Ship Trajectory Tracking Event-Triggered Control Method and System with Performance Game Mechanism

Abstract

An embodiment of the present invention discloses a ship trajectory tracking event-triggered control method and system with a performance game mechanism. The method includes: S1, determining the position error and attitude error corresponding to the ship; S2, designing a first performance index and a first value function; S3, designing the negative gradient estimate of the first value function, the optimal virtual control law, and the online learning law; S4, obtaining the dynamic reference signal and the dynamic control error; S5, defining a second performance index and the corresponding second value function; S6, designing the negative gradient estimate corresponding to the second value function, the optimal control input, and the optimal trigger error; S7, determining whether the trigger rule is satisfied; S8, changing the ship state and continuing to determine whether the navigation task is completed. If not, reconfirm the current state of the ship and return to S1. The present invention solves the problems in the prior art that "it is difficult for operators to obtain the best trigger effect and control accuracy" and "the ship trajectory tracking controller has weak robustness in the marine environment interference".

Description

Technical Field

[0001] The present invention relates to the technical fields of ship control engineering and ship automatic navigation equipment, and particularly relates to a ship trajectory tracking event-triggered control method and system with a performance game mechanism. Background Technique

[0002] In the field of ship motion control, the guidance algorithm is one of the important key technologies for solving ship path-keeping control (which can be divided into two categories: indirect path control and direct path control). The existing guidance algorithms have been introduced from the field of missile shooting guidance research into the field of ship navigation, that is, the so-called Line of sight (LOS) algorithm that we usually mention. It solves the problem of calculating the ship's guiding course using the track deviation and course deviation in indirect path-keeping control, and it is also an algorithm widely adopted in current shipborne autopilots. At the same time, the specific technical features of the LOS algorithm will be briefly introduced in this application:

[0003] The variable LOS radius and waypoint switching boundary ring are two important concepts or variables in the LOS algorithm. The purpose of the LOS algorithm is to deduce the course reference command ψ los for completing the control task requirements in path-keeping control. Using the existing ship course-keeping controller to drive the rudder actuator, the ship's course tracks the reference command ψ los , reduces the track deviation, and finally realizes the automatic navigation of the ship along the planned route. Figure 1 The basic guidance principle diagram of the LOS algorithm is given. In navigation practice, the planned route is usually designed by the driver by setting waypoints, such as Figure 1 the (x i-1 , y i-1 ), (x i , y i ), and (x i+1 , y i+1 ) in i-1 P i . Taking the current ship position (x, y) as the center and drawing an arc with the LOS radius R, on the premise of appropriately selecting the LOS radius, it can intersect the planned route P i-1 P i at points A B and A F . The line segment starting from the current ship position (x, y) and ending at point A F is defined as the LOS line, and the corresponding azimuth angle is ψ los , which can be calculated by Equation (1) and ψ los ∈<-π, π>. Usually, there are three ways to take R: 1) Traditional LOS algorithm: R = αL pp , L ppis the length between perpendiculars of the ship. In this case, it is necessary to require that α > 1, otherwise the ship will fluctuate frequently around the planned route; 2) Improve the LOS algorithm: R = d + L pp , where d is the projection distance from the current ship position to the planned course, that is, the track deviation. Such a selection can ensure that R > d always holds, ensuring the existence of the LOS line; 3) The exponential convergence LOS algorithm, as shown in Equation (2). Among them, lambertw is the inverse function of the function f(x) = xe x , and the minimum LOS radius R min = 1.7L pp , and the coefficient b is the exponential convergence factor, b = 0.05.

[0004]

[0005]

[0006] The LOS guidance algorithm can realize the navigation and guidance of the ship on a straight-line route and finally achieve the track-keeping control task. However, when the ship approaches the waypoint, that is, Figure 1 at the P i position, a waypoint conversion is required. This involves the concept of the waypoint switching boundary loop, that is, a circular area centered at (x i , y i ) with a radius of δ i . When the ship enters this area, the reference planned route switches from the track segment {(x i-1 , y i-1 ), (x i , y i )} to the track segment {(x i , y i ), (x i+1 , y i+1 ), and the switching condition is Equation (3).

[0007]

[0008] At the same time, in the field of ship motion control, the main design idea of the trajectory tracking control algorithm is to design a virtual control law based on the position and attitude errors, thereby obtaining the dynamic velocity error, and further designing a ship controller. To solve the problems of ship actuator wear and resistance to ocean environment interference, the existing ship trajectory tracking control technologies have proposed event-triggered control algorithms and disturbance observers.

[0009] Although the event-triggered control algorithm can prevent the controller from generating real-time control commands by reducing the control accuracy and decreasing the update frequency of the control input, the adjustment of the event-triggered threshold parameter is uncertain and subjective. It is difficult for the operator to balance the control accuracy and the triggering effect, and there is no standard for evaluating the control accuracy and the triggering effect. In addition, due to the highly nonlinear and variable characteristics of the real marine environment, it is difficult to apply the disturbance observer to navigation practice.

[0010] Based on the above analysis, it can be determined that the existing ship trajectory tracking control algorithms mainly have the following two defects:

[0011] 1) The existing ship trajectory tracking event-triggered control algorithm cannot balance the triggering effect and the control accuracy. When the operator adjusts the triggering threshold parameter, it completely depends on the trial-and-error method and experience, resulting in two extreme situations: it is easy to obtain a good triggering effect and poor control accuracy, or high control accuracy and poor triggering effect. Therefore, it is difficult for the operator to obtain the best triggering effect and control accuracy with the existing ship motion control engineering practice technology;

[0012] 2) The existing ship ocean environment disturbance observer cannot be directly applied to navigation practice. The main reason is that when facing the complex and variable ocean environment, the disturbance observer often fails to achieve the observation effect, and the designed ship trajectory tracking controller does not have strong robustness, that is, the ship trajectory tracking controller has weak robustness in the ocean environment disturbance. Summary of the Invention

[0013] Based on this, in order to solve the deficiencies of the existing technology, a ship trajectory tracking event-triggered control method with a performance game mechanism is specifically proposed.

