A ship heading control method with rudder angle constraint and unknown control gain

Abstract

The present invention discloses a rudder angle constrained ship heading control method with unknown control gain, S1: setting a nonlinear ship motion mathematical model; S2: determining a reference heading; S3: designing a heading error virtual controller to stabilize the heading error; S4: simplifying the heading error virtual controller; S5: designing a steering angle virtual controller to stabilize the steering angle error and process the first unknown control gain; S6: simplifying the steering angle virtual controller; S7: designing a heading holder to process the second unknown control gain in the nonlinear ship motion mathematical model and constrain the actual rudder angle. The present invention introduces the Nussbaum function to solve the problem of unknown control gain direction, while avoiding the singularity problem that may occur when the controller faces complex dynamics; Lyapunov function is used to constrain the rudder angle, thereby reducing the steering frequency and energy consumption of the steering gear; and finally realizing precise heading control under the conditions of unknown control gain and rudder angle constraints, thereby improving the safety and reliability of ship navigation.

Description

Technical Field

[0001] The invention relates to the technical field of heading control, and in particular to a rudder angle constrained ship heading control method with unknown control gain. Background Art

[0002] With the continuous expansion of global economic integration and trade, ocean transportation, as a key link connecting the world, has become increasingly strategic. The exploration and development of marine resources, the booming international trade, and the increasing complexity of the global supply chain have all put forward more stringent requirements for the shipping industry. However, the complexity and unpredictability of the marine environment pose a severe challenge to the safety of ship navigation, especially under the influence of bad weather, current changes, and the nonlinear dynamic characteristics of ships, it becomes crucial to maintain the stability and accuracy of the ship's heading.

[0003] In actual navigation, ships also need to deal with practical engineering problems such as input dead zone, unknown control gain and rudder angle constraints, especially the problem of heading control in complex environments such as unknown ship parameters, changing navigation conditions and narrow waterways. In the prior art, although studies have proposed a variety of dead zone compensation schemes and adaptive control strategies, most of these methods require the measurement of ship control gain to achieve heading control, and the ship control gain may become unknown or change due to changes in ship loading conditions, wear of the hull or changes in sea conditions, which increases the uncertainty of heading control and affects the safety and reliability of ship navigation. Summary of the invention

[0004] The present invention provides a rudder angle constrained ship heading control method with unknown control gain, so as to overcome the technical problem that most of the prior arts need to measure the ship control gain first to achieve heading control, which will affect the safety and reliability of ship navigation due to the limitation of the known nature of the control gain.

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

[0006] A rudder angle constrained ship heading control method with unknown control gain, the specific steps comprising:

[0007] S1: Setting a nonlinear ship motion mathematical model with dead zone;

[0008] S2: Setting the reference model and determining the reference heading in combination with the given initial value of the ship command heading;

[0009] S3: obtaining a heading error based on the actual heading of the nonlinear ship motion mathematical model and the reference heading, and designing a heading error virtual controller according to the heading error to stabilize the heading error;

[0010] S4: introducing a first first-order filter to simplify the heading error virtual controller, and using a radial basis function to approximate the first nonlinear term in the nonlinear ship motion mathematical model;

[0011] S5: Based on the actual steering angular velocity in the nonlinear ship motion mathematical model and the first first-order filter, a steering angular velocity error is obtained, and a steering angle virtual controller is designed according to the steering angle error and combined with the Nussbaum function to stabilize the steering angle error and process the first unknown control gain in the nonlinear ship motion mathematical model;

[0012] S6: introducing a second first-order filter to simplify the steering angle virtual controller, and using a radial basis function to approximate the second nonlinear term in the nonlinear ship motion mathematical model;

[0013] S7: Based on the actual rudder angle in the nonlinear ship motion mathematical model and the second first-order filter, a rudder angle error is obtained, and a heading keeper is designed according to the rudder angle error and combined with the Nussbaum function and the obstacle Lyapunov function to process the second unknown control gain in the nonlinear ship motion mathematical model and constrain the actual rudder angle;

[0014] S8: Determine whether the set simulation time has been reached. If so, complete the heading keeping task. Otherwise, repeat steps S3-S7.

