Ship course automatic switching toughness strengthening control method under network attack

Abstract

The invention discloses a ship course automatic switching toughness strengthening control method under network attack, which comprises the following steps: constructing a ship robust controller according to a nonlinear Nomoto ship model based on a first-order closed-loop gain forming algorithm and a course switching mechanism; constructing an automatic switching controller under the network attack according to the ship robust controller; performing nonlinear modification on the control input of the automatic switching controller, and optimizing the control input of the automatic switching controller after nonlinear modification by adopting a zero-order retainer to obtain the optimized control input of the automatic switching controller; and marine environment interference in the course process of the ship is considered, rudder angle / rudder speed limitation is carried out on the optimization control input of the automatic switching controller, and final ship control input is obtained. The problems that when uncertain factors such as network attacks are faced, the control precision requirement is difficult to meet due to the fact that ship collision avoidance sometimes needs a large angle, and the ship navigation stability cannot be kept under the conditions of network attacks and large-angle collision avoidance are solved.

Description

Technical Field

[0001] The present invention relates to the field of ship control technology, and in particular to a ship heading automatic switching resilience enhancement control method under network attacks. Background Art

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

[0003] Traditional heading control algorithms, such as proportional-integral-derivative (PID) control, often have difficulty meeting control accuracy requirements when faced with uncertainties such as cyber attacks, as ship collision avoidance sometimes requires large angles. In the event of cyber attacks and large-angle collision avoidance, the ship's heading control not only takes a long time to adjust and is unable to maintain the ship's navigation stability (resilience) and safety, but also lacks the ability to save energy and reduce carbon emissions. Summary of the invention

[0004] The present invention provides a method for strengthening the resilience of automatic switching of ship heading under network attacks to overcome the above technical problems.

[0005] In order to achieve the above object, the technical solution of the present invention is:

[0006] A method for strengthening the resilience of automatic switching of ship heading under network attack specifically comprises the following steps:

[0007] S1: Construct nonlinear Nomoto ship model;

[0008] Obtain the heading error between the ship's desired heading and actual heading to build a heading switching mechanism;

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

[0010] S2: Construct an automatic switching controller under network attack and obtain the initial control input of the automatic switching controller according to the ship robust controller;

[0011] S3: Based on the nonlinear modification technology, the initial control input of the automatic switching controller is nonlinearly modified, and the control input of the automatic switching controller after nonlinear modification is optimized by using a zero-order holder to obtain the optimized control input of the automatic switching controller;

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

[0013] The ship's heading at the next moment under the cyber attack is obtained according to the final ship control input, so as to realize the automatic switching of the ship's heading and enhance the resilience control.

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

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

[0016]

[0017] Where: ψ represents the heading angle of the ship; δ represents the rudder angle input of the ship; K, T represent the turning index and maneuverability index of the ship motion maneuverability respectively; α, β represent the nonlinear parameters of the ship model; Represents the first derivative of the ship's heading angle ψ; Represents the second derivative of the ship's heading angle and heading ψ;

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

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

[0020] The heading switching mechanism: taking the actual heading of the ship as the heading starting point and the expected heading of the ship as the heading ending point, respectively obtaining the first heading difference and the second heading difference according to the counterclockwise rotation and the clockwise rotation;

[0021] Comparing the absolute value of the first heading difference with the absolute value of the second heading difference;

[0022] The rotation direction corresponding to the heading difference with the smallest absolute value is selected as the rotation direction for switching the ship's heading;

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

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

[0025]

[0026] Where: K represents the cyclotonicity index; K c represents the input of the ship robust controller; ρ represents the positive design parameter for improving the dynamic performance of the ship system; s represents the complex variable of the Laplace transform.

[0027] Furthermore, the automatic switching controller under the network attack constructed in S2 is expressed as

[0028]

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

[0030] The initial control input of the automatic switching controller is obtained according to the ship robust controller, and its expression is:

[0031] δ=K c 'e.

