An unmanned underwater vehicle trajectory tracking method with anti-dos attack and disturbance compensation capability

Abstract

This invention discloses a trajectory tracking method for unmanned underwater vehicles (UUVs) with anti-DoS attack and disturbance compensation capabilities, relating to the field of control technology. It includes establishing a kinematic and dynamic model of the UUV, estimating external disturbances, solving a disturbance compensation optimization problem to obtain disturbance compensation control inputs, embedding the disturbance compensation control inputs into the input constraints of a disturbance compensation model predictive control optimization problem, and solving for the optimal control input sequence. To resist DoS attacks, a packet transmission strategy based on the total predictive control sequence is designed. This strategy includes the actuator receiving and buffering the total predictive control sequence when communication is normal; when communication is interrupted by an attack, the actuator reconstructs the current control command using the buffered sequence to maintain control continuity. This application can achieve robust and safe trajectory tracking of UUVs in complex environments with both unknown disturbances and DoS attacks, exhibiting good trajectory tracking stability.

Description

Technical Field

[0001] This invention relates to the field of control technology, and in particular to a method for tracking the trajectory of an unmanned underwater vehicle with anti-DoS attack and disturbance compensation capabilities. Background Technology

[0002] Uncrewed Underwater Vehicles (UUVs), as important intelligent marine equipment, have been widely used in fields such as marine exploration, underwater infrastructure inspection, and environmental monitoring. With the development of UUV technology, their control systems are increasingly integrated with communication systems, enabling information exchange with the control center or mother ship via communication links to support navigation, monitoring, and emergency or backup control functions. However, due to the complexity of the marine environment and factors such as limited bandwidth, high latency, and insufficient reliability of underwater acoustic communication, UUV communication links are prone to network anomalies and even denial-of-service (DoS) attacks. DoS attacks significantly degrade control system performance by blocking control information transmission, and in severe cases, may lead to system instability.

[0003] To address the control problem of marine robots under DoS attacks, existing research mainly employs non-optimization methods such as event-triggered control, sliding mode control, observer-compensated control, and fuzzy control. These methods improve system robustness through fixed control laws or switching mechanisms, but they struggle to systematically consider input and state constraints. When attacks are prolonged or complex, control performance and safety are difficult to guarantee. Furthermore, UUVs are inevitably affected by external factors such as ocean current disturbances during actual operation. When DoS attacks and external disturbances coexist, existing methods still fall short in terms of trajectory tracking accuracy, system robustness, and constraint satisfaction. A unified control framework that can balance performance and safety is still lacking.

[0004] Therefore, the low accuracy and poor stability of unmanned underwater vehicle trajectory tracking in the presence of both DoS attacks and external disturbances have become urgent technical problems that need to be solved. Summary of the Invention

[0005] This invention provides a trajectory tracking method for unmanned underwater vehicles with anti-DoS attack and disturbance compensation capabilities, solving the technical problem of poor trajectory tracking stability of unmanned underwater vehicles when DoS attacks and external disturbances coexist.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] A method for tracking the trajectory of an unmanned underwater vehicle with anti-DoS attack and disturbance compensation capabilities includes the following steps:

[0008] Step 1: Construct the kinematic and dynamic models of the unmanned underwater vehicle and form a planar mathematical model. Discretize the planar mathematical model to obtain a predictive model for trajectory tracking control.

[0009] Step 2: Obtain the actual state of the unmanned underwater vehicle at the current moment, the system state at the previous moment, and the control input at the previous moment. Combine the dynamic model of the unmanned underwater vehicle to calculate the disturbance value at the previous moment and use it as the estimated value of the disturbance at the current moment. Construct a disturbance compensation mechanism. Based on the estimated value of the disturbance at the current moment, construct the cost function and input constraints for disturbance compensation and solve for the disturbance compensation control input.

[0010] Step 3: Obtain the cost function and input constraints of the disturbance compensation model predictive control and form a trajectory tracking control strategy. Embed the disturbance compensation control input into the input constraints of the disturbance compensation model predictive control of the trajectory tracking control strategy, and iteratively solve to obtain the optimal control input sequence.

[0011] Step 4: Add the disturbance compensation control input to the optimal control input sequence to obtain the total predictive control sequence. Based on the total predictive control sequence, design the packet transmission strategy. The packet transmission strategy includes the actuator receiving and buffering the total predictive control sequence when communication is normal.

