thereby improving the flexibility and versatility of the attacker's system attack. Furthermore, the method basically does not produce unnecessary tampering of the input matrix and the output matrix. Since the generated attack matrix is ​​less different from the original matrix, the attack intention is more difficult to detect, thereby greatly improving the success rate of the attack. Finally, the method can help strengthen the defense strategy of the target UAV flight control system, provide additional protection and monitoring for the key positions of the target UAV flight control system, and prevent the attacker from causing various accidents. The method solves the problem that the current countermeasures in the field of UAV countermeasures are single and lack of pertinence, resulting in poor attack effects and inability to accurately interfere with the target UAV.

[0154] With the same inventive concept, an embodiment of the present invention provides a device for attacking a UAV flight control system. Since the principle of solving the technical problem of the device is similar to that of a method for attacking a UAV flight control system, the implementation of the device can refer to the implementation of the method, and the repeated parts will not be repeated.

[0155] Figure 2 A schematic diagram of the structure of an attack device of a UAV flight control system provided by an embodiment of the present invention is shown in FIG. Figure 2 As shown, the device includes: an establishing unit 201, a constructing unit 202, a first obtaining unit 203, a second obtaining unit 204 and a tampering unit 205.

[0156] An establishing unit 201 is used to receive an attack instruction, obtain internal parameters of a target UAV flight control system according to the attack instruction, and establish an initial system model of the target UAV flight control system according to the internal parameters, wherein the internal parameters include an initial system matrix, an initial input matrix, and an initial output matrix;

[0157] A construction unit 202 is used to obtain a system model in a new linear space including a Jordan block according to the initial system model and the initial system matrix subjected to Jordan standard modification, and to construct a candidate matrix according to the system model in the new linear space, the system matrix in the new space, the input matrix in the new space, the output matrix in the new space and the Jordan block;

[0158] The first obtaining unit 203 is used to combine the key row vector and the key column vector of the candidate matrix to obtain a key matrix according to the PBH rank criterion, determine the norm of each row vector included in the key matrix, rearrange the norms in ascending order to obtain an optimal attack matrix, set the first k rows of the optimal attack matrix to zero, and obtain the tampered optimal attack matrix; wherein k represents a positive integer, and k is less than the number of rows of the optimal attack matrix;

[0159] The second obtaining unit 204 is used to return the tampered optimal attack matrix to the input matrix in the new space and the output matrix in the new space, to obtain the input matrix in the judgment space and the output matrix in the judgment space, wherein the input matrix in the judgment space is transformed to obtain the tampered input matrix, and the output matrix in the judgment space is transformed to obtain the tampered output matrix;

[0160] The tampering unit 205 is used to obtain the tampering parameters of the input matrix according to the relationship between the tampered input matrix and the initial input matrix, obtain the tampering parameters of the output matrix according to the relationship between the tampered output matrix and the initial output matrix, and tamper with the internal parameters of the target UAV flight control system according to the tampering parameters of the input matrix and the tampering parameters of the output matrix.

[0161] It should be understood that the units included in the above drone flight control system attack device are only logical divisions based on the functions implemented by the device. In actual applications, the above units can be superimposed or split. In addition, the functions implemented by the drone flight control system attack device provided in this embodiment correspond to the drone flight control system attack method provided in the above embodiment. The more detailed processing flow implemented by the device has been described in detail in the above method embodiment 1 and will not be described in detail here.

[0162] Another embodiment of the present invention also provides a computer device, which includes: a processor and a memory; the memory is used to store computer program code, and the computer program code includes computer instructions; when the processor executes the computer instructions, the electronic device executes each step of a method for attacking a drone flight control system in the method flow described in the above method embodiment.

[0163] Another embodiment of the present invention further provides a computer-readable storage medium, which stores computer instructions. When the computer instructions are executed on a computer device, the computer device executes each step of a method for attacking a drone flight control system in the method flow described in the above method embodiment.

