Ship toughness strengthening course keeping control method under network attack

Abstract

The invention discloses a ship toughness strengthening course keeping control method under network attacks, which comprises the following steps: establishing a response type nonlinear Nomoto model as a ship motion mathematical model to obtain a simplified transfer function; based on a second-order closed-loop gain shaping algorithm, constructing a ship course robust controller according to the simplified transfer function; obtaining a ship course error under the condition of considering the ship network attack so as to carry out nonlinear modification on control input of a ship course robust controller; an equivalent transformation model for performing input signal feedback on control input of the ship course robust controller after nonlinear modification is obtained; according to the equivalent transformation model, a zero-order retainer is adopted to optimize control output of a ship course robust controller, and optimized rudder angle control output is obtained; and obtaining the final ship navigation course according to the optimized rudder angle control output by considering the marine environment interference. The technical problem that a traditional ship control strategy cannot resist network attacks to guarantee the ship course and the collision prevention control function is solved.

Description

Technical Field

[0001] The present invention relates to the field of ship motion control and modeling, and in particular to a ship resilience enhanced heading keeping control method under network attacks. Background Art

[0002] As the intelligence of ships continues to increase, their control systems are increasingly dependent on the network. However, this also makes ships face the potential threat of cyber attacks during navigation. Once attacked by a cyber attack, traditional ship control strategies are often difficult to deal with, which can easily lead to loss of control of the ship's heading and inability to achieve effective collision avoidance operations, seriously affecting the safety of ship navigation. For example, in some cases, a cyber attack may cause the measurement information of the control system to be tampered with, causing the ship to receive incorrect navigation data and make incorrect heading adjustment decisions, which is extremely dangerous for ships sailing in complex sea conditions. Therefore, there is an urgent need for a new control method that can resist cyber attacks and ensure the ship's heading and collision avoidance control functions. Summary of the invention

[0003] The present invention provides a ship resilience enhanced course keeping control method under network attack to overcome the above technical problems.

[0004] In order to achieve the above object, the technical solution of the present invention is:

[0005] A ship resilience enhanced course keeping control method under network attack specifically comprises the following steps:

[0006] S1: Establish a responsive nonlinear Nomoto model as a mathematical model of ship motion;

[0007] S2: Obtain simplified transfer functions for controller design based on the mathematical model of ship motion;

[0008] S3: Based on the second-order closed-loop gain shaping algorithm, a ship heading robust controller is constructed according to the simplified transfer function;

[0009] S4: Obtain the ship heading error considering the ship network attack;

[0010] According to the ship heading error, the control input of the ship heading robust controller is modified nonlinearly;

[0011] Obtain the ship heading robust controller after nonlinear modification and perform an equivalent transformation model for input signal feedback;

[0012] According to the equivalent transformation model, the zero-order holder is used to optimize the control output of the ship heading robust controller to obtain the optimized rudder angle control output;

[0013] S5: Considering the marine environment interference, the final ship navigation heading is obtained according to the optimized rudder angle control output;

[0014] The marine environmental disturbance at least includes sea wind disturbance and sea wave disturbance.

[0015] Furthermore, the response-type nonlinear Nomoto model constructed in S1 is expressed as

[0016]

[0017] Where: ψ represents the ship's heading angle; The first derivative of ψ is the rate of change of heading; represents the second-order derivative of ψ, i.e., the heading angular acceleration; K0 and T0 represent the ship turning index and following index, respectively; δ represents the ship rudder angle; α and β represent the nonlinear parameters of the ship model.