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

[0033] S31: Based on the nonlinear modification technology, the initial control input δ of the automatic switching controller is nonlinearly modified, and the expression is:

[0034] δ0=arctan(aK c 'e)

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

[0036] S32: Get the transfer function G of the zero-order holder h (s), whose expression is

[0037]

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

[0039] The transfer function G of the zero-order holder h (s) is expanded by Taylor series to obtain a simplified form of the zero-order holder, which is expressed as

[0040]

[0041] S33: Optimize the control input of the automatic switching controller after nonlinear modification according to the simplified zero-order holder to obtain the optimized control input δ of the automatic switching controller c , whose expression is

[0042]

[0043] Furthermore, in S4, the marine environment interference during the ship's heading process is considered, and the limiting condition for the rudder angle / rudder speed limit of the optimized control input of the automatic switching controller is:

[0044]

[0045] Where: δ represents the final ship control input, i.e., the ship rudder angle input; δ max Indicates the maximum rudder angle value of the ship.

[0046] Beneficial effect: The present invention provides a control method for enhancing the resilience of automatic switching of ship heading under network attacks. Through the heading switching mechanism, when the ship faces a large-angle collision avoidance turn, the large-angle collision avoidance is converted into a small-angle turn. At the same time, a ship robust controller is obtained based on a first-order closed-loop gain shaping algorithm to construct an automatic switching controller under network attacks. By simulating network attacks, the measured signal is inverted and equivalent to the positive feedback control situation. An automatic switching function of ship heading positive and negative feedback is designed, so that when the ship is attacked by a network, the resilience of the ship in heading maintenance and large-angle collision avoidance switching is improved. By adding a nonlinear modification driven by an inverse tangent function and a zero-order holder to the automatic switching controller to modify its control input, the controller output amplitude is greatly reduced and the rudder swing frequency is reduced. It can effectively cope with network attacks, quickly realize heading switching during large-angle collision avoidance, and reduce energy consumption while reducing rudder wear. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0048] Figure 1 This is a flow chart of a method for strengthening control of automatic switching resilience of ship heading under network attack according to the present invention;

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

[0050] Figure 3 This is a simulation diagram of the gyration test of the "Yupeng" under ballasting in this embodiment;

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

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

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

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

[0055] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0056] This embodiment provides a method for strengthening the resilience of ship heading automatic switching under network attacks. Figure 1 to Figure 2 As shown, the specific steps include:

[0057] S1: Construct nonlinear Nomoto ship model;

[0058] Obtain the heading error between the ship's desired heading and actual heading to build a heading switching mechanism;

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

[0060] The specific steps include:

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

[0062]

[0063] The ship motion model used in this embodiment is a nonlinear response model. However, this model is relatively simple and has a certain distance from the real ship. In order to build a more realistic mathematical model of ship motion so that it can better simulate the operation of the ship in reality, a nonlinear function is needed. To replace the in

[0064]

[0065] Then the nonlinear Nomoto ship model is constructed, and the expression of the nonlinear Nomoto ship model is:

[0066]

[0067] Where: ψ represents the heading angle of the ship; δ represents the rudder angle input of the ship; K, T represent the turning index and maneuverability index of the ship motion maneuverability respectively; α, β represent the nonlinear parameters of the ship model; Represents the first derivative of the ship's heading angle ψ; Represents the second derivative of the ship's heading angle and heading ψ;

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

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

[0070] The heading switching mechanism: taking the actual heading of the ship as the heading starting point and the expected heading of the ship as the heading ending point, respectively obtaining the first heading difference and the second heading difference according to the counterclockwise rotation and the clockwise rotation; wherein obtaining the heading difference by rotating in the counterclockwise direction or the clockwise direction is an existing well-known technical means, which will not be described in detail here;

[0071] Comparing the absolute value of the first heading difference with the absolute value of the second heading difference;

[0072] The rotation direction corresponding to the heading difference with the smallest absolute value is selected as the rotation direction for switching the ship's heading;

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

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

[0075]

[0076] δ=K c e

[0077] Where: K represents the cyclotonicity index; K c represents the input of the ship robust controller; ρ represents the positive design parameter for improving the dynamic performance of the ship system; s represents the complex variable of the Laplace transform.

