A control method for automatically switching ship heading under network attacks to enhance resilience

Abstract

This invention discloses a robust control method for automatic course switching of ships under cyberattacks. The method includes: constructing a robust ship controller based on a first-order closed-loop gain shaping algorithm and a course switching mechanism, using a nonlinear Nomoto ship model; constructing an automatic course switching controller under cyberattacks based on the robust ship controller; nonlinearly modifying the control input of the automatic course switching controller, and optimizing the nonlinearly modified control input using a zero-order hold to obtain the optimized control input; considering marine environmental disturbances during the ship's course, limiting the optimized control input of the automatic course switching controller by rudder angle / rudder speed to obtain the final ship control input. This method solves the problem that, when facing uncertainties such as cyberattacks, the ship's collision avoidance sometimes requires large angles that are difficult to control accurately, resulting in the inability to maintain ship navigation stability under cyberattacks and large-angle collision avoidance scenarios.

Description

Technical Field

[0001] This invention relates to the field of ship control technology, and in particular to a resilient control method for automatic course switching of ships under cyberattacks. Background Technology

[0002] Ship motion is highly nonlinear and uncertain, and course control is a key technical means to ensure ship navigation safety, improve ship maneuverability, and enhance shipping economy.

[0003] Traditional heading control algorithms, such as proportional-integral-derivative (PID) control, often struggle to achieve the required control precision when facing uncertainties such as cyberattacks. This is because collision avoidance sometimes requires large angles, and under cyberattack and large-angle collision avoidance scenarios, ship heading control not only has long adjustment times and cannot maintain ship navigation stability (resilience) and safety, but also lacks energy-saving and carbon-reducing capabilities. Summary of the Invention

[0004] This invention provides a robust control method for automatic course switching of ships under cyberattacks to overcome the aforementioned technical problems.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A method for enhancing the resilience of automatic course switching of ships under cyberattacks, specifically including the following steps:

[0007] S1: Construct a nonlinear Nomoto ship model;

[0008] To obtain the heading error between the ship's desired heading and its actual heading, in order to construct a heading switching mechanism;

[0009] Based on the first-order closed-loop gain shaping algorithm and the heading switching mechanism, a robust ship controller is constructed according to the nonlinear Nomoto ship model.

[0010] S2: Construct an automatic switching controller under network attacks, and obtain the initial control input of the automatic switching controller based on the ship's robust controller;

[0011] S3: Based on nonlinear modification technology, the initial control input of the automatic switching controller is nonlinearly modified, and a zero-order hold is used to optimize the control input of the nonlinearly modified automatic switching controller to obtain the optimized control input of the automatic switching controller.

[0012] S4: Considering the marine environmental interference during the ship's course, the rudder angle / rudder speed is limited to the optimized control input of the automatic switching controller to obtain the final ship control input;

[0013] The ship's course at the next moment under a cyberattack is obtained based on the final ship control input, so as to achieve automatic course switching and resilience enhancement control of the ship.

[0014] Furthermore, S1 specifically includes the following steps:

[0015] S11: Construct a nonlinear Nomoto ship model, and the expression for the nonlinear Nomoto ship model is as follows:

[0016]

[0017] In the formula: ψ represents the ship's heading angle; δ represents the ship's rudder angle input; K and T represent the turning index and maneuvering index of the ship's motion control, respectively; α and β represent the nonlinear parameters of the ship model; The first derivative representing the heading angle ψ of a ship; The second derivative of the heading angle ψ of a ship;

[0018] S12: Obtain the heading error e between the ship's desired heading and actual heading, where e = ψ r -ψ;

[0019] Construct a heading switching mechanism based on the heading error e;

[0020] The heading switching mechanism is as follows: taking the ship's actual heading as the heading start point and the ship's desired heading as the heading end point, the first heading difference and the second heading difference are obtained respectively when rotating in a counterclockwise direction and rotating in a clockwise direction.

[0021] Compare the absolute values ​​of the first heading difference and the second heading difference.

