A trajectory tracking control method for networked unmanned ships under replay attack

Abstract

The present application provides a trajectory tracking control method for a networked unmanned ship under a replay attack. The method provided by the present application includes: establishing a dynamic and kinematic mathematical model based on the motion information of a three-degree-of-freedom fully-driven ship, and tracking the expected state information and the real state information of the fully-driven ship in real time; replacing the saturated nonlinearity with a smooth function based on the saturation constraint of the control input of the fully-driven ship; analyzing the action mechanism of the replay attack, and establishing a replay attack mathematical model in combination with Bernoulli random variables; establishing an adaptive neural network state observer; designing an adaptive neural network output feedback tracking control law based on the adaptive neural network state observer; establishing a periodic event triggering mechanism based on the unknown timing characteristics corresponding to the real state information under the replay attack and the feedback tracking control law of the adaptive neural network output. The method provided by the present application can complete the reliable control of the unmanned ship under a replay attack.

Description

Technical Field

[0001] The present application relates to the technical field of autonomous control of unmanned ships, and in particular to a trajectory tracking control method for a networked unmanned ship under a replay attack. Background Art

[0002] For unmanned surface autonomous ships, intelligent autonomous safe navigation control is a core module, which relies on the key technology - wireless network communication. In network communication, the position, speed status and control information of the unmanned ship must reach the receiving end through the wireless network; in an open and shared network environment, these transmission channels are fragile and susceptible to network attacks. Among them, replay attacks are cunning and vicious, which seriously threatens the safety of unmanned ship navigation control.

[0003] When a replay attack occurs, the replay position and speed attack information will enter the control system along with the sensor information, causing serious degradation of system performance. In order to solve the replay attack, the academic community has proposed various methods to achieve safe control of networked control systems, including state estimation, attack detection, system switching, etc. However, these solutions require accurate prior information about the target system or affect the system control performance. In actual navigation, unmanned ships will be disturbed by the marine environment and the perturbation of ship parameters, so the accurate information requirements cannot always be met.

[0004] In addition, in practice, the actuator needs high-frequency response control instructions to compensate for external disturbances or attack interference, which exacerbates the problem of actuator wear; at the same time, in the control design algorithm, the calculated control instructions will inevitably exceed the physical limitations of the unmanned ship actuator, resulting in output saturation. This will have an adverse effect on the control performance of the unmanned ship. Summary of the invention

[0005] In view of this, the present application provides a trajectory tracking control method for a networked unmanned ship under a replay attack, which can achieve reliable control of the unmanned ship under a replay attack.

[0006] Specifically, the present application is implemented through the following technical solutions:

[0007] The first aspect of the present application provides a trajectory tracking control method for a networked unmanned ship under a replay attack, the method comprising:

[0008] A dynamic and kinematic mathematical model is established according to the motion information of the three-degree-of-freedom fully-driven ship, and the desired state information and the actual state information of the fully-driven ship are tracked in real time; according to the saturation constraint of the control input of the fully-driven ship, a smooth function is used to replace the saturation nonlinearity;

[0009] Analyze the mechanism of replay attack, combine Bernoulli random variables, and establish a mathematical model of replay attack;

[0010] Establishing an adaptive neural network state observer according to the dynamics and kinematics mathematical model, the replay attack mathematical model and the neural network system;

[0011] Based on the adaptive neural network state observer, in the framework of vector backstepping method, combined with neural network and minimum parameter learning technology, an adaptive neural network output feedback tracking control law is designed;

[0012] Based on the unknown timing characteristics corresponding to the real state information under the replay attack and the feedback tracking control law output by the adaptive neural network, a periodic event triggering mechanism is established.

[0013] The second aspect of the present application provides a networked unmanned ship trajectory tracking control device under a replay attack, the device comprising a tracking module, a processing module and a design module, wherein:

[0014] The tracking module is used to establish dynamic and kinematic mathematical models according to the motion information of the three-degree-of-freedom all-drive ship, and to track the expected state information and the actual state information of the all-drive ship in real time; according to the saturation constraint of the control input of the all-drive ship, a smooth function is used to replace the saturation nonlinearity;

[0015] The processing module is used to analyze the mechanism of replay attack and establish a replay attack mathematical model in combination with Bernoulli random variables;

[0016] The processing module is further used to establish an adaptive neural network state observer according to the dynamics and kinematics mathematical model, the replay attack mathematical model and the neural network system;

[0017] The design module is also used to design an adaptive neural network output feedback tracking control law based on the adaptive neural network state observer in the framework of vector backstepping method, combined with neural network and minimum parameter learning technology;

[0018] The processing module is further used to establish a periodic event triggering mechanism based on the unknown timing characteristics corresponding to the real state information under the replay attack and the feedback tracking control law output by the adaptive neural network.

[0019] The third aspect of the present application provides a networked unmanned ship trajectory tracking control device under a replay attack, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of any one of the methods provided in the first aspect of the present application are implemented.

[0020] The fourth aspect of the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of any one of the methods provided in the first aspect of the present application.