[0012] Step 5: When communication is interrupted due to a DoS attack, the actuator reconstructs the control input at the current moment based on the cached total predictive control sequence.

[0013] A further technical solution is that, in step 1, the planar mathematical model of the unmanned underwater vehicle is Equation (3).

[0014]

[0015] (3)

[0016] In equation (3), For planar kinematics model, This represents the position and orientation vector of an unmanned underwater vehicle in an inertial coordinate system. This represents the velocity vector of the unmanned underwater vehicle in volume coordinates. For rotation matrix, The heading angle of the unmanned underwater vehicle; For dynamic model, It is the inertia matrix. It is the Coriolis force-centripetal force matrix. It is the hydrodynamic damping matrix. This represents the control input vector of an unmanned underwater vehicle.

[0017] The prediction model used for trajectory tracking control is Equation (4).

[0018] (4)

[0019] Equation (4) is the prediction model used for trajectory tracking control under nominal conditions. In equation (4), This indicates the nominal status of the unmanned underwater vehicle. For the control input of unmanned underwater vehicles, This is a discretized dynamic model for an unmanned underwater vehicle.

[0020] A further technical solution is that, in step 2, the disturbance value at the previous moment is calculated according to equation (6).

[0021] (6)

[0022] In equation (6), This represents the actual disturbance at the previous moment. For unmanned underwater vehicles at all times The actual state This represents the system state at the previous moment. To control the input, Discretized dynamic model for unmanned underwater vehicles;

[0023] According to equation (7), the disturbance value of the previous moment is used as the estimated value of the disturbance at the current moment.

[0024] (7)

[0025] In equation (7), It is a disturbance The estimate;

[0026] The cost function and input constraints for disturbance compensation are given by equation (8).

[0027]

[0028] (8)

[0029] In equation (8), This represents the cost function for perturbation compensation. Indicates the sampling interval. Let be the inertia matrix of the dynamic model of the unmanned underwater vehicle. Input constraints for disturbance compensation. For disturbance compensation control input; and These represent the minimum and maximum values ​​of the disturbance compensation control input, respectively.

[0030] A further technical solution is that, in step 3, the cost function of the disturbance compensation model predictive control is given by equation (9).

[0031] (9)

[0032] In equation (9), It predicts the time domain. Indicates in The sampling state at any given time. Indicates in The first thing to do at any moment Predicted state at any given time It is a predictive control sequence; and These represent the stage cost function and the terminal cost function, respectively. Represents reference path information, matrix , and It is a positive definite weighted matrix;

[0033] The trajectory tracking control strategy is given by equation (10).

[0034]

[0035]

[0036] ,

[0037] ,

[0038] (10)

[0039] In equation (10), This represents the optimal control input sequence. and These represent the minimum and maximum values ​​of the control input for the unmanned underwater vehicle, respectively. Input constraints for predictive control of the disturbance compensation model; optimal control input sequence .

[0040] A further technical solution is that, in step 4, the total predictive control sequence is given by equation (11).

[0041] (11)

[0042] In equation (11), This is the overall predictive control sequence;

[0043] The packet transmission strategy also includes sending the entire predictive control sequence to the actuator and buffering it when communication is normal. The current control input of the unmanned underwater vehicle uses the first value of the overall predictive control sequence. When communication is interrupted, the actuator selects the control input from the most recent successful transmission moment based on the cached total predictive control sequence for the current control cycle.

[0044] A further technical solution is that, in step 5, reconstructing the control input at the current moment includes selecting the control input at the moment of the most recent successful transmission.

[0045] The beneficial effects of adopting the above technical solution are as follows:

[0046] A trajectory tracking method for unmanned underwater vehicles (UUVs) with DoS attack resistance and disturbance compensation capabilities is proposed. First, a kinematic and dynamic model of the UUV is established. Second, after estimating external disturbances, a disturbance compensation optimization problem is solved to obtain the disturbance compensation control input. The disturbance compensation control input is then embedded into the input constraints of a disturbance compensation model predictive control optimization problem to obtain the optimal control input sequence. To resist DoS attacks on the communication channel between the remote control center and the actuator, a packet transmission strategy based on the total predictive control sequence is designed. This strategy includes the actuator receiving and buffering the total predictive control sequence when communication is normal; when communication is interrupted by an attack, the actuator reconstructs the current control command using the buffered sequence to maintain control continuity. This application enables robust and safe trajectory tracking of UUVs in complex environments with both unknown disturbances and DoS attacks, exhibiting good trajectory tracking stability. Attached Figure Description