[0022] And select the rotation direction corresponding to the smaller absolute value of the heading difference as the rotation direction for the ship's heading change;

[0023] When the absolute value of the first heading difference is equal to the absolute value of the second heading difference, either the counterclockwise or clockwise direction is randomly selected as the turning direction for the ship's heading change.

[0024] S13: Based on a first-order closed-loop gain shaping algorithm and a heading switching mechanism, a robust ship controller is constructed according to the nonlinear Nomoto ship model. The expression of the robust ship controller is as follows:

[0025]

[0026] In the formula: K represents the cyclicity index; K c ρ represents the input of the ship's robust controller; ρ represents the positive design parameters that improve the dynamic performance of the ship's system; and s represents the complex variable of the Laplace transform.

[0027] Furthermore, the automatic switching controller under network attack constructed in S2 has the following expression:

[0028]

[0029] Where: K c ' represents the control input of the ship's robust controller under cyberattack; G represents the open-loop transfer function;

[0030] The initial control input for the automatic switching controller is obtained from the ship's robust controller, and its expression is:

[0031] δ=K c 'e.

[0032] Furthermore, S3 specifically includes the following steps:

[0033] S31: The initial control input δ of the automatic switching controller is nonlinearly modified using nonlinear modification techniques, and the expression is as follows:

[0034] δ0=arctan(aK c 'e)

[0035] In the formula: δ0 represents the control input after nonlinear modification; arctan(au) represents the modification function and u=K c 'e;

[0036] S32: Obtain the transfer function G of the zeroth-order hold h (s), whose expression is

[0037]

[0038] In the formula: a represents the sampling period of the configured ship system; s represents the complex variable of the Laplace transform;

[0039] The transfer function G of the zero-order hold h (s) Perform a Taylor series expansion to obtain the simplified form of the zero-order hold, whose expression is:

[0040]

[0041] S33: Optimize the control input of the nonlinearly modified automatic switching controller based on the simplified zero-order hold to obtain the optimized control input δ of the automatic switching controller. c Its expression is

[0042]

[0043] Furthermore, S4 considers marine environmental disturbances during the ship's course and imposes rudder angle / rudder speed limits on the optimized control input of the automatic switching controller as follows:

[0044]

[0045] In the formula: δ represents the final ship control input, i.e., the ship's rudder angle input; δ max This indicates the maximum rudder angle limit for a vessel.

[0046] Beneficial Effects: This invention provides a robust control method for automatic course switching under cyberattacks. By employing a course switching mechanism, when a ship faces a large-angle collision avoidance maneuver, it converts the large-angle collision avoidance maneuver into a small-angle maneuver. Simultaneously, a robust ship controller is obtained based on a first-order closed-loop gain shaping algorithm to construct an automatic switching controller under cyberattacks. By simulating a cyberattack and equating the inversion of the measurement signal to a positive feedback control situation, an automatic course positive and negative feedback switching function is designed. This improves the ship's resilience in maintaining course and switching between large-angle collision avoidance when facing cyberattacks. By adding nonlinear modifications driven by an arctangent function and modifying the control input with a zero-order hold in the automatic switching controller, the controller output amplitude and rudder frequency are significantly reduced. This effectively addresses the challenges of rapidly switching course during large-angle collision avoidance under cyberattacks, while also reducing rudder wear and energy consumption. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 The flowchart shows the ship's automatic course switching resilience enhancement control method under network attacks according to the present invention.

[0049] Figure 2 This is a simulation block diagram of the switching control for the ship's automatic course switching resilience enhancement control in this embodiment;

[0050] Figure 3 This is a simulation diagram of the ballast rotation test of the "Yupeng" wheel in this embodiment;

[0051] Figure 4 This is a simulation diagram of the 10° / 10° Z-shaped test in this embodiment;

[0052] Figure 5 This is a simulation diagram of the switching control output of the system with nonlinear modification of the arctangent function in this embodiment;

[0053] Figure 6 This is a simulation diagram of the ship's rudder angle change in this embodiment;

[0054] Figure 7 This is a simulation block diagram of the automatic switching controller in this embodiment. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] This embodiment provides a method for enhancing the resilience of automatic course switching control of ships under network attacks, such as... Figures 1 to 2 As shown, the specific steps include:

[0057] S1: Construct a nonlinear Nomoto ship model;

[0058] To obtain the heading error between the ship's desired heading and its actual heading, in order to construct a heading switching mechanism;

[0059] Based on the first-order closed-loop gain shaping algorithm and the heading switching mechanism, a robust ship controller is constructed according to the nonlinear Nomoto ship model.

