Method and device for controlling ship formation under network and physical attacks

Abstract

The invention relates to the field of artificial intelligence, and provides a ship formation control method and device under network and physical attacks, electronic equipment and a computer readable storage medium. The method comprises the following steps: determining network attack information according to a preset network attack model and actually measured position-course data, and obtaining a target input control signal under a network attack; and obtaining predicted position-course data and predicted speed state data of each ship, substituting the predicted position-course data and the predicted speed state data into a preset expansion state observer, and performing compensation control on the ship formation based on the preset expansion state observer. The method has the technical effects that the multi-ship formation can be stably controlled in a complex navigation environment including network attack and physical attack, and the navigation safety of the ship formation is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of ship control, in particular to a ship formation control method and device under network and physical attacks, electronic equipment and computer readable storage medium. BACKGROUND

[0002] With the development of intelligent shipping technology, inland autonomous ship formation has become a research hotspot in the water transport field due to its efficiency and flexibility in logistics transportation, environmental monitoring and channel maintenance. Multi-ship formation has the advantages of reducing maintenance cost, improving fault tolerance and improving operation efficiency.

[0003] With the increasing openness of the network and the continuous expansion of the network scale, it will inevitably increase the possibility of network attacks, such as denial of service attacks, deception attacks and replay attacks. Denial of service attacks will occupy communication channels and consume network bandwidth, resulting in normal communication being blocked. Deception attacks will inject false information in shared data transmission channels, misleading ship control operations. Replay attacks will constantly replay previously recorded data to prevent ships from obtaining real-time and accurate data from their neighbors. Even the inevitable transmission delay in network communication also brings challenges to multi-ship formation control.

[0004] In addition, multi-ship formation may also be subject to accidental physical attacks when performing tasks, such as enemy ship collisions, weapon attacks, underwater artificial obstacles, etc. Under these physical attacks, the hull of the ship will be deformed, bent or even broken. During the navigation of the multi-ship formation, the working performance of the sensors and actuators directly affects the maintenance of the formation pattern, so the influence of physical attacks on sensors and actuators cannot be ignored.

[0005] Therefore, how to control multi-ship formation in a complex navigation environment containing network attacks and physical attacks is a problem to be solved in the field of ship motion control. SUMMARY

[0006] Therefore, it is necessary to provide a ship formation control method and device under network and physical attacks, electronic equipment and computer readable storage medium, to realize stable control of multi-ship formation in a complex navigation environment containing network attacks and physical attacks, and to improve the navigation safety of ship formation.

[0007] In order to achieve the above technical effects, in a first aspect, the present application provides a ship formation control method under network and physical attacks, applied to control a ship formation including a plurality of ships, characterized in that it comprises: The position-course data of each ship is sampled to obtain measured position-course data, network attack information is determined according to a preset network attack model and the measured position-course data, the network attack information is substituted into a preset controller model to obtain a target input control signal under network attack; The target input control signal is substituted into a preset dynamic system model to obtain predicted position-course data and predicted speed state data of each ship, the preset dynamic system model includes a relationship model of the predicted position-course data of each ship and an input control signal, and a relationship model of the predicted speed state data of each ship and an input control signal; The predicted position-course data and the predicted speed state data are substituted into a preset extended state observer, and compensation control is performed on the ship formation based on the preset extended state observer.

[0008] In a possible embodiment, the sampling of the position-course data of each ship to obtain measured position-course data includes: The position-course data of each ship is sampled based on a preset sampling time sequence, and a sampling time is recorded, and the position-course data and the sampling time are taken as the measured position-course data.

[0009] In a possible embodiment, the control method of the ship formation under network and physical attack further includes: A communication topology relationship between each ship is constructed; The measured position-course data is encrypted to form a position-course data packet, and the position-course data packet is sent to other ships according to the communication topology relationship.

