Distributed security control method for coordinated attack of drones with random switching topology

Abstract

The present invention discloses a distributed security control method for coordinated attack of drones with random switching topology, comprising the following steps: using graph theory technology and Markov random theory to establish a dynamic model of a drone swarm with random switching topology; based on actual attack scenarios, establishing a mathematical model of coordinated attack under complex constraints; based on the dynamic model of the drone swarm with random switching topology and the mathematical model of coordinated attack, constructing a distributed security consistency protocol in a limited time domain of drones; calculating and solving the gain of the security controller to be designed in the distributed security consistency protocol to achieve consistency control of the drone swarm. The present invention solves the problems that the existing drone system security control method is difficult to apply to the drone system model with time-varying parameters and communication topology switching, ignores the complex constraints in the actual attack scenario, and causes poor robustness and instability of the drone system.

Description

Technical Field

[0001] The present invention relates to the technical field of drone safety control, and in particular to a distributed safety control method for coordinated attack of drones with random switching topology. Background Art

[0002] As an important technical embodiment of artificial intelligence, drones play a very important role in national security, national economic construction, and national defense and military fields. With their advantages of low cost, easy deployment, high flexibility, and strong adaptability, drones have become an important support and strategic key point in application fields such as forest fire rescue, harmful gas leak detection, and earthquake search and rescue. It is worth noting that these applications are all based on ensuring system security, otherwise they will bring unpredictable harm to national construction and people's lives and property. In recent years, with the continuous expansion of the scale of drone swarms, the heterogeneity of nodes has become prominent, which has magnified the overall vulnerability of the system and made it extremely vulnerable to network security threats. Therefore, the research on drone safety issues has important practical significance and theoretical value.

[0003] Based on actual engineering application scenarios, the safety control method technology of UAV systems in complex communication network environments has the following shortcomings: First, the actual operating environment of UAVs is harsh, and the controlled parameters change in real time due to the influence of operating environment factors. In addition, it is worth noting that UAV equipment exposed to the actual operating environment cannot avoid network attacks, physical channel instability, limited communication distance and other constraints that cause random changes in network communication topology. However, the existing safety control methods are difficult to apply to UAV system models with time-varying parameters and communication topology switching. Second, most of the existing results focus on the research of safety control methods under a single attack mode in an ideal attack scenario, ignoring the many actual constraints for attackers to successfully implement attacks in actual attack scenarios, and also do not consider the difficulties brought to the design of safety control strategies by coordinated attacks with complex attack modes. Third, the existing research process for the safety control of UAV systems does not fully consider the impact of uncertain factors such as unknown external interference and random attacks on system performance, which leads to problems such as poor robustness and instability of the control system. Fourth, most of the existing safety control schemes are for infinite time domains, which are difficult to meet the actual needs of completing specific tasks within a certain period of time. Summary of the invention

[0004] In view of the above-mentioned defects, the present invention proposes a distributed security control method for coordinated attack of drones with random switching topology, aiming to solve the problems that the existing drone system security control methods are difficult to apply to drone system models with time-varying parameters and communication topology switching, ignore the complex constraints in actual attack scenarios, and cause poor robustness and instability of the drone system.

[0005] To achieve this object, the present invention adopts the following technical solutions:

[0006] The distributed security control method for coordinated attack of drones with random switching topology includes the following steps:

[0007] Step S1: Using graph theory and Markov random theory to establish a dynamic model of a drone swarm with random switching topology;

[0008] Step S2: Based on the actual attack scenario, a mathematical model of coordinated attack under complex constraints is established;

[0009] Step S3: Based on the dynamic model of the drone swarm with random switching topology and the mathematical model of coordinated attack, a distributed security consensus protocol within the limited time domain of drones is constructed;

[0010] Step S4: Calculate and solve the gain of the safety controller to be designed in the distributed safety consistency protocol to achieve consistent control of the drone swarm.