[0014] In order to achieve the above object, the corresponding technical solution of the present invention is:

[0015] A ship trajectory tracking event-triggered control method with a performance game mechanism, characterized by including:

[0016] S1. Based on the three-degree-of-freedom planar motion model of the ship, determine the corresponding position error and attitude error of the ship;

[0017] S2. Based on the position error and the attitude error, design a first performance index and a corresponding first value function;

[0018] S3. Design a first negative gradient estimate value corresponding to the first value function, determine the optimal virtual control law based on the first negative gradient estimate value, and design an online learning law;

[0019] S4. Based on the dynamic surface technology, reduce the order of the derivative of the optimal virtual control law to obtain the corresponding dynamic reference signal, and further obtain the dynamic control error;

[0020] S5. Based on the input - end event - triggered mechanism and the dynamic control error, define the second performance index and the corresponding second value function, where the second performance index is used to describe the relationship of the zero - sum game between the control input and the differential of the triggering error;

[0021] S6. Design the second negative - gradient estimate, the optimal control input, and the optimal triggering error corresponding to the second value function;

[0022] S7. Based on the determined design parameters in S6, judge whether the triggering rule is satisfied. If so, determine the optimal control input as the control input estimate value corresponding to the next triggering moment and execute S8; otherwise, determine the optimal control input as the control input estimate value corresponding to the current triggering moment and execute S8.

[0023] S8. Change the ship state and continue to judge whether the navigation task is completed. If not, re - confirm the current ship state and return to S1 to re - determine the position error and attitude error corresponding to the ship.

[0024] Optionally, in one embodiment, the formulas of the performance index and the corresponding value function in S2 are shown as the following formulas (9) and (10);

[0025]

[0026]

[0027] In the formula, J u1 (z e , α u ) and J r1 (ψ e , α r ) are the performance indices of the position error and the attitude error respectively; and are the value functions of J u1 (z e , α u ) and J r1 (ψ e , α r ) respectively; α u and α r are the virtual control laws of u and r respectively; and are α u1 and α r1 when J u and J r reach the minimum values respectively, z eand ψ e are the ship position error and attitude error respectively.

[0028] Optionally, in one embodiment, the calculation formula of the first negative gradient estimate value corresponding to the first value function in S3 is as shown in the following formula (1-3);

[0029]

[0030] In the formula, are respectively negative gradient estimates. k u , k r are the virtual control parameters of the surge and yaw degrees of freedom respectively. are the radial basis neural network weight critic estimates of the surge and yaw degrees of freedom respectively, S u1 , S r1 are respectively the activation functions of the radial basis neural network weights ;

[0031] The calculation formulas of the optimal virtual control law estimate value and the online learning law are as shown in the following formulas (1-4) and (1-5);

[0032]

[0033]

[0034] In the formula, are respectively the estimates of the optimal virtual control law ; are respectively the actor estimates of the radial basis neural networks of the surge and yaw degrees of freedom; k uc1 , k rc1 , k ua1 , k ra1 is the online learning rate; and are respectively the critic learning law and the actor learning law of the radial basis neural networks of the surge and yaw degrees of freedom; I is the identity matrix; σ j1 is a constant greater than 0 of the online learning law ;

[0035] Optionally, in one embodiment, S4 includes the following steps

[0036] S41. Based on the dynamic surface technology, reduce the order of the derivative of the optimal virtual control law to obtain the corresponding dynamic reference signal, and the corresponding formula is as shown below,

[0037]

[0038] wherein, ∈ u , ∈ r are respectively filter time constants of; β u , β r are respectively kinetic reference signals obtained after filtering;

[0039] S42. Based on the three-degree-of-freedom planar motion model of the ship and the kinetic reference signal, define the ship kinetic control error, and the corresponding formula is shown as follows

[0040] u e = β u - u,r e = β r - r

[0041] where u e , r e are respectively the forward speed error and yaw speed error of the kinetic control;

[0042] And obtain the derivative form of the aforementioned ship kinetic control error, and the corresponding formula is shown as follows

[0043]

[0044] Optionally, in one embodiment, the formula corresponding to the input end event trigger mechanism in the S5 is shown as follows

[0045]

[0046] wherein, is the control input after triggering, is the trigger error, t represents continuous time, is the trigger moment;

[0047] The corresponding formulas of the second performance index and the second value function are as shown in formulas (1-8) and (1-9)

[0048]

[0049]

[0050] wherein, J u2 , J r2 are respectively the performance indexes of the forward speed and yaw speed errors of the kinetic control, are respectively u2 , J r2 value functions of, γ u , γ r are respectively the event trigger threshold parameters of the propeller and the rudder, is the optimal control input.

[0051] Optionally, in one embodiment, the value function in S6 The second negative gradient estimate value of is as shown in the following formula (1-10)

[0052]

[0053] In the formula, are respectively the negative gradient estimate values of the value function , k ue , k re are respectively the speed control parameters of τ u , τ r ; is the estimated value of the extreme ocean disturbance acting on the hull forward and yaw free; is the estimated value of the radial basis neural network weights of the recombinant dynamics forward and yaw degrees of freedom, is the critic estimated value of the radial basis neural network weights of the forward and yaw degrees of freedom; b u , b r are respectively the constants greater than 0 in the negative gradient estimate value of the value function ;

[0054] The optimal control input estimate value and the optimal trigger error estimate value are as shown in the following formula (1-11)),

[0055]

[0056] In the formula, are respectively the estimated values of the optimal control input and the optimal trigger error, is the actor estimated value of the radial basis neural network weights of the forward and yaw degrees of freedom;

[0057] Among them, the online learning laws of the actor estimated value of the radial basis neural network weights of the forward and yaw degrees of freedom and the estimated value of the extreme ocean disturbance acting on the hull forward and yaw free are as shown in formulas (1-12) (1-13),

[0058]

[0059]

[0060] In the formula, are respectively the critic learning law and the actor learning law of the radial basis neural network weights , is the learning law of the radial basis neural network weights of the recombinant dynamics nonlinear term, Learning law for extreme marine disturbances. k jc2 , k ja2 , Γ j , Γ wj are respectively learning rates, σ j2 is a constant greater than 0 in the online learning law , σ Wj , σ wj are respectively constants greater than 0 in the online learning law , are respectively initial values.