[0018] Further, in S2, a transfer function for controller design is obtained according to the mathematical model of ship motion, which specifically includes the following steps:

[0019] S21: Based on the mathematical model of ship motion, the Laplace operator s is introduced to obtain the initial transfer function, which is expressed as follows:

[0020]

[0021] S22: Omit the nonlinear parameters α, βs of the initial transfer function 3 ψ 3 , to obtain the simplified transfer function G(s), which is expressed as

[0022]

[0023] Furthermore, the S3 specifically includes the following steps:

[0024] S31: Get the second-order closed-loop gain shaping algorithm model, which is expressed as

[0025]

[0026] Where: T1 represents the time constant; s represents the Laplace operator; G represents the closed-loop transfer function; K represents the input of the heading controller to be designed;

[0027] S32: Based on the simplified transfer function G(s) and the second-order closed-loop gain shaping algorithm model, a ship heading controller is constructed, and its expression is:

[0028]

[0029] S33: In order to avoid the influence of static error in the ship heading controller on the ship control system, the simplified transfer function G(s) is rewritten as

[0030]

[0031] Where: ε represents the constant term of the influence of static error on ship motion;

[0032] S34: According to the rewritten simplified transfer function G' and the ship heading controller, the ship heading robust controller is obtained, and its expression is:

[0033]

[0034] Furthermore, the S4 specifically includes the following steps:

[0035] S41: Obtain the ship heading error e under the consideration of ship network attack and e=ψ r -ψ;

[0036] Among them, ψ r represents the desired heading of the ship ψ r ; ψ represents the actual heading under the consideration of the ship’s cyber attack;

[0037] Based on the ship heading error e, the control input of the ship heading robust controller is nonlinearly modified according to the nonlinear modification function f(u);

[0038] And the expression for nonlinear modification is

[0039] δ=K c e

[0040] f(u)=arctan(aδ) / b

[0041] Where: a and b both represent setting parameters;

[0042] S42: Obtain the ship heading robust controller after nonlinear modification and perform the equivalent transformation model of input signal feedback, which is expressed as follows:

[0043]

[0044] Where: K' represents the control input of the ship heading robust controller after nonlinear modification; represents the transfer function of the closed-loop control system under the consideration of ship network attack, that is, the positive feedback term of the ship heading robust controller; represents the negative feedback term of the ship heading robust controller;

[0045] S43: According to the equivalent transformation model, a zero-order holder is used to optimize the control output of the ship heading robust controller to obtain an optimized rudder angle control output;

[0046] The optimized rudder angle control output δ r The expression is

[0047] δ r =arctan(aK c e) / b*K e

[0048]

[0049] Where: K e represents the transfer function of the zero-order holder; T represents the set sampling period of the ship control system; s represents the Laplace operator.

[0050] Furthermore, the S5 specifically includes the following steps:

[0051] S51: Obtain the equivalent rudder angle δ considering the sea breeze disturbance w1 according to the optimized rudder angle control output s ;

[0052] The sea breeze disturbance w1 is an equivalent angle synthesized by a set white noise and an equivalent rudder angle representing the wind level;

[0053] The equivalent rudder angle δ s The expression is

[0054] δ s =δ r +w1

[0055] S52: Set the equivalent rudder angle δ s The output heading angle of the ship is obtained by inputting it into the mathematical model of ship motion, and the output heading angle is added to the considered wave disturbance w2 to obtain the final ship navigation heading output after considering the wind and wave disturbance. The wave disturbance w2 is the equivalent angle obtained by the second-order oscillation link driven by white noise certified by ITTC.

[0056] Beneficial effect: The present invention provides a method for ship resilience enhanced heading keeping control under network attack. Based on a second-order closed-loop gain shaping algorithm, a ship heading robust controller is obtained according to a constructed simplified transfer function, and then the control input of the ship heading robust controller after nonlinear modification is obtained under the consideration of the ship network attack, and an equivalent transformation model is used to perform input signal feedback. By simulating various possible network attack scenarios, the equivalent transformation model is used to optimize the automatic switching function of the ship heading positive and negative feedback, so that the ship control system can respond quickly and accurately when facing similar network attack interference, and automatically switch to the correct feedback mode to ensure stable control of the ship heading; a robust controller is designed by using a second-order closed-loop gain shaping algorithm, and a nonlinear modification driven by a nonlinear modification function and a zero-order holder are added after the robust controller to reduce the controller output amplitude, which not only effectively reduces the output rudder angle amplitude and the rudder turning frequency, but also ensures that the ship can still maintain a stable heading in a complex and changeable network attack environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] 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.