[0060] Specifically, it includes the following steps:

[0061] S11: The mathematical model of ship motion in this embodiment adopts the second-order Nomoto model, and the expression is as follows:

[0062]

[0063] The ship motion model used in this embodiment is a nonlinear response model. However, this model is relatively simple and differs somewhat from real ships. To construct a more realistic mathematical model of ship motion that can better simulate the actual operation of ships, a nonlinear function is needed. to replace the in equation (1) in

[0064]

[0065] Furthermore, a nonlinear Nomoto ship model is constructed, and the expression for the nonlinear Nomoto ship model is as follows:

[0066]

[0067] In the formula: ψ represents the ship's heading angle; δ represents the ship's rudder angle input; K and T represent the turning index and maneuvering index of the ship's motion control, respectively; α and β represent the nonlinear parameters of the ship model; The first derivative representing the heading angle ψ of a ship; The second derivative of the heading angle ψ of a ship;

[0068] S12: Obtain the heading error e between the ship's desired heading and actual heading, where e = ψ r -ψ;

[0069] Construct a heading switching mechanism based on the heading error e;

[0070] The heading switching mechanism is as follows: taking the ship's actual heading as the heading start point and the ship's desired heading as the heading end point, the first heading difference and the second heading difference are obtained by rotating counterclockwise and clockwise respectively; obtaining the heading difference by rotating counterclockwise or clockwise is a known technical means and will not be elaborated on here.

[0071] Compare the absolute values ​​of the first heading difference and the second heading difference.

[0072] And select the rotation direction corresponding to the smaller absolute value of the heading difference as the rotation direction for the ship's heading change;

[0073] When the absolute value of the first heading difference is equal to the absolute value of the second heading difference, either the counterclockwise or clockwise direction is randomly selected as the turning direction for the ship's heading change.

[0074] S13: Based on a first-order closed-loop gain shaping algorithm and a heading switching mechanism, a robust ship controller is constructed according to the nonlinear Nomoto ship model. The expression of the robust ship controller is as follows:

[0075]

[0076] δ=K c e

[0077] In the formula: K represents the cyclicity index; K c ρ represents the input of the ship's robust controller; ρ represents the positive design parameters that improve the dynamic performance of the ship's system; and s represents the complex variable of the Laplace transform.

[0078] S2: Construct an automatic switching controller under network attacks, and obtain the initial control input of the automatic switching controller based on the ship's robust controller;

[0079] Specifically, cyberattacks on ships take many forms, targeting their communication, control, or data systems. Some common forms include: untargeted attacks, targeted attacks (such as proactive attacks, exploiting vulnerabilities in ship communication protocols, and insider attacks via USB drives through Wi-Fi, high-frequency radio, and commercial satellite communications), and other forms of attacks (such as interfering with the Automatic Identification System (AIS) and ransomware attacks). Signal inversion is a significant type of attack. In control theory, negative feedback involves creating a feedback loop to continuously adjust the input amplitude, reducing the error between the input and output, ultimately achieving the ideal output. The positive feedback concept used in this embodiment is an equivalent transformation of negative feedback, used to simulate the situation where a hacker inverts the measured signal during a cyberattack (negative feedback involves inverting the measured signal; a negative equals a positive, equivalent to positive feedback). For a negative feedback loop, the transfer function of the closed-loop control system can be expressed as... Positive feedback is equivalent to changing the denominator from positive to negative and the numerator from negative to negative; it is essentially an equivalent transformation. For the controller K', this can also be achieved by adding a negative sign. That is: first, the feedback signal is changed from negative to positive feedback; then, the controller of the original negative feedback control method is multiplied by -1 to become a positive feedback controller; finally, the system output is multiplied by -1, ultimately achieving the equivalent transformation between negative and positive feedback. This allows for the acquisition of an automatic switching controller under network attacks based on a robust ship controller, the expression of which is:

[0080]

[0081] Where: K c ' represents the control input of the ship's robust controller under network attack; G represents the open-loop transfer function. The left side of this automatic switching controller expression is the transfer function of the negative feedback control system, and the right side is the transfer function of the positive feedback control system. When the controller is positive feedback, the output of the positive feedback system differs from the output of the negative feedback system by a negative sign; the equation on the right side of the equation is used for the switching control scheme when the measured signal is negative; -K' is the controller under positive feedback. Theoretically, any system that can be controlled by negative feedback has an equivalent positive feedback control system, and ultimately, under the action of positive feedback and nonlinear feedback, a system like... Figure 7 The simulation module shown;

[0082] The initial control input for the automatic switching controller is obtained from the ship's robust controller, and its expression is:

[0083] δ=K c 'e

[0084] S3: Based on nonlinear modification technology, the initial control input of the automatic switching controller is nonlinearly modified, and a zero-order hold is used to optimize the control input of the nonlinearly modified automatic switching controller to obtain the optimized control input of the automatic switching controller.

[0085] Specifically, it includes the following steps:

[0086] S31: The initial control input δ of the automatic switching controller is nonlinearly modified using nonlinear modification techniques, and the expression is as follows:

[0087] δ0=arctan(aK c 'e)

[0088] In the formula: δ0 represents the control input after nonlinear modification; arctan(au) represents the modification function and u=K c 'e;

[0089] S32: Because the zero-order hold has the characteristic that its amplitude decays rapidly as the frequency increases, it has good low-pass filtering properties, which is consistent with the characteristic that ship control signals play a significant role in the low-frequency range. In addition, the zero-order hold can reduce the steering frequency to protect the steering gear from wear. Therefore, by incorporating the zero-order hold into the controller, the transfer function of the zero-order hold can be obtained, and its expression is:

[0090]

[0091] In the formula: a represents the sampling period of the configured ship system; s represents the complex variable of the Laplace transform;

[0092] The transfer function G of the zero-order hold h (s) Perform a Taylor series expansion to obtain the simplified form of the zero-order hold, whose expression is:

[0093]

[0094] S33: Optimize the control input of the nonlinearly modified automatic switching controller based on the simplified zero-order hold to obtain the optimized control input δ of the automatic switching controller. c Its expression is

[0095]

[0096] This embodiment demonstrates the impact of adding the arctangent function on the steady state of the ship control system as follows:

[0097] Suppose a step signal is used as the input signal with amplitude r. Assume the error of the ship control system is within an acceptable range and the change in the input signal causes the value of u to be very small. Then, according to the Taylor series expansion, arctan(au) ≈ au. According to the mean value theorem, under given conditions, the output ψ of the ship control system is...

[0098]

[0099] Therefore, the steady-state error of the ship control system output is 0, which indicates that modifying the controller output with the arctangent function under specific conditions will not affect the steady state of the system. After repeated selection and experimental verification of a, the control effect is better when a = 0.4. Therefore, the final nonlinear modification form is arctan(0.4u).

[0100] S4: Considering the marine environmental interference during the ship's course, the rudder angle / rudder speed is limited to the optimized control input of the automatic switching controller to obtain the final ship control input;

[0101] The ship's course at the next moment under a cyberattack is obtained based on the final ship control input, so as to achieve automatic course switching and resilience enhancement control of the ship.

[0102] In a specific embodiment, S4 considers marine environmental disturbances during the ship's course and imposes rudder angle / rudder speed limits on the optimized control input of the automatic switching controller as follows:

[0103]

[0104] In the formula: δ represents the final ship control input, i.e., the ship's rudder angle input; δ max This indicates the maximum rudder angle limit for a vessel.