[0010] In a possible embodiment, the determination of network attack information according to a preset network attack model and the measured position-course data includes: For any ship, after receiving the position-course data packet sent by other ships, a receiving time when the position-course data packet is received is recorded, and the position-course data packet is decrypted to obtain the position-course data and the sampling time; A total attack duration of the network attack is determined according to the preset sampling time sequence, the receiving time and the sampling time, and a network attack probability is determined according to the total attack duration and a total sampling duration of the preset sampling time sequence; The network attack probability is substituted into the preset network attack model to obtain the network attack information subject to Bernoulli distribution.

[0011] In one possible embodiment, the preset controller model includes a control gain. Substituting the network attack information into the preset controller model yields a target input control signal under the network attack, including: Based on the network attack information, the target control gain is obtained by solving linear matrix inequalities. The target control gain and the network attack information are substituted into the preset controller model to obtain the target input control signal.

[0012] In one possible embodiment, the preset dynamic system model includes: ; in, The position-heading data of the vessel. Inject signals to the unknown control bias generated by physical attacks. Let be a rotation matrix, and = , Let be the heading angle of the vessel. The speed state data, Inject signals to the unknown control biases caused by model errors and environmental disturbances. The inertia matrix, For the specified command control input, Inject signals to unknown control biases generated by cyberattacks.

[0013] In one possible embodiment, the preset extended state observer includes: ; in, For Laplace matrix, For oscillation speed, = , = . Unmeasurable ASV velocity The estimate; Indicates unknown input The estimate; and express and The estimate; and This represents the specified positive compensation matrix.

[0014] Secondly, this application provides a control device for a ship formation under cyber and physical attacks, used to control a ship formation comprising several ships, including: a data sampling module, configured to sample position and heading data of each ship to obtain measured position and heading data; a control signal generation module, configured to determine network attack information according to a preset network attack model and the measured position and heading data, and to obtain target input control signals under network attack by substituting the network attack information into a preset controller model; a data prediction module, configured to substitute the target input control signals into a preset dynamic system model to obtain predicted position and heading data and predicted speed state data of each ship, the preset dynamic system model including a relationship model between the predicted position and heading data and input control signals of each ship and a relationship model between the predicted speed state data and input control signals of each ship; a compensation control module, configured to substitute the predicted position and heading data and predicted speed state data into a preset extended state observer to perform compensation control on the ship formation based on the preset extended state observer.

[0015] In a third aspect, the present application also provides an electronic device, including a memory and a processor, wherein, the memory is configured to store a program; the processor is coupled to the memory and is configured to execute the program stored in the memory to implement the steps of the network and physical attack under ship formation control method described in any of the implementation manners.

[0016] In a fourth aspect, the present application also provides a computer readable storage medium for storing computer readable programs or instructions, which can implement the steps of the network and physical attack under ship formation control method described in any of the implementation manners when executed by a processor.

[0017] The present application has the following beneficial effects: Compared with the related art, in the network and physical attack under ship formation control method, device, electronic equipment and computer readable storage medium provided by the application, during the sailing of the ship formation, the position-course data of each ship is sampled to obtain the measured position-course data, the network attack information received by the ship formation can be determined based on the preset network attack model according to the measured position-course data, the network attack information is substituted into the preset controller model, the target input control signal related to the network attack information can be generated by the preset controller module, then the target input control signal is substituted into the preset dynamics system model, the predicted position-course data and the predicted speed state data of each ship can be obtained, finally the predicted position-course data and the predicted speed state data are substituted into the preset extended state observer, the preset extended state observer can compensate and control the ship formation based on the preset extended state observer. Since the dynamics system of the ship is closely related to the physical attack received by the ship, the predicted position-course data and the predicted speed state data generated according to the preset dynamics system model are also related to the physical attack received by the ship, since the target input control signal for generating the predicted position-course data and the predicted speed state data is related to the network attack information, finally the preset extended state observer can compensate and control the physical attack and the network attack received by the ship, so as to realize stable control of the multi-ship formation in the complex sailing environment containing the network attack and the physical attack, and improve the sailing safety of the ship formation. BRIEF DESCRIPTION OF DRAWINGS

[0018] In order to more clearly illustrate the technical solutions in the embodiments of the application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the application, and other drawings can be obtained by those skilled in the art without creative labor.