[0021] The trajectory tracking control method for a networked unmanned ship under a replay attack provided by the present application is different from the existing observer. The present invention adopts the finite coverage principle and the neural network estimation technology to make the proposed adaptive neural network state observer have dual benefits. One is that it is independent of the controller design, and the other is that it does not require the precise position signal of the unmanned ship. Furthermore, the present invention utilizes the reconstruction capability of the observer to restore the true speed information of the unmanned ship, thereby replacing the damaged speed signal under the replay attack to enter the control system, further ensuring the control performance of the unmanned ship under the replay attack. Furthermore, the present invention reduces the number of responses of the driver to the control command and alleviates mechanical wear by establishing a periodic event trigger mechanism between the controller and the driver; in addition, the selection mechanism has the advantages of not requiring real-time monitoring of the trigger conditions and not requiring differentiation of the control command under the replay attack, thereby avoiding the occurrence of the Zeno phenomenon. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 A flow chart of a networked unmanned ship trajectory tracking control method under a replay attack provided by an exemplary embodiment of the present application;

[0023] Figure 2 A module diagram of a networked unmanned ship trajectory tracking control system under a replay attack provided by an exemplary embodiment of the present application;

[0024] Figure 3 An ideal and actual track tracking curve diagram of an unmanned ship provided by an exemplary embodiment of the present application;

[0025] Figure 4 A graph showing the position error of an unmanned ship provided by an exemplary embodiment of the present application;

[0026] Figure 5 A graph of error estimation between actual and estimated speeds of an unmanned ship provided by an exemplary embodiment of the present application;

[0027] Figure 6 An unmanned ship control input curve diagram provided for an exemplary embodiment of the present application;

[0028] Figure 7 An adaptive parameter estimation curve diagram of an unmanned ship provided by an exemplary embodiment of the present application;

[0029] Figure 8 A schematic diagram of periodic event triggering time and interval provided for an exemplary embodiment of the present application;

[0030] Fig. 9A hardware structure diagram of the networked unmanned ship trajectory tracking control device under replay attack in this application;

[0031] Fig.10 This is a structural diagram of Embodiment 1 of the networked unmanned ship trajectory tracking control device under replay attack provided in this application. DETAILED DESCRIPTION

[0032] Here, exemplary embodiments are described in detail, and examples thereof are shown in the accompanying drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The implementations described in the following exemplary embodiments do not represent all implementations consistent with the present application.

[0033] The terms used in this application are only for the purpose of describing specific embodiments and are not intended to limit this application. The singular forms of "a", "said" and "the" used in this application are also intended to include plural forms, unless the context clearly indicates other meanings. It should also be understood that the term "and / or" used in this article refers to and includes any or all possible combinations of one or more associated listed items.

[0034] It should be understood that although the terms first, second, third, etc. may be used in the present application to describe various information, these information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of the present application, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining".

[0035] The method provided in the present application can be used together with data sensors, shore-based control centers, ship-borne actuators and wireless transmission networks.

[0036] In a specific implementation, the data sensor collects the state information of the ship's movement and transmits the ship's state information to a shore-based control center via a wireless transmission network;

[0037] The shore-based control center processes the collected ship motion state information and completes the adaptive neural network output feedback control of the networked unmanned ship in the unknown random replay attack scenario;

[0038] The shore-based control center includes:

[0039] Construct a mathematical model of trajectory tracking control between the input and output relationship of the ship through the ship's kinematic and dynamic information;

[0040] The adaptive neural network state observer is constructed by obtaining the unknown ship position signal in the replay attack scenario through the limited coverage principle and reconstructing the unknown composite function by the neural network system.

[0041] By using observer estimation information to compensate for the impact of position attacks, neural network systems, adaptive and single-parameter online learning technologies are used to handle unknown ship dynamics and external environmental disturbances, and an adaptive neural network trajectory tracking controller for ships is constructed.

[0042] The wear effect of high-frequency disturbance on actuators is alleviated by periodic event triggering mechanism;

[0043] The ship-borne actuator executes control instructions sent by the controller fed back by the wireless transmission network, specifically including rudder angle instructions of the steering gear and thrust instructions of the propeller, so as to realize ship adaptive neural network trajectory tracking control triggered by periodic events under replay attack.

[0044] Specific embodiments are given below to introduce the technical solution of the present application in detail.

[0045] Figure 1 This is a flow chart of a networked unmanned ship trajectory tracking control method under a replay attack provided by an exemplary embodiment of the present application. Figure 1 , the method provided in this embodiment may include:

[0046] S101. A dynamic and kinematic mathematical model is established according to the motion information of a three-degree-of-freedom all-drive ship, and the desired state information and the actual state information of the all-drive ship are tracked in real time; and a smooth function is used to replace the saturation nonlinearity according to the saturation constraint of the control input of the all-drive ship.

[0047] Optionally, the motion information of the three-degree-of-freedom fully-driven ship includes ship posture, angular velocity, and control torque.

[0048] Optionally, the dynamics and kinematics mathematical model is established based on a first formula, wherein the first formula is:

[0049] ;

[0050] Among them, the is the ship pose vector, including the ship position ( x , y ) and heading angle ψ ; is the ship velocity vector, including surge, sway and pitch angular velocity; τ is the control input vector; is the external disturbance vector; is the inertia matrix; is the Coriolis centripetal matrix; is the nonlinear hydrodynamic damping matrix; J ( ψ ) is a rotation matrix that satisfies , the rotation matrix expression is the second formula, and the second formula is:

[0051] ;

[0052] Among them, the ψ is the heading angle.