[0105] Compared with existing technologies, this embodiment transforms large-angle collision avoidance maneuvers into small-angle maneuvers through a course switching mechanism. Simultaneously, it uses a first-order closed-loop gain shaping algorithm to obtain a robust ship controller, constructing an automatic switching controller under cyberattacks. By simulating a cyberattack and equating the inversion of measurement signals to positive feedback control, an automatic switching function for positive and negative course feedback is designed. This improves the ship's resilience in maintaining course and switching between large-angle collision avoidance when facing cyberattacks. By adding nonlinear modifications driven by an arctangent function and modifying the control input with a zero-order hold in the automatic switching controller, the controller output amplitude and rudder frequency are significantly reduced, effectively coping with rapid course switching during large-angle collision avoidance under cyberattacks, while also reducing rudder wear and energy consumption.

[0106] This embodiment aims to verify the effectiveness of the established nonlinear Nomoto ship model, such as... Figures 3 to 4 As shown, taking "Yupeng" as the research object, a 35° turn simulation test and a 10° / 10° Z-shaped test under full load were carried out based on Matlab and compared with the actual ship data. The ship parameters under ballast are shown in Table 1, and the characteristic parameters of each turn are listed in Table 1.

[0107] Table 1. Parameter values ​​of the “Yupeng” wheel

[0108]

[0109] Ballasting 35° right turn simulation experiment: The nonlinear Nomoto model was used to simulate the ballasting 35° right turn of the "Yupeng" vessel. The value of the dimensionless crossflow coefficient C was adjusted to make the simulation close to the actual ship. At the same time, the crossflow parameter was tested multiple times using the bisection method. It was found that the simulation effect was better when C = 0.6. Figure 1 A comparison of the turning circles of the actual ship and the simulation.

[0110] Table 2. Simulation results of the turning inballast for the “Yupeng” wheel.

[0111]

[0112] And verification was performed based on the definition of compliance in ship motion control:

[0113]

[0114] In the formula: A d1 Indicates the actual ship rotation advance; A d2 D represents the advance distance in the model rotation simulation; T1 D represents the initial diameter of the actual ship's turn; T2 D1 represents the simulated gyroscope diameter; D2 represents the actual ship gyroscope diameter; D3 represents the simulated gyroscope diameter. Calculations show that the nonlinear Nomoto model gyroscope simulation and the actual ship test have good agreement under ballast wind conditions of force 6. The specific results are shown in Table 2.

[0115] 10° / 10° Z-shaped simulation test under ballast: A 10° / 10° Z-shaped simulation test was conducted on the "Yupeng" vessel under ballast conditions. The simulation test results are as follows: Figure 2As shown in Table 3, a comparison between the 10° / 10° Z-shaped simulation test and the actual ship data is given. According to MSC.137(76), in the test, L / V=21, V=9.0m / s, L=189m. According to the regulations, the first overshoot angle should not exceed 5°+0.5L / V=15.5°, and the second overshoot angle should not exceed 17.5°+0.75L / V=33.25°;

[0116] Table 3. Comparison of 10° / 10° Zig-Zagmaneuvertest overshoot angle

[0117]

[0118] The controller in this embodiment combines a first-order closed-loop gain shaping algorithm, nonlinear modification, and a zero-order hold. The zero-order hold can reduce the rudder frequency, while the controller designed with the closed-loop gain shaping algorithm has strong robustness. These characteristics demonstrate the controller's significant practical value in maritime navigation. This embodiment uses the Simulink toolbox of Matlab to conduct simulation experiments on the "Yupeng" vessel of Dalian Maritime University. A traditional PID controller without nonlinear modification is selected as a reference to determine the degree of improvement of the controller in this embodiment. The expression for the traditional controller is:

[0119]

[0120] In the formula: u(t) is the control output; e(t) is the control input, i.e., the deviation between the controlled variable and the setpoint; K p T i T d These are the proportional coefficient, integral time constant, and derivative time constant, respectively.

[0121] By consulting relevant materials, the ship's parameters were obtained. The main parameters of the "Yupeng" are shown in Table 1. The ship's maneuverability index and following index are K = 0.21 and T = 107.78, respectively. The rudder angle is 3°. For the nonlinear terms of the ship model, α = 13.17 and β = 16323.89 can be obtained using the least squares method. The simulation time was set to 1600s, the simulation step size was variable, and the solver was ode45. The pulsating wind in the sea breeze encountered by the ship during navigation was handled using the white noise method proposed by Astorm and Kallstrom.