[0015] Furthermore, in S1, the nonlinear ship motion mathematical model with dead zone is expressed as:

[0016] (1)

[0017] In the formula, is the heading angle; is the first derivative of the heading angle; is the bow angular velocity; is the first derivative of the bow angular velocity; is an unknown disturbance, ; and are all unknown control gains, , ; and All are nonlinear terms; is the command rudder angle; is the actual rudder angle; is the first derivative of the actual rudder angle; K.T Parameters that reflect the maneuverability of the ship; To control the gain, is the time constant;

[0018] The input of the dead zone, i.e. the command rudder angle, is expressed as:

[0019] (3)

[0020] In the formula, , is a bounded disturbance in the dead zone; m is the dead zone slope; and represent the right slope of the dead zone and the left slope of the dead zone respectively, and ; and are all dead zone breakpoints, and , ; Input to the system.

[0021] Furthermore, in S2, the reference model is set as:

[0022] (4)

[0023] (5)

[0024] In the formula, is the reference command signal, is the reference heading; and They are The first and second derivatives of .

[0025] Further, in S3, the process of obtaining a heading error based on the actual heading of the nonlinear ship motion mathematical model and the reference heading, and designing a heading error virtual controller according to the heading error is:

[0026] The heading error obtained by the actual heading based on the nonlinear ship motion mathematical model and the reference heading is expressed as:

[0027] (6)

[0028] In the formula, is the actual heading, i.e. the heading angle, is the reference heading;

[0029] Taking the derivative of the above formula, we get:

[0030] (7)

[0031] Design of virtual controller for heading error To process the heading error, it is expressed as:

[0032] (8)

[0033] In the formula, is a positive control parameter, for The first derivative of .

[0034] Furthermore, in S4, the process of introducing a first first-order filter to simplify the heading error virtual controller and using a radial basis function to approximate the first nonlinear term in the nonlinear ship motion mathematical model is as follows:

[0035] Let the heading error virtual controller The time constant is The first order filter , expressed as:

[0036] (9)

[0037] In the formula, for The first derivative of

[0038] The filter error is calculated as:

[0039] ;

[0040] According to formula (9), The differential expression of is:

[0041] (10)

[0042] In the formula, is a continuous function, , whose maximum value is ;

[0043] for The first derivative of for The first derivative of

[0044] The first nonlinear term is transformed into Approximately:

[0045] (14)

[0046] in, ; ,but , ;

[0047] By introducing the robust neural damping technology, we get:

[0048] (15)

[0049] In the formula, ; ; is the weight matrix; is the radial basis function neural network vector; To have an upper bound The unknown random error constant.

[0050] Furthermore, in S5, based on the actual steering angular velocity in the nonlinear ship motion mathematical model and the first order filter, the steering angular velocity error is obtained. The process of designing the steering angle virtual controller according to the steering angle error and the Nussbaum function is as follows:

[0051] The steering angular velocity error is defined as:

[0052] (16)

[0053] Taking the derivative of the above formula, we get:

[0054] (17)

[0055] In the formula, for The first derivative of

[0056] According to (14) and (15), we can further obtain:

[0057] (18)

[0058] Considering the first unknown control gain The sign of is unknown, so the Nussbaum function is used to deal with this problem and the steering angle virtual controller is designed. And the adaptive control law is:

[0059] (19)

[0060] In the formula, It is a parameter set by humans; N is the Nussbaum function; is the radial basis function neural network vector; yes The estimated value of ; for The first derivative of yes The first derivative of .