[0019] Figure 1 The flowchart of the network and physical attack under ship formation control method provided by an embodiment of the application; Figure 2 The structural diagram of the network and physical attack under ship formation control device provided by an embodiment of the application; Figure 3 The structural diagram of the electronic equipment provided by an embodiment of the application. DETAILED DESCRIPTION

[0020] With reference to the drawings and briefly describing the technical schemes in the embodiments of the present application, the technical schemes in the embodiments of the present application will be described clearly and completely. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person skilled in the art without creative work fall within the scope of protection of the present application.

[0021] In the description of the embodiments of the present application, unless otherwise specified, the meaning of "multiple" is two or more than two. The association relationship of the associated objects is described, which means that there can be three relationships, for example: A and / or B, which can mean that A exists alone, A and B exist together, and B exists alone.

[0022] The "first", "second" and the like described in the embodiments of the present application are only for the purpose of description, and cannot be understood as indicating or implying the relative importance of the indicated technical features or implicitly indicating the number of the indicated technical features. Therefore, the technical features limited by "first" and "second" can explicitly or implicitly include at least one of the features.

[0023] In this document, referring to "embodiments" means that the specific features, structures or properties described in connection with the embodiments can be included in at least one embodiment of the present application. The appearance of this phrase in various places in the specification does not necessarily mean the same embodiment, nor is it independent or alternative to other embodiments. A person skilled in the art explicitly and implicitly understands that the embodiments described herein can be combined with other embodiments.

[0024] The present application provides a network and physical attack under ship formation control method, device, electronic equipment and computer readable storage medium, the following are described respectively.

[0025] Please refer to Figure 1 The network and physical attack under ship formation control method provided by the embodiment can specifically include the following steps. Step S101: sampling the position and heading data of each ship to obtain measured position and heading data.

[0026] In this step, each ship (also referred to as ASV, Autonomous Surface Vehicle, in this document) can specifically sample the position and heading data of each ship based on a pre-set preset sampling time sequence when reaching the sampling time point in the preset sampling time sequence, to obtain measured position and heading data (t). Wherein, the measured position and heading data (t) can include the position coordinates of the ship and the heading angle of the ship , i.e. . For the sake of distinction, in the present application, a certain specific measured position-heading data record can be denoted as .

[0027] In the present step, while the measured position-heading data (t) is collected, the sampling time can be recorded. For the sake of distinction, the measured position-heading data corresponding sampling time can be recorded as . Further, in the present step, after the measured position-heading data and the sampling time are sampled, the measured position-heading data and the sampling time can be encrypted and packed, and labeled to form a position-heading data packet . Then, based on the communication relationship between each ship in the ship formation, the position-heading data packet is sent to other ships in the ship formation.

[0028] In the ship formation, before the communication between each ship in the ship formation, the communication topology relationship can be constructed based on whether the communication between each ship can be carried out. After the position-heading data packet is formed , the position-heading data packet can be sent to other ships according to the communication topology relationship.

[0029] Specifically, for a multi-ship system consisting of one leader and N followers, the interaction directed topology is represented by a directed graph , where denotes the set of nodes (i.e. ships), represents the follower set; denotes the edge set, where edge , indicates that node can receive information from node ; denotes the adjacency matrix of the leader, if cannot receive information from , , otherwise ; denotes the non-negative weighted adjacency matrix, when , , when , ; the Laplacian matrix , whose elements satisfy:

[0030] The follower ASV tracks the leader state , the platoon error converges: wherein, is a preset platoon offset, is an allowed error upper bound.

[0031] Step S102: Determine network attack information according to a preset network attack model and measured position-course data.

[0032] In this step, for each ship, a constant and can be set at initialization. After receiving the position-course data packet sent by other ships, the data such as , , in the position-course data packet can be read. If the receiving time of the received position-course data packet satisfies , then can be calculated, and is updated, m=m+1, m is the sampling number. If the receiving time of the received position-course data packet does not satisfy , it can be further determined whether satisfies. If yes, the ship sending the position-course data packet is not attacked by DoS. If satisfies, then , are updated; if 0 satisfies, then , are updated. Further, the relevant data of network attack can be calculated according to the formula , , , . Among them, represents the maximum allowed continuous attack number of replay attack, represents the occurrence probability of replay attack, represents the maximum allowed continuous attack number of DoS attack, represents the occurrence probability of DoS attack.