[0122] The transfer function h(s) of the wave model obtained under force 6 wind is:

[0123]

[0124] Where ξ6 represents wave disturbance under sea state 6, and ζ represents white noise.

[0125] Regarding the controller's control performance, three metrics—Mean Absolute Error (MAE), Mean Integrate Absolute (MIA), and Mean Total Variation (MTV)—were selected for quantitative analysis and comparison. MAE measures the system output response time, while MIA and MTV measure energy consumption related to the input rudder angle and the smoothness of the corresponding algorithm.

[0126]

[0127] Where: t0, t ∞ These are the initial and final times, respectively; ψ r Here, ψ(t) is the set reference heading; δ(t) is the ship's heading angle at time t; and t is time. To verify the energy-saving effect of the controller after nonlinear modification, a specific energy index is used to compare the energy consumption during the unmanned vessel's navigation process:

[0128] J=∫δ 2 dt

[0129] In the formula: J is an indicator for measuring energy consumption.

[0130] The evaluation index is not actual energy; it only indicates, in terms of numerical magnitude, that the nonlinearly modified heading control outperforms conventional feedback under the influence of factors such as rudder angle, maximum rudder angle, and adjustment time. Therefore, this embodiment uses existing rudder drag energy consumption calculation formulas to calculate the energy consumption of the nonlinearly modified controller and the controller in this embodiment, thereby more accurately demonstrating its energy-saving advantages. Rudder drag is the resistance to the ship's forward movement caused by the water flow impacting the rudder blades during steering. It interacts with the component of the rudder force in the ship's forward direction; therefore, rudder drag energy consumption can effectively describe the work done by the steering gear. Its calculation formula is as follows:

[0131]

[0132] in,

[0133] In the formula: T0 = 1600s is the simulation time, X HR Let V be the drag force of the water on the rudder during longitudinal motion, V be the speed, ρ be the density of seawater, and A be the density of the water. R f is the rudder area. aThe slope of the rudder lift coefficient at a = 0 is calculated using the Fujii formula in this embodiment, where λ is the rudder aspect ratio and γ is the slope. R C is the rectification factor. b l is the square coefficient. R It can be considered as the longitudinal coordinate of the rudder, but according to the literature, it is generally twice -L / 2. R ' indicates that it is dimensionless, and r' is the dimensionless turning angular velocity, and the above parameters are all reflected in Table 1.

[0134] This experiment simulates a ship's network attack by introducing positive and negative signal switching into the loop during a simulation duration of 800 seconds. A positive and negative feedback switching control was designed to address the issue of reversed signal readings. The ship's initial heading is set to 0°, and the desired heading ψ... r The angle is 20°. Simulating ship motion over 800 seconds, the ship needs to switch to 340° to avoid collisions. If a conventional control algorithm is used, the ship would need to turn 320°, a slow and lengthy process. This embodiment treats 340° as -20°, requiring only a 40° turn. However, during the course switch, the control system is attacked by a cyberattack. The hacker reverses the measurement signal, turning the original negative feedback system into a positive feedback system. Figure 5 It can be seen that the method of this embodiment can bring the ship's heading angle to the expected course in a very short time and stabilize it near the desired course quickly without much fluctuation. This result shows that, in the face of adverse situations where network attacks cause measurement signal reversal, the automatic switching control method proposed in this embodiment can respond immediately and quickly correct the course, thereby effectively avoiding the risk of the ship yawing. Figure 6 It is clear from the above that the method in this embodiment can better reduce the rudder angle and reduce rudder damage.

[0135] Table 4. Comparison of simulation results under Beaufortwind of No. 6

[0136]

[0137] After reaching the predetermined course, the heading angle fluctuated somewhat, but the system still maintained good stability. Using the controller of this embodiment, in sea state VI, the maximum rudder angle decreased by 61.87%, MAE increased slightly, MIA decreased by 45.04%, MTV decreased by 38.22%, the energy consumption indicator J decreased by 70.35%, and rudder drag energy consumption decreased by 74.52%. Quantitative analysis of the experimental results shows that the controller of this embodiment can effectively achieve energy-saving goals. The MAE indicator, mainly used to measure the system's output response time or error magnitude, may reflect a certain degree of trade-off made by the controller in pursuing higher energy efficiency regarding the smoothness of the rudder angle input curve, as both the energy consumption indicator J and rudder drag energy consumption were significantly reduced.