[0047] Figure 1 This is a flowchart of the application;

[0048] Figure 2 A data graph showing the inertial coordinate system and the volume coordinate system;

[0049] Figure 3 This is a data flow diagram illustrating the overall control of this application under a DoS attack. Detailed Implementation

[0050] The purpose of this application is to address the limitations of non-optimization methods, which struggle to systematically consider input and state constraints and lack the ability to handle DoS attacks. This application employs a model predictive control (MPC) optimization method. Due to its predictive characteristics and rolling optimization mechanism, MPC can compensate for intermittent data loss using future information while explicitly handling input and state constraints. Furthermore, it incorporates disturbances in the marine environment into the design of the disturbance compensation optimization problem, overcoming the limitations of existing methods in terms of anti-interference capabilities. This method overcomes the limitations of existing research, improves the trajectory tracking accuracy of UUVs, ensures the safety and robustness of trajectory tracking control, and enhances the mission execution capabilities of UUVs in complex underwater environments.

[0051] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit this application or its application or use. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0052] Many specific details are set forth in the following description in order to provide a full understanding of this application. However, this application may also be implemented in other ways different from those described herein. Those skilled in the art can make similar extensions without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0053] Example 1:

[0054] like Figure 1 As shown, this invention discloses a method for tracking the trajectory of an unmanned underwater vehicle with anti-DoS attack and disturbance compensation capabilities, comprising the following steps:

[0055] Step 1: Construct UUV kinematic, dynamic, and predictive models.

[0056] The kinematic and dynamic models of the unmanned underwater vehicle are constructed, and a predictive model for trajectory tracking control is obtained, as detailed below.

[0057] Step 1-1: The planar kinematic model of a UUV is defined as follows:

[0058] (1)

[0059] In equation (1), This represents the position and orientation vector of an unmanned underwater vehicle in an inertial coordinate system. This represents the velocity vector of the unmanned underwater vehicle in volume coordinates. Let the rotation matrix be defined as follows:

[0060]

[0061] in, The heading angle of the unmanned underwater vehicle.

[0062] like Figure 2 As shown in the diagram, the data from the inertial coordinate system and the volume coordinate system can be seen... The distribution and relationships of.

[0063] Step 1-2: Establish the dynamic model of the UUV as follows:

[0064] (2)

[0065] Equation (2) is the original dynamic model of the unmanned underwater vehicle. In equation (2), It is the inertia matrix. It is the Coriolis force-centripetal force matrix. It is the hydrodynamic damping matrix. These matrices represent the control input vectors of the unmanned underwater vehicle, and their detailed definitions are as follows:

[0066]

[0067]

[0068]

[0069] in, , , Indicates mass as The inertial term. , , , and , These represent the hydrodynamic damping coefficients in the directions of surge, sway, and yaw, respectively.

[0070] In summary, the planar mathematical model of UUV is defined as:

[0071]

[0072] (3)

[0073] In equation (3), For planar kinematics model, This represents the position and orientation vector of an unmanned underwater vehicle in an inertial coordinate system. This represents the velocity vector of the unmanned underwater vehicle in volume coordinates. For rotation matrix, The heading angle of the unmanned underwater vehicle; For dynamic model, It is the inertia matrix. It is the Coriolis force-centripetal force matrix. It is the hydrodynamic damping matrix. This represents the control input vector of the unmanned underwater vehicle.

[0074] Steps 1-3: Discretize equation (3) and write it in a concise form to obtain the prediction model for trajectory tracking control, see equation (4):

[0075] (4)

[0076] (5)

[0077] Equation (4) is the prediction model used for trajectory tracking control under nominal conditions. In equation (4), This indicates the nominal status of the unmanned underwater vehicle. For the control input of unmanned underwater vehicles, For the discretized dynamic model of the unmanned underwater vehicle, In this context, d stands for discrete.

[0078] Equation (5) is the model used for state updates. In equation (5), This indicates the actual state of an unmanned underwater vehicle, including disturbances. This indicates an external disturbance.