[0053] Optionally, the step of replacing the saturation nonlinearity with a smooth function according to the saturation constraint of the full-drive ship control input comprises:

[0054] The calculation process of the saturation constraint is the third formula, which is:

[0055] ;

[0056] Among them, the yes i The upper limit of the control force or torque in the direction, It is the control instruction for subsequent design;

[0057] The fourth formula is introduced as a hyperbolic tangent smooth function, and the fourth formula is:

[0058] ;

[0059] Combined with the mean value theorem, the control input at this time satisfies the fifth formula, which is:

[0060] ;

[0061] in, , , ; ,

[0062] Said Bounded and satisfied ; is the approximation error, satisfying , Bounded.

[0063] S102. Analyze the mechanism of replay attack, combine Bernoulli random variables, and establish a replay attack mathematical model.

[0064] Optionally, the replay attack mathematical model is established based on a sixth formula, which is:

[0065] ;

[0066] Among them, the is an unknown position signal received by the observer; η is the real position signal of the all-drive vessel; To replay the attack signal; The time for the attacker to record the attack signal and meet , t is the time when the attacker sends the attack signal, Represents the time interval between the attacker recording and sending the replay attack signal; Bernoulli random variable σ is the occurrence indicator of the replay attack, σ 1 indicates that the attack is active. σ 0 means the attack is dormant, with a probability of .

[0067] S103, establishing an adaptive neural network state observer according to the dynamics and kinematics mathematical model, the replay attack mathematical model and the neural network system.

[0068] Optionally, construct a first-order filter to obtain a derivative of the replayed attack signal;

[0069] Based on the replay attack mathematical model, combined with the finite coverage principle, the unknown replay attack signal derivative is covered;

[0070] On the basis of the covered ship position signal of the all-drive ship, the adaptive neural state observer is constructed in combination with the neural network system.

[0071] Optionally, constructing a first-order filter to obtain a derivative of the replayed attack signal includes:

[0072] The replay attack signal derivative is obtained based on the seventh formula, and the seventh formula is:

[0073] ;

[0074] Among them, the is the filtering constant; the attack signal derivative quilt replace.

[0075] Optionally, based on the replay attack mathematical model, combined with the finite coverage principle, covering the unknown replay attack signal derivative includes:

[0076] Starting from delay 0, divide N Known delay interval To cover the unknown replay attack delay to a limited extent ; and , is the maximum delay that the control system can tolerate; There is a delay interval Just delay the unknown replay attack Coverage, that is, there is a bounded range of states that can be obtained , so that The eighth formula is satisfied, and the eighth formula is:

[0077] ;

[0078] Among them, the .

[0079] Optionally, the adaptive neural state observer is constructed based on the covered ship position signal of the all-drive ship in combination with the neural network system, including:

[0080] The ship dynamics and kinematics mathematical equations are rewritten based on the ninth formula, which is:

[0081] ;

[0082] Among them, the ; ; is an unknown function, and is approximated based on the neural network system, and the process is shown in the tenth formula, which is:

[0083] ;

[0084] Among them, the is the ideal weight matrix, is the basis function vector, To approximate the error vector and satisfy , is a normal number.

[0085] In the replay attack scenario, the unknown ship position signal containing the replay attack signal enters the observer system, causing the unknown dynamic composite term The eleventh formula is included, and the eleventh formula is:

[0086] ;

[0087] Among them, the ;

[0088] Using neural network system to predict unknown compound terms The approximation is performed, and the process is represented by the twelfth formula, which is:

[0089] ;

[0090] Among them, the is the ideal weight matrix, is the basis function vector, To approximate the error vector and satisfy , is a positive constant;

[0091] make , , , ; and stated represent the estimated values ​​of the ship's position and speed respectively, and stated It is obtained by the adaptive neural network state observer of the thirteenth formula, and the thirteenth formula is:

[0092] ;

[0093] The adaptive law is the fourteenth formula and the fifteenth formula, and the fourteenth formula is:

[0094] ;

[0095] The fifteenth formula is:

[0096] ;

[0097] in, , ; κ >0, k 1>0 and k 2>0 is the observer gain; is an auxiliary variable; is the rotation matrix after the attack, For the The transpose of and is a positive design matrix, and are all positive constants; k 3 and k 4 is a positive design parameter; For vector traces;

[0098] For the adaptive neural network state observer, the design parameters satisfy the following inequality, at which the observation error is and stated and the neural network weight estimation error is bounded, based on the sixteenth formula, which is:

[0099] ;

[0100] in, and are the number of neurons in the corresponding neural network systems;

[0101] The state observation error dynamic equation of the adaptive neural network state observer is the seventeenth formula and the eighteenth formula, and the seventeenth formula is:

[0102] ;

[0103] The eighteenth formula is:

[0104] ;

[0105] in, ;

[0106] The Lyapunov function is constructed to analyze the performance of the adaptive neural network state observer, as shown in the nineteenth formula, which is:

[0107] ;

[0108] Combining the seventeenth formula and the eighteenth formula to derive the nineteenth formula, a twentieth formula is obtained, and the twenty-first formula is:

[0109] ;

[0110] according to‖ J ( ψ )‖=1 and ‖ υ ‖≤ υ m , wherein the υ m is the maximum speed of the ship, and the 21st formula is obtained. The 21st formula is:

[0111] ;

[0112] in, , ;

[0113] Said The 20th formula can be written as the 22nd formula according to the 17th formula to the 21st formula, and the 22nd formula is:

[0114] ;

[0115] in, ;

[0116] The twenty-third formula is obtained by solving the twenty-second formula, and the twenty-third formula is:

[0117] ;

[0118] Among them, the is the initial value; when t When it approaches ∞, ,therefore , are all bounded; when t When it approaches ∞, the twenty-fourth formula is obtained according to the nineteenth formula and the twenty-third formula, and the twenty-fourth formula is:

[0119] ;

[0120] Among them, select the preset design parameters κ , k 1, k 2, k 3 and k 4, and ensure that the sixteenth formula is established, the state observation error is and stated Can converge to a first preset range.

[0121] S104. Based on the adaptive neural network state observer, in the framework of vector backstepping method, combined with neural network and minimum parameter learning technology, an adaptive neural network output feedback tracking control law is designed.

[0122] Optionally, in the design framework of the backstepping method, in order to avoid the virtual control law α f The complex derivative operation introduces the first-order filter of the seventh formula to obtain its filtered version α The specific process is shown in the twenty-fifth formula, which is:

[0123] ;

[0124] Where T is the filter constant; the filter error is ,at this time ;

[0125] Defining the attitude error of the unmanned ship and speed error As shown in the twenty-sixth formula, the twenty-sixth formula is:

[0126] ;

[0127] The attitude error is differentiated to obtain the twenty-seventh formula, which is:

[0128] ;

[0129] The virtual control law is the twenty-eighth formula, which is:

[0130] ;

[0131] Among them, the is a positive design matrix;

[0132] Substituting the twenty-eighth formula into the twenty-seventh formula yields the twenty-ninth formula, which is:

[0133] ;

[0134] in, ;make , is a positive constant;

[0135] According to the first formula and the fifth formula, a thirtieth formula is obtained, and the thirtieth formula is:

[0136] ;

[0137] in, , there exists a normal number Make ; , there exists a normal number Make .

[0138] The 31st formula is obtained by derivatizing the speed error, and the 31st formula is:

[0139] ;

[0140] in, ; Use neural network system to analyze unknown composite functions The thirty-second formula is estimated and is:

[0141] ;

[0142] in, is the ideal weight matrix, is the basis function vector; To approximate the error and satisfy , is a normal number.

[0143] make , the thirty-third formula is obtained, and the thirty-third formula is:

[0144] ;

[0145] in, ;

[0146] According to the 31st formula to the 33rd formula, the 34th formula is obtained, and the 34th formula is:

[0147] ;

[0148] Design the following control law and adaptive law as shown in the 35th and 36th formulas, and the 35th formula is:

[0149] ;

[0150] The thirty-sixth formula is:

[0151] ;

[0152] in, All are designed positive diagonal matrices; , βc The estimated value is , , The estimated value is ,in ;definition .

[0153] S105: Establish a periodic event triggering mechanism based on the unknown timing characteristics corresponding to the real state information under the replay attack and the feedback tracking control law output by the adaptive neural network.

[0154] Optionally, the periodic event trigger mechanism is established based on Formula 37 and Formula 38, and the Formula 37 is:

[0155] ;

[0156] The thirty-eighth formula is:

[0157] ;

[0158] in, is the measurement error of the control command, The control law for the design; is the design parameter, Q The minimum trigger period defined by the user, n is the minimum trigger period multiple, k is the sampling times.

[0159] Figure 2 This is a module diagram of a networked unmanned ship trajectory tracking control system under a replay attack provided by an exemplary embodiment of the present application. Figure 2 This embodiment provides a networked unmanned ship trajectory tracking control system under a replay attack, which is used to implement the control method of Example 1, including: the data sensor collects the state information of the ship's motion, and transmits the ship's state information to the shore-based control center through the wireless transmission network; the shore-based control center processes the collected ship motion state information, and completes the networked unmanned ship adaptive neural network output feedback control under the unknown random replay attack scenario; the ship-borne actuator executes the control instructions sent by the controller fed back by the wireless transmission network, specifically including the rudder angle instructions of the steering gear and the thrust instructions of the propeller, so as to realize the ship adaptive neural network trajectory tracking control triggered by periodic events under the replay attack.

[0160] In this embodiment, the new information collected about the ship's motion includes: the position, attitude, and longitudinal, lateral, and bow (angular) velocities of the ship measured by the sensor module; the unmanned ship sensor module includes a GPS positioning unit, an IMU inertial measurement unit, a radar, and a high-definition image sensor.