[0164] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0165] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A method for attacking a UAV flight control system, characterized in that: include: An attack instruction is received, internal parameters of a flight control system of a target UAV are obtained according to the attack instruction, and an initial system model of the flight control system of the target UAV is established according to the internal parameters, wherein the internal parameters include an initial system matrix, an initial input matrix, and an initial output matrix; According to the initial system model and the initial system matrix subjected to Jordan standard modification, a system model in a new linear space including a Jordan block is obtained, and a candidate matrix is ​​constructed according to the system model in the new linear space, the system matrix in the new space, the input matrix in the new space, the output matrix in the new space and the Jordan block; According to the PBH rank criterion, the key row vector and the key column vector of the candidate matrix are combined to obtain a key matrix, the norm of each row vector included in the key matrix is ​​determined, and the optimal attack matrix is ​​obtained by rearranging the vectors in ascending order according to the norms, and the first k rows of the optimal attack matrix are set to zero to obtain the tampered optimal attack matrix; wherein k represents a positive integer, and k is less than the number of rows of the optimal attack matrix; Returning the tampered optimal attack matrix to the input matrix in the new space and the output matrix in the new space, obtaining the input matrix in the judgment space and the output matrix in the judgment space, wherein the input matrix in the judgment space is transformed to obtain the tampered input matrix, and the output matrix in the judgment space is transformed to obtain the tampered output matrix; According to the relationship between the tampered input matrix and the initial input matrix, the tampered parameters of the input matrix are obtained; according to the relationship between the tampered output matrix and the initial output matrix, the tampered parameters of the output matrix are obtained; according to the tampered parameters of the input matrix and the tampered parameters of the output matrix, the internal parameters of the target UAV flight control system are tampered.

2. The method according to claim 1, characterized in that The step of combining the key row vector and the key column vector of the candidate matrix according to the PBH rank criterion to obtain a key matrix specifically includes: According to the PBH rank criterion, determine the i-th Jordan block J i The last row in the table affects the controllability of the UAV flight control system. The i-th Jordan block J i The first column affects the observability of the UAV flight control system, and the i-th Jordan block J i The last row in is determined as the key row vector, and the i-th Jordan block J i The first column is determined as a key column vector, and the key row vector and the key column vector are combined to obtain a key matrix; The key matrix is ​​as follows: Among them, represents the key matrix, represents the corresponding key row vector in represents the multiple row vectors corresponding to J i corresponding to the multiple row vectors, represents the corresponding key column vector in represents the multiple column vectors corresponding to J i corresponding to the multiple column vectors, J i represents the i-th Jordan block, represents the input matrix in the new space, represents the output matrix in the new space, represents the l-th row vector in the key row vector in represents the l-th column vector in the key column vector in, γ represents the dimension of J i l represents the number of Jordan blocks, 1 ≤ l < n, and n represents a positive integer.

3. The method according to claim 1, characterized in that The PBH rank criterion is as follows: Among them, K c represents the controllability matrix, K o represents the observability matrix, I represents the identity matrix, represents the system matrix under the judgment space, represents the input matrix under the judgment space, represents the output matrix under the judgment space, λ i represents the eigenvalue of the initial system matrix, 1 ≤ i ≤ l < n, n represents a positive integer, i represents the serial number of the Jordan block, s represents the complex variable, and λ l represents the lth eigenvalue of the initial system matrix, Represents the input matrix in the judgment space The row vector consisting of all elements in the nth row of , Represents the output matrix in the judgment space The column vector consisting of all elements in the nth column of , where l represents the number of Jordan blocks.

4. The method according to claim 1, characterized in that The system model under the new linear space including the Jordan block is as follows: in, represents the system state at time k in the new linear space, represents the system state at time k+1 in the new linear space, y k represents the system measurement output at time k in the new linear space, represents the system matrix in the new space, represents the input matrix in the new space, represents the output matrix in the new space, u k represents the initial system control input at time k, J i represents the \(i\)-th Jordan block, \(l\) represents the number of Jordan blocks, represents the i corresponding multiple row vectors, represents the i corresponding multiple column vectors, \(1\leq i\leq l < n\), \(n\) represents a positive integer.