[0079] The predictive model is the nominally undisturbed state formula (4). Formula (5) is written here because it is used in formula (6) to estimate the disturbance. It is a model used for state updates. So, to summarize, formula (5) has two uses. First, it is used for the state update model, not for the predictive model of trajectory tracking control. Second, it is used for the calculation of the disturbance at the previous time step, see formula (6).

[0080] Step 2: Construct a disturbance compensation mechanism.

[0081] External disturbances are estimated, a disturbance compensation mechanism is constructed, and corresponding disturbance compensation control inputs are generated, as detailed below.

[0082] Step 2-1: For low-frequency disturbances in the marine environment, construct a disturbance estimation mechanism based on the system state and dynamics model. At any time, using unmanned underwater vehicles at any time actual state The system state at the previous moment and control input Combining known dynamic models of unmanned underwater vehicles Calculating the disturbance from the previous moment, we obtain:

[0083] (6)

[0084] In equation (6), This represents the actual disturbance at the previous moment. For unmanned underwater vehicles at all times The actual state This represents the system state at the previous moment. For controlling input.

[0085] Furthermore, based on the characteristics of slow changes in the marine environment and limited amplitude of disturbance changes within adjacent sampling times, the disturbance value calculated at the previous time step is used as the estimated value of the disturbance at the current time step, that is:

[0086] (7)

[0087] In equation (7), It is a disturbance The estimate.

[0088] Step 2-2: After obtaining the estimated value of the disturbance, design the disturbance compensation optimization problem, including the cost function and input constraints of the disturbance compensation optimization problem, specifically defined as:

[0089]

[0090] (8)

[0091] In equation (8), Let represent the cost function of the perturbation compensation optimization problem. Indicates the sampling time. This indicates the disturbance compensation control input. Input constraints for disturbance compensation. and These represent the minimum and maximum values ​​of the disturbance compensation control input, respectively.

[0092] Solve the disturbance compensation control input optimization problem to obtain the disturbance compensation control input.

[0093] Step 3: Construct a trajectory tracking control strategy based on a prediction model.

[0094] The disturbance compensation control input is embedded into the input constraints of the disturbance compensation model predictive control optimization problem to construct a trajectory tracking control strategy based on the predictive model. The optimal control input sequence is obtained by solving it online, as detailed below.

[0095] Step 3-1: Design the cost function for the predictive control optimization problem of the disturbance compensation model, specifically defined as:

[0096] (9)

[0097] In equation (9), It predicts the time domain. Indicates in The sampling state at any given time. Indicates in The first thing to do at any moment Predicted state at any given time It is a predictive control sequence; and These represent the stage cost function and the terminal cost function, respectively. Represents reference path information, matrix , and It is a positive definite weighted matrix.

[0098] Step 3-2: Design the disturbance compensation model predictive control optimization problem, embedding the disturbance compensation control input into the input constraints of the disturbance compensation model predictive control optimization problem; based on the prediction model of formula (4), iteratively solve the optimal control input sequence; the definition of the disturbance compensation model predictive control optimization problem is as follows:

[0099]

[0100]

[0101] ,

[0102] ,

[0103] (10)

[0104] In equation (10), This represents the optimal control input sequence. and These represent the minimum and maximum values ​​of the control input for the unmanned underwater vehicle, respectively. The input constraints for disturbance compensation model predictive control are defined; the optimal control input sequence is obtained by solving the disturbance compensation model predictive control optimization problem. .

[0105] Equation (10) as a whole is referred to as the perturbation compensation model predictive control optimization problem. Equation (9) is the cost function of the perturbation compensation model predictive control optimization problem. Equation (9) is included in Equation (10) because the first term of Equation (10) , here It is the cost function of the perturbation compensation model predictive control optimization problem. Therefore, formula (10) is the perturbation compensation model predictive control optimization problem.

[0106] The input constraints for the disturbance compensation model predictive control optimization problem are in equation (10). The disturbance compensation input constraints are in formula (8), and there is a difference between the two. Solving the disturbance compensation optimization problem will yield the following results. , and then This is placed into the input constraints of the predictive control optimization problem of the disturbance compensation model, that is, in formula (10). and Include .

[0107] Step 4: Transmit and cache the total predictive control sequence when communication between the remote control center and the actuator is normal.

[0108] The total predictive control sequence is obtained from the disturbance compensation control input and the optimal control input sequence. A group transmission strategy is designed based on the total predictive control sequence. When communication is normal, the actuator receives and buffers the total predictive control sequence, as detailed below.