[0061] Optionally, in one embodiment, the steps corresponding to S1 include:

[0062] S11. Create a three-degree-of-freedom planar motion model of the ship, and its corresponding model formula is

[0063]

[0064] where

[0065]

[0066] In the above formula, x, y, ψ are respectively the x-axis coordinate, y-axis coordinate and heading angle of the ship in the earth coordinate system; v = [u, v, r] T is the ship speed matrix, where u, v, r are respectively the ship's forward speed, transverse drift speed and yaw speed; f u (v), f v (v), f r (v) are respectively the dynamic nonlinear terms of the ship's forward, transverse drift and yaw degrees of freedom; m u , m v , m r are respectively the displacements of the ship in the forward, transverse drift and yaw degrees of freedom, d wu , d wv , d wr are respectively the disturbances of the marine environment acting on the ship's forward, transverse drift and yaw motion directions; τ u , τ r are respectively the propulsive force provided by the propeller and the turning moment generated by the rudder blade, as the control inputs of the ship motion control system; d u1 , d u2 , d u3 are respectively the 1st, 2nd and 3rd order hydrodynamic derivatives of the ship's forward degree of freedom, d v1 , d v2 , d v3 are respectively the 1st, 2nd and 3rd order hydrodynamic derivatives of the ship's transverse drift degree of freedom, d r1 , dr2 , d r3 are the 1st, 2nd, and 3rd order hydrodynamic derivatives of the yaw degree of freedom of the ship respectively;

[0067] S12. Based on the planar motion model of the ship with three degrees of freedom, determine the relationship between the ship coordinates and the virtual ship coordinates, and then obtain the reference heading angle;

[0068] Assume that the reference trajectory of the ship is generated by real-time planning of the virtual ship and determine the relationship between the ship coordinates and the virtual ship coordinates, as shown in the following formula (1-16),

[0069]

[0070] where x r , y r , ψ r are the x-axis coordinate, y-axis coordinate, and heading angle of the virtual ship in the earth coordinate system respectively; u r , r r are the forward speed and yaw speed of the virtual ship respectively;

[0071] Then, according to the relationship between the ship coordinates and the virtual ship coordinates, obtain the reference heading angle, as shown in the following formula (1-17);

[0072]

[0073] where x e , y e are the coordinate errors of the x-axis and y-axis of the ship, and ψ d is the reference heading angle;

[0074] S13. Based on the planar motion model of the ship with three degrees of freedom and the reference heading angle, determine the corresponding position error and attitude error of the ship, and the corresponding calculation formula is shown in the following formula (1-18);

[0075]

[0076] where z e and ψ e are the position error and attitude error of the ship respectively.

[0077] In addition, to solve the deficiencies of the traditional technology, a ship trajectory tracking event-triggered control system implementing the foregoing design scheme is also proposed, which is characterized by including:

[0078] The first data acquisition unit is used to determine the corresponding position error and attitude error of the ship based on the planar motion model of the ship with three degrees of freedom;

[0079] The first data design unit is configured to design a first performance index and a corresponding first value function based on the position error and the attitude error;

[0080] The second data design unit is configured to design a first negative gradient estimate, an optimal virtual control law, and an online learning law corresponding to the first value function, and the optimal virtual control law and the online learning law are used to obtain an index value corresponding to the minimum first performance index;

[0081] The second data acquisition unit is configured to perform a reduced-order processing on the derivative of the optimal virtual control law based on the dynamic surface technology to obtain a corresponding dynamic reference signal, and further obtain a dynamic control error;

[0082] The third data design unit is configured to define a second performance index and a corresponding second value function based on the input terminal event triggering mechanism and the obtained dynamic control error;

[0083] The fourth data design unit is configured to design a second negative gradient estimate, an optimal control input, and an optimal triggering error corresponding to the second value function;

[0084] The first data judgment unit is configured to judge whether the triggering rule is satisfied based on the design parameters of the fourth data design unit. If so, execute S8; otherwise, execute S8.

[0085] The second data judgment unit is configured to change the ship state and continue to judge whether the navigation task is completed. If not, reconfirm the current ship state and re-determine the corresponding position error and attitude error of the ship through the first data acquisition unit.

[0086] In addition, to solve the deficiencies existing in the traditional technology when facing, a computer-readable storage medium is also proposed, including computer instructions, which when run on a computer, cause the computer to execute the method described above.

[0087] Implementing the embodiments of the present invention will have the following beneficial effects:

[0088] 1. The present invention solves the problems that the existing event-triggered control method cannot balance the control accuracy and the triggering effect and the triggering threshold parameter adjustment is complex. That is, according to the differential game and zero-sum game theories, the present invention establishes a second performance index describing the relationship between the dynamic control error, the continuous control input, and the event-triggered error, and through the min-max strategy, obtains the event-triggered error that can make the control effect the worst, that is, the optimal triggering error, and the continuous control input that can make the control effect the best, that is, the optimal control input. This design can ensure high control accuracy while minimizing the wear of the ship's propeller and rudder to the greatest extent.

[0089] 2. Regarding the problem of the interference of the marine environment on ship motion control, the present invention also provides a parameter estimation method for compensating for marine environmental interference. That is, the present invention additionally introduces an extreme marine interference estimate value into the value function of the dynamic error and designs a learning law based on the dynamic control error and the extreme marine interference estimate value to achieve the compensation of the ship for the extreme marine environment. The extreme marine interference estimate value introduced by this additional design will directly compensate the control input. When the ship's dynamic control error is large, it can significantly increase the control input, accelerate the response of the ship's propeller and rudder to the external environment, and achieve the rapid stabilization of the control error. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0091] Wherein:

[0092] Figure 1 is the basic guidance principle diagram of the -LOS algorithm mentioned in the prior art;

[0093] Figure 2 is the execution flowchart of the ship trajectory tracking control algorithm corresponding to the embodiment of the control method of the present invention;

[0094] Figure 3 is the wind field plan view and wave three-dimensional view under sea state 3 corresponding to the embodiment of the control method of the present invention;

[0095] Figure 4 is the trajectory tracking result diagram of the ship corresponding to the embodiment of the control method of the present invention under sea state 3;

[0096] Figure 5 is the ship trajectory tracking error curve graph corresponding to the embodiment of the control method of the present invention;

[0097] Figure 6 is the ship control input curve graph corresponding to the embodiment of the control method of the present invention;

[0098] Figure 7 is the event trigger interval graph corresponding to the embodiment of the control method of the present invention;

[0099] Figure 8 is the extreme marine environment interference estimate curve graph corresponding to the embodiment of the control method of the present invention;

