Ship course keeping control method for resilience enhancement under cyber attack

Abstract

The application discloses a ship resilience reinforcement course keeping control method under network attack, comprising the following steps: establishing a responsive nonlinear Nomoto model as a ship motion mathematical model to obtain a simplified transfer function; constructing a ship course robust controller according to the simplified transfer function based on a second-order closed-loop gain shaping algorithm; obtaining a ship course error under consideration of ship network attack to perform nonlinear modification on the control input of the ship course robust controller; obtaining the control input of the ship course robust controller after nonlinear modification, and performing equivalent transformation model of input signal feedback; optimizing the control output of the ship course robust controller according to the equivalent transformation model by using a zero-order holder to obtain optimized rudder angle control output; and obtaining a final ship navigation course according to the optimized rudder angle control output in consideration of marine environmental interference. The technical problem that the traditional ship control strategy cannot resist network attack to guarantee the ship course and collision avoidance control functions is solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of ship motion control and modeling, and particularly relates to a ship resilience enhanced course keeping control method under network attack. BACKGROUND

[0002] With the continuous improvement of the intelligence level of ships, the dependence of its control system on the network is also increasing. However, this also makes the ship face potential threats of network attacks during navigation. Once subjected to network attacks, the traditional ship control strategy is often difficult to deal with, which easily leads to the loss of control of the ship's course and the inability to achieve effective collision avoidance operations, seriously affecting the safety of ship navigation. For example, in some cases, network attacks may cause the measurement information of the control system to be tampered with, so that the ship receives incorrect navigation data and then makes incorrect course adjustment decisions, which is extremely dangerous for ships navigating in complex sea conditions. Therefore, there is an urgent need for a new control method that can resist network attacks and protect the ship's course and collision avoidance control functions. SUMMARY

[0003] The present application 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 purpose, the technical scheme of the present application is:

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

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

[0007] S2: obtaining a simplified transfer function for controller design according to the ship motion mathematical model;

[0008] S3: constructing a ship course robust controller according to the simplified transfer function based on a second-order closed-loop gain shaping algorithm;

[0009] S4: obtaining a ship course error considering the ship network attack;

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

[0011] The ship course robust controller after nonlinear modification is obtained, and an equivalent transformation model of input signal feedback is performed;

[0012] According to the equivalent transformation model, a zero-order holder is used to optimize the control output of the ship course robust controller, and an optimized rudder angle control output is obtained;

[0013] S5: Considering the interference of the marine environment, 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’s turning index and following index, respectively; δ represents the ship’s rudder angle; α and β represent the nonlinear parameters of the ship model.

[0018] Furthermore, in S2, the 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, which is expressed as

[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] In the formula: ε represents a constant term of the influence of static error on ship movement;

[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] Further, the S4 specifically includes the following steps

[0035] S41: Obtain the ship heading error e considering the ship network attack, and e = ψ r -ψ;

[0036] Wherein, ψ r represents the expected ship heading ψ r ; ψ represents the actual heading considering the ship network 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 of nonlinear modification is

[0039] δ = K c e

[0040] f(u) = arctan(aδ) / b

[0041] In the formula: a and b represent set parameters;

[0042] S42: Obtain the nonlinearly modified ship heading robust controller, and perform equivalent transformation model of input signal feedback, and its expression is

[0043]

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

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

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

[0047] δ r = arctan (aK c e) / b*K e

[0048]

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

[0050] Further, the S5 specifically comprises the following steps

[0051] S51: obtaining the equivalent rudder angle δ s under the sea wind disturbance w1 according to the optimized rudder angle control output;

[0052] The sea wind disturbance w1 is an equivalent angle composed of a set white noise and an equivalent rudder angle representing the wind scale.

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

[0054] δ s = δ r + w1

[0055] S52: inputting the equivalent rudder angle δ s to the ship motion mathematical model to obtain the ship output heading angle, and adding the output heading angle to the considered sea wave disturbance w2 to obtain the final ship sailing heading after considering the wind wave disturbance, and the sea wave disturbance w2 is an equivalent angle obtained by driving a second-order oscillation link with the ITTC-recognized white noise.