[0011] Preferably, step S1 specifically includes the following sub-steps:

[0012] Step S11: Calculate and obtain the kinematic model of each UAV in the UAV group. The kinematic model of each UAV is expressed as follows:

[0013]

[0014] Among them, x i (k) represents the state of the i-th UAV, x i The specific formula of (k) is as follows:

[0015] x i (k) = [p i (k), v i (k)],p i (k) represents the position vector of the i-th UAV; v i (k) represents the velocity vector of the i-th UAV;

[0016] u i (k) represents the control input vector of the i-th UAV; y i (k) represents the measurement output vector of the i-th UAV; w i (k) represents unknown and bounded external interference; A(k), B(k), C(k) and D(k) are all known time-varying parameter matrices;

[0017] Step S12: construct a random switching topology graph, and use the random switching topology graph to describe the communication interaction structure between the kinematic models of each UAV, so as to obtain a dynamic model of the UAV swarm with random switching topology;

[0018] The expression of random switching topology graph is as follows:

[0019]

[0020] in, Represents the random switching topology at time k; Represents the vertex set under the switching topology; Represents the edge set under the switching topology; represents the adjacency matrix between drone groups under the switching topology; w k represents the Markov chain at time k, w k The transition probability is as follows:

[0021] P{w k+1 =t|w k =s} =π st

[0022] Among them, π st represents the transition probability of the drone from state s at time k to state t at time k+1, π st >0.

[0023] Preferably, in step S2, the mathematical model of coordinated attack under complex constraints is expressed as follows:

[0024]

[0025] in, represents the measurement output vector of the i-th drone after being attacked; represents the control input vector of the i-th drone after being attacked; u i (k) represents the control input vector of the i-th UAV; y i (k) represents the measurement output vector of the i-th UAV; represents the attack vector injected by the attacker in the feedforward measurement channel; The attack vector injected by the attacker in the feedback control channel; α i (k) and β i (k) are all random variables that obey the Bernoulli distribution.

[0026] Preferably, in step S3, the expression of the distributed security consistency protocol within the limited time domain of the drone is as follows:

[0027]

[0028] in, represents the measurement output vector of the i-th drone after being attacked; represents the control input vector of the i-th drone after being attacked; represents the measurement output vector of the jth UAV after being attacked; represents the vertex set of the i-th UAV under the switching topology; K(k) represents the gain of the safety controller to be designed.

[0029] Preferably, in step S3, the following steps are also included:

[0030] By analyzing the distributed safety consistency protocol in the limited time domain of the UAV, the closed-loop system equation of the i-th UAV is obtained, where the expression of the closed-loop system equation of the i-th UAV is as follows:

[0031]

[0032] Among them, x i (k) represents the state of the i-th drone; and Both represent the time-varying parameter matrix of the UAV system after dimension expansion; The parameter matrix representing the attack vector suffered by the measurement channel after dimension expansion; Represents the parameter matrix of the attack vector of the feedback control channel after dimension expansion; a y (k) represents the attack vector suffered by the measurement channel after dimension expansion; a u (k) represents the attack vector on the feedback control channel after dimension expansion.

[0033] Preferably, in step S4, the following sub-steps are specifically included:

[0034] Given a scalar γ>0 and a positive definite symmetric matrix R, when the state of the UAV closed-loop system tends to be consistent in a finite time domain, if there exists a positive definite matrix {P k} k∈[0，T] , the matrix {G k} k∈[0，T] , the matrix Ω l and the safety controller gain K(k) to be designed, and the scalars π1>0 and π2>0 so that the following recursive linear matrix inequality holds;

[0035]

[0036] P0<γ 2 R;

[0037] Then the safety controller gain K(k) to be designed can be obtained by solving the following formula:

[0038]

[0039] Among them, G 1，k+1 represents a free matrix; represents the matrix to be calculated; Represents a matrix block in a matrix inequality; Represents a matrix block in a matrix inequality;

[0040] represents a matrix block in a matrix inequality,

[0041] Represents a matrix block The sub-blocks in

[0042]

[0043] Represents a matrix block The sub-blocks in

[0044] A'(k) represents the matrix sub-block A matrix element in ;

[0045]

[0046] Among them, I N Represents the N-dimensional identity matrix; represents the Kronecker product; q k+1 represents any matrix; o k+1 represents a non-singular matrix; represents the Laplace matrix; C(k) represents the time-varying parameter matrix;

[0047] Represents a matrix subblock A matrix element in ;

[0048]

[0049] in, represents the success probability matrix of the attack on the measurement channel;

[0050] Represents a matrix subblock A matrix element in ;

[0051]

[0052] Among them, H N Represents state x i (k) and its average state The relationship matrix between them; B(k) represents the time-varying parameter matrix;

[0053] D'(k) represents the matrix sub-block A matrix element in ;

[0054]

[0055] Represents a matrix subblock Matrix block elements in ;

[0056] Represents a matrix subblock The matrix block elements in .