[0161] In this embodiment, the shore-based control center module includes: constructing a trajectory tracking control mathematical model between the input and output relationship of the ship through the ship's kinematic and dynamic information; obtaining the unknown ship position signal in the replay attack scenario through the finite coverage principle, and reconstructing the unknown composite function by the neural network system to construct an adaptive neural network state observer; compensating the impact of the position attack through the observer estimation information, and processing the unknown dynamics of the ship and the external environment disturbance by the neural network system, adaptive and single-parameter online learning technology; combining the periodic event trigger mechanism to construct a ship adaptive neural network trajectory tracking controller.

[0162] In this embodiment, the parameters to be designed of the adaptive neural network state observer and the adaptive neural network output feedback tracking controller and their respective adaptive laws are selected as shown in Table 1:

[0163] Table 1

[0164]

[0165] In this embodiment, the shipborne actuator executes the control instructions sent by the controller of the transmission network feedback, specifically including the rudder angle instructions of the steering gear and the thrust instructions of the propeller, so as to realize the ship adaptive neural network trajectory tracking control triggered by periodic events under replay attack.

[0166] In this embodiment, numerical simulation is performed using the Matlab platform, and a model ship is used as an example to verify the effectiveness of the control algorithm of this embodiment. The expected trajectory of the ship is and ,in The initial state of the unmanned ship is set to , , , , . External disturbance wave model generation. The control force (moment) is limited to Neural Networks , and The number of neurons is 10, and their centers are evenly distributed , , , with a width of 1.

[0167] Figure 3 An ideal and actual track tracking curve diagram of an unmanned ship provided for an exemplary embodiment of the present application. Figure 4 A graph showing the position error of an unmanned ship provided by an exemplary embodiment of the present application. Figure 5 A graph of the error between the actual and estimated speeds of an unmanned ship provided by an exemplary embodiment of the present application. Figure 6 A control input curve diagram of an unmanned ship provided for an exemplary embodiment of the present application. Figure 7 An adaptive parameter estimation curve diagram of an unmanned ship provided by an exemplary embodiment of the present application. Figure 8 This is a schematic diagram of the periodic event triggering time and interval provided by an exemplary embodiment of the present application. Figures 3 to 8 The periodic event-triggered adaptive neural network trajectory tracking control method has a good control effect. Even in the unknown random replay attack scenario, the unmanned ship can still track the expected trajectory with a small tracking error and navigate safely, and has good control performance; the adaptive neural network state observer can restore the state information of the unmanned ship more accurately; the periodic event trigger mechanism greatly reduces the number of actuator responses.

[0168] The trajectory tracking control method for a networked unmanned ship under a replay attack provided in the present application restores the true speed information of the unmanned ship under the replay attack by constructing an adaptive neural network state observer, avoids damaged signals containing unknown random replay attack signals from entering the control system from the speed channel, and compensates for the impact of the replay attack on the replay position; by establishing a periodic event trigger mechanism, the drive wear is alleviated, and the performance of the unmanned ship control system is further guaranteed.

[0169] In summary, the present invention successfully restores the true speed of the unmanned ship under the replay attack through an adaptive neural network state observer, avoids the degradation of control performance caused by the inclusion of the replay attack speed into the control system along with the sensor signal, and effectively compensates for the impact of the position replay attack; by combining the periodic event trigger mechanism, the number of high-frequency responses of the actuator is reduced and mechanical wear is alleviated, further ensuring the control performance of the system.

[0170] Corresponding to the aforementioned embodiment of a method for tracking and controlling a trajectory of a networked unmanned ship under a replay attack, the present application also provides an embodiment of a device for tracking and controlling a trajectory of a networked unmanned ship under a replay attack.

[0171] The embodiment of the present application of a networked unmanned ship trajectory tracking control device under replay attack can be applied to a networked unmanned ship trajectory tracking control device under replay attack. The device embodiment can be implemented by software, or by hardware or a combination of software and hardware. Taking software implementation as an example, as a device in a logical sense, it is formed by the processor of the networked unmanned ship trajectory tracking control device under replay attack in which it is located reading the corresponding computer program instructions in the non-volatile memory into the memory for execution. From the hardware level, if Fig. 9 As shown, it is a hardware structure diagram of the networked unmanned ship trajectory tracking control device under replay attack of the present application, except Fig. 9 In addition to the processor, memory, network interface, and non-volatile memory shown, the networked unmanned ship trajectory tracking control device under replay attack in which the device in the embodiment is located may also include other hardware, which will not be elaborated here.

[0172] Fig.10 This is a schematic diagram of the structure of the first embodiment of the networked unmanned ship trajectory tracking control device under replay attack provided by this application. Fig.10 The device provided in this embodiment includes a tracking module 1010, a processing module 1020 and a design module 1030, wherein:

[0173] The tracking module 1010 is used to establish a dynamic and kinematic mathematical model according to the motion information of the three-degree-of-freedom fully-driven ship, and to track the desired state information and the actual state information of the fully-driven ship in real time; according to the saturation constraint of the control input of the fully-driven ship, a smooth function is used to replace the saturation nonlinearity;

[0174] The processing module 1020 is used to analyze the mechanism of replay attack and establish a replay attack mathematical model in combination with Bernoulli random variables;

[0175] The processing module 1020 is further used to establish an adaptive neural network state observer according to the dynamics and kinematics mathematical model, the replay attack mathematical model and the neural network system;

[0176] The design module 1030 is further used to design an adaptive neural network output feedback tracking control law based on the adaptive neural network state observer in the framework of vector backstepping method, combined with neural network and minimum parameter learning technology;

[0177] The processing module 1020 is further used to establish a periodic event triggering mechanism based on the unknown timing characteristics corresponding to the real state information under the replay attack and the feedback tracking control law output by the adaptive neural network.