[0100] Figure 9This is the trajectory diagram of the unmanned boat INAC-5 corresponding to the embodiment of the control method of the present invention;

[0101] Figure 10 This is the state diagram of the unmanned boat passing through each waypoint from the perspective of a fixed camera position corresponding to the embodiment of the control method of the present invention;

[0102] Figure 11 This is the trajectory tracking error diagram of the unmanned boat INAC-5 corresponding to the embodiment of the control method of the present invention;

[0103] Figure 12 This is the control command diagram of the unmanned boat INAC-5 corresponding to the embodiment of the control method of the present invention;

[0104] Figure 13 This is the schematic diagram of the basic process corresponding to the control method of the present invention. Detailed implementation manners

[0105] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0106] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the technical field to which the present invention belongs. The terms used in the description of the present invention in this specification are only for the purpose of describing specific embodiments and are not intended to limit the present invention. It can be understood that the terms "first", "second", etc. used in the present invention can be used herein to describe various elements, but these elements are not limited by these terms. These terms are only used to distinguish one element from another. For example, without departing from the scope of the present application, the first element can be called the second element, and similarly, the second element can be called the first element. Both the first element and the second element are elements, but they are not the same element.

[0107] In view of the deficiencies of the existing technology, in this embodiment, a performance game control method based on differential game theory for realizing the ship trajectory tracking task is specifically proposed. That is, this method takes into account the two problems of "it is difficult for operators to obtain the best trigger effect and control accuracy" and "the ship trajectory tracking controller is less robust in marine environment interference" in the practice of ship motion control engineering, and proposes a ship trajectory tracking event-triggered control method based on differential game to solve the ship trajectory tracking control problem.

[0108] Specifically, as Figure 13 shown, the control method is characterized by including the following steps:

[0109] S1. Determine the corresponding position error and attitude error of the ship based on the three-degree-of-freedom planar motion model of the ship;

[0110] S2. Design a first performance index and a corresponding first value function based on the position error and attitude error, where the first performance index is used to describe the performance index corresponding to the position error and attitude error;

[0111] S3. Design a first negative gradient estimate corresponding to the first value function, determine an optimal virtual control law based on the first negative gradient estimate, and design an online learning law;

[0112] S4. Based on the dynamic surface technology, reduce the order of the derivative of the optimal virtual control law to obtain a corresponding dynamic reference signal, and then obtain a dynamic control error;

[0113] S5. Define a second performance index and a corresponding second value function based on the input terminal event-triggering mechanism and the dynamic control error, where the second performance index is used to describe the relationship between the control input and the trigger error differential zero-sum game;

[0114] S6. Design a second negative gradient estimate, an optimal control input, and an optimal trigger error corresponding to the second value function;

[0115] S7. Determine whether the trigger rule is satisfied based on the design parameters determined in S6. If so, determine the optimal control input as the control input estimate value corresponding to the next trigger moment ( ) and execute S8. Otherwise, determine the optimal control input as the control input estimate value corresponding to the current trigger moment ( ) and execute S8;

[0116] S8. Change the ship state and continue to determine whether the navigation task is completed. If not, reconfirm the current ship state and return to S1 to re-determine the corresponding position error and attitude error of the ship.

[0117] In some specific embodiments, the steps corresponding to S1 include:

[0118] S11. Create a three-degree-of-freedom planar motion model of the ship, and its corresponding model formula is

[0119]

[0120] where

[0121]

[0122] In the formula, x, y, and ψ are respectively the x-axis coordinate, y-axis coordinate, and heading angle of the ship in the earth coordinate system; v = [u, v, r]T is the ship speed matrix, where \(u\), \(v\), and \(r\) are the ship's forward speed, sway speed, and yaw speed respectively; \(f\) u (v), \(f\) v (v), \(f\) r (v) are the dynamic nonlinear terms of the ship's forward, sway, and yaw degrees of freedom respectively, which can be approximated online by a radial basis neural network. For a detailed introduction to the principle, please refer to references [1][2]; \(m\) u , \(m\) v , \(m\) r are the displacements of the ship in the forward, sway, and yaw degrees of freedom respectively, \(d\) wu , \(d\) wv , \(d\) wr are the disturbances of the marine environment acting on the ship's forward, sway, and yaw motion directions respectively; \(\tau\) u , \(\tau\) r are the propulsive force provided by the propeller and the turning moment generated by the rudder respectively, serving as the control inputs of the ship motion control system; \(d\) u1 , \(d\) u2 , \(d\) u3 are the first, second, and third order hydrodynamic derivatives of the ship's forward degree of freedom respectively, \(d\) v1 , \(d\) v2 , \(d\) v3 are the first, second, and third order hydrodynamic derivatives of the ship's sway degree of freedom respectively, \(d\) r1 , \(d\) r2 , \(d\) r3 are the first, second, and third order hydrodynamic derivatives of the ship's yaw degree of freedom respectively.

[0123] The literature information mentioned in the previous paragraph: [1] Guoxing Wen, Shuzhi Sam Ge, C.L.Philip Chen, Fangwen Tu and ShengnanWang. Adaptive Tracking Control of Surface Vessel Using Optimized BacksteppingTechnique. IEEE Transactions on Cybernetics, 2019, 49(9): 3420 - 3431.

[0124] [2] Jiqiang Li, Guoqing Zhang, Cheng Liu and Weidong Zhang. COLREGs-Constrained Adaptive Fuzzy Event-Triggered Control for Underactuated Surface Vessels With the Actuator Failures. IEEE Transactions on Fuzzy System. 2021, 29(12): 3822-3832.

[0125] S12. Based on the three-degree-of-freedom planar motion model of the ship, determine the relationship between the ship coordinates and the virtual ship coordinates, and then obtain the reference heading angle.

[0126] Assume that the reference trajectory of the ship is generated in real time by the virtual ship and the relationship between the ship coordinates and the virtual ship coordinates is determined as shown in the following equation (6).

[0127]

[0128] where x r , y r , ψ r are the x-axis coordinate, y-axis coordinate, and heading angle of the virtual ship in the earth coordinate system, respectively; u r , r r are the forward speed and yaw speed of the virtual ship, respectively.

[0129] Then, according to the relationship between the ship coordinates and the virtual ship coordinates, the reference heading angle is obtained as shown in the following equation (7).