[0061] Further, in S6, the process of introducing a second first-order filter to simplify the steering angle virtual controller and using a radial basis function to approximate the second nonlinear term in the nonlinear ship motion mathematical model is as follows:

[0062] Make the steering angle virtual controller The time constant is The second first-order filter , expressed as:

[0063] (20)

[0064] In the formula, yes The first derivative of

[0065] The filter error is calculated as:

[0066] ;

[0067] According to formula (20), The differential expression of is:

[0068] (twenty one)

[0069] In the formula, is a continuous function with unknown upper bound, ;

[0070] yes The first derivative of yes The first derivative of

[0071] The second nonlinear term is transformed into Approximately:

[0072] (twenty two)

[0073] In the formula, ; ; So we can get ; ;

[0074] By introducing the robust neural damping technology, we can get:

[0075] (twenty three)

[0076] In the formula, , ; is the weight matrix; is the radial basis function neural network vector; To have an upper bound The unknown random error constant.

[0077] Furthermore, in S7, the rudder angle error is obtained based on the actual rudder angle in the nonlinear ship motion mathematical model and the second first-order filter. The process of designing the heading keeper according to the rudder angle error and combining the Nussbaum function and the obstacle Lyapunov function is as follows:

[0078] Define the following variables:

[0079] (twenty four)

[0080] (25)

[0081] In the formula, , and is a positive constant;

[0082] Substituting (24) into (25) we can obtain:

[0083] (26)

[0084] The actual rudder angle in the nonlinear ship motion mathematical model is compared with the second first-order filter The rudder angle error is defined as:

[0085] ;

[0086] Taking the derivative of the above formula, we get:

[0087] (27)

[0088] According to (22) and (23), we can further obtain:

[0089] (28)

[0090] According to the rudder angle error and combined with the Nussbaum function and the obstacle Lyapunov function, the heading keeper and the adaptive control law are designed as follows:

[0091] (29)

[0092] In the formula, It is a parameter set by humans; is satisfied A positive integer, for The first derivative of yes The first derivative of

[0093] and .

[0094] Beneficial effects: The present invention designs a steering angle virtual controller according to the steering angle error and in combination with the Nussbaum function, and processes the steering angle error and the first unknown control gain in the mathematical model of nonlinear ship motion; designs a heading holder according to the rudder angle error and in combination with the Nussbaum function and the obstacle Lyapunov function, processes the unknown control gain in the mathematical model of nonlinear ship motion and constrains the actual rudder angle, and effectively solves the problem of unknown control gain direction by introducing the Nussbaum function, ensures that the heading control can still be achieved when the ship control gain is unknown, and avoids the singularity problem that may occur in the controller when facing complex dynamics; in addition, the obstacle Lyapunov function is used to constrain the rudder angle, which reduces the steering frequency and energy consumption of the steering gear, makes the control action more in line with the operating habits of the crew, and improves the comfort and safety of ship control; at the same time, the radial basis function is used to approximate the nonlinear terms in the mathematical model of nonlinear ship motion, which reduces the complexity of the controller, and finally realizes precise heading control under the conditions of unknown control gain and rudder angle constraints, thereby improving the safety and reliability of ship navigation. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] 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.

[0096] Figure 1 It is a flow chart of a method for controlling a ship's heading with rudder angle constraint and unknown control gain in the present invention;

[0097] Figure 2 is a dead zone nonlinear diagram in an embodiment of the present invention;

[0098] Figure 3 is the expected heading of the ship in the embodiment of the present invention and actual heading Experimental results graph;

[0099] Figure 4 is the ship heading error in the embodiment of the present invention Experimental results graph;

[0100] Figure 5 Graph showing the results of a ship turning angular velocity experiment in an embodiment of the present invention;

[0101] Figure 6 is the actual rudder angle of the ship in the embodiment of the present invention Experimental results graph;

[0102] Figure 7 is the command rudder angle in the embodiment of the present invention and actual rudder angle Experimental comparison chart;

[0103] Figure 8 is the actual heading under different algorithms in the embodiments of the present invention Experimental comparison chart;

[0104] Fig. 9 is the heading error under different algorithms in the embodiments of the present invention Experimental comparison chart;

[0105] Fig.10 This is a comparison diagram of steering angular velocity experiments under different algorithms in an embodiment of the present invention;

[0106] Fig.11 is the actual rudder angle under different algorithms in the embodiments of the present invention Experimental comparison chart. DETAILED DESCRIPTION

[0107] 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.