[0078] S2: Construct an automatic switching controller under network attack and obtain the initial control input of the automatic switching controller according to the ship robust controller;

[0079] Specifically, there are various forms of cyber attacks on ships, which may target the ship's communication system, control system or data system, etc. The following are some common forms of cyber attacks on ships: untargeted attacks, targeted attacks (such as active attacks, exploiting vulnerabilities in ship communication protocols, invading through WIFI, high-frequency radio and commercial satellite communications, insider attacks using USB flash drives, etc.). Other forms of attacks (such as interference with the ship's automatic identification system (AIS), ransomware attacks, etc.). Among them, signal reversal is an important one. In control theory, negative feedback is to form a feedback loop and continuously adjust the amplitude of the input to reduce the error between the input and the output, so that the system finally achieves the ideal output. The positive feedback concept adopted in this embodiment is another form of equivalent transformation of negative feedback, which is used to simulate the situation when the hacker reverses the measured signal during a cyber attack (negative feedback is the reversal of the measured signal, negative and negative equals positive, which is equivalent to the situation of 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 while the numerator becomes negative. It is essentially an equivalent change. For the controller K', a negative sign can also be added. That is, first, the feedback signal is changed from negative feedback to positive feedback, and then the controller of the original negative feedback control method is multiplied by -1 to become a positive feedback controller, and then the system output is multiplied by -1, and finally the equivalent transformation of negative feedback and positive feedback is realized. Then, the automatic switching controller under network attack is obtained based on the ship robust controller. Its expression is:

[0080]

[0081] Where: K c ' represents the control input of the ship robust controller under network attack; G represents the open-loop transfer function. The left side of the 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 it is a positive feedback controller, the output of the positive feedback system differs from the output of the negative feedback system by a negative sign; the formula on the right side of the equal sign is used to measure the switching control scheme when the signal is negative; -K' is the controller under positive feedback. In theory, any system that can be controlled by negative feedback has an equivalent positive feedback control system. Finally, under the action of positive feedback and nonlinear feedback, a system like Figure 7 The simulation module shown;

[0082] The initial control input of the automatic switching controller is obtained according to the ship robust controller, and its expression is:

[0083] δ=K c 'e

[0084] S3: Based on the nonlinear modification technology, the initial control input of the automatic switching controller is nonlinearly modified, and the control input of the automatic switching controller after the nonlinear modification is optimized by using a zero-order holder to obtain the optimized control input of the automatic switching controller;

[0085] The specific steps include:

[0086] S31: Based on the nonlinear modification technology, the initial control input δ of the automatic switching controller is nonlinearly modified, and the expression is:

[0087] δ0=arctan(aK c 'e)

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

[0089] S32: Since the zero-order holder has the characteristic that the amplitude decays rapidly as the frequency increases, it has good low-pass filtering performance, which is consistent with the characteristic that the ship control signal plays a greater role in the low-frequency band. In addition, the zero-order holder has the function of reducing the steering frequency to protect the steering gear from wear. Therefore, the zero-order holder is incorporated into the controller to obtain the transfer function of the zero-order holder, which is expressed as

[0090]

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

[0092] The transfer function G of the zero-order holder h (s) is expanded by Taylor series to obtain a simplified form of the zero-order holder, which is expressed as

[0093]

[0094] S33: Optimize the control input of the automatic switching controller after nonlinear modification according to the simplified zero-order holder to obtain the optimized control input δ of the automatic switching controller c , whose expression is

[0095]

[0096] In this example, the effect of adding the inverse tangent function on the steady state of the ship control system is as follows:

[0097] Assume that a step signal is used as the input signal with an amplitude of r. Assuming that the error of the ship control system is within an acceptable range and that the change in the input signal causes the value of u to be very small, then according to the expansion of the Taylor series, 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 output steady-state error of the ship control system is 0, which shows that under certain conditions, using the inverse tangent function to modify the output of the controller 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, so the final nonlinear modification form is arctan(0.4u);

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

[0101] The ship's heading at the next moment under the cyber attack is obtained based on the final ship control input, so as to realize the automatic switching of the ship's heading and strengthen the control of resilience;

[0102] In a specific embodiment, in S4, considering the marine environment interference during the ship's heading process, the limiting condition for limiting the rudder angle / rudder speed of the optimized control input of the automatic switching controller is:

[0103]

[0104] Where: δ represents the final ship control input, i.e., the ship rudder angle input; δ max Indicates the maximum rudder angle value of the ship.