[0033] In this step, different preset network attack models can be constructed according to different types of network attacks. For example, for an energy-limited DoS attack model, a group of random variables subject to Bernoulli distribution can be introduced, wherein is the sampling time. exist Take the value from, satisfying ,in This represents the known attack probability. For a deception attack model, a set of random variables following a Bernoulli distribution is defined. This is used to describe the occurrence of deception attacks. Among them... Sampling time, exist Take the value from, satisfying ,in Let represent the known attack probability. For the replay attack model, define a set of random variables that follow a Bernoulli distribution. This is used to describe the occurrence of deception attacks. Among them... Sampling time, exist Take the value from, satisfying ,in This indicates the known probability of an attack.

[0034] As shown above, by substituting the relevant network attack data obtained from the analysis of measured position-heading data into the preset network attack model, the corresponding network attack information can be obtained. .

[0035] Step S103: Substitute the network attack information into the preset controller model to obtain the target input control signal under the network attack.

[0036] In this step, for The preset controller model is as follows: ; in, ,and , .

[0037] Network attack information Substituting these values ​​into the above formula yields the target input control signal under the corresponding network attack. .

[0038] Furthermore, the aforementioned preset controller model includes control gain. In specific embodiments of this application, the network attack information can be based on the leader's network attack information within the network attack information. , and The target control gain is obtained by solving linear matrix inequalities. Specifically, if a positive definite symmetric matrix exists... , The following conditions must be met: 5

[0039] wherein , , BY , j = 4, 5,..., 3 ,

[0040] , ,

[0041] , ,

[0042] , j = 5, 6,...,

[0043]

[0044] I ,

[0045]

[0046] ,

[0047] , , }

[0048] to j=5,6,…, and

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055] Then the closed-loop system is with Performance level of mean square asymptotic stability, the controller gain is K = Y .

[0056] Step S104: Substitute the target input control signal into the preset dynamic system model to obtain the predicted position-course data and the predicted speed state data of each ship.

[0057] In this step, the preset dynamic system model comprises: ; Wherein, is the position-course data of the ship, is an unknown control bias injection signal generated by a physical attack, is a rotation matrix, and = , is the heading angle of the ship, is the speed state data, is an unknown control bias injection signal generated by a model error and environmental disturbance, is an inertia matrix, is a designated command control input, is an unknown control bias injection signal generated by a network attack.

[0058] Specifically, it can be obtained according to the following manner.

[0059] The origin O of the earth-fixed coordinate system is selected at an arbitrary point on the sea level, the X axis points to the north direction, the Y axis points to the east direction, and the Z axis is perpendicular to OXY and points to the earth surface; The kinematic model of the ship is expressed as: ; The following formula is used to describe the relationship between system input and ship motion dynamics: = ; Wherein, represents the position state of the i-th ship, represents the speed state of the i-th ship, , , , respectively represent the positions of the ship in the X axis and the Y axis, represents the heading angle, , , are the surge speed, the sway speed and the yaw angle speed, respectively. is the inertia matrix, is the Coriolis matrix and the centripetal matrix of the th ship. is the nonlinear damping matrix; represents the control input, is the external environmental disturbance caused by wind, wave, and current, denotes the unknown model dynamics.

[0060] is the rotation matrix, and is expressed as:

[0061] The leader trajectory state is expressed as:

[0062] For the sensor, the sensor attack model is specifically:

[0063] where, denotes the position- heading actual measurement data, denotes the unknown measurement bias injection signal caused by malicious sensor attacks.

[0064] For the actuator, the actuator attack model is specifically:

[0065] where, denotes the specified command control input, denotes the unknown control bias injection signal caused by malicious actuator attacks.