[0108] This embodiment provides a method for controlling a ship's heading with rudder angle constraints and unknown control gains. Figure 1 As shown, the specific steps include:

[0109] S1: Setting a nonlinear ship motion mathematical model with dead zone;

[0110] Specifically, this scheme designs a rudder angle constrained heading control method with unknown control gain, so that the actual heading angle of the ship With reference signal As a track, to meet the heading requirements during navigation.

[0111] In a specific embodiment, the set nonlinear ship motion mathematical model with dead zone is expressed as:

[0112] (1)

[0113] In the formula, is the heading angle; is the first derivative of the heading angle; is the bow angular velocity; is the first derivative of the bow angular velocity; is an unknown disturbance, ; and are all unknown control gains, , ; and All are nonlinear terms; is the command rudder angle; is the actual rudder angle; is the first derivative of the actual rudder angle; K.T Parameters that reflect the maneuverability of the ship; K is the cyclotonicity index, K The larger the value, the greater the rudder moment and the smaller the damping moment; T is the followability index, T The larger the value of , the greater the inertia and the smaller the damping torque; To control the gain, is the time constant;

[0114] For real ships, T The sign of is undefined because when T When is positive, the boat is stable. T When it is negative, the ship is unstable. During steering, a larger steering range may cause the ship to lose balance, so the steering angle should be limited to a certain extent. In this embodiment, the actual steering angle is limited to , the dead zone input is the command rudder angle It is expressed as:

[0115] (2)

[0116] In the formula, and represent the right slope of the dead zone and the left slope of the dead zone respectively, and ; m is the dead zone slope; and are all dead zone breakpoints, and , ; Input to the system.

[0117] Specifically, Figure 2 As shown, the dead zone is represented as a combination of linear input and bounded disturbance. Therefore, based on formula (2), the input of the dead zone is Expressed as ,in

[0118] (3)

[0119] In the formula, , is a bounded disturbance in the dead zone.

[0120] S2: Setting the reference model and determining the reference heading in combination with the given initial value of the ship command heading;

[0121] Considering the actual performance of the ship, if the reference command heading is tracked directly, the initial error of the algorithm will be large and the controller input will be oversaturated. Therefore, in order to avoid this phenomenon and make the heading transition smoother, the reference model set in this embodiment is expressed as:

[0122] (4)

[0123] (5)

[0124] In the formula, is the reference command signal, is the reference heading; and They are The first and second derivatives of .

[0125] S3: obtaining a heading error based on the actual heading of the nonlinear ship motion mathematical model and the reference heading, and designing a heading error virtual controller according to the heading error to stabilize the heading error;

[0126] In a specific embodiment, in S3, the process of obtaining a heading error based on the actual heading of the nonlinear ship motion mathematical model and the reference heading, and designing a heading error virtual controller according to the heading error is:

[0127] The heading error obtained by the actual heading based on the nonlinear ship motion mathematical model and the reference heading is expressed as:

[0128] (6)

[0129] In the formula, is the actual heading, i.e. the heading angle, is the reference heading;

[0130] Taking the derivative of the above formula, we get:

[0131] (7)

[0132] Design of virtual controller for heading error To process the heading error, it is expressed as:

[0133] (8)

[0134] In the formula, is a positive control parameter, for The first derivative of .

[0135] S4: Introducing the first first-order filter Simplifying the heading error virtual controller, and using radial basis function to approximate the first nonlinear term in the nonlinear ship motion mathematical model;

[0136] In a specific embodiment, in S4, a first order filter is introduced Simplify the heading error virtual controller and use radial basis function to solve the first nonlinear term in the nonlinear ship motion mathematical model The approximate processing process is:

[0137] In order to avoid the "complexity explosion" problem, in this embodiment, the heading error virtual controller The time constant is The first order filter , as shown in formula (9), thereby simplifying the heading error virtual controller and avoiding repeated derivation of the heading error virtual controller:

[0138] (9)

[0139] In the formula, for The first derivative of

[0140] The filter error is calculated as:

[0141] ;

[0142] According to formula (9), The differential expression of is:

[0143] (10)

[0144] In the formula, is a continuous function, , whose maximum value is ; for The first derivative of for The first derivative of

[0145] In this embodiment, based on Lemma 1, radial basis functions are used to approximate the first nonlinear term in the nonlinear ship motion mathematical model. , to resolve structural and parameter uncertainties.