[0058] Figure 1 This is a flow chart of the ship resilience enhanced heading keeping control method under network attack of the present invention;

[0059] Figure 2 This is the core block diagram of the ship toughness enhanced heading keeping control method in this embodiment;

[0060] Figure 3 This is a simulation diagram of the 35° right turn experiment of KVLCC2 in this embodiment;

[0061] Figure 4 This is a simulation diagram of the 10° / 10° Z-shaped experiment of KVLCC No. 2 in this embodiment;

[0062] Figure 5 This is a simulation diagram of the course change under level 5 sea conditions in this embodiment;

[0063] Figure 6 This is a simulation diagram of the rudder angle change under level 5 sea conditions in this embodiment;

[0064] Figure 7 This is a simulation diagram of ship heading change based on the equivalent transformation model under level 5 sea conditions in this embodiment;

[0065] Figure 8This is a feedback loop block diagram constructed using the equivalent transformation model in this embodiment. DETAILED DESCRIPTION

[0066] 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.

[0067] This embodiment provides a ship resilience enhanced course keeping control method under network attack, such as Figure 1 to Figure 2 As shown, the specific steps include:

[0068] S1: Establish a responsive nonlinear Nomoto model as a mathematical model of ship motion;

[0069] Specifically, in this embodiment, it is crucial to establish a mathematical model with satisfactory accuracy and appropriate complexity for the closed-loop performance study of the system. It is necessary to consider the influence of environmental factors on the ship motion parameters and the ship shape and its own structural characteristics. In this embodiment, the responsive nonlinear Nomoto mathematical model is selected as the ship motion mathematical model. By using the actual ship parameters for modeling, the tedious mechanical analysis and the process of establishing a complex state space model are avoided, making the description of the ship's motion response more accurate and convenient.

[0070] The constructed responsive nonlinear Nomoto model is expressed as

[0071]

[0072] Where: ψ represents the ship's heading angle; The first derivative of ψ is the rate of change of heading; represents the second-order derivative of ψ, i.e., the heading angular acceleration; K0 and T0 represent the ship turning index and following index, respectively; δ represents the ship rudder angle; α and β represent the nonlinear parameters of the ship model;

[0073] S2: Obtain simplified transfer functions for controller design based on the mathematical model of ship motion;

[0074] The specific steps include:

[0075] S21: Based on the mathematical model of ship motion, the Laplace operator s is introduced to obtain the initial transfer function, which is expressed as follows:

[0076]

[0077] S22: To facilitate controller design, the model is simplified, that is, the nonlinear parameters α, βs of the initial transfer function are omitted. 3 ψ 3 , to obtain the simplified transfer function G(s), which is expressed as

[0078]

[0079] S3: Based on the second-order closed-loop gain shaping algorithm, a ship heading robust controller is constructed according to the simplified transfer function;

[0080] In this embodiment, in order to realize the ship heading keeping control, a second-order closed-loop gain shaping algorithm is used to design the controller. The algorithm reversely infers the controller by constructing the desired system closed-loop transfer function. The characteristics of the algorithm are that the physical concept of the theory is clear and the solution process is extremely simple.

[0081] The specific steps include:

[0082] S31: Get the second-order closed-loop gain shaping algorithm model, which is expressed as

[0083]

[0084] Where: T1 represents the time constant; s represents the Laplace operator; G represents the closed-loop transfer function; K represents the input of the heading controller;

[0085] S32: Based on the simplified transfer function G(s) and the second-order closed-loop gain shaping algorithm model, a ship heading controller is constructed, and its expression is:

[0086]

[0087] S33: This embodiment is a controller designed using a second-order closed-loop gain control algorithm, which can eliminate the influence of static errors on the system. A very small constant term is added to the denominator of the transfer function of the ship motion model to reproduce the influence of uncertain constant value interference on the ship motion. The simplified transfer function G(s) is rewritten as