[0138] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for enhancing the resilience of ship course switching under cyberattacks, characterized in that, Specifically, the following steps are included: S1: Constructing a nonlinear structure Ship models; To obtain the heading error between the ship's desired heading and its actual heading, in order to construct a heading switching mechanism; Based on a first-order closed-loop gain shaping algorithm and a heading switching mechanism, and according to nonlinear... Ship model construction for robust ship controllers; S2: Construct an automatic switching controller under network attacks, and obtain the initial control input of the automatic switching controller based on the ship's robust controller; S3: Based on nonlinear modification technology, the initial control input of the automatic switching controller is nonlinearly modified, and a zero-order hold is used to optimize the control input of the nonlinearly modified automatic switching controller to obtain the optimized control input of the automatic switching controller. S4: Considering the marine environmental interference during the ship's course, the rudder angle / rudder speed is limited to the optimized control input of the automatic switching controller to obtain the final ship control input; The ship's course at the next moment under a cyberattack is obtained based on the final ship control input, so as to achieve automatic course switching and resilience enhancement control of the ship. S1 specifically includes the following steps. S11: Constructing Nonlinearity Ship model, and nonlinear The expression for the ship model is: In the formula: Indicates the ship's heading angle; Indicates the input of the ship's rudder angle; The turning index and the maneuverability index respectively represent the ship's maneuverability. Represents the nonlinear parameters of the ship model; Indicates the heading angle of the ship. The first derivative; Indicates the heading angle of the ship. The second derivative; S12: Obtain the heading error between the ship's desired heading and actual heading. ,and ; According to heading error Establish a course switching mechanism; The heading switching mechanism is as follows: taking the ship's actual heading as the heading start point and the ship's desired heading as the heading end point, the first heading difference and the second heading difference are obtained respectively when rotating in a counterclockwise direction and rotating in a clockwise direction. Compare the absolute values ​​of the first heading difference and the second heading difference. And select the rotation direction corresponding to the smaller absolute value of the heading difference as the rotation direction for the ship's heading change; When the absolute value of the first heading difference is equal to the absolute value of the second heading difference, either the counterclockwise or clockwise direction is randomly selected as the turning direction for the ship's heading change. S13: Based on a first-order closed-loop gain shaping algorithm and heading switching mechanism, according to nonlinear... A robust ship controller is constructed using a ship model. The expression for the robust ship controller is as follows: In the formula: Represents the cyclicity index; Indicates the input of the ship's robust controller; These represent positive design parameters that improve the dynamic performance of a ship's systems. The complex variable represents the Laplace transform; the automatic switching controller under the network attack constructed in S2 has the following expression: In the formula: This represents the control input of the ship's robust controller under cyberattack. Represent the open-loop transfer function; The initial control input for the automatic switching controller is obtained from the ship's robust controller, and its expression is: ； S3 specifically includes the following steps. S31: Initial control input for the automatic switching controller based on nonlinear modification technology To perform non-linear modification, the expression is: In the formula: This represents the control input after nonlinear modification; Indicates that the function is modified and ; S32: Obtain the transfer function of the zeroth-order hold Its expression is In the formula: Indicates the sampling period of the configured ship system; Represent the complex variable of the Laplace transform; Transfer function of zero-order hold Perform a Taylor series expansion to obtain the simplified form of the zero-order hold, whose expression is: S33: Optimize the control input of the nonlinearly modified automatic switching controller based on the simplified zero-order hold to obtain the optimized control input of the automatic switching controller. Its expression is ； S4 considers marine environmental disturbances during the ship's course, and imposes rudder angle / rudder speed limits on the optimized control input of the automatic switching controller under the following constraints: In the formula: This indicates the final ship control input, i.e., the ship's rudder angle input; This indicates the maximum rudder angle limit for a vessel.

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