[0056] Beneficial effects: the application provides a ship resilience enhanced course keeping control method under network attack, based on a second-order closed-loop gain shaping algorithm, a ship course robust controller is obtained according to a constructed simplified transfer function, then a control input of the ship course robust controller considering the ship network attack is obtained, an equivalent transformation model of the input signal feedback is carried out, by simulating various possible network attack scenes, the equivalent transformation model is used to optimize the ship course positive and negative feedback automatic switching function, so that the ship control system can quickly and accurately respond when facing similar network attack interference, and automatically switch to the correct feedback mode, ensuring the stable control of the ship course; by using the second-order closed-loop gain shaping algorithm to design the robust controller, and adding the nonlinear modification function driven by the nonlinear modification and zero-order holder to the robust controller, the controller output amplitude is reduced, not only effectively reducing the output rudder angle amplitude and rudder turning frequency, but also ensuring that the ship can still maintain a stable course under the complex and variable network attack environment. BRIEF DESCRIPTION OF DRAWINGS

[0057] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiment or prior art description. Obviously, the drawings described below are some embodiments of the present application, and those skilled in the art can obtain other drawings according to these drawings without creative labor.

[0058] Figure 1 The flow chart of the ship resilience enhanced course keeping control method under network attack of the present application;

[0059] Figure 2 The core block diagram of the ship resilience enhanced course keeping control method in the present embodiment;

[0060] Figure 3 The KVLCC2 No. 35 right rotation experiment simulation diagram in the present embodiment;

[0061] Figure 4 The KVLCC2 No. 10 / 10 Z-shaped experiment simulation diagram in the present embodiment;

[0062] Figure 5 The course change simulation diagram under 5-level sea state in the present embodiment;

[0063] Figure 6 The rudder angle change simulation diagram under 5-level sea state in the present embodiment;

[0064] Figure 7 The ship course change simulation diagram based on the equivalent transformation model under 5-level sea state in the present embodiment;

[0065] Figure 8An equivalent transformation model is utilized to construct a feedback loop block diagram in the embodiment. DETAILED DESCRIPTION

[0066] To make the objectives, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0067] The embodiment provides a ship resilience reinforcement course keeping control method under a network attack, as shown in Figures 1 to 2 The method comprises the following steps.

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

[0069] Specifically, the embodiment establishes a mathematical model with required precision and appropriate complexity, which is crucial for system closed-loop performance research. The influence of environmental factors on ship motion parameters needs to be considered, and the ship shape and its structure characteristics also need to be considered. The embodiment selects a responsive nonlinear Nomoto mathematical model as the ship motion mathematical model. The model is established by using real ship parameters, avoiding the cumbersome mechanical analysis and the process of establishing a complex state space model, and making the description of the ship motion response more accurate and convenient.

[0070] The responsive nonlinear Nomoto model is constructed, and its expression is

[0071]

[0072] In the formula, ψ represents a ship heading angle; represents a first-order derivative of ψ, that is, a heading rate of change; represents a second-order derivative of ψ, that is, a heading angle acceleration; K0 and T0 represent a ship turning index and a following index respectively; δ represents a ship rudder angle; and α and β represent nonlinear parameters of the ship model.

[0073] S2: obtaining a simplified transfer function for controller design according to the ship motion mathematical model;

[0074] The method comprises the following steps.

[0075] S21: based on the ship motion mathematical model, introducing a Laplace operator s to obtain an initial transfer function, and the expression is

[0076]

[0077] S22: For the convenience of controller design, the model is simplified, that is, the nonlinear parameters a, b of the initial transfer function are omitted 3 3 to obtain the simplified transfer function G(s), the expression of which is

[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, the second-order closed-loop gain shaping algorithm is used to design the controller for realizing the ship heading keeping control. The algorithm is to back-propagate the controller by constructing the expected system closed-loop transfer function, and the feature is that the physical concept is clear and the solving process is extremely simple;

[0081] Specifically, the following steps are included

[0082] S31: The model of the second-order closed-loop gain shaping algorithm is obtained, the expression of which is

[0083]