[0088]

[0089] Where: ε represents the constant term of the influence of the static error uncertainty constant value disturbance on the ship motion;

[0090] S34: According to the rewritten simplified transfer function G' and the ship heading controller, the ship heading robust controller is obtained, and its expression is:

[0091]

[0092] S4: nonlinear modification of the control input of the ship heading robust controller;

[0093] Considering the ship network attack, the ship heading robust controller after nonlinear modification is obtained, and the equivalent transformation model of input signal feedback is performed;

[0094] According to the equivalent transformation model, the zero-order holder is used to optimize the control output of the ship heading robust controller to obtain the optimized rudder angle control output;

[0095] The specific steps include:

[0096] S41: Obtain the ship heading error e under the consideration of ship network attack and e=ψ r -ψ;

[0097] Among them, ψ r represents the desired heading of the ship ψ r ; ψ represents the actual heading under the consideration of the ship’s cyber attack;

[0098] Based on the ship heading error e, the control input of the ship heading robust controller is nonlinearly modified according to the nonlinear modification function f(u);

[0099] And the expression for nonlinear modification is

[0100] δ=K c e

[0101] f(u)=arctan(aδ) / b

[0102] This embodiment also includes the analysis of the impact of nonlinear feedback on the ship heading keeping control system:

[0103] The Taylor series expansion of the nonlinear modification function f(u) is performed at u=0:

[0104]

[0105] Where: a and b are setting parameters, which have different effects on the performance of the ship heading keeping control system. The Taylor series is retained to the first order and arctan(au) / b≈au / b=ω;

[0106] Let the system frequency of the ship heading keeping control system ω=0.6a / b, and analyze the system:

[0107] 1) Analyze the steady-state performance of the ship heading keeping control system, ignoring the high-order terms in the nonlinear feedback, and the system steady-state error e ss (∞) is approximately:

[0108]

[0109] Where:r It means the set heading is the desired heading of the ship, and the final system output steady-state error is 0, which proves that nonlinear feedback has no effect on the steady state of the system;

[0110] 2) Analyze the influence of the dynamic performance of the ship heading keeping control system, and its expression is:

[0111]

[0112] Among them, when a / b = 1, it is equivalent to the output response of the original robust control system; when a / b≠1, the appropriate selection of the values ​​of a and b can change the dynamic response performance of the system to meet actual needs;

[0113] 3) The influence on the control output of the ship's heading keeping control system, and the system input ψ r The transfer function to the controller output δ is

[0114]

[0115] It can be seen from the transfer function that the numerator decreases more significantly than the denominator, so adjusting the values ​​of the setting parameters a and b will reduce the rudder angle and reduce the control output;

[0116] S42: Obtain the ship heading robust controller after nonlinear modification and perform the equivalent transformation model of input signal feedback, which is expressed as follows:

[0117]

[0118] Where: K' represents the control input of the ship heading robust controller after nonlinear modification; represents the transfer function of the closed-loop control system under the consideration of ship network attack, that is, the positive feedback term of the ship heading robust controller; represents the negative feedback term of the ship heading robust controller;