[0057] The technical solution provided by the embodiments of the present application may have the following beneficial effects:

[0058] This scheme can describe the random switching of UAV swarm communication topology under the constraints of actual working environment factors by introducing graph theory technology and Markov random theory. By establishing a mathematical model of coordinated attack, the complex constraints in actual attack scenarios are fully considered. By solving the gain of the security controller, it is ensured that the state of the UAV swarm can be consistent within a limited time domain under random switching topology, coordinated attack and unknown external interference, which is conducive to the stability of the UAV system and improves the robustness of the UAV system. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a flow chart of the steps of a distributed security control method for coordinated attack of drones with random switching topology. DETAILED DESCRIPTION

[0060] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals represent the same or similar elements or elements having the same or similar functions from beginning to end. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.

[0061] The distributed security control method for coordinated attack of drones with random switching topology includes the following steps:

[0062] Step S1: Using graph theory and Markov random theory to establish a dynamic model of a drone swarm with random switching topology;

[0063] Step S2: Based on the actual attack scenario, a mathematical model of coordinated attack under complex constraints is established;

[0064] Step S3: Based on the dynamic model of the drone swarm with random switching topology and the mathematical model of coordinated attack, a distributed security consensus protocol within the limited time domain of drones is constructed;

[0065] Step S4: Calculate and solve the gain of the safety controller to be designed in the distributed safety consistency protocol to achieve consistent control of the drone swarm.

[0066] The distributed security control method of this scheme with coordinated attack of UAVs with random switching topology, such as Figure 1 As shown, the first step is to use graph theory technology and Markov random field theory to establish a dynamic model of a drone swarm with random switching topology. Specifically, considering the constraints such as source search, target tracking and sudden changes in the working environment in actual engineering applications, the drone swarm needs to change the communication topology in real time to complete the target task. It is worth noting that the existing control method for fixed topology drone systems is difficult to apply to drone systems with random switching topology. Therefore, this scheme considers a time-varying drone system with a random switching topology, introduces graph theory technology and Markov random theory to describe the topological structure of switching between drones, and graph theory technology and Markov random theory are both existing technologies. By establishing a dynamic model of a drone swarm with random switching topology, it is prepared for the subsequent study of the cooperative control problem under network attacks when multiple drones cooperate to complete designated tasks in a complex network environment. The second step is to establish a mathematical model of cooperative attack under complex constraints based on actual attack scenarios. In this embodiment, the establishment of a mathematical model of cooperative attack can quantify the false data injection attack suffered by the feedforward transmission channel and feedback transmission channel of the drone, which is convenient for observing the tampering of the attacked measurement data and the tampering of the control signal. The third step is to construct a distributed security consistency protocol for drones in a limited time domain based on the dynamic model of drone swarms with random switching topologies and the mathematical model of coordinated attacks. In this embodiment, the establishment of a distributed security consistency protocol is conducive to preparing for the subsequent design of a security controller, thereby ensuring that the drone swarm can converge to a consensus within a limited time. The fourth step is to calculate and solve the gain of the security controller to be designed in the distributed security consistency protocol to achieve consistent control of the drone swarm. In this embodiment, the security control problem of drones with random switching topologies under coordinated attacks is transformed into a security controller solution problem. The gain of the security controller to be designed is solved using the recursive linear matrix inequality technology, and the security controller is designed based on the gain of the security controller to be designed to ensure that the state of the drone swarm under random switching topologies, coordinated attacks and unknown external interference can converge to a consensus within a limited time domain, while satisfying H. ∞ performance.