[0178] The device of this embodiment can be used to perform Figure 1 The steps, specific implementation principles and implementation processes of the method embodiment shown are similar and will not be repeated here.

[0179] Please continue to refer to Fig. 9 The present application also provides a networked unmanned ship trajectory tracking control device under a replay attack, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of any one of the methods provided in the first aspect of the present application are implemented.

[0180] The present application also provides a computer-readable storage medium having a computer program stored thereon, and when the program is executed by a processor, the steps of any one of the methods provided in the present application are implemented.

[0181] The implementation process of the functions and effects of each unit in the above-mentioned device is specifically described in the implementation process of the corresponding steps in the above-mentioned method, and will not be repeated here.

[0182] For the device embodiment, since it basically corresponds to the method embodiment, the relevant parts can refer to the partial description of the method embodiment. The device embodiment described above is only schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the present application scheme. A person of ordinary skill in the art can understand and implement it without paying any creative work.

[0183] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present application shall be included in the scope of protection of the present application.

Claims

1. A networked unmanned ship trajectory tracking control method under replay attack, characterized in that: The method comprises: A dynamic and kinematic mathematical model is established according to the motion information of the three-degree-of-freedom fully-driven ship, and the desired state information and the actual state information of the fully-driven ship are tracked in real time; according to the saturation constraint of the control input of the fully-driven ship, a smooth function is used to replace the saturation nonlinearity; Analyze the mechanism of replay attack, combine Bernoulli random variables, and establish a mathematical model of replay attack; Establishing an adaptive neural network state observer according to the dynamics and kinematics mathematical model, the replay attack mathematical model and the neural network system; Based on the adaptive neural network state observer, in the framework of vector backstepping method, combined with neural network and minimum parameter learning technology, an adaptive neural network output feedback tracking control law is designed; The design of the adaptive neural network output feedback tracking control law includes: Obtaining estimated values ​​of the ship position and speed of the all-drive ship based on the adaptive neural network state observer, and calculating the feedback tracking control law in combination with the observer gain of the adaptive neural network state observer; Based on the unknown timing characteristics corresponding to the real state information under the replay attack and the feedback tracking control law output by the adaptive neural network, a periodic event triggering mechanism is established.

2. The method according to claim 1, characterized in that The motion information of the three-degree-of-freedom fully-driven ship includes ship posture, angular velocity, and control torque.

3. The method according to claim 1, characterized in that: The dynamics and kinematics mathematical model is established according to the motion information of the three-degree-of-freedom fully-driven ship, including: The dynamic and kinematic mathematical model is established based on the first formula, and the first formula is: ； Among them, the is the ship pose vector, containing the ship position and heading angle ; is the derivative of the ship's posture vector; is the derivative of the ship velocity vector; , is the ship velocity vector, including surge, sway and pitch angular velocity; τ is the control input vector; ; d is the external disturbance vector; , M is the inertia matrix; is the Coriolis centripetal matrix; is the nonlinear hydrodynamic damping matrix; is a rotation matrix that satisfies , the rotation matrix expression is the second formula, and the second formula is: ； Among them, the is the rotation matrix, is the heading angle.

4. The method according to claim 1, characterized in that: The method of replacing the saturation nonlinearity with a smooth function according to the saturation constraint of the full-drive ship control input comprises: The calculation process of the saturation constraint is the third formula, which is: ； Among them, the is the actual control instruction; yes i The upper limit of the control force or torque in the direction, It is the control instruction for subsequent design; The fourth formula is introduced as a hyperbolic tangent smooth function, and the fourth formula is: ； Combined with the mean value theorem, the control input at this time satisfies the fifth formula, which is: ； Among them, the is the smoothed calculated value of the control input, satisfying , is the corresponding initial value; is the actual control instruction; is a bounded variable, and its operation rule is ,satisfy , ; is a bounded approximation error that satisfies ; It is the control instruction for subsequent design.

5. The method according to claim 1, characterized in that The analysis of the replay attack mechanism is combined with Bernoulli random variables to establish a replay attack mathematical model, including: The replay attack mathematical model is established based on the sixth formula, which is: ； Among them, the is an unknown position signal received by the observer; η is the real position signal of the all-drive vessel; To replay the attack signal; The time for the attacker to record the attack signal and meet , t is the time when the attacker sends the attack signal, represents the time interval between the attacker recording and sending the replay attack signal; the Bernoulli random variable σ is the occurrence indicator of the replay attack, σ 1 indicates that the attack is active. σ 0 means the attack is dormant, with a probability of .