[0109] Step 4-1: Based on the disturbance compensation control input obtained in Step 2-2 and the optimal control input sequence obtained in Step 3-2, since the disturbance is low-frequency, it will not deviate too much within a prediction time domain. Therefore, the disturbance compensation control input... It can be applied to the entire prediction time domain. Adding the disturbance compensation control input to the optimal control input sequence yields the total predictive control sequence, expressed as:

[0110] (11)

[0111] In equation (11), This is the overall predictive control sequence.

[0112] Step 4-2: To defend against DoS attacks on the communication channel between the remote control center and the actuator, a packet transmission strategy based on the total predictive control sequence is designed, as detailed below:

[0113] when When communication is normal, the actuator can directly receive the total predictive control sequence sent from the remote control center. The actuators of the unmanned underwater vehicle use the first control signal of the total predictive control sequence as input:

[0114] (12)

[0115] In equation (12), This is the first control input signal of the overall predictive control sequence.

[0116] At the same time, the received total prediction control sequence Update the buffer and update the time of the most recent successful transfer from the remote control center to the actuator. .

[0117] Step 5: When communication between the remote control center and the actuator is interrupted due to a DoS attack, the actuator reconstructs the control input at the current moment based on the cached total predictive control sequence.

[0118] When communication is interrupted due to a DoS attack, the actuator reconstructs the control input at the current moment based on the cached total predictive control sequence in order to maintain the continuity and stability of the unmanned underwater vehicle trajectory tracking control, as detailed below.

[0119] when When communication is interrupted, the communication channel is blocked, and the actuator cannot receive information from the remote control center. The actuators of unmanned underwater vehicles are used in… The total predictive control sequence received at each time step reconstructs the control command at the current time step, as shown in Equation (13), in order to maintain control continuity.

[0120] (13)

[0121] In equation (13), This refers to the control input signal at the moment of the most recent successful transmission of the overall predictive control sequence. This indicates the time of the most recent successful transmission.

[0122] The basic idea of ​​this application is as follows: to establish a kinematic and dynamic model of an unmanned underwater vehicle; to estimate low-frequency disturbances in the marine environment; to design a cost function for a disturbance compensation optimization problem based on the disturbance estimate; to complete the design of the disturbance compensation optimization problem by combining the input constraints of the disturbance compensation optimization problem; to embed the disturbance compensation control input into the input constraints of the disturbance compensation model predictive control optimization problem; to design a cost function; and to solve for the optimal control input sequence.

[0123] like Figure 3As shown, the DoS attack occurs on the communication channel between the remote control center and the actuator. A packet transmission strategy based on the total predictive control sequence is designed to resist the impact of the DoS attack. By solving a two-layer optimization problem and implementing the packet transmission strategy, robust and safe trajectory tracking of the unmanned underwater vehicle can be achieved in a complex environment where unknown disturbances and DoS attacks coexist.

[0124] Compared with the prior art, the beneficial technical effects of this application are as follows.

[0125] 1. This application introduces a packet transmission strategy based on total predictive control sequence. When the communication channel between the remote control center and the actuator is subjected to a DoS attack, the actuator can still use the predicted and cached control sequence to maintain continuous system control, avoid control failure caused by communication interruption, and improve the trajectory tracking reliability and system resilience of UUV in network attack environment.

[0126] 2. This application introduces a disturbance compensation optimization problem. By combining disturbance estimation, compensation mechanism and rolling time-domain optimization, it can effectively suppress unknown bounded disturbances and ensure the convergence of trajectory tracking error and the stability of control performance even under complex environmental disturbances such as ocean currents.

[0127] 3. Based on the multi-constraint optimization characteristics of model predictive control, this application integrates control input constraints and system dynamic constraints into the optimization solution process. Even when dealing with DoS attacks and external disturbances, it can still ensure that the control input meets the physical constraints, making the method engineering feasible in actual unmanned underwater vehicle systems.