[0067] This scheme can describe the random switching of UAV swarm communication topology under the constraints of actual working environment factors by introducing graph theory technology and Markov random theory. By establishing a mathematical model of coordinated attack, the complex constraints in actual attack scenarios are fully considered. By solving the gain of the security controller, it is ensured that the state of the UAV swarm can be consistent within a limited time domain under random switching topology, coordinated attack and unknown external interference, which is conducive to the stability of the UAV system and improves the robustness of the UAV system.

[0068] Preferably, step S1 specifically includes the following sub-steps:

[0069] Step S11: Calculate and obtain the kinematic model of each UAV in the UAV group. The kinematic model of each UAV is expressed as follows:

[0070]

[0071] Among them, x i (k) represents the state of the i-th UAV, x i The specific formula of (k) is as follows:

[0072] x i (k) = [p i (k), v i (k)],p i (k) represents the position vector of the i-th UAV; v i (k) represents the velocity vector of the i-th UAV;

[0073] u i (k) represents the control input vector of the i-th UAV; y i (k) represents the measurement output vector of the i-th UAV; w i (k) represents unknown and bounded external interference; A(k), B(k), C(k) and D(k) are all known time-varying parameter matrices;

[0074] Step S12: construct a random switching topology graph, and use the random switching topology graph to describe the communication interaction structure between the kinematic models of each UAV, so as to obtain a dynamic model of the UAV swarm with random switching topology;

[0075] The expression of random switching topology graph is as follows:

[0076]

[0077] in, Represents the random switching topology at time k; Represents the vertex set under the switching topology; Represents the edge set under the switching topology; represents the adjacency matrix between drone groups under the switching topology; w k represents the Markov chain at time k, w k The transition probability is as follows:

[0078] P{w k+1 =t|w k =s} =π st

[0079] Among them, π strepresents the transition probability of the drone from state s at time k to state t at time k+1, π st >0.

[0080] In this embodiment, considering that in actual engineering applications, the tasks and working environments of drone swarms are constantly changing, these performance constraints and other factors cause the cooperative formations between drone swarms to change, which in turn causes the communication topology between drone swarms to change in real time. Here, the Markov chain w is introduced k Characterize the random switching topology that changes over time. By constructing a random switching topology graph, we can describe the communication interaction between drone groups. When , it means that the drones communicate with each other; when When , it means that there is no information exchange between drones.

[0081] Preferably, in step S2, the mathematical model of coordinated attack under complex constraints is expressed as follows:

[0082]

[0083] in, represents the measurement output vector of the i-th drone after being attacked; represents the control input vector of the i-th drone after being attacked; u i (k) represents the control input vector of the i-th UAV; y i (k) represents the measurement output vector of the i-th UAV; represents the attack vector injected by the attacker in the feedforward measurement channel; The attack vector injected by the attacker in the feedback control channel; α i (k) and β i (k) are all random variables that obey the Bernoulli distribution.

[0084] Specifically, in an open network communication environment, unprotected feedforward measurement channels and feedback control channels in drone interactions will inevitably be subject to security threats brought by network attacks. If any drone in a drone group is successfully attacked and invaded, it is possible to destroy the stability of the entire system, and even make it difficult for the entire drone group interconnected via the network to work normally. Therefore, in this embodiment, the situation where the drone feedforward channel and feedback control channel are subjected to coordinated attacks is taken into account, and a reasonable coordinated attack mathematical model is constructed for it.

[0085] Further explanation: considering that it is difficult for attackers to obtain all the knowledge of the UAV system in practice, we assume that the attack vector and is a bounded nonlinear function.

[0086] Due to the influence of safety protection equipment and network communication constraints on drone systems, the false information sent by attackers over a period of time may not be successful. Therefore, in order to describe this actual attack situation, a random variable α that follows a Bernoulli distribution is introduced. i (k) and β i (k) describes the random characteristics of the success rate of the attacker's coordinated attack. For the sake of generality, we assume that the random variable α i (k) and β i (k) are independent of each other.