[0146] Lemma 1: For the definition on a compact set Any given continuous function have , by combining radial basis functions and continuous function separation technology, it can be approximated with arbitrary accuracy, as shown in formula (11):

[0147] (11)

[0148] In the formula, is the radial basis function neural network vector, is an upper bound The unknown random error constant is:

[0149] (12)

[0150] In the formula, is the number of nodes in the neural network, As the center, is the width of the Gaussian function. is the state vector The dimension of is, A is the weight matrix, expressed as:

[0151] (13)

[0152] because is an unknown smooth function, so it can be approximated by the radial basis function as:

[0153] (14)

[0154] in, ; ,but , .

[0155] In order to avoid the heavy calculation of real-time update of neural network weights, the robust neural damping technology is introduced, which can be obtained:

[0156] (15)

[0157] In the formula, ; ; is the weight matrix; is the radial basis function neural network vector; To have an upper bound The unknown random error constant.

[0158] S5: Based on the actual steering angular velocity of the nonlinear ship motion mathematical model and the first first-order filter, the steering angular velocity error is obtained, and the steering angle virtual controller is designed according to the steering angle error and combined with the Nussbaum function to stabilize the steering angle error and process the first unknown control gain in the nonlinear ship motion mathematical model;

[0159] Specifically, in this embodiment, the Nussbaum function is used to process the ship following index T The problem of unknown control coefficients in the direction is solved, avoiding the singularity problem in the controller.

[0160] In a specific embodiment, in S5, the actual steering angular velocity based on the nonlinear ship motion mathematical model and the first order filter The steering angular velocity error is obtained. The process of designing the steering angle virtual controller based on the steering angle error and the Nussbaum function is as follows:

[0161] The steering angular velocity error is defined as:

[0162] (16)

[0163] Taking the derivative of the above formula, we get:

[0164] (17)

[0165] In the formula, for The first derivative of

[0166] According to (14) and (15), we can further obtain:

[0167] (18)

[0168] Considering the first unknown control gain The sign of is unknown, so the Nussbaum function is used to deal with this problem and the steering angle virtual controller is designed. And the adaptive control law is:

[0169] (19)

[0170] In the formula, It is a parameter set by humans; N is the Nussbaum function; is the radial basis function neural network vector; yes The estimated value of ; for The first derivative of yes The first derivative of .

[0171] S6: Introducing the second first-order filter The steering angle virtual controller is simplified to stabilize the steering angle error, and the second nonlinear term in the nonlinear ship motion mathematical model is approximated by using radial basis function;

[0172] In a specific embodiment, in S6, a second first-order filter is introduced Simplify the steering angle virtual controller and use radial basis function to solve the second nonlinear term in the nonlinear ship motion mathematical model The approximate processing process is:

[0173] In order to simplify the derivation process, let the steering angle virtual controller The time constant is The second first-order filter , expressed as:

[0174] (20)

[0175] In the formula, yes The first derivative of

[0176] The filter error is calculated as:

[0177] ;

[0178] According to formula (20), The differential expression of is:

[0179] (twenty one)

[0180] In the formula, is a continuous function with unknown upper bound, ; yes The first derivative of yes The first derivative of .

[0181] In this embodiment, based on Lemma 1, the second nonlinear term is converted into Approximately:

[0182] (twenty two)

[0183] In the formula, ; ; So we can get ; .

[0184] By introducing the robust neural damping technology, we can get:

[0185] (twenty three)

[0186] In the formula, , ; is the weight matrix; is the radial basis function neural network vector; To have an upper bound The unknown random error constant.