[0105] Compared with the prior art, this embodiment converts large-angle collision avoidance into small-angle steering through a heading switching mechanism when the ship faces a large-angle collision avoidance steering. At the same time, a ship robust controller is obtained based on a first-order closed-loop gain shaping algorithm to construct an automatic switching controller under network attacks. By simulating network attacks, the measured signal is inverted and equivalent to the positive feedback control situation. An automatic switching function of ship heading positive and negative feedback is designed, so that when the ship is attacked by a network, the ship's heading maintenance and large-angle collision avoidance switching resilience is improved. By adding a nonlinear modification driven by an inverse tangent function and a zero-order holder to the automatic switching controller to modify its control input, the controller output amplitude is greatly reduced and the rudder swing frequency is reduced. It can effectively cope with network attacks, quickly realize heading switching during large-angle collision avoidance, and reduce energy consumption while reducing rudder wear.

[0106] In order to verify the validity of the established nonlinear Nomoto ship model, Figure 3 to Figure 4 As shown, taking the "Yupeng" as the research object, a 35° turning simulation test and a 10° / 10° Z-shaped test were carried out under full load 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 turning circle are listed in Table 1;

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

[0108]

[0109] Simulation experiment of right turn at 35° under ballast: The nonlinear Nomoto model was used to simulate the right turn at 35° under ballast of the Yupeng ship. The value of the dimensionless cross-flow coefficient C was adjusted to make the simulation close to the actual ship. At the same time, the cross-flow parameters were selected multiple times by dichotomy. It was found that when C = 0.6, the simulation effect was better. Figure 1 Comparison of the turning circles of the real ship and the simulation.

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

[0111]

[0112] And according to the definition of compliance in ship motion control, verification is carried out:

[0113]

[0114] Where: A d1 Indicates the actual ship rotation advance; A d2 Indicates the model rotation simulation distance; D T1 Indicates the initial turning diameter of the actual ship; D T2 It indicates the initial diameter of the simulated turning; D1 indicates the turning diameter of the actual ship; D2 indicates the simulated turning diameter. It is calculated that under the condition of ballast level 6 wind, the nonlinear Nomoto model turning simulation and the actual ship test have a good agreement. The specific results are shown in Table 2.

[0115] 10° / 10°Z-shape simulation test under ballast: When the ship is under ballast, the "Yupeng" ship is subjected to a 10° / 10°Z-shape simulation test. The simulation test results are as follows: Figure 2As shown in Table 3, the 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-Zag maneuvertest overshoot angle

[0117]

[0118] The controller in the method of this embodiment combines a first-order closed-loop gain shaping algorithm, nonlinear modification and a zero-order holder. The zero-order holder can reduce the rudder frequency, and the controller designed by the closed-loop gain shaping algorithm has strong robustness. These characteristics show that the controller has strong practical significance for navigation. This embodiment uses Matlab's Simulink toolbox to conduct a simulation experiment on the "Yupeng Ship" of Dalian Maritime University, and selects a traditional PID controller that has not been improved by nonlinear modification as a reference object to judge the improvement degree of the controller of this embodiment. The expression of the traditional controller is:

[0119]

[0120] Where: u(t) is the control output; e(t) is the control input, that is, the deviation between the controlled quantity and the given value; K p , T i , T d They are the proportional coefficient, integral time constant and differential time constant respectively.

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

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

[0123]

[0124] Among them, ξ6 represents the wave interference under sea condition level 6, and ζ represents white noise.

[0125] In terms of the control performance of the controller, in order to quantitatively analyze and compare the control performance of the controller, three indicators, namely Mean Absolute Error (MAE), Mean Integrate Absolute (MIA) and Mean Total Variation (MTV), are used for quantitative analysis. Among them, MAE is used to measure the response time of the system output, and MIA and MTV are used to measure the energy consumption related to the input rudder angle and the smoothness of the corresponding algorithm.