[0087] Preferably, in step S3, the expression of the distributed security consistency protocol in the limited time domain of the drone is as follows:

[0088]

[0089] in, represents the measurement output vector of the i-th drone after being attacked; represents the control input vector of the i-th drone after being attacked; represents the measurement output vector of the jth UAV after being attacked; represents the vertex set of the i-th UAV under the switching topology; K(k) represents the gain of the safety controller to be designed.

[0090] In this embodiment, the coordinated attack and external unknown interference are taken into consideration, and a distributed safety consistency control protocol within a limited time domain of the UAV is constructed using distributed control technology.

[0091] Preferably, in step S3, the following steps are also included:

[0092] By analyzing the distributed safety consistency protocol in the limited time domain of the UAV, the closed-loop system equation of the i-th UAV is obtained, where the expression of the closed-loop system equation of the i-th UAV is as follows:

[0093]

[0094] Among them, x i (k) represents the state of the i-th drone; and Both represent the time-varying parameter matrix of the UAV system after dimension expansion; The parameter matrix representing the attack vector suffered by the measurement channel after dimension expansion; Represents the parameter matrix of the attack vector of the feedback control channel after dimension expansion; a y (k) represents the attack vector suffered by the measurement channel after dimension expansion; a u (k) represents the attack vector on the feedback control channel after dimension expansion.

[0095] In this embodiment, by establishing the closed-loop system equation of the drone, the state of the closed-loop system of the drone tends to be consistent within a limited time domain.

[0096] Preferably, in step S4, the following sub-steps are specifically included:

[0097] Given a scalar γ>0 and a positive definite symmetric matrix R, when the state of the UAV closed-loop system tends to be consistent in a finite time domain, if there exists a positive definite matrix {P k} k∈[0，T] , the matrix {G k} k∈[0，T] , the matrix Ω l and the safety controller gain K(k) to be designed, as well as the scalars π1>0 and π2>0 so that the following recursive linear matrix inequality holds:

[0098]

[0099] P0<γ 2 R;

[0100] Then the safety controller gain K(k) to be designed can be obtained by solving the following formula:

[0101]

[0102] Among them, G 1，k+1 represents a free matrix; represents the matrix to be calculated; Represents a matrix block in a matrix inequality; Represents a matrix block in a matrix inequality;

[0103] represents a matrix block in a matrix inequality,

[0104] Represents a matrix block The sub-blocks in

[0105]

[0106] Represents a matrix block The sub-blocks in

[0107] A'(k) represents the matrix sub-block A matrix element in ;

[0108]

[0109] Among them, I N Represents the N-dimensional identity matrix; represents the Kronecker product; qk+1 represents any matrix; o k+1 represents a non-singular matrix; represents the Laplace matrix; C(k) represents the time-varying parameter matrix;

[0110] Represents a matrix subblock A matrix element in ;

[0111]

[0112] in, represents the success probability matrix of the attack on the measurement channel;

[0113] Represents a matrix subblock A matrix element in ;

[0114]

[0115] Among them, H N Represents state x i (k) and its average state The relationship matrix between them; B(k) represents the time-varying parameter matrix;

[0116] D'(k) represents the matrix sub-block A matrix element in ;

[0117]

[0118] Represents a matrix subblock Matrix block elements in ;

[0119] Represents a matrix subblock The matrix block elements in .

[0120] In this embodiment, the gain K(k) of the safety controller to be designed is solved by recursive linear matrix inequality technology, which can ensure that the state of the drone group can be consistent in a limited time domain under random topology switching, coordinated attack and unknown external interference, and satisfy H ∞ performance.