[0084] In the formula, 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: According to the simplified transfer function G(s) and the model of the second-order closed-loop gain shaping algorithm, the ship heading controller is constructed, the expression of which is

[0086]

[0087] S33: The controller designed by using the second-order closed-loop gain control algorithm can eliminate the influence of static error on the system, and can reproduce the influence of uncertain constant disturbance on ship motion by adding a very small constant term to the denominator of the transfer function of the ship motion model. The simplified transfer function G(s) is rewritten as

[0088]

[0089] In the formula, e represents the constant term of the influence of static error and uncertain constant disturbance on ship motion;

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

[0091]

[0092] S4: The control input of the ship heading robust controller is nonlinearly modified;​

[0093] An equivalent transformation model of input signal feedback is performed on the nonlinear modified ship course robust controller under ship network attack;

[0094] According to the equivalent transformation model, a zero-order holder is used to optimize the ship course robust controller control output, and an optimized rudder angle control output is obtained;

[0095] Specifically, the following steps are included

[0096] S41: Obtain the ship course error e under ship network attack, and e = ψ r - ψ;

[0097] Wherein, ψ r represents the expected ship course ψ r ; ψ represents the actual course under consideration of ship network attack;

[0098] Based on the ship course error e, the control input of the ship course 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] The embodiment also includes analysis of the influence of nonlinear feedback on the ship course keeping control system:

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

[0104]

[0105] In the formula: a and b represent set parameters, which have different effects on the performance of the ship course keeping control system. Retain the Taylor series to the first order, and let arctan(au) / b ≈ au / b = ω;

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

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

[0108]

[0109] In the formula: ψr represents the set course, i.e. the desired course of the ship, and the final system output steady-state error is 0, which proves that the nonlinear feedback has no effect on the system steady state;

[0110] 2) Analysis of the influence on the dynamic performance of the ship course keeping control system, which is expressed as

[0111]

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

[0113] 3) Influence on the control output of the ship course keeping control system, and the transfer function from the system input ψ r to the controller output δ is

[0114]

[0115] As can be seen from the transfer function, the numerator decreases more obviously than the denominator, so adjusting the values of the set parameters a and b will reduce the rudder angle and the control output;

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

[0117]

[0118] In the formula: K' represents the control input of the ship course robust controller after nonlinear modification; represents the positive feedback term of the ship course robust controller considering the transfer function of the closed-loop control system under the ship network attack; represents the negative feedback term of the ship course robust controller;

[0119] The task of the heading controller in the ship heading keeping control system is to adjust the rudder angle of the ship according to the deviation of the heading, so that the ship can keep 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 which has a certain functional relationship with the deviation, and correct the heading deviation by adjusting the rudder angle. In actual application, the control input of the controller may be changed from positive to negative due to hacker network attack, which is equivalent to positive feedback, causing abnormal system behavior, and even leading to safety accidents. The embodiment of the application can still work normally even if hacker attack occurs, because the error is offset by the minus sign designed at the time. From the safety and reliability point of view, 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 the safety and efficiency of navigation. In control theory, the negative feedback of the equivalent transformation model means that the ship heading keeping control system feeds back its output to the system input to suppress the influence of input changes, so that the system is more stable, that is, the positive feedback concept adopted in the embodiment is the equivalent transformation of the negative feedback form. For negative feedback, the transfer function of the closed-loop control system is The positive feedback is equivalent to changing the feedback signal from negative to positive, then multiplying the controller of the original negative feedback control method by-1 to become the controller of the positive feedback, and then multiplying the system output by-1, so as to realize the equivalent transformation of negative feedback and positive feedback. Among them, in the positive and negative feedback theory, the system that can be controlled by negative feedback has an equivalent positive feedback control system, so that under the action of positive feedback and nonlinear feedback, the feedback loop can be obtained by using the equivalent transformation model when the input signal changes sign, and then the simulation module of the simulation block diagram as shown in Figure 8 is constructed;

[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, and an optimized rudder angle control output is obtained;

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

[0122] δ r = arctan (aK c e) / b*K e

[0123]

[0124] In the formula: K ea transfer function representing a zero-order hold; T represents a set sampling period of a ship control system; and s represents a Laplace operator;