[0119] In the ship heading keeping control system of this embodiment, the task of the heading controller is to adjust the rudder angle of the ship according to the deviation of the heading so that the ship maintains the predetermined heading. In a standard negative feedback control system, if the ship deviates from the set heading, the ship heading keeping control system will obtain a rudder angle adjustment amount that has a certain functional relationship with the deviation, and correct the heading deviation by adjusting the rudder angle. In practical applications, the control input of the controller may be changed from positive to negative due to a hacker network attack, which is equivalent to a positive feedback situation, causing abnormal system behavior and even leading to safety accidents. In this embodiment, through the positive feedback control of the equivalent transformation model, the ship heading keeping control system can still work normally even if it encounters a hacker attack, because this error is offset by the negative sign during design. From the perspective of safety and reliability, the positive feedback control mechanism of the equivalent transformation model significantly improves the robustness of the ship heading keeping control system and improves the overall safety of the system. This additional safety measure can ensure that the ship can reliably maintain the predetermined heading, thereby ensuring navigation safety and efficiency. In control theory, the negative feedback of the equivalent transformation model refers to the ship heading keeping control system feeding back its output to the system input to suppress the impact of input changes, thereby making the system more stable. That is, the positive feedback concept adopted in this embodiment is an equivalent transformation of the negative feedback form. For negative feedback, the closed-loop control system transfer function is Positive feedback is equivalent to changing the feedback signal from negative to positive, then multiplying the original negative feedback control method controller by -1 to change it to a positive feedback controller, and then multiplying the system output by -1, and finally realizing the equivalent transformation of negative feedback and positive feedback. In theory, all systems that can be controlled by negative feedback have an equivalent positive feedback control system. Therefore, under the action of positive feedback and nonlinear feedback, the equivalent transformation model can be used to obtain the feedback loop when the input signal is reversed, and then the following can be constructed: Figure 8 The simulation module of the simulation block diagram shown;

[0120] S43: According to the equivalent transformation model, a zero-order holder is used to optimize the control output of the ship heading robust controller to obtain an optimized rudder angle control output;

[0121] The optimized rudder angle control output δ r The expression is

[0122] δ r =arctan(aK c e) / b*K e

[0123]

[0124] Where: K erepresents the transfer function of the zero-order holder; T represents the set sampling period of the ship control system; s represents the Laplace operator;

[0125] In order to reduce the steering frequency of the ship, this embodiment converts discrete digital signals into continuous analog signals by introducing a zero-order holder. In the steering system, it can hold discrete steering commands. After receiving a steering command, the zero-order holder will keep the command value unchanged for a period of time, so that the steering actuator does not need to respond frequently to rapidly changing commands. This reduces the number of actions of the steering actuator, thereby reducing the steering frequency. Therefore, integrating the zero-order holder into the controller can not only maintain the accurate transmission of the control signal, but also effectively extend the service life of the steering gear and improve the reliability and durability of the entire ship control system;

[0126] S5: Considering the marine environmental disturbance, obtaining the final ship navigation direction according to the optimized rudder angle control output; the marine environmental disturbance at least includes sea wind disturbance and sea wave disturbance;

[0127] The specific steps include:

[0128] S51: Obtain the equivalent rudder angle δ considering the sea breeze disturbance w1 according to the optimized rudder angle control output s ;

[0129] The sea breeze disturbance w1 is an equivalent angle synthesized by a set white noise and an equivalent rudder angle representing the wind level. The equivalent rudder angle δ s The expression is

[0130] δ s =δ r +w1

[0131] S52: Set the equivalent rudder angle δ s The output heading angle of the ship is obtained by inputting it into the mathematical model of ship motion, and the output heading angle is added to the considered wave disturbance w2 to obtain the final ship navigation heading output after considering the wind and wave disturbance. The wave disturbance w2 is the equivalent angle obtained by the second-order oscillation link driven by white noise certified by ITTC.

[0132] In this embodiment, the existing ship controller is combined with a second-order closed-loop gain shaping algorithm, nonlinear modification and a zero-order holder to obtain a ship resilience enhanced heading keeping control method under a network attack to maintain the ship's navigation course. The use of a zero-order holder can reduce the rudder frequency, and the controller designed with the second-order closed-loop gain shaping algorithm has strong robustness, so that the obtained ship heading robust controller has strong navigation practice significance. This embodiment takes the impact of network attacks on ship control systems into overall consideration. First, by simulating various possible network attack scenarios, a highly robust ship heading controller is constructed using advanced control algorithms. For example, the use of a second-order closed-loop gain shaping algorithm, combined with nonlinear feedback driven by an inverse tangent function and a zero-order holder, effectively reduces the ship's output rudder angle amplitude and steering frequency, reduces unnecessary consumption of ship energy, and also reduces mechanical wear and operational risks that may be caused by frequent steering. In terms of simulating network attacks, we conducted in-depth research on the typical attack situation of measurement information reversal, constructed an equivalent transformation model, and simulated the controller input signal under network attack as equivalent to the positive feedback situation. Through the equivalent transformation model, we optimized the automatic switching function of positive and negative feedback of the ship's heading, and accurately adjusted the control design parameters, so that the ship control system can respond quickly and accurately when facing similar network attack interference, automatically switch to the correct feedback mode, and ensure stable control of the ship's heading.