[0130]

[0131] where x e , y e are the errors of the ship's x-axis and y-axis coordinates, and ψ d is the reference heading angle.

[0132] S13. Based on the three-degree-of-freedom planar motion model (4) of the ship and the reference heading angle (7), determine the corresponding position error and attitude error of the ship, and the corresponding calculation formulas are shown in the following equation (8).

[0133]

[0134] where z e and ψ e are the ship position error and attitude error, respectively.

[0135] In some specific embodiments, the steps corresponding to S2 include:

[0136] S2. Based on the position error and attitude error (see Equation (8)), design a first performance index and a corresponding first value function, where the first performance index is used to describe the performance index corresponding to the ship position error and attitude error to be considered;

[0137] The formulas of the first performance index and the corresponding first value function are shown in the following Equations (9) and (10);

[0138]

[0139]

[0140] In the formula, J u1 (z e , α u ) and J r1 (ψ e , α r ) are the performance indexes of the position error and attitude error respectively; and are the value functions of J u1 (z e , α u ) and J r1 (ψ e , α r ) respectively; α u and α r are the virtual control laws of u and r respectively; and are α u1 and α r1 when J u and J r reach the minimum values respectively, that is, the optimal virtual control laws, t is time, and s is a certain moment.

[0141] In some specific embodiments, the steps corresponding to S3 include: designing a first negative gradient estimate value corresponding to the first value function, determining the optimal virtual control law and the online learning law based on the first negative gradient estimate value; so as to obtain the index value of the minimum first performance index through the optimal virtual control law and the online learning law; wherein,

[0142] Considering that the first negative gradient estimate value of the value function is:

[0143]

[0144] In the formula, are the negative gradient estimate values of respectively, ku , k r are the virtual control parameters for the surge and yaw degrees of freedom respectively, are the critic estimated values of the radial basis neural network weights for the surge and yaw degrees of freedom, S u1 , S r1 are the radial basis neural network weights respectively activation functions.

[0145] To obtain the minimum value of the performance index, the optimal virtual control law estimate shown in Equation (12) and the online learning law shown in Equation (13) are designed.

[0146]

[0147]

[0148] In the formula, are the estimates of the optimal virtual control law respectively , are the actor estimated values of the radial basis neural network for the surge and yaw degrees of freedom respectively, k uc1 , k rc1 , k ua1 , k ra1 is online learning rate of and are the critic learning law and actor learning law of the radial basis neural network for the surge and yaw degrees of freedom respectively, I is the identity matrix, σ j1 is the online learning law constant greater than 0.

[0149] In some specific embodiments, since the optimal virtual control law will cause a large computational load problem in the next derivative calculation, the dynamic surface technology needs to be introduced to reduce the order of the derivative of the optimal virtual control law. The specific steps corresponding to S4 include:[[]]

[0150] S41. Based on the dynamic surface technology, reduce the order of the derivative of the optimal virtual control law to obtain the corresponding dynamic reference signal. The corresponding formula is shown as follows

[0151]

[0152] In the formula, ∈ u , ∈ r are filtering time constants respectively; β u , β r are dynamical reference signals obtained after filtering;

[0153] S42. Based on the ship three-degree-of-freedom planar motion model - Equation (4) and the dynamic reference signal - Equation (14), define the ship dynamic control error, and the corresponding formula is shown as follows

[0154] u e =β u -u,r e =β r -r

[0155] where u e ,r e are the dynamic control forward speed error and the yaw speed error respectively

[0156] According to Equation (4), the derivative form of the dynamic control error is obtained as follows

[0157]

[0158] In some specific embodiments, to reduce actuator wear and avoid unnecessary actuator braking, the following input-end event-triggering mechanism is introduced, and the corresponding formula is shown as follows

[0159]

[0160] In the formula is the control input after triggering is the triggering error, t represents continuous time is the triggering moment; by adopting the event-triggering mechanism (16), it can be ensured that the control input remains unchanged within the triggering time period For the event-triggering mechanism, the larger the triggering error means the longer the triggering period and the worse the control accuracy. Therefore, it is desired to obtain the optimal triggering error that can balance the control accuracy and the triggering period, that is

[0161] Considering the event-triggering mechanism (16) and the radial basis neural network, Equation (15) can be expressed as

[0162]

[0163] In the formula, W j ,S j (v) are the radial basis neural network weights and activation functions for reconstructing the ship dynamic nonlinear terms respectively, and ε j is the neural network approximation error

[0164] Considering the zero-sum game relationship between the control input and the triggering error, define the second performance index and the second value function of the differential zero-sum game of the control input and the triggering error as in Equations (18) and (19)

[0165]

[0166]

[0167] In the formula, J u2 , J r2 are respectively the performance indexes of the kinetic control forward speed and the yaw speed error. are respectively the value functions of J u2 , J r2 , γ u , γ r are respectively the event trigger threshold parameters of the propeller and the rudder. is the optimal control input.

[0168] In some specific embodiments, the steps corresponding to S6 include:

[0169] Considering that the second negative gradient estimate of the value function is:

[0170]

[0171] In the formula, are respectively the negative gradient estimates of the value function , k ue , k re are respectively the speed control parameters of τ u , τ r , is the estimated value of the extreme ocean disturbance acting on the forward movement and yaw freedom of the hull. is the estimated value of the radial basis neural network weight for reorganizing the kinetic forward and yaw freedoms. is the critic estimate of the radial basis neural network weight for the forward and yaw freedoms, b u , b r are respectively the constants greater than 0 in the negative gradient estimate of the value function .

[0172] The estimated value of the optimal control input and the estimated value of the optimal trigger error are as shown in formula (21).

[0173]

[0174] In the formula, are respectively the estimated values of the optimal control input and the optimal trigger error. is the actor estimate of the radial basis neural network weight for the forward and yaw freedoms.

[0175] The online learning laws of the weight estimation value of the radial basis neural network and the extreme marine interference estimation value involved therein are shown in Eqs. (22) and (23).

[0176]

[0177]

[0178] Wherein, are respectively the critic learning law and the actor learning law of the weights of the radial basis neural network , is the learning law of the weights of the radial basis neural network for the recombined kinetic nonlinear term, is the learning law of the extreme marine interference, k jc2 , k ja2 , Γ j , Γ wj are respectively learning rates, σ j2 is a constant greater than 0 in the online learning law , σ Wj , σ wj are respectively constants greater than 0 in the online learning law . are respectively initial values.