[0128] Example 2:

[0129] like Figure 1 As shown, this invention discloses a method for tracking the trajectory of an unmanned underwater vehicle with anti-DoS attack and disturbance compensation capabilities, comprising the following steps:

[0130] Step 1: Obtain the system state information of the unmanned underwater vehicle and construct a predictive model for trajectory tracking control based on its kinematic and dynamic characteristics;

[0131] Step 2: To address external disturbances in the marine environment, a disturbance compensation mechanism is constructed, the disturbance is estimated, and the corresponding disturbance compensation control input is generated;

[0132] Step 3: Based on disturbance compensation, construct a trajectory tracking control strategy based on a prediction model, and generate an optimal control input sequence containing control inputs at multiple future time points through rolling optimization;

[0133] Step 4: Based on the overall predictive control sequence, design a packet transmission strategy to resist DoS attacks, and transmit and buffer the overall predictive control sequence when communication between the remote control center and the actuator is normal;

[0134] Step 5: When communication between the remote control center and the actuator is interrupted due to a DoS attack, the actuator reconstructs the control input at the current moment based on the cached total predictive control sequence in order to maintain the continuity and stability of the unmanned underwater vehicle trajectory tracking control.

[0135] This method first establishes a kinematic and dynamic model of the unmanned underwater vehicle (UUV). Second, after estimating external disturbances, it solves a disturbance compensation optimization problem to obtain the disturbance compensation control input. The disturbance compensation control input is then embedded into the input constraints of the disturbance compensation model predictive control optimization problem, and the optimal control input sequence is obtained through online solution. To defend against DoS attacks on the communication channel between the remote control center and the actuator, a packet transmission strategy based on the total predictive control sequence is designed: when communication is normal, the actuator receives and buffers the total predictive control sequence; when communication is interrupted by an attack, the actuator reconstructs the current control command using the buffered sequence to maintain control continuity. This application enables robust and safe trajectory tracking of the UUV in complex environments where both unknown disturbances and DoS attacks coexist.

[0136] Based on Embodiment 2, the disturbance compensation mechanism described in step 2 first converts the actual disturbance from the previous moment into an estimate for the current moment. ,in This represents the actual disturbance at the previous moment. Estimate the disturbance at the current time; then design the cost function based on the disturbance estimate. ,in The sampling interval is... Let be the inertia matrix of the dynamic model of the unmanned underwater vehicle. The disturbance compensation control input is used; the disturbance compensation optimization problem is solved, and the resulting disturbance compensation control input is used. This is introduced into the trajectory tracking control optimization problem.

[0137] Further based on Example 2, step 3, based on the prediction model... The trajectory tracking control strategy is a model predictive control strategy, in which... This indicates the nominal status of the unmanned underwater vehicle. This represents the control input vector of the unmanned underwater vehicle; firstly, the trajectory tracking control performance indicators are designed. ,in and These represent the stage cost function and the terminal cost function, respectively. Represents reference path information, matrix , and It is a positive definite weighted matrix; then, the optimal control input sequence is generated by solving the disturbance compensation model predictive control problem online. And it is updated at each step of the optimization solution.

[0138] Furthermore, based on Example 2, the total predictive control sequence described in step 4 is the optimal control input sequence. With disturbance compensation control input The sum of, i.e. .

[0139] Based on Embodiment 2, the anti-DoS attack packet transmission strategy in step 4 further includes: when communication is normal, the total prediction control sequence... The entire sequence is sent to the actuator and buffered. The current control input of the unmanned underwater vehicle uses the first value of the total predictive control sequence. When communication is interrupted, the actuator selects the control input for the corresponding moment based on the buffered total predictive control sequence for the current control cycle. , This is the time of the most recent successful transmission of the overall predictive control sequence.

[0140] Furthermore, based on Embodiment 2, the occurrence of the DoS attack is random and appears intermittently over time.

Claims

1. A method for tracking the trajectory of an unmanned underwater vehicle with anti-DoS attack and disturbance compensation capabilities, characterized in that: Includes the following steps, Step 1: Construct the kinematic and dynamic models of the unmanned underwater vehicle and form a planar mathematical model. Discretize the planar mathematical model to obtain a predictive model for trajectory tracking control. Step 2: Obtain the actual state of the unmanned underwater vehicle at the current moment, the system state at the previous moment, and the control input at the previous moment. Combine the dynamic model of the unmanned underwater vehicle to calculate the disturbance value at the previous moment and use it as the estimated value of the disturbance at the current moment. Construct a disturbance compensation mechanism. Based on the estimated value of the disturbance at the current moment, construct the cost function and input constraints for disturbance compensation and solve for the disturbance compensation control input. Step 3: Obtain the cost function and input constraints of the disturbance compensation model predictive control and form a trajectory tracking control strategy. Embed the disturbance compensation control input into the input constraints of the disturbance compensation model predictive control of the trajectory tracking control strategy, and iteratively solve to obtain the optimal control input sequence. Step 4: Add the disturbance compensation control input to the optimal control input sequence to obtain the total predictive control sequence. Based on the total predictive control sequence, design the packet transmission strategy. The packet transmission strategy includes the actuator receiving and buffering the total predictive control sequence when communication is normal. Step 5: When communication is interrupted due to a DoS attack, the actuator reconstructs the control input at the current moment based on the cached total predictive control sequence.