[0187] S7: Actual rudder angle and second order filter based on nonlinear ship motion mathematical model The rudder angle error is obtained, and a heading keeper is designed according to the rudder angle error in combination with the Nussbaum function and the obstacle Lyapunov function to handle the second unknown control gain in the mathematical model of nonlinear ship motion and constrain the actual rudder angle;

[0188] Specifically, in this embodiment, according to the characteristics of the ship and the actual steering habits, the obstacle Lyapunov is used to limit the rudder angle. While limiting the rudder angle, the rotation rate of the rudder is also limited, which is more in line with the actual situation of marine engineering.

[0189] In a specific embodiment, in S7, the actual rudder angle in the nonlinear ship motion mathematical model is compared with the second first-order filter. The rudder angle error is obtained. The process of designing the heading keeper based on the rudder angle error and combining the Nussbaum function and the obstacle Lyapunov function is as follows:

[0190] In order to ensure that the ship with unknown control gain and input dead zone can navigate along the reference course without violating the rudder angle constraint, in this embodiment, a adaptive heading keeping control scheme based on obstacle Lyapunov function and Nussbaum function is designed by comprehensively applying dynamic surface technology and neural network technology, including:

[0191] First, to achieve the control objectives, define the following variables:

[0192] (twenty four)

[0193] (25)

[0194] In the formula, , and is a positive constant;

[0195] Substituting (24) into (25) we can obtain:

[0196] (26)

[0197] The actual rudder angle in the nonlinear ship motion mathematical model is compared with the second first-order filter The rudder angle error is defined as:

[0198] ;

[0199] Taking the derivative of the above formula, we get:

[0200] (27)

[0201] According to (22) and (23), we can further obtain:

[0202] (28)

[0203] Considering the second unknown control gain The sign of is unknown and the rudder angle is constrained. The Nussbaum function and the obstacle Lyapunov function are used to deal with the problem. Therefore, the heading keeper and the adaptive control law are designed as follows:

[0204] (29)

[0205] In the formula, It is a parameter set by humans; is satisfied A positive integer, for The first derivative of yes The first derivative of

[0206] and .

[0207] S8: Determine whether the set simulation time has been reached. If so, complete the heading keeping task. Otherwise, repeat steps S3-S7.

[0208] Specifically, in order to verify the effectiveness of the rudder angle constrained ship heading control method with unknown control gain proposed in the present invention, the "Yukun" was taken as the research object, and a series of experiments and comparative simulations were carried out on the MATLAB simulation platform, including: the specific simulation results of maintaining the heading are as follows: Figure 3-7 As shown, Figure 3 The desired heading and actual heading under the control algorithm are shown. It can be seen from the figure that the entire navigation process includes eight rudder angle changes, corresponding to the eighth-order change. The desired heading trajectory guided by the command navigation starts from zero and is smoother overall. Based on the method proposed in this embodiment, the actual heading can quickly track the desired heading to meet the command requirements. The result of the heading error is shown in Figure 4 As shown in the figure, it can be observed that the heading error decreases rapidly at the initial moment, indicating that the system responds quickly to the control command. During the subsequent entire navigation process, the heading error remains within a reasonable range with small oscillations, which is a typical feature of the control system, indicating that the designed controller can effectively stabilize the system tracking the reference signal. Figure 5The corresponding steering angular velocity is given. It can be observed from the figure that during the entire steering process, the angular velocity remains within a reasonable boundary, which is consistent with engineering practice. Figure 6 It can be seen that the actual servo rudder angle is always within the predefined range, thereby ensuring the constraint of the partial state. In addition, in the subsequent navigation process, the heading is effectively maintained within the range of 25 degrees through the method proposed in this embodiment. Figure 7 is the command rudder angle and actual rudder angle ,It can be seen from the figure that when the command rudder angle passes through the servo system of the ,actual rudder angle signal obtained is constrained, and the response signal ,is more suitable for the actual steering, which can effectively reduce the wear of the rudder ,system.