[0179] Based on the same inventive concept, the present invention also proposes a ship trajectory tracking event-triggered control system with a performance game mechanism:

[0180] A first data acquisition unit, which is used to determine the corresponding position error and attitude error of the ship based on the three-degree-of-freedom planar motion model of the ship;

[0181] A first data design unit, which is used to design a first performance index and a corresponding first value function based on the position error and the attitude error;

[0182] A second data design unit, which is used to design a first negative gradient estimate value, an optimal virtual control law and an online learning law corresponding to the first value function;

[0183] A second data acquisition unit, which is used to perform a reduced-order processing on the derivative of the optimal virtual control law based on the dynamic surface technology to obtain a corresponding kinetic reference signal, and further obtain a kinetic control error;

[0184] A third data design unit, which is used to define a second performance index and a corresponding second value function based on the input-end event-triggered mechanism and the obtained kinetic control error;

[0185] The fourth data design unit is configured to design a second negative gradient estimate, an optimal control input, and an optimal triggering error corresponding to the second value function;

[0186] The first data determination unit is configured to determine whether a triggering rule is satisfied based on the design parameters of the fourth data design unit. If so, it determines that the optimal control input is the control input estimate corresponding to the next triggering moment, and the second data determination unit continues to determine whether the navigation task is completed. Otherwise, it determines that the optimal control input is the control input estimate corresponding to the current triggering moment, and the second data determination unit continues to determine whether the navigation task is completed;

[0187] The second data determination unit is configured to change the ship state and continue to determine whether the navigation task is completed. If not, it reconfirms the current ship state and redetermines the position error and attitude error corresponding to the ship through the first data acquisition unit.

[0188] Based on the same inventive concept, the present invention also provides a computer-readable storage medium, including computer instructions, which when run on a computer, cause the computer to execute the method described above.

[0189] For verifying Figure 2 the effectiveness of the ship trajectory tracking control algorithm proposed by the present invention as shown, the applicant uses Matlab to conduct computer simulation experiments and compares them with existing conventional algorithms. At the same time, to further verify that the ship trajectory tracking control algorithm proposed by the present invention has the value of algorithm engineering development, the applicant conducts full-scale ship verification experiments at the Lingshui Wharf of Dalian Maritime University.

[0190] The relevant experimental design process and verification process are as follows:

[0191] Experiment 1:

[0192] Condition setting:

[0193] Set the initial state of the virtual ship as [x r (0), y r (0), ψ r (0), u r (0), r r (0)] = [0 m, 0 m, 45 deg, 3 m / s, 0 deg / s], the initial state of the ship [x(0), y(0), ψ(0), u(0), v(0), r(0)] = [-20 m, 0 m, 0 deg, 0 m / s, 0 m / s, 0 deg / s]. The forward speed and yaw speed of the virtual ship are designed and expressed by Equation (23), and the corresponding formula is as follows

[0194]

[0195] Purpose of the experiment: Through the ship trajectory tracking control algorithm proposed by the present invention, the position and attitude of the ship are tracked on the virtual ship, and compared with the existing control algorithm in the aforementioned literature [1], so as to verify the superiority of the ship trajectory tracking control algorithm proposed by the present invention.

[0196] The verification results are as follows:

[0197] Figures 3 - 8 They are respectively the ship trajectory tracking simulation results under sea state 3 simulated on the matlab simulation platform; among them, Figure 3 is the simulation environment used on the matlab simulation platform, that is, the planar view of the wind field and the three-dimensional view of the waves under sea state 3, Figure 3 in which (a) is the schematic planar diagram of the wind field with a wind direction of 150°, and (b) is the three-dimensional schematic diagram of wind-generated waves; Figure 4 is the ship trajectory tracking result. Both the ship trajectory tracking control algorithm proposed by the present invention and the algorithm in the literature [1] can achieve ship trajectory tracking, but the ship adopting the ship trajectory tracking control algorithm proposed by the present invention is closer to the virtual ship and has better trajectory tracking performance; Figure 5 is the position error and attitude error diagram of ship trajectory tracking. Among them, (a) is the position error diagram, and (b) is the attitude error diagram. It can be seen that the control error of the ship trajectory tracking control algorithm proposed by the present invention is smaller than that in the literature [1], especially the attitude error is much smaller than the algorithm proposed in the literature [1]; Figure 6 is the curve graph of the control inputs provided by the two control algorithms for the ship. Among them, (a) is the propeller propulsion force graph, and (b) is the rudder turning moment graph; among them, the control input provided by the control algorithm in the literature [1] is a time-varying continuous input, and this input will continuously send control commands to the propeller and the rudder, causing unnecessary wear. However, the control input of the control algorithm proposed by the present invention is an intermittent trigger type input. This input method only sends new control commands to the propeller and the rudder at the trigger time point, greatly reducing equipment wear; the number of triggers and the trigger interval between two adjacent trigger time points are as Figure 7 shown ( Figure 7 in which: (a) the trigger effect of the propeller input. (b) the trigger effect of the rudder input), among which the control input of the propeller was triggered 203 times in total, and the control input of the rudder was triggered 1037 times in total. For the algorithm in the literature [1], the control inputs of the rudder and the propeller were each triggered 15,000 times in total. Figure 8 is the estimation result of the proposed ship trajectory tracking control algorithm for extreme ocean disturbances ((a) the estimated value of ocean disturbance in the forward degree of freedom the estimated value of ocean disturbance in the yaw degree of freedom curve), it can be seen that compared with the forward motion direction of the ship, the ship needs to make more compensation for non-linearity and disturbances in the yaw motion direction.

[0198] Experiment 2:

[0199] Key points of experimental design:

[0200] In this experiment, the unmanned boat "INAC-5" was used as the experimental object, and the DVS guidance algorithm was used to generate a virtual ship to guide the unmanned boat "INAC-5". The main parameters of the unmanned boat "INAC-5" are shown in Table 1. At the same time, the relevant content of the experimental object (for details, see the literature [3] Guoqing Zhang, Shang Liu, Jiangshuai Huang and Weidong Zhang. Dynamic event-triggered path-following control of underactuated surface vehicle with the experiment verification. IEEE Transactions on Vehicular Technology, 2022, 71(10): 10415–10425.); The relevant technology of using the DVS guidance algorithm to generate a virtual ship to guide the unmanned boat "INAC-5" can be found in the literature [4] Guoqing Zhang and Xianku Zhang. A novel DVS guidance principle and robust adaptive path-following control for underactuated ships using low frequency gain-learning. ISA Transactions, 2015, 56: 75-86.