6. The method according to claim 1, characterized in that The method of establishing an adaptive neural network state observer according to the dynamics and kinematics mathematical model, the replay attack mathematical model and the neural network system comprises: Construct a first-order filter to obtain the derivative of the replayed attack signal; Based on the replay attack mathematical model, combined with the finite coverage principle, the unknown replay attack signal derivative is covered; On the basis of the covered ship position signal of the all-drive ship, the adaptive neural state observer is constructed in combination with the neural network system.

7. The method according to claim 6, characterized in that The step of constructing a first-order filter to obtain a derivative of a replayed attack signal includes: The replay attack signal derivative is obtained based on the seventh formula, and the seventh formula is: ； Among them, the is the filtering constant; The time when the attacker records the attack signal; η is the real position signal of the all-drive vessel; To replay the attack signal; is the replayed attack signal after replacement; the attack signal derivative quilt replace.

8. The method according to claim 6, characterized in that Based on the replay attack mathematical model, combined with the finite coverage principle, the unknown replay attack signal derivative is covered, including: Starting from delay 0, divide N Known delay interval To cover the unknown replay attack delay to a limited extent ; and , is the maximum delay that the control system can tolerate; There is a delay interval Just delay the unknown replay attack Coverage, that is, there is a bounded range of states that can be obtained , so that The eighth formula is satisfied, and the eighth formula is: ； Among them, the is the attack signal derivative; is a bounded coverage signal interval that satisfies .

9. The method according to claim 6, characterized in that The method of constructing the adaptive neural state observer based on the covered ship position signal of the fully-driven ship and combining the neural network system comprises: The ship dynamics and kinematics mathematical equations are rewritten based on the ninth formula, which is: ； Among them, the is the derivative of the ship's posture vector; is the rotation matrix; is the ship velocity vector; is the derivative of the ship velocity vector; is a class perturbation vector; ; ; is an unknown function, and is approximated based on the neural network system, and the process is shown in the tenth formula, which is: ； Among them, the is a composite uncertainty term containing unknown dynamics and additional mass; is an ideal weight matrix that satisfies , is the transpose of the ideal weight matrix; is a basis function vector that satisfies ; is the input vector of the neural network, satisfying ; To approximate the error vector and satisfy , is a positive constant; In the replay attack scenario, the unknown ship position signal containing the replay attack signal enters the observer system, causing the unknown dynamic composite term The eleventh formula is included, and the eleventh formula is: ； Among them, the ; is an unknown composite dynamic; express and multiply; express and multiply; The delay interval The starting value of Using neural network system to predict unknown compound terms Approximation is performed, and the process is represented by the twelfth formula, which is: ； Among them, the is an unknown composite dynamic; ; is the approximation value of the neural network; is the ideal weight matrix, is the basis function vector, To approximate the error vector and satisfy , is a positive constant; make , , , ; and stated represent the estimated values ​​of the ship's position and speed respectively, and stated It is obtained by the adaptive neural network state observer of the thirteenth formula, and the thirteenth formula is: ； Among them, the is an estimated value of the ship position of the all-drive ship, is an estimated value of the ship speed of the all-drive ship; is the derivative of the pose error estimate; is the rotation matrix after the attack, For the The transpose of is the estimated error of the position signal; for The estimated value of ; yes The estimated value of ; k 1. k 2. κ are the designed observer gains; is an auxiliary variable; is the transpose of the ideal weight estimate of the tenth formula; is the transpose of the ideal weight matrix estimate; The adaptive law is the fourteenth formula and the fifteenth formula, and the fourteenth formula is: ； The fifteenth formula is: ； Among them, the ; is an estimate of the ideal weight matrix; is the transpose of the estimated error of the position signal; is the derivative of the ideal weight estimate; yes An estimated value of , ; κ>0, k1>0 and k2>0 are observer gains; is an auxiliary variable; is the rotation matrix after the attack, For the The transpose of and stated For a positive design matrix, and are all positive constants; k 3 and k 4 is a positive design parameter; For vector traces; For the adaptive neural network state observer, the design parameters satisfy the following inequality, and the observation error is and stated and the neural network weight estimation error and is bounded, based on the sixteenth formula, which is: ； Among them, the κ , k 1 and as stated k 2 is the observer gain; k 3 and as stated k 4 is a positive design parameter; and stated are the number of neurons in the corresponding neural network systems; The state observation error dynamic equation of the adaptive neural network state observer is the seventeenth formula and the eighteenth formula, and the seventeenth formula is: ； The eighteenth formula is: ； Among them, the is the derivative of the position estimation error; express and multiply; express and multiply; is the estimated error of the position signal; is the derivative of the velocity estimation error; yes ; k1, k2 and κ are designed observer gains; ; The Lyapunov function is constructed to analyze the performance of the adaptive neural network state observer, as shown in the nineteenth formula, which is: ； Among them, the is the constructed Lyapunov function; is the estimated error of the position signal; is the transpose of the estimated error of the position signal; is the speed estimation error; is an estimate of the ideal weight matrix; combining the seventeenth formula and the eighteenth formula to derive the nineteenth formula, the twentieth formula is obtained, and the twenty-first formula is: ； Among them, the is the derivative of the nineteenth formula; express and multiply; κ is the designed observer gain; is the basis function vector; is the heading angle after the attack; is the estimated value of; according to J(ψ) ‖=1 and ‖ υ ‖≤ υm , wherein the υm is the maximum speed of the ship, and the 21st formula is obtained. The 21st formula is: ； Among them, the ; yes The square of the norm; yes The square of the norm; yes The norm of yes An estimated value of , ; Said and is a positive constant; The 20th formula can be written as the 22nd formula according to the 17th formula to the 21st formula. The 22nd formula is: ； Among them, the is the derivative of the nineteenth formula; is the constructed Lyapunov function; ; The twenty-third formula is obtained by solving the twenty-second formula, and the twenty-third formula is: ； Among them, the is the constructed Lyapunov function; is the initial value; when t When it approaches ∞, ,therefore , are all bounded; when t When it approaches ∞, the twenty-fourth formula is obtained according to the nineteenth formula and the twenty-third formula, and the twenty-fourth formula is: ； Among them, the is the norm of the attitude estimation error; is the norm of the speed estimation error; the κ is a preset design parameter; the preset design parameter is selected κ , k 1, k 2, k 3 and k 4, and ensure that the sixteenth formula is established, the state observation error is and stated Can converge to a first preset range.