[0066] The physical attack is introduced into the ship dynamics system model to obtain:

[0067] where, is the unknown control bias injection signal generated by the model error and environmental disturbance.

[0068] Step S105: Substitute the predicted position- heading data and the predicted speed state data into the preset extended state observer, and perform compensation control on the ship formation based on the preset extended state observer.

[0069] In this step, the preset extended state observer includes: ; where, is the Laplace matrix, ,​​​​ unmeasurable ASV velocity estimation of the unknown input estimation of the unknown input

[0070] In this step, based on the above preset extended state observer, the external disturbance (such as physical attack and network attack) of the ship formation and the internal unmodeled dynamics (such as nonlinear term, parameter variation) are unified as a “total disturbance”, and the “total disturbance” is taken as an extended state (additional state variable) of the ship formation. Through the preset extended state observer, the original state of the ship formation and the extended “total disturbance state” are estimated at the same time, so as to perform compensation control on the ship formation.

[0071] Compared with the related art, in the ship formation control method under network and physical attack provided in the embodiments of the present application, the position-course data of each ship is sampled during the navigation of the ship formation to obtain measured position-course data, the network attack information received by the ship formation can be determined according to the measured position-course data based on a preset network attack model, the network attack information is substituted into a preset controller model, the target input control signal related to the network attack information can be generated by the preset controller module, then the target input control signal is substituted into a preset dynamics system model, the predicted position-course data and the predicted speed state data of each ship can be obtained, and finally the predicted position-course data and the predicted speed state data are substituted into a preset extended state observer, the preset extended state observer can perform compensation control on the ship formation based on the preset extended state observer. Since the dynamics system of the ship is closely related to the physical attack received by the ship, the predicted position-course data and the predicted speed state data generated according to the preset dynamics system model are also related to the physical attack received by the ship, since the target input control signal used to generate the predicted position-course data and the predicted speed state data is related to the network attack information, the preset extended state observer can finally perform compensation control on the physical attack and the network attack received by the ship at the same time, so as to realize stable control of the multi-ship formation in a complex navigation environment containing network attack and physical attack, and improve the navigation safety of the ship formation.

[0072] In order to better implement the ship formation control method under network and physical attack in the embodiments of the present application, on the basis of the ship formation control method under network and physical attack, correspondingly, such as​​​​​​​​​Figure 2 As shown, the embodiment of the present application further provides a network and physical attack under ship formation control device, the network and physical attack under ship formation control device comprises: The data sampling module 201 is configured to sample the position and heading data of each ship to obtain measured position and heading data. The control signal generation module 202 is configured to determine network attack information according to a preset network attack model and the measured position and heading data, and substitute the network attack information into a preset controller model to obtain a target input control signal under network attack. The data prediction module 203 is configured to substitute the target input control signal into a preset dynamic system model to obtain predicted position and heading data and predicted speed state data of each ship, and the preset dynamic system model comprises a relationship model between the predicted position and heading data of each ship and the input control signal, and a relationship model between the predicted speed state data of each ship and the input control signal. The compensation control module 204 is configured to substitute the predicted position and heading data and the predicted speed state data into a preset extended state observer to perform compensation control on the ship formation based on the preset extended state observer.

[0073] The network and physical attack under ship formation control device provided by the above embodiment can implement the technical solutions described in the network and physical attack under ship formation control method embodiment, and the principles of the implementation of the above modules or units can be referred to the corresponding content in the network and physical attack under ship formation control method embodiment, which will not be described here.

[0074] Please refer to Figure 3 The present application also provides an electronic device 300. The electronic device 300 comprises a processor 301, a memory 302 and a display 303. Figure 3 Only part of the components of the electronic device 300 are shown, but it should be understood that all the shown components are not required, and more or less components can be alternatively implemented.

[0075] The processor 301 can be a central processing unit (CPU), a microprocessor or other data processing chip in some embodiments, used to run the program code or process data stored in the memory 302, such as the network and physical attack under ship formation control method in the present application.