[0209] To further demonstrate the performance of this embodiment, it is compared with the robust neural network adaptive algorithm used in the literature (Qiang et a., 2019) and the event-triggered algorithm used in the literature (Zhang et a., 2022). Figure 8 The trajectory of the actual heading of the ship under different algorithms is described. It can be seen from the figure that the algorithms are not much different. Fig. 9 The heading error is given , it can be seen that the error is very stable within a very small range. Fig.10 is the trajectory of the steering angular velocity. It can be clearly seen that the steering angular velocity converges quickly to the reference value. Fig.11 is the actual rudder angle under different algorithms. The results show that the embodiment can accurately control the rudder angle within 30°, and is particularly outstanding in achieving small rudder angles. This feature not only reduces energy consumption, but also reduces the wear of the steering gear, thereby reducing the burden on the ship's power system and enhancing the practicability of engineering applications.

[0210] 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 controlling a ship's heading with rudder angle constraints and unknown control gain, characterized in that: The specific steps include: S1: Setting a nonlinear ship motion mathematical model with dead zone; S2: Setting the reference model and determining the reference heading in combination with the given initial value of the ship command heading; S3: obtaining a heading error based on the actual heading of the nonlinear ship motion mathematical model and the reference heading, and designing a heading error virtual controller according to the heading error to stabilize the heading error; S4: introducing a first first-order filter to simplify the heading error virtual controller, and using a radial basis function to approximate the first nonlinear term in the nonlinear ship motion mathematical model; In S4, the process of introducing the first first-order filter to simplify the heading error virtual controller and using the radial basis function to approximate the first nonlinear term in the nonlinear ship motion mathematical model is as follows: Let the heading error virtual controller α r The time constant is τ r The first order filter β r , expressed as: In the formula, β r The first derivative of The filter error is calculated as: y r ＝β r -α r According to formula (9), y r The differential expression of is: In the formula, B r (·) is a continuous function, Its maximum value is M r ; for y r The first derivative of is α r The first derivative of The first nonlinear term f(r) is approximated by radial basis function as: f(r)=S r (r)A r r+ε(r) =S r (r)A r (r e +b r )+ε(r) =S r (r)A r b r +b r S r (r)w r +ε(r) (14) Among them, b r =||A r ||; but ; By introducing the robust neural damping technology, we get: In the formula, A r is the weight matrix; S r (r) is the radial basis function neural network vector; ε(r) is the upper bound The unknown random error constant of S5: Based on the actual steering angular velocity in the nonlinear ship motion mathematical model and the first first-order filter, a steering angular velocity error is obtained, and a steering angle virtual controller is designed according to the steering angle error and combined with the Nussbaum function to stabilize the steering angle error and process the first unknown control gain in the nonlinear ship motion mathematical model; In S5, the steering angle velocity error is obtained based on the actual steering angle velocity in the nonlinear ship motion mathematical model and the first order filter. The process of designing the steering angle virtual controller according to the steering angle error and the Nussbaum function is as follows: The steering angular velocity error is defined as: r e ＝r-β r (16) In the formula, β r is the first order filter; r is the actual steering angular velocity; Taking the derivative of the above formula, we get: In the formula, For r e The first derivative of wr is the unknown disturbance; g2 is the first unknown control gain; δ is the actual rudder angle; According to (14) and (15), we can further obtain: Considering that the sign of the first unknown control gain g2 is unknown, the Nussbaum function is used to deal with this problem and the steering angle virtual controller is designed. And the adaptive control law is: Where c2, Γ 21 , Γ 22 , σ 12 , σ 22 is a parameter set artificially; N is the Nussbaum function; S r (r) is the radial basis function neural network vector; is an estimate of for The first derivative of yes The first derivative of S6: introducing a second first-order filter to simplify the steering angle virtual controller, and using a radial basis function to approximate the second nonlinear term in the nonlinear ship motion mathematical model; S7: Based on the actual rudder angle in the nonlinear ship motion mathematical model and the second first-order filter, a rudder angle error is obtained, and a heading keeper is designed according to the rudder angle error and combined with the Nussbaum function and the obstacle Lyapunov function to process the second unknown control gain in the nonlinear ship motion mathematical model and constrain the actual rudder angle; S8: Determine whether the set simulation time has been reached. If so, complete the heading keeping task. Otherwise, repeat steps S3-S7.