[0125] The embodiment is to reduce the steering frequency of the ship by introducing a zero-order hold to convert discrete digital signals into continuous analog signals. In the steering system, it can hold the discrete steering instructions. When a steering instruction is received, the zero-order hold will keep the instruction value unchanged for a period of time, so that the steering actuator does not need to respond to the rapidly changing instructions frequently. In this way, the number of actions of the steering actuator is reduced, thereby reducing the steering frequency. Therefore, integrating the zero-order hold into the controller can not only maintain the accurate transmission of the control signal, but also effectively prolong the service life of the steering gear and improve the reliability and durability of the entire ship control system;

[0126] S5: considering the sea environment interference, obtaining the final ship sailing heading according to the optimized rudder angle control output; the sea environment interference at least includes sea wind interference and sea wave interference;

[0127] Specifically includes the following steps

[0128] S51: obtaining the equivalent rudder angle δ s under the sea wind interference w1 according to the optimized rudder angle control output

[0129] And the sea wind interference w1 is an equivalent angle composed of a set white noise and an equivalent rudder angle representing the wind level, and the expression of the equivalent rudder angle δ s is

[0130] δ s = δ r +w1

[0131] S52: inputting the equivalent rudder angle δ s to the ship motion mathematical model to obtain the ship output heading angle, and adding the output heading angle and the considered sea wave interference w2 to obtain the final ship sailing heading output after considering the wind wave interference, and the sea wave interference w2 is an equivalent angle obtained by driving a second-order oscillation link with an ITTC-identified white noise.

[0132] In this embodiment, the existing ship controller is combined with the second-order closed-loop gain shaping algorithm, nonlinear modification and zero-order holder to obtain a ship robustness reinforcement course keeping control method under network attack. The zero-order holder can reduce the rudder frequency, and the controller designed by the second-order closed-loop gain shaping algorithm has strong robustness, so that the obtained ship course robust controller has strong maritime practical significance. In this embodiment, the influence of network attack on the ship control system is considered as a whole. First, by simulating various possible network attack scenarios, an advanced control algorithm is used to construct a ship course controller with high robustness. For example, by using the second-order closed-loop gain shaping algorithm, combining the nonlinear feedback driven by the arctangent function and the zero-order holder, the ship output rudder angle amplitude and the rudder turning frequency are effectively reduced, the unnecessary consumption of ship energy is reduced, and the mechanical wear and operation risk caused by frequent rudder turning are also reduced. In terms of simulating network attacks, a typical attack case of inverting the measured information is studied in depth, an equivalent transformation model is constructed, the controller input signal under network attack is equivalent to the positive feedback case, the automatic switching function of the ship course positive and negative feedback is optimized through the equivalent transformation model, and the control design parameters are accurately adjusted, so that the ship control system can quickly and accurately respond when facing similar network attack interference, automatically switch to the correct feedback mode, and ensure the stable control of the ship course.

[0133] Simulation experiment: In this embodiment, the 300,000-ton oil tanker KVLCC2, which is one of the international standard ship models, is used as the simulation object. The real ship data and the nonlinear Nomoto model are used to perform 35° right turning experiment and 10° / 10° Z-shaped experiment simulation respectively, and the results are compared.

[0134] As shown in Figure 3 , in this embodiment, the nonlinear Nomoto model is used to perform the simulation experiment of KVLCC2 ballast right turning 35°, the value of the dimensionless cross-flow coefficient C is adjusted to make the simulation close to the real ship, and the cross-flow parameter is valued multiple times by dichotomy. It is found that when C=0.6, the simulation effect is good.

[0135] Table 1. KVLCC2 turning test under ballast

[0136]

[0137] Among them, according to the definition of compliance in ship motion control, the expression is:

[0138]

[0139] In the formula: A d1 represents the turning approach of the real ship; A d2D represents the simulation turning diameter; D1 represents the actual ship turning diameter; D2 represents the simulation turning diameter. T1 D represents the simulation turning diameter; D1 represents the actual ship turning diameter; D2 represents the simulation turning diameter. T2 D represents the simulation turning diameter; D1 represents the actual ship turning diameter; D2 represents the simulation turning diameter. The simulation turning test results of the KVLCC2 under the condition of the ballast state are shown in Table 2, and the main parameters of the KVLCC2 are shown in Table 3.