[0126]

[0127] Where: t0, t ∞ are the initial time and the end time respectively; ψ r is the set reference heading; ψ(t) is the ship heading angle at time t; δ(t) is the rudder angle at time t; t is time; In order to verify the energy-saving effect of the controller after nonlinear modification, a specific energy indicator is used to compare the energy consumption of the unmanned ship during navigation:

[0128] J = ∫δ 2 dt

[0129] Where: J is an indicator to measure energy consumption.

[0130] The evaluation index is not the real energy. It only shows in numerical value that the index of heading control after nonlinear modification under the influence of factors such as rudder angle, maximum rudder angle, and adjustment time is better than conventional feedback. Therefore, this embodiment draws on the existing rudder resistance energy consumption calculation formula to calculate the energy consumption of the nonlinear modification and the controller of this embodiment, so as to more accurately illustrate its advantages in energy saving effect. The rudder resistance is the resistance of the ship to the forward movement of the water flow impacting the rudder blade when the ship is steering. The rudder resistance and the component force of the rudder force in the forward direction of the ship are interactive forces. Therefore, the rudder resistance energy consumption can well describe the work done by the steering gear. The calculation formula is as follows:

[0131]

[0132] in,

[0133] Where: T0 = 1600s is the simulation time, X HR is the water resistance to the rudder in longitudinal motion, V is the ship speed, ρ is the seawater density, A R is the rudder area, f ais the slope of the rudder lift coefficient at a=0. This embodiment uses Fujii's formula for calculation, λ is the rudder aspect ratio, γ R is the rectification coefficient, C b is the square coefficient, l R It can be regarded as the longitudinal coordinate of the rudder, but according to the description in the literature, it is generally twice -L / 2, l R ' represents the dimensionless transformation, r' is the dimensionless bow angular velocity, and the above parameters are reflected in Table 1.

[0134] In this experiment, the positive and negative switching of the signal is added to the loop when the simulation time is 800s to simulate the attack on the ship network, and the switching control of positive and negative feedback is designed to solve the problem of the reverse sign of the measured signal. r The ship needs to switch to 340° for collision avoidance at 800s. If the conventional control algorithm is used, the ship needs to turn to 320°, and the turning process is slow and long. In this embodiment, 340° is processed as -20°, so it only needs to turn 40°. When the heading is switched, the control system encounters a network attack, and the hacker reverses the measurement signal, and the original negative feedback system becomes a positive feedback system. Figure 5 It can be seen that the method of this embodiment can make the ship's heading angle reach the expected heading in a very short time, and stabilize near the expected heading at a very fast speed without much fluctuation. This result shows that in the face of the adverse situation of the measurement signal reversal caused by network attacks, the automatic switching control method proposed in this embodiment can respond immediately and quickly correct the heading, thereby effectively avoiding the risk of the ship yaw. Figure 6 It can be seen intuitively that the method of this embodiment can better reduce the steering angle and reduce rudder damage.

[0135] Tab.4 Comparison of simulation results under Beaufort wind of No.6

[0136]

[0137] After reaching the set heading, the heading angle fluctuates to a certain extent, but the system still has good stability. After using the controller of this embodiment, under the sixth level sea condition, the maximum rudder angle is reduced by 61.87%, MAE increases slightly, MIA decreases by 45.04%, MTV decreases by 38.22%, the index J measuring energy consumption decreases by 70.35%, and the rudder resistance energy consumption decreases by 74.52%. Through the quantitative analysis of the test results, it can be seen that the use of the controller of this embodiment can effectively achieve the energy-saving goal. The MAE index is mainly used to measure the response time or error size of the system output. Its increase may reflect that the controller has made a certain degree of trade-off on the smoothness of the rudder angle input curve when pursuing higher energy-saving effects, because the index J measuring energy consumption and the rudder resistance energy consumption are significantly reduced.