[0076] In some embodiments, the processor 301 can be a single server or a group of servers. The group of servers can be centralized or distributed. In some embodiments, the processor 301 can be local or remote. In some embodiments, the processor 301 can be implemented in a cloud platform. In an embodiment, the cloud platform can include a private cloud, a public cloud, a hybrid cloud, a community cloud, a distributed cloud, an inter-organizational cloud, a multi-cloud, or the like, or any combination thereof.

[0077] The memory 302 can be an internal storage unit of the electronic device 300, such as a hard disk or a memory of the electronic device 300, in some embodiments. The memory 302 can also be an external storage device of the electronic device 300, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) card, a Flash Card, or the like, equipped on the electronic device 300, in other embodiments.

[0078] Further, the memory 302 can include both an internal storage unit and an external storage device of the electronic device 300. The memory 302 is used to store application software and various data installed on the electronic device 300.

[0079] The display 303 can be an LED display, a liquid crystal display, a touch liquid crystal display, an OLED (Organic Light-Emitting Diode) touch, or the like, in some embodiments. The display 303 is used to display information of the electronic device 300 and to display a visualized user interface. The components 301-303 of the electronic device 300 communicate with each other through a system bus.

[0080] In an embodiment, when the processor 301 executes the control program of the ship formation under network and physical attacks in the memory 302, the following steps can be implemented: The position and heading data of each ship are sampled to obtain measured position and heading data, network attack information is determined according to a preset network attack model and the measured position and heading data, the network attack information is substituted into a preset controller model to obtain a target input control signal under network attack; The target input control signal is substituted into a preset dynamic system model to obtain predicted position and heading data and predicted speed state data of each ship, the preset dynamic system model includes a relationship model of the predicted position and heading data of each ship and the input control signal, and a relationship model of the predicted speed state data of each ship and the input control signal; The predicted position and heading data and the predicted speed state data are substituted into a preset extended state observer, and the ship formation is compensated and controlled based on the preset extended state observer.

[0081] It should be understood that, in addition to the above functions, the processor 301 can also implement other functions when executing the control program of the ship formation under network and physical attacks in the memory 302. For details, refer to the description of the corresponding method embodiments.

[0082] Further, the type of the electronic device 300 mentioned in the embodiments of the present application is not specifically limited, and the electronic device 300 can be a mobile phone, a tablet computer, a personal digital assistant (PDA), a wearable device, a laptop, or the like. Exemplary embodiments of the portable electronic device include, but are not limited to, a portable electronic device running an IOS, android, microsoft, or other operating system. The above portable electronic device can also be other portable electronic devices, such as a laptop having a touch-sensitive surface (e.g., a touch panel). It should also be understood that in some other embodiments of the present application, the electronic device 300 can also be a desktop computer having a touch-sensitive surface (e.g., a touch panel).

[0083] Correspondingly, the embodiments of the present application also provide a computer-readable storage medium for storing computer-readable programs or instructions, which, when executed by a processor, can implement the steps or functions in the control method of the ship formation under network and physical attacks provided by the above method embodiments.

[0084] Those skilled in the art can understand that all or part of the processes of the above-mentioned embodiments can be completed by a computer program instructing related hardware (such as a processor, a controller, etc.) to complete. The computer program can be stored in a computer-readable storage medium. The computer-readable storage medium includes a magnetic disk, an optical disk, a read-only memory, or a random access memory, etc.

[0085] The network and physical attack control method, device, electronic device, and storage medium of the ship formation provided by the present application are described in detail above, and the principles and implementation modes of the present application are described by applying specific examples. The above description of the embodiments is only used to help understand the method and its core idea of the present application; at the same time, for those skilled in the art, according to the idea of the present application, the specific implementation mode and application range will be changed; in conclusion, the content of the specification should not be understood as a limitation of the present application.