[0140] The simulation turning test results of the KVLCC2 under the condition of the ballast state are shown in Table 2, and the main parameters of the KVLCC2 are shown in Table 3. Figure 4 The simulation turning test results of the KVLCC2 under the condition of the ballast state are shown in Table 2, and the main parameters of the KVLCC2 are shown in Table 3.

[0141] The simulation turning test results of the KVLCC2 under the condition of the ballast state are shown in Table 2, and the main parameters of the KVLCC2 are shown in Table 3.

[0142] Table 2. 10° / 10° Z-shaped test overshoot angle comparison

[0143]

[0144] The simulation test of the KVLCC2 with a capacity of 300,000 tons is performed by using the Simulink function in MATLAB, the expected heading is set to 60° before 2500s, and the control input is changed from 60° to -60° due to a hacker attack at 2500s. The positive feedback control method is adopted, i.e., the equivalent transformation model, so that the ship can still maintain the heading of 60° when the control input is changed to -60° due to the network attack. The nonlinear parameters a = 31.31 and β = 1054564.00 in the response type nonlinear Nomoto model are obtained by using the ship parameters in Table 3, the K0 = 0.05, T0 = 201.73 and ε = 0.00001 in the simplified transfer function, and the set parameters a = 0.3 and b = 1 in the nonlinear modification function f(u). The simulation time is set to 5000s, and the simulation step is 0.1s. At the same time, in order to meet the actual navigation, the maximum rudder angle of 35° and the maximum rudder rate of 5° / s are added.

[0145] In this embodiment, the environmental disturbance is equivalent to a white noise and an equivalent rudder angle representing the wind level, and the sea wave disturbance w2 is equivalent to a second-order oscillation link driven by a white noise recognized by the international ITTC, and a 5-level sea condition is selected as a general sea condition for simulation considering the actual navigation. In the ship motion mathematical model, the sea wave disturbance is represented as:

[0146]

[0147] wherein: ξ5 represents sea wave disturbance under 5th sea state; ξ represents white noise;

[0148] Table 3. Main particulars of“KVLCC2”ship

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

[0150]

[0151] As shown in Fig. 6, the variation of the heading within 7000s under 5th sea state is shown in Fig. 7, the variation of the rudder angle within 7000s is shown in Fig. 8, and it can be seen from Fig. 9 that both the controller without nonlinear feedback and the controller of the embodiment can achieve the control target, Figure 5 Figure 5 Figure 5 Figure 6 It can be seen that the controller of the embodiment can better reduce the rudder angle and reduce the rudder loss. For the controller, the stability, accuracy and rapidity of the control system should be met. For the ship heading switching system, the rudder angle should be small, and the rudder frequency should also be small, so as to achieve the effect of energy saving and emission reduction and reducing the wear of the rudder system. Therefore, in order to better compare which one has better comprehensive performance between the controller of the embodiment and the controller without nonlinear feedback, the error formula is introduced for comparison, and the error formula is:

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

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

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

[0155] W = ∫δ 2 (t)dt

[0156] wherein: W represents total energy consumption index; δ(t) represents rudder angle. The values of e R (t), e C (t) and δ of the two controllers can be directly calculated in Simulink in MATLAB, and the total error E 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 smaller than that of the controller without nonlinear feedback. Furthermore, the energy consumption index W1 = 25.2 of the controller in this embodiment with nonlinear feedback is approximately 81.63% lower than the energy consumption index W2 = 137.2 of the controller without nonlinear feedback. Therefore, it can be concluded that the overall performance of the controller in this embodiment with nonlinear feedback is superior to that 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, and 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 above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above 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 robustness enhanced course keeping control method under cyber attack, characterized in that, Specifically comprising the following steps: S1: establishing a responsive nonlinear Nomoto model as a ship motion mathematical model; S2: obtaining a simplified transfer function for controller design according to the ship motion mathematical model; S3: constructing a ship heading robust controller according to the simplified transfer function based on a second-order closed-loop gain shaping algorithm; S4: obtaining a ship heading error considering ship cyber attacks; According to the ship heading error, the control input of the ship heading robust controller is nonlinearly modified; Obtain the nonlinearly modified ship heading robust controller, and perform an equivalent transformation model of input signal feedback; According to the equivalent transformation model, the ship heading robust controller control output is optimized by using a zero-order holder to obtain an optimized rudder angle control output; S5: considering the sea environment disturbance, obtaining the final ship navigation heading according to the optimized rudder angle control output; The sea environment disturbance at least includes sea wind disturbance and sea wave disturbance.