10. The method according to claim 1, characterized in that The design of the adaptive neural network output feedback tracking control law includes: In the design framework of the backstepping method, in order to avoid the virtual control law α f The complex derivative operation of the seventh formula is introduced to obtain its filtered version by introducing the first-order filter of the seventh formula α The specific process is shown in the twenty-fifth formula, and the seventh formula is: ； Among them, the is the filtering constant; The time when the attacker records the attack signal; η is the real position signal of the all-drive vessel; To replay the attack signal; is the replayed attack signal after replacement; the attack signal derivative quilt replace; The twenty-fifth formula is: ； Among them, the yes α The derivative of is a filtered version of the virtual control law; is the virtual control law; T is the filter constant; the filter error is ,at this time ; Defining the attitude error of the unmanned ship and speed error As shown in the twenty-sixth formula, the twenty-sixth formula is: ； The attitude error is differentiated to obtain the twenty-seventh formula, which is: ； The virtual control law is the twenty-eighth formula, which is: ； Among them, the is the estimated error of the position signal corresponding to the position of the all-drive ship; is the ideal position of the ship; is a filtered version of the virtual control law; is the derivative of the ship attitude tracking error; is the virtual control law; is the derivative of the ideal position of the ship; is a positive design matrix; ; Substituting the twenty-eighth formula into the twenty-seventh formula yields the twenty-ninth formula, which is: ； Among them, the is the derivative of the ship attitude tracking error; A is a bounded unknown composite term; ;make , is a positive constant; According to the first and fifth formulas, we get the 30th formula: The first formula is: ； Among them, the is the ship pose vector, containing the ship position and heading angle ; is the derivative of the ship's posture vector; is the derivative of the ship velocity vector; , is the ship velocity vector, including surge, sway and pitch angular velocity; τ is the control input vector; ; d is the external disturbance vector; , M is the inertia matrix; is the Coriolis centripetal matrix; is the nonlinear hydrodynamic damping matrix; is the rotation matrix; The fifth formula is: ； Among them, the is the smoothed calculated value of the control input, satisfying , is the corresponding initial value; is the actual control instruction; is a bounded variable, and its operation rule is ,satisfy , ; is a bounded approximation error that satisfies ; It is the control instruction for subsequent design; The 30th formula is: ； Among them, the is a bounded variable; yes The column vector composed of , there exists a normal number Make ; , there exists a normal number Make ; The 31st formula is obtained by derivatizing the speed error, and the 31st formula is: ； Among them, the is the derivative of the ship speed tracking error; ; Use neural network system to analyze unknown composite functions The thirty-second formula is estimated and is: ； Among them, the is the input vector of the above neural network; is the basis function; is the ideal weight; is the ideal weight matrix, is the basis function vector; εc is the approximation error and satisfies , is a positive constant; make , the thirty-third formula is obtained, and the thirty-third formula is: ； Among them, the is the transpose of the ship speed tracking error; is an unknown constant; is the kernel function; ; According to the 31st formula to the 33rd formula, the 34th formula is obtained, and the 34th formula is: ； Design the following control law and adaptive law as shown in the 35th and 36th formulas, and the 35th formula is: ； The thirty-sixth formula is: ； Among them, the is the feedback tracking control law; yes The estimated value of is calculated as follows: ,satisfy ; yes ; yes ; yes The estimated value of yes The estimated value of ; yes The derivative of are all designed positive diagonal matrices; definition .

11. The method according to claim 1, characterized in that The periodic event triggering mechanism is established based on the unknown timing characteristics corresponding to the real state information under the replay attack and the feedback tracking control law output by the adaptive neural network, including: The periodic event trigger mechanism is established based on the 37th formula and the 38th formula, and the 37th formula is: ； The thirty-eighth formula is: ； Among them, the It is the control instruction of the subsequent design; yes i direction k The triggering moment of the second; is the measurement error of the control command, The control law for the design; is the design parameter, Q The minimum trigger period defined by the user, n is the minimum trigger period multiple, k is the sampling times.

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