5. The method according to claim 1, characterized in that The step of constructing a candidate matrix according to the system model in the new linear space, the system matrix in the new space, the input matrix in the new space, the output matrix in the new space and the Jordan block includes: will be combined with the i-th Jordan block J i The corresponding input matrix in the new space Multiple row vectors of the i-th Jordan block J i The output matrix corresponding to the new space The candidate matrix is ​​obtained by combining multiple column vectors of , which is shown as follows: Among them, M represents the candidate matrix, represents the multiple row vectors corresponding to J i corresponding to represents the multiple column vectors corresponding to J i corresponding to, J i represents the i-th Jordan block, represents the γ-th row vector in represents the γ-th column vector in, γ represents the dimension of J i where l represents the number of Jordan blocks, 1 ≤ i ≤ l < n, and n represents a positive integer, represents the transpose of.

6. The method according to claim 1, characterized in that The determining of the norm of each row vector included in the key matrix, rearranging the norms in ascending order to obtain an optimal attack matrix, setting the first k rows of the optimal attack matrix to zero, and obtaining the tampered optimal attack matrix specifically includes: Determine the norm of each row vector included in the key matrix, and sort them in ascending order according to the size of the norm, and the matrix obtained after sorting is the optimal attack matrix; The first k rows of the optimal attack matrix are all set to zero to obtain a tampered optimal attack matrix, wherein the number of rows and the number of columns of the optimal attack matrix are respectively equal to the number of rows and the number of columns of the tampered optimal matrix.

7. The method according to claim 1, characterized in that The input matrix in the judgment space is transformed to obtain a tampered input matrix, and the output matrix in the judgment space is transformed to obtain a tampered output matrix, which is specifically shown as follows: The tampering parameters of the input matrix are obtained according to the relationship between the tampered input matrix and the initial input matrix, and the tampering parameters of the output matrix are obtained according to the relationship between the tampered output matrix and the initial output matrix, as shown below: Among them, B′ represents the tampered input matrix, C′ represents the tampered output matrix, B represents the initial input matrix, C represents the initial output matrix, ΔB represents the tampered parameter of the input matrix, ΔC represents the tampered parameter of the output matrix, represents the input matrix in the judgment space, represents the output matrix in the judgment space, Q represents the reversible transformation matrix of the initial system matrix, Q -1 Represents the inverse matrix of matrix Q.

8. An attack device for a UAV flight control system, characterized in that: include: An establishing unit, configured to receive an attack instruction, obtain internal parameters of a target UAV flight control system according to the attack instruction, and establish an initial system model of the target UAV flight control system according to the internal parameters, wherein the internal parameters include an initial system matrix, an initial input matrix, and an initial output matrix; A construction unit is used to obtain a system model in a new linear space including a Jordan block according to the initial system model and the initial system matrix subjected to Jordan standard modification, and to construct a candidate matrix according to the system model in the new linear space, the system matrix in the new space, the input matrix in the new space, the output matrix in the new space and the Jordan block; The first obtaining unit is used to combine the key row vector and the key column vector of the candidate matrix to obtain a key matrix according to the PBH rank criterion, determine the norm of each row vector included in the key matrix, rearrange the norms in ascending order to obtain an optimal attack matrix, set the first k rows of the optimal attack matrix to zero, and obtain the tampered optimal attack matrix; wherein k represents a positive integer, and k is less than the number of rows of the optimal attack matrix; The second obtaining unit is used to return the tampered optimal attack matrix to the input matrix in the new space and the output matrix in the new space, to obtain the input matrix in the judgment space and the output matrix in the judgment space, wherein the input matrix in the judgment space is transformed to obtain the tampered input matrix, and the output matrix in the judgment space is transformed to obtain the tampered output matrix; The tampering unit is used to obtain the tampering parameters of the input matrix according to the relationship between the tampered input matrix and the initial input matrix, obtain the tampering parameters of the output matrix according to the relationship between the tampered output matrix and the initial output matrix, and tamper with the internal parameters of the flight control system of the target UAV according to the tampering parameters of the input matrix and the tampering parameters of the output matrix.

9. A computer device, characterized in that: The computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor executes a method for attacking a drone flight control system as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that: A computer program is stored, and when the computer program is executed by a processor, the processor executes a method for attacking a drone flight control system as described in any one of claims 1 to 7.

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