Claims

1. A control method of a ship formation under cyber and physical attacks, applied to control of a ship formation including a plurality of ships, characterized by, The method comprises the following steps: sampling position and heading data of each ship to obtain measured position and heading data, determining network attack information according to a preset network attack model and the measured position and heading data, substituting the network attack information into a preset controller model to obtain target input control signals under network attack; substituting the target input control signals into a preset dynamic system model to obtain predicted position and heading data and predicted speed state data of each ship, the preset dynamic system model comprising a relationship model between predicted position and heading data and input control signals of each ship and a relationship model between predicted speed state data and input control signals of each ship; substituting the predicted position and heading data and the predicted speed state data into a preset extended state observer to perform compensation control on the ship formation based on the preset extended state observer.

2. The control method of a fleet of ships under cyber-physical attack according to claim 1, characterized in that, The sampling of the position and heading data of each ship to obtain the measured position and heading data comprises the following steps: sampling the position and heading data of each ship based on a preset sampling time sequence, and recording sampling time, and taking the position and heading data and the sampling time as the measured position and heading data.

3. The method of controlling a formation of ships under cyber and physical attacks according to claim 2, wherein, The control method of the ship formation under network and physical attack further comprises the following steps: constructing a communication topology relationship between each ship; encrypting the measured position and heading data to form a position and heading data packet, and sending the position and heading data packet to other ships according to the communication topology relationship.

4. The method of controlling a formation of ships under cyber and physical attacks according to claim 3, wherein The determination of the network attack information according to the preset network attack model and the measured position and heading data comprises the following steps: for any ship, after receiving the position and heading data packet sent by other ships, recording a receiving time of receiving the position and heading data packet, and decrypting the position and heading data packet to obtain the position and heading data and the sampling time; determining a total attack duration of the network attack according to the preset sampling time sequence, the receiving time and the sampling time, and determining a network attack probability according to the total attack duration and a total sampling duration of the preset sampling time sequence; substituting the network attack probability into the preset network attack model to obtain the network attack information subject to Bernoulli distribution.

5. The method of claim 3, wherein, The preset controller model comprises control gains, and the substitution of the network attack information into the preset controller model to obtain the target input control signals under network attack comprises the following steps: obtaining target control gains by linear matrix inequality solving according to the network attack information; substituting the target control gains and the network attack information into the preset controller model to obtain the target input control signals.

6. The method of claim 1, wherein, The preset dynamic system model comprises: ； in, The position-heading data of the vessel. Inject signals to the unknown control bias generated by physical attacks. Let be a rotation matrix, and = , Let be the heading angle of the vessel. The speed state data, Inject signals to the unknown control biases caused by model errors and environmental disturbances. The inertia matrix, For the specified command control input, Inject signals to unknown control biases generated by cyberattacks.

7. The method of controlling a formation of ships under cyber and physical attacks according to claim 6, wherein, The preset extended state observer comprises: ； where is the Laplace matrix, is the surge velocity, Unmeasurable ASV velocity estimates; denotes the estimate of the unknown input and denotes the estimate of and and denotes the prescribed positive compensation matrix.​​​​​​ 8. A control device for a ship formation under cyber and physical attacks, applied to control a ship formation including a plurality of ships, characterized by, The method comprises the following steps: a data sampling module for sampling position and heading data of each ship to obtain measured position and heading data; The control signal generation module is configured to determine network attack information according to a preset network attack model and the measured position-course data, and to obtain target input control signals under network attacks by substituting the network attack information into a preset controller model; The data prediction module is configured to obtain predicted position-course data and predicted speed state data of each ship by substituting the target input control signals into a preset dynamic system model, wherein the preset dynamic system model comprises a relationship model between the predicted position-course data and the input control signals of each ship, and a relationship model between the predicted speed state data and the input control signals of each ship; The compensation control module is configured to perform compensation control on the ship formation based on the preset extended state observer by substituting the predicted position-course data and the predicted speed state data into the preset extended state observer.

9. An electronic device, comprising: comprising a memory and a processor, wherein, the memory is configured to store a program; the processor, coupled with the memory, is configured to execute the program stored in the memory to implement the steps of the control method for the ship formation under network and physical attacks according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, a computer readable program or instruction for storing, which can implement the steps of the control method for the ship formation under network and physical attacks according to any one of claims 1 to 7 when executed by a processor.

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