[0133] Simulation experiment: This embodiment uses the 300,000-ton oil tanker KVLCC2, one of the international standard ship models, as the simulation object, and uses the actual ship data and the nonlinear Nomoto model to perform 35° right turn experiment and 10° / 10° Z-shaped experiment simulation and compare the obtained results.

[0134] like Figure 3 As shown, in this embodiment, the nonlinear Nomoto model is used to carry out a simulation experiment of KVLCC2 ballast right turn of 35°, and the value of the dimensionless cross-flow coefficient C is adjusted to make the simulation close to the actual ship. At the same time, the cross-flow parameters are taken multiple times through the dichotomy method, and it is found that when C=0.6, the simulation effect is better.

[0135] Table 1. KVLCC2 slewing test during ballast

[0136]

[0137] The definition of compliance in ship motion control is used for verification, and its expression is:

[0138]

[0139] Where: A d1 Indicates the actual ship rotation advance; A d2Indicates the model rotation simulation distance; D T1 Indicates the initial turning diameter of the actual ship; D T2 It represents the initial diameter of the simulated turning; D1 represents the turning diameter of the actual ship; D2 represents the simulated turning diameter. The ballast can be calculated. Under the condition of force 6 wind, the nonlinear Nomoto model turning simulation has a good agreement with the actual ship test. The specific results are shown in Table 1.

[0140] In this embodiment, a 10° / 10° Z-shaped simulation test was conducted on KVLCC2 under ballast conditions. The simulation test results are shown in the figure. Figure 4 Table 2 shows the comparison data between the 10° / 10° Z-shaped simulation test and the actual ship data. Table 3 shows the main parameters of KVLCC2. In the test, L / V=39, and the preset first overshoot angle should not exceed 5°+0.5L / V=23°, and the second overshoot angle should not exceed 17.5°+0.75L / V

[0141] =46.75°.

[0142] Table 2. Comparison of overrun angles in 10° / 10° Z-shaped tests

[0143]

[0144] This embodiment uses the Simulink function in MATLAB to conduct a simulation experiment on the 300,000-ton KVLCC2. The desired heading is set to 60° before 2500s. At 2500s, a hacker attack causes the control input to change from 60° to -60°. The positive feedback control method, i.e., the equivalent transformation model, is adopted to enable the ship to maintain a heading of 60° when the control input changes to -60° under a network attack. The nonlinear parameters α=31.31, β=1054564.00 in the responsive nonlinear Nomoto model are obtained using the ship parameters in Table 3, K0=0.05, T0=201.73, ε=0.00001 in the simplified transfer function, and the setting parameters a=0.3, b=1 in the nonlinear modification function f(u). The simulation time is set to 5000s, and the simulation step length is 0.1s. At the same time, in order to meet the actual navigation situation, the maximum rudder angle of 35° and the maximum steering rate of 5° / s are added.