2. The method for tracking the trajectory of an unmanned underwater vehicle with anti-DoS attack and disturbance compensation capabilities according to claim 1, characterized in that: In step 1, the planar mathematical model of the unmanned underwater vehicle is given by equation (3). (3) In equation (3), For planar kinematics model, This represents the position and orientation vector of an unmanned underwater vehicle in an inertial coordinate system. This represents the velocity vector of the unmanned underwater vehicle in volume coordinates. For rotation matrix, The heading angle of the unmanned underwater vehicle; For dynamic model, It is the inertia matrix. It is the Coriolis force-centripetal force matrix. It is the hydrodynamic damping matrix. This represents the control input vector of an unmanned underwater vehicle. The prediction model used for trajectory tracking control is Equation (4). (4) Equation (4) is the prediction model used for trajectory tracking control under nominal conditions. In equation (4), This indicates the nominal status of the unmanned underwater vehicle. For the control input of unmanned underwater vehicles, This is a discretized dynamic model for an unmanned underwater vehicle.

3. The method for tracking the trajectory of an unmanned underwater vehicle with anti-DoS attack and disturbance compensation capabilities according to claim 1, characterized in that: In step 2, the disturbance value of the previous moment is calculated according to equation (6). (6) In equation (6), This represents the actual disturbance at the previous moment. For unmanned underwater vehicles at all times The actual state This represents the system state at the previous moment. To control the input, Discretized dynamic model for unmanned underwater vehicles; According to equation (7), the disturbance value of the previous moment is used as the estimated value of the disturbance at the current moment. (7) In equation (7), It is a disturbance The estimate; The cost function and input constraints for disturbance compensation are given by equation (8). (8) In equation (8), This represents the cost function for perturbation compensation. Indicates the sampling interval. Let be the inertia matrix of the dynamic model of the unmanned underwater vehicle. Input constraints for disturbance compensation. For disturbance compensation control input; and These represent the minimum and maximum values ​​of the disturbance compensation control input, respectively.

4. The method for tracking the trajectory of an unmanned underwater vehicle with anti-DoS attack and disturbance compensation capabilities according to claim 1, characterized in that: In step 3, the cost function of the disturbance compensation model predictive control is given by equation (9). (9) In equation (9), It predicts the time domain. Indicates in The sampling state at any given time. Indicates in The first thing to do at any moment Predicted state at any given time It is a predictive control sequence; and These represent the stage cost function and the terminal cost function, respectively. Represents reference path information, matrix , and It is a positive definite weighted matrix; The trajectory tracking control strategy is given by equation (10). ， ， (10) In equation (10), This represents the optimal control input sequence. and These represent the minimum and maximum values ​​of the control input for the unmanned underwater vehicle, respectively. Input constraints for predictive control of the disturbance compensation model; optimal control input sequence .

5. The method for tracking the trajectory of an unmanned underwater vehicle with anti-DoS attack and disturbance compensation capabilities according to claim 1, characterized in that: In step 4, the overall predictive control sequence is given by equation (11). (11) In equation (11), This is the overall predictive control sequence; The packet transmission strategy also includes sending the entire predictive control sequence to the actuator and buffering it when communication is normal. The current control input of the unmanned underwater vehicle uses the first value of the overall predictive control sequence. When communication is interrupted, the actuator selects the control input from the most recent successful transmission moment based on the cached total predictive control sequence for the current control cycle.

6. The method for tracking the trajectory of an unmanned underwater vehicle with anti-DoS attack and disturbance compensation capabilities according to claim 1, characterized in that: In step 5, reconstructing the control input at the current moment includes selecting the control input at the moment of the most recent successful transmission.

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