2. The ship's course keeping control method for resiliency enhancement under cyber attack according to claim 1, wherein, The responsive nonlinear Nomoto model constructed in S1 has an expression of where: ψ represents the heading angle of the ship; represents the first derivative of ψ, i.e. the rate of change of heading; represents the second derivative of ψ, i.e. the acceleration of the heading angle; K0and T0represent the turning quality index and the following quality index of the ship, respectively; δ represents the rudder angle of the ship; and α and β represent the nonlinear parameters of the ship model.

3. The ship's course keeping control method for resiliency enhancement under cyber attack according to claim 2, wherein, In S2, the transfer function for controller design is obtained according to the ship motion mathematical model, specifically comprising the following steps S21: based on the ship motion mathematical model, an initial transfer function is obtained by introducing a Laplace operator s, and the expression is S22: omit the nonlinear parameters a, b of the initial transfer function 3 Ψ 3 to obtain a simplified transfer function G(s) whose expression is 4. The ship's course keeping control method for resiliency enhancement under cyber attack according to claim 3, wherein, The S3 specifically comprises the following steps S31: obtain a second-order closed-loop gain shaping algorithm model, and the expression is In the formula: T1 represents a time constant; s represents a Laplace operator; G represents a closed-loop transfer function; K represents the input of the heading controller to be designed; S32: according to the simplified transfer function G(s) and the second-order closed-loop gain shaping algorithm model, a ship heading controller is constructed, and the 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 In the formula: ε represents a constant term of static error uncertainty constant disturbance affecting ship motion; S34: according to the rewritten simplified transfer function G' and the ship heading controller, a ship heading robust controller is obtained, and the expression is 5. The ship's course keeping control method for resiliency enhancement under cyber attack according to claim 4, wherein, The S4 specifically comprises the following steps S41: Obtain the ship heading error e considering the ship network attack, and e = ψ r - ψ; where ψ r represents the desired course of the ship ψ r ; ψ represents the actual course considering the cyber attack on the ship network; 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 the non-linear modification is δ = K c e f(u) = arctan(aδ) / b In the formula: a and b represent set parameters; S42: obtain the nonlinearly modified ship heading robust controller, and perform an equivalent transformation model of input signal feedback, and the expression is In the formula, K' represents the control input of the ship course robust controller after nonlinear modification; represents the positive feedback term of the ship course robust controller considering the transfer function of the closed-loop control system under ship network attacks; represents the negative feedback term of the ship course robust controller. S43: according to the equivalent transformation model, the ship heading robust controller control output is optimized by using a zero-order holder 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 hold; T represents the set sampling period of the ship control system; and s represents the Laplace operator.

6. The ship's course keeping control method for resiliency enhancement under cyber attack according to claim 5, wherein, The S5 specifically comprises the following steps S51: Obtain the equivalent rudder angle δ under the consideration of sea wind disturbance w1 according to the optimized rudder angle control output s ; And the sea wind disturbance w1 is a set white noise and an equivalent angle composed of an equivalent rudder angle representing the wind level; The equivalent rudder angle δ s The expression for δ s = δ r + w1 S52: input the equivalent rudder angle δ s The input is input to the ship motion mathematical model to obtain the ship output heading angle, and the output heading angle is added to the considered sea wave disturbance w2 to obtain the final ship sailing heading after considering the wind wave disturbance, and the sea wave disturbance w2 is the equivalent angle obtained by driving the second-order oscillation link with ITTC recognized white noise.

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