[0145] In this embodiment, for environmental interference, the sea breeze interference w1 is equivalently described as a synthesis of a white noise and an equivalent rudder angle representing the wind level through nonlinear modification; for wave interference w2, the second-order oscillation link driven by white noise recognized by the International ITTC is used to represent it. Considering the actual navigation needs, the level 5 sea condition is selected as the general sea condition for simulation. In the mathematical model of ship motion, the level 5 sea condition is simulated, and the wave interference is represented as:

[0146]

[0147] Where: ξ5 represents the wave interference under level 5 sea conditions; ξ represents white noise;

[0148] Table 3. Main parameters of KVLCC2

[0149] Tab3.Main particulars of “KVLCC2” ship

[0150]

[0151] like Figure 5 The following shows the course change within 7000s under sea condition level 5. Figure 5 The figure shows the change of rudder angle within 7000s. Figure 5 It can be seen that both the controller without nonlinear feedback and the controller of this embodiment can achieve the control target. Figure 6 It can be seen that the controller of this embodiment can better reduce the rudder angle and reduce rudder damage. For the controller, the stability, accuracy and speed of the control system must be met. For the ship heading switching system, the rudder angle should be smaller and the rudder frequency should also be smaller to achieve energy saving and emission reduction and reduce the wear of the rudder system. Therefore, in order to better compare which of the controllers of this embodiment and the controller without nonlinear feedback has better comprehensive performance, an error formula is introduced for comparison, and the error formula is:

[0152] E=Pe R (t)+Qe C (t)

[0153] Where: E represents the total error; e R (t) represents the rudder angle error expressed in root mean square; e C (t) represents the heading error; P and Q represent weights, with P = 0.7 and Q = 0.3, to adjust the balance between control effect and energy saving and emission reduction.

[0154] In order to accurately compare the energy-saving effect between the controller with nonlinear feedback and the controller without nonlinear feedback in this embodiment, the total energy consumption index formula is used for calculation, and its expression is:

[0155] W = ∫δ 2 (t)dt

[0156] Where: W represents the total energy consumption index; δ(t) represents the steering angle. The e of the two controllers can be directly calculated by using Simulink in MATLAB. R (t), e C Substituting the values ​​of (t) and δ into the error formula and the total energy consumption index formula, we can obtain the total error E of the controller without nonlinear feedback. R=12.041, the total error E of the controller with nonlinear feedback added in this embodiment C =8.584, the error of the controller in this embodiment is less than the error of the controller without nonlinear feedback. At the same time, the energy consumption index W1=25.2 of the controller with nonlinear feedback in this embodiment is about 81.63% lower than the energy consumption index W2=137.2 of the controller without nonlinear feedback. Therefore, it can be concluded that the comprehensive performance of the controller with nonlinear feedback in this embodiment is better than the comprehensive performance of the controller without nonlinear feedback.

[0157] Depend on Figure 7 As shown, it can be seen that when the negative feedback control method is attacked by hackers, the control input changes from positive to negative, the system output changes from 60° to -60°, and the hacker attack is successful; under the resilience enhanced heading keeping control method proposed in this embodiment, when attacked by hackers, the system automatically switches from negative feedback to positive feedback, and the system output changes from -60° to 60° in a short time, keeping the original heading unchanged. This shows that the system resilience (stability) can be enhanced and the system security can be enhanced by automatically switching the system, that is, the equivalent transformation model.

[0158] 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 ship resilience enhanced heading keeping control method under network attack, characterized in that: The specific steps include: S1: Establish a responsive nonlinear Nomoto model as a mathematical model of ship motion; S2: Obtain simplified transfer functions for controller design based on the mathematical model of ship motion; S3: Based on the second-order closed-loop gain shaping algorithm, a ship heading robust controller is constructed according to the simplified transfer function; S4: Obtain the ship heading error considering the ship network attack; According to the ship heading error, the control input of the ship heading robust controller is modified nonlinearly; Obtain the ship heading robust controller after nonlinear modification and perform an equivalent transformation model for input signal feedback; According to the equivalent transformation model, the zero-order holder is used to optimize the control output of the ship heading robust controller to obtain the optimized rudder angle control output; S5: Considering the marine environment interference, the final ship navigation heading is obtained according to the optimized rudder angle control output; The marine environmental disturbance at least includes sea wind disturbance and sea wave disturbance.