[0138] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements 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 strengthening the resilience of ship heading automatic switching under network attacks, characterized in that: The specific steps include: S1: Construct nonlinear Nomoto ship model; Obtain the heading error between the ship's desired heading and actual heading to build a heading switching mechanism; Based on the first-order closed-loop gain shaping algorithm and heading switching mechanism, a ship robust controller is constructed according to the nonlinear Nomoto ship model. S2: Construct an automatic switching controller under network attack and obtain the initial control input of the automatic switching controller according to the ship robust controller; S3: Based on the nonlinear modification technology, the initial control input of the automatic switching controller is nonlinearly modified, and the control input of the automatic switching controller after the nonlinear modification is optimized by using a zero-order holder to obtain the optimized control input of the automatic switching controller; S4: Considering the marine environment interference during the ship's heading process, the rudder angle / rudder speed is limited on the optimized control input of the automatic switching controller to obtain the final ship control input; The ship's heading at the next moment under the cyber attack is obtained according to the final ship control input, so as to realize the automatic switching of the ship's heading and enhance the resilience control.

2. According to the method for strengthening the control of ship heading automatic switching resilience under network attack in claim 1, it is characterized in that: The S1 specifically includes the following steps S11: Construct a nonlinear Nomoto ship model, and the expression of the nonlinear Nomoto ship model is Where: ψ represents the heading angle of the ship; δ represents the rudder angle input of the ship; K, T represent the turning index and maneuverability index of the ship motion maneuverability respectively; α, β represent the nonlinear parameters of the ship model; Represents the first derivative of the ship's heading angle ψ; Represents the second derivative of the ship's heading angle and heading ψ; S12: Obtain the heading error e between the ship's desired heading and actual heading, and e=ψ r -ψ; Construct a heading switching mechanism based on the heading error e; The heading switching mechanism: taking the actual heading of the ship as the heading starting point and the expected heading of the ship as the heading ending point, respectively obtaining the first heading difference and the second heading difference according to the counterclockwise rotation and the clockwise rotation; Comparing the absolute value of the first heading difference with the absolute value of the second heading difference; The rotation direction corresponding to the heading difference with the smallest absolute value is selected as the rotation direction for switching the ship's heading; When the absolute value of the first heading difference is equal to the absolute value of the second heading difference, either the counterclockwise direction or the clockwise direction is randomly selected as the rotation direction for switching the ship's heading; S13: Based on the first-order closed-loop gain shaping algorithm and the heading switching mechanism, a ship robust controller is constructed according to the nonlinear Nomoto ship model. The expression of the ship robust controller is: δ=K c e Where: K represents the cyclotonicity index; K c represents the input of the ship robust controller; ρ represents the positive design parameter for improving the dynamic performance of the ship system; s represents the complex variable of the Laplace transform.

3. According to the method for strengthening the control of the ship's heading automatic switching resilience under network attack in claim 2, it is characterized in that: The automatic switching controller under the network attack constructed in S2 is expressed as Where: K c ' represents the control input of the ship robust controller under cyber attack; G represents the open-loop transfer function; The initial control input of the automatic switching controller is obtained according to the ship robust controller, and its expression is δ = K c 'e.

4. According to the method for strengthening the control of ship heading automatic switching resilience under network attack in claim 3, it is characterized in that: S3 specifically includes the following steps S31: Based on the nonlinear modification technology, the initial control input δ of the automatic switching controller is nonlinearly modified, and the expression is δ0=arctan(aK c 'e) Where: δ0 represents the control input after nonlinear modification; arctan(au) represents the modification function and u = K c 'e; S32: Get the transfer function G of the zero-order holder h (s), whose expression is Where: a represents the sampling period of the configured ship system; s represents the complex variable of Laplace transform; The transfer function G of the zero-order holder h (s) is expanded by Taylor series to obtain a simplified form of the zero-order holder, which is expressed as S33: Optimize the control input of the automatic switching controller after nonlinear modification according to the simplified zero-order holder to obtain the optimized control input δ of the automatic switching controller c , whose expression is 5. According to the method for strengthening the control of ship heading automatic switching resilience under network attack in claim 4, it is characterized in that: In S4, the marine environment disturbance during the ship's heading process is considered, and the limiting condition for the rudder angle / rudder speed limit on the optimized control input of the automatic switching controller is: Where: δ represents the final ship control input, i.e., the ship rudder angle input; δ max Indicates the maximum rudder angle value of the ship.

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