[0201]

[0202] Selection of experimental parameters:

[0203] In the experiment, the following 5 waypoints were selected: W1(38.8650188°N, 121.5333179°E), W2(38.8648882°N, 121.5336210°E), W3(38.86551169°N, 121.5341547°E), W4(38.8656234°N, 121.5338168°E), W5(38.8650188°N, 121.5333179°E). The starting position of the unmanned boat is (38.8650175°N, 121.5333118°E); meanwhile, in this experiment, the forward speed of the virtual ship is 2 m / s. In order to generate control commands for the unmanned boat "INAC-5", the control algorithm proposed in the present invention was embedded into the main processing unit of the personal computer through Visual Basic 2015, and at the same time, the personal computer was connected to the on-board wireless local area network to transmit control commands to the unmanned boat "INAC-5". In addition, in order to implement the event trigger mechanism, so that the personal computer sends the same control command within the trigger interval period, the on-board industrial control box and the steering gear servo implement the execution of the control command by the propeller and the steering gear. To record the experiment process, the state of the unmanned boat "INAC-5" passing through each waypoint was recorded at a fixed position near waypoint W1.

[0204] Purpose of the experiment: Through this experiment, it is hoped that the unmanned boat can autonomously sail along a closed route composed of 5 waypoints and pass through the 5 waypoints in sequence.

[0205] The verification results are as follows:

[0206] Figures 9 - 12 For the experimental results of this experiment; among them Figure 9 is the trajectory result of the unmanned boat "INAC-5" sailing along the route. It can be seen that the unmanned boat "INAC-5" can autonomously complete the trajectory tracking tasks of straight sailing and turning paths. The turning states of the unmanned boat "INAC-5" at waypoints W1 - W5 are as Figure 10 shown. From Figure 11 ((a) position error, (b) attitude error in the figure), it can be seen that when the unmanned boat "INAC-5" adopts the control algorithm proposed in the present invention, it can stabilize the position error below 3 m and the attitude error below ±20°. Figure 12 ((a) telegraph order, (b) rudder order in the figure) shows the control commands generated by the control algorithm proposed in the present invention. A total of 53 control commands were generated for the propeller and 587 control commands were generated for the steering gear in this experiment.

[0207] In summary, combining the above verification experiments and comparing with the existing technologies, implementing the embodiments of the present invention will have the following beneficial effects:

[0208] (1) The ship trajectory tracking control algorithm / method proposed by the present invention solves the defect that "it is difficult for the event-triggered trajectory tracking control algorithm to obtain the best triggering effect and control accuracy", realizes the performance game and trade-off between the control accuracy and the triggering effect, can optimize the ship's autopilot performance, and has the characteristics of high control accuracy and greenness;

[0209] (2) The ship trajectory tracking control algorithm / method proposed by the present invention involves a parameter estimation compensation method for ocean environmental disturbances, enabling the present invention to consider the relationship between ocean environmental disturbances and dynamic control errors, and having the ability to resist extreme ocean environmental disturbances. The ship path tracking controller designed accordingly has strong robustness, which is of great significance to ship engineering with high requirements for navigation accuracy;

[0210] (1) At present, the research on event-triggered and game control theories is becoming increasingly prosperous, but their applications in ship control engineering are few. The ship trajectory tracking control algorithm / method proposed by the present invention has been verified by actual ship experiments, providing the possibility for the application of the present invention's achievements in ship control engineering practice.

[0211] The above embodiments only represent several implementation manners of the present application. The description is relatively specific and detailed, but it should not be construed as a limitation to the patent scope of the present application. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several deformations and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the appended claims.

Claims

1. A ship trajectory tracking event-triggered control method with a performance game mechanism, characterized in that, Including: S1. Based on the three-degree-of-freedom planar motion model of the ship, determine the corresponding position error and attitude error of the ship; S2. Based on the position error and attitude error, design a first performance index and a corresponding first value function, where the first performance index is used to describe the performance index corresponding to the position error and attitude error; S3. Design a first negative gradient estimate corresponding to the first value function, determine an optimal virtual control law based on the first negative gradient estimate, and design an online learning law; S4. Based on the dynamic surface technology, reduce the order of the derivative of the optimal virtual control law to obtain a corresponding dynamic reference signal, and further obtain a dynamic control error; S5. Based on the input-end event-triggering mechanism and the dynamic control error, define a second performance index and a corresponding second value function, where the second performance index is used to describe the relationship of the zero-sum game between the control input and the derivative of the triggering error; S6. Design a second negative gradient estimate corresponding to the second value function, and determine an optimal control input and an optimal triggering error based on the second negative gradient estimate; S7. Based on the design parameters determined in S6, judge whether the triggering rule is satisfied. If so, determine the optimal control input as the control input estimate corresponding to the next triggering moment and execute S8. Otherwise, determine the optimal control input as the control input estimate corresponding to the current triggering moment and execute S8; S8. Change the ship state and continue to judge whether the navigation task is completed. If not, reconfirm the current ship state and return to S1 to re-determine the corresponding position error and attitude error of the ship.

2. The ship trajectory tracking event-triggered control method with a performance game mechanism according to claim 1, characterized in that The formulas of the first performance index and the corresponding first value function in S2 are shown as the following formulas (1-1) and (1-2); where J u1 (z e ,α u ) and J r1 (ψ e ,α r ) are the performance indices of the position error and the attitude error, respectively; and are the value functions of J u1 (z e ,α u ) and J r1 (ψ e ,α r ), respectively; α u and α r are the virtual control laws of u and r, respectively; and are α u1 and α r1 when J u and J r reach their minimum values, respectively; z e and ψ e are the position error and the attitude error of the ship, respectively; t is the time, and s is a certain moment.