2. According to the method for ship resilience enhancement and heading keeping control under network attack in claim 1, it is characterized in that: The response-type nonlinear Nomoto model constructed in S1 is expressed as Where: ψ represents the ship's heading angle; The first derivative of ψ is the rate of change of heading; represents the second-order derivative of ψ, i.e., the heading angular acceleration; K0 and T0 represent the ship turning index and following index, respectively; δ represents the ship rudder angle; α and β represent the nonlinear parameters of the ship model.

3. According to the method for ship resilience enhancement and heading keeping control under network attack in claim 2, it is characterized in that: In S2, the transfer function for controller design is obtained according to the mathematical model of ship motion, which specifically includes the following steps: S21: Based on the mathematical model of ship motion, the Laplace operator s is introduced to obtain the initial transfer function, which is expressed as follows: S22: Omit the nonlinear parameters α, βs of the initial transfer function 3 ψ 3 , to obtain the simplified transfer function G(s), which is expressed as 4. According to the method for ship resilience enhancement and heading keeping control under network attack in claim 3, it is characterized in that: S3 specifically includes the following steps S31: Get the second-order closed-loop gain shaping algorithm model, which is expressed as Where: T1 represents the time constant; s represents the Laplace operator; G represents the closed-loop transfer function; K represents the input of the heading controller to be designed; S32: Based on the simplified transfer function G(s) and the second-order closed-loop gain shaping algorithm model, a ship heading controller is constructed, and its expression is: S33: In order to avoid the influence of static error in the ship heading controller on the ship control system, the simplified transfer function G(s) is rewritten as Where: ε represents the constant term of the influence of the static error uncertainty constant value disturbance on the ship motion; S34: According to the rewritten simplified transfer function G' and the ship heading controller, the ship heading robust controller is obtained, and its expression is:

5. According to the method for ship resilience enhancement and heading keeping control under network attack in claim 4, it is characterized in that: The S4 specifically includes the following steps S41: Obtain the ship heading error e under the consideration of ship network attack and e=ψ r -ψ; Among them, ψ r represents the desired heading of the ship ψ r ; ψ represents the actual heading under the consideration of the ship’s cyber attack; Based on the ship heading error e, the control input of the ship heading robust controller is nonlinearly modified according to the nonlinear modification function f(u); And the expression for nonlinear modification is δ=K c e f(u)=arctan(aδ) / b Where: a and b both represent setting parameters; S42: Obtain the ship heading robust controller after nonlinear modification and perform the equivalent transformation model of input signal feedback, which is expressed as follows: Where: K' represents the control input of the ship heading robust controller after nonlinear modification; represents the transfer function of the closed-loop control system under the ship network attack, that is, the positive feedback term of the ship heading robust controller; represents the negative feedback term of the ship heading robust controller; S43: According to the equivalent transformation model, a zero-order holder is used to optimize the control output of the ship heading robust controller to obtain an optimized rudder angle control output; The optimized rudder angle control output δ r The expression of δ r =arctan(aK c e) / b*K e Where: K e represents the transfer function of the zero-order holder; T represents the set sampling period of the ship control system; s represents the Laplace operator.

6. According to the method of ship resilience enhancement heading keeping control under network attack in claim 5, it is characterized in that: S5 specifically includes the following steps S51: Obtain the equivalent rudder angle δ considering the sea breeze disturbance w1 according to the optimized rudder angle control output s ; The sea breeze disturbance w1 is an equivalent angle synthesized by a set white noise and an equivalent rudder angle representing the wind level; The equivalent rudder angle δ s The expression of δ s =δ r +w1 S52: Set the equivalent rudder angle δ s The output heading angle of the ship is obtained by inputting it into the mathematical model of ship motion, and the output heading angle is added to the considered wave disturbance w2 to obtain the final ship navigation heading output after considering the wind and wave disturbance. The wave disturbance w2 is the equivalent angle obtained by the second-order oscillation link driven by white noise certified by ITTC.

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