2. A method for controlling a ship's heading with rudder angle constraint and unknown control gain according to claim 1, characterized in that: In S1, the mathematical model of nonlinear ship motion with dead zone is expressed as: Where ψ is the heading angle; is the first derivative of the heading angle; r is the bow angular velocity; is the first derivative of the bow angular velocity; d wr is the unknown disturbance, d wr =Δ wr / T; g2 and g3 are both unknown control gains, g2=K / T, g3=K E / T E ; f(r) and f(δ) are both nonlinear terms; δ E is the command rudder angle; δ is the actual rudder angle; is the first derivative of the actual rudder angle; K and T are parameters reflecting the maneuverability of the ship; K E is the control gain, T E is the time constant; The dead zone input is the command rudder angle δ E It is expressed as: In the formula, ω is the bounded disturbance in the dead zone; m is the dead zone slope; m r and m l Respectively represent the right slope of the dead zone and the left slope of the dead zone, and m r =m l =m>0; b r and b l are all dead zone breakpoints, and b r >0,b l >0; u(t) is the system input.

3. A method for controlling a ship's heading with rudder angle constraint and unknown control gain according to claim 2, characterized in that: In S2, the reference model is set as: In the formula, ψ r is the reference command signal, ψ d is the reference heading; and They are respectively d The first and second derivatives of .

4. A method for controlling a ship's heading with rudder angle constraint and unknown control gain according to claim 3, characterized in that: In S3, the process of obtaining a heading error based on the actual heading of the nonlinear ship motion mathematical model and the reference heading, and designing a heading error virtual controller according to the heading error is as follows: The heading error obtained by the actual heading based on the nonlinear ship motion mathematical model and the reference heading is expressed as: ψ e =ψ-ψ d (6) Where ψ is the actual heading, i.e. the heading angle, d is the reference heading; Taking the derivative of the above formula, we get: Design of virtual controller α for heading error r To process the heading error, it is expressed as: In the formula, c1 is the positive control parameter; is e The first derivative of .

5. A method for controlling a ship's heading with rudder angle constraint and unknown control gain according to claim 4, characterized in that: In S6, the process of introducing a second first-order filter to simplify the steering angle virtual controller and using a radial basis function to approximate the second nonlinear term in the nonlinear ship motion mathematical model is as follows: Make the steering angle virtual controller The time constant is τ δ The second first-order filter β δ , expressed as: In the formula, Is β δ The first derivative of The filter error is calculated as: According to formula (20), y δ The differential expression of is: In the formula, B δ (·) is a continuous function with unknown upper bound, Yes δ The first derivative of yes The first derivative of The second nonlinear term f(δ) is approximated by radial basis function as: f(δ)=S δ (d)A δ b δ +b δ S δ (d)w δ +e(d) (22) Where b δ =||A δ ||; So we can get b δ w δ =A δ δ e ; By introducing robust neural damping technology, we can get: In the formula, A δ is the weight matrix; S δ (δ) is the radial basis function neural network vector; ε(δ) is the upper bound The unknown random error constant.

6. A method for controlling a ship's heading with rudder angle constraint and unknown control gain according to claim 5, characterized in that: In S7, the rudder angle error is obtained based on the actual rudder angle in the nonlinear ship motion mathematical model and the second first-order filter. The process of designing the heading keeper according to the rudder angle error and combining the Nussbaum function and the obstacle Lyapunov function is as follows: Define the following variables: In the formula, l aδ and l bδ is a positive constant; Substituting (24) into (25) we can obtain: The actual rudder angle in the nonlinear ship motion mathematical model is compared with the second first-order filter β δ The rudder angle error is defined as: d e =δ-β δ Taking the derivative of the above formula, we get: According to (22) and (23), we can further obtain: According to the rudder angle error and combined with the Nussbaum function and the obstacle Lyapunov function, the heading keeper and the adaptive control law are designed as follows: Where c3, Γ 31 , Γ 32 , σ 31，32 is a parameter set artificially; k is a positive integer satisfying 2k≥n+2, for The first derivative of yes The first derivative of and

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