3. A ship trajectory tracking event-triggered control method with a performance game mechanism according to claim 1, characterized in that, The calculation formula of the first negative gradient estimate corresponding to the first value function in S3 is shown as the following formula (1-3); In the formula, are respectively negative gradient estimates, k u , k r are respectively the virtual control parameters of the surge and yaw degrees of freedom, are respectively the radial basis neural network weight critic estimates of the surge and yaw degrees of freedom, S u1 , S r1 are respectively the activation functions of the radial basis neural network weights ; The calculation formulas of the optimal virtual control law estimate and the online learning law are shown as the following formulas (1-4) and (1-5); In the formula, are the optimal virtual control laws respectively estimates; are the actor estimates of the radial basis function neural networks for the surge and yaw degrees of freedom respectively; k uc1 , k rc1 , k ua1 , k ra1 is online learning rate; and are the critic learning law and actor learning law of the radial basis function neural networks for the surge and yaw degrees of freedom respectively; I is the identity matrix; σ j1 is the online learning law constant greater than 0.

4. A ship trajectory tracking event-triggered control method with a performance game mechanism according to claim 1, characterized in that S4 includes the following steps S41. Based on the dynamic surface technology, reduce the order of the derivative of the optimal virtual control law to obtain a corresponding dynamic reference signal, and the corresponding formula is shown as the following formula; where ∈ u , ∈ r are respectively filter time constants; β u , β r are respectively the dynamic reference signals obtained after filtering; S42. Based on the three-degree-of-freedom planar motion model of the ship and the dynamic reference signal, define the ship dynamic control error, and the corresponding formula is shown as the following formula; u e = β u - u,r e = β r - r where u e , r e are the advancing speed error and yaw rate error under dynamic control respectively; And obtain the derivative form of the aforementioned ship dynamic control error, and its corresponding formula is shown as the following formula; 5. A ship trajectory tracking event-triggered control method with a performance game mechanism according to claim 1, characterized in that, The formula corresponding to the input-end event-triggering mechanism in S5 is shown as the following formula wherein, is the control input after triggering, is the triggering error, t represents continuous time, is the triggering moment; The formulas of the second performance index and the second value function are shown as the following formulas (1-8) and (1-9); where, J u2 , J r2 are the performance indexes of the kinematic control forward speed and the yaw speed error respectively, are the value functions of J u2 , J r2 respectively, γ u , γ r are the event-triggered threshold parameters of the propeller and the rudder respectively, is the optimal control input.

6. A ship trajectory tracking event-triggered control method with a performance game mechanism according to claim 1, characterized in that The second value function in S6 The second negative gradient estimate value, and the corresponding formula is as follows, formula (1-10) In the formula, are respectively the negative gradient estimation values of the value function , k ue , k re are respectively the velocity control parameters of τ u , τ r ; is the estimated value of the extreme ocean disturbance acting on the forward motion and yaw freedom of the hull; is the estimated value of the radial basis neural network weights for the forward motion and yaw freedom of the recombination dynamics, is the critic estimated value of the radial basis neural network weights for the forward motion and yaw freedom; b u , b r are respectively the constants greater than 0 in the negative gradient estimation value of the value function ; The formulas of the optimal control input estimate and the optimal triggering error estimate are shown as the following formula (1-11); wherein, are respectively the estimated values of the optimal control input and the optimal triggering error, is the actor estimated value of the radial basis neural network weights for the surge and yaw degrees of freedom, Among them, the online learning laws of the actor estimate of the radial basis neural network weight of the forward and yaw degrees of freedom and the estimate of the extreme ocean disturbance acting on the forward and yaw freedoms of the hull are shown as the following formulas (1-12) and (1-13); In the formula, are the weights of the radial basis neural network of the critic learning law and the actor learning law, is the learning law of the weights of the radial basis neural network for the recombined kinetic nonlinear term, is the learning law of the extreme ocean disturbance, k jc2 , k ja2 , Γ j , Γ wj are respectively learning rates of j2 is the online learning law a constant greater than 0 in Wj , σ wj are respectively the online learning laws a constant greater than 0 in are respectively initial values of 7. A ship trajectory tracking event-triggering control method with a performance game mechanism according to claim 1, characterized in that The steps corresponding to S1 include: S11. Create a three - degree - of - freedom planar motion model of the ship, and its corresponding model formula is where In the above formula, x, y, and ψ are the x-axis coordinate, y-axis coordinate, and heading angle of the ship in the geodetic coordinate system, respectively; v = [u, v, r] T is the ship speed matrix, where u, v, and r are the ship's forward speed, transverse drift speed, and yaw rate, respectively; f u (v), f v (v), f r (v) are the dynamic nonlinear terms of the ship's forward, transverse drift, and yaw degrees of freedom, respectively; m u , m v , m r are the displacements of the ship in the forward, transverse drift, and yaw degrees of freedom, respectively, d wu , d wv , d wr are the disturbances of the marine environment acting on the ship's forward, transverse drift, and yaw motion directions, respectively; τ u , τ r are the propulsive force provided by the propeller and the turning moment generated by the rudder blade, respectively, as the control inputs of the ship motion control system; d u1 , d u2 , d u3 are the 1st, 2nd, and 3rd order hydrodynamic derivatives of the ship's forward degree of freedom, d v1 , d v2 , d v3 are the 1st, 2nd, and 3rd order hydrodynamic derivatives of the ship's transverse drift degree of freedom, d r1 , d r2 , d r3 are the 1st, 2nd, and 3rd order hydrodynamic derivatives of the ship's yaw degree of freedom, respectively; S12. Based on the three - degree - of - freedom planar motion model of the ship, determine the relationship between the ship's coordinates and the virtual ship's coordinates, and then obtain the reference heading angle; Assume that the reference trajectory of the ship is generated in real - time by the virtual ship and the relationship between the ship's coordinates and the virtual ship's coordinates is determined as shown in the following formula (1 - 16), where x r , y r , ψ r are respectively the x-axis coordinate, y-axis coordinate and heading angle of the virtual ship in the geodetic coordinate system; u r , r r are respectively the forward speed and yaw rate of the virtual ship; then according to the relationship between the ship's coordinates and the virtual ship's coordinates, the reference heading angle is obtained as shown in the following formula (1 - 17); where x e , y e are the coordinate errors of the ship's x-axis and y-axis, and ψ d is the reference heading angle; S13. Based on the three - degree - of - freedom planar motion model of the ship and the reference heading angle, determine the corresponding position error and attitude error of the ship, and the