[0121] In addition, each functional unit in each embodiment of the present invention may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into one module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0122] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A distributed security control method for coordinated attack of drones with random switching topology, characterized by: The following steps are involved: Step S1: Using graph theory and Markov random theory to establish a dynamic model of a drone swarm with random switching topology; Step S2: Based on the actual attack scenario, a mathematical model of coordinated attack under complex constraints is established; Step S3: Based on the dynamic model of the drone swarm with random switching topology and the mathematical model of coordinated attack, a distributed security consensus protocol within the limited time domain of drones is constructed; Step S4: Calculate and solve the gain of the safety controller to be designed in the distributed safety consistency protocol to achieve consistency control of the drone swarm; In step S3, the expression of the distributed security consensus protocol in the limited time domain of the drone is as follows: in, represents the measurement output vector of the i-th drone after being attacked; represents the control input vector of the i-th drone after being attacked; represents the measurement output vector of the jth UAV after being attacked; represents the vertex set of the i-th drone under the switching topology; represents the gain of the safety controller to be designed; In step S3, the following steps are also included: By analyzing the distributed safety consistency protocol in the limited time domain of the UAV, the closed-loop system equation of the i-th UAV is obtained, where the expression of the closed-loop system equation of the i-th UAV is as follows: = + + + ； in, Indicates the state of the i-th drone; , and Both represent the time-varying parameter matrix of the UAV system after dimension expansion; The parameter matrix representing the attack vector of the measurement channel after dimension expansion; The parameter matrix representing the attack vector of the feedback control channel after dimension expansion; Indicates the attack vector suffered by the measurement channel after dimension expansion; It indicates that the feedback control channel is attacked by the attack vector after dimension expansion.

2. The distributed security control method for coordinated attack of drones with random switching topology according to claim 1 is characterized in that: In step S1, the following sub-steps are specifically included: Step S11: Calculate and obtain the kinematic model of each UAV in the UAV group. The kinematic model of each UAV is expressed as follows: in, represents the state of the i-th drone, The specific formula is as follows: = , represents the position vector of the i-th drone; represents the velocity vector of the i-th UAV; represents the control input vector of the i-th UAV; represents the measurement output vector of the i-th UAV; Represents unknown and bounded external interference; , , and All are known time-varying parameter matrices; Step S12: construct a random switching topology graph, and use the random switching topology graph to describe the communication interaction structure between the kinematic models of each UAV, so as to obtain a dynamic model of the UAV swarm with random switching topology; The expression of random switching topology graph is as follows: = in, Represents the random switching topology at time k; Represents the vertex set under the switching topology; Represents the edge set under the switching topology; represents the adjacency matrix between drone groups under the switching topology; represents the Markov chain at time k, The transition probability is as follows: in, represents the transition probability of the drone from state s at time k to state t at time k+1, >

0.

3. The distributed security control method with coordinated attack of UAVs with random switching topology according to claim 1 is characterized in that: In step S2, the mathematical model of coordinated attack under complex constraints is expressed as follows: in, represents the measurement output vector of the i-th drone after being attacked; represents the control input vector of the i-th drone after being attacked; represents the control input vector of the i-th UAV; represents the measurement output vector of the i-th UAV; represents the attack vector injected by the attacker in the feedforward measurement channel; Attack vectors injected by attackers in the feedback control channel; and are all random variables that follow a Bernoulli distribution.

4. The distributed security control method for coordinated attack of drones with random switching topology according to claim 1 is characterized in that: In step S4, the following sub-steps are specifically included: Given a scalar > 0 and positive definite symmetric matrix R, when the state of the UAV closed-loop system tends to be consistent in a finite time domain, if there exists a positive definite matrix ,matrix ,matrix and the gain of the safety controller to be designed , and the scalar >0 and >0 makes the following recursive linear matrix inequality hold: ＜0； ＜ ； Then the gain of the safety controller to be designed is It can be solved by the following formula: = ； in, represents a free matrix; represents the matrix to be calculated; Represents a matrix block in a matrix inequality; Represents a matrix block in a matrix inequality; represents a matrix block in a matrix inequality, = ; Represents a matrix block The sub-blocks in = ; Represents a matrix block The sub-blocks in = + ; Represents a matrix subblock A matrix element in ; = + ； in, Represents the N-dimensional identity matrix; represents the Kronecker product; represents an arbitrary matrix; represents a non-singular matrix; represents the Laplacian matrix; represents the time-varying parameter matrix; Represents a matrix subblock A matrix element in ; = ； in, represents the success probability matrix of the attack on the measurement channel; Represents a matrix subblock A matrix element in ; = ； in, Indicates status With its average state The relationship matrix between them; represents the time-varying parameter matrix; Represents a matrix subblock A matrix element in ; ； Represents a matrix subblock Matrix block elements in ; Represents a matrix subblock The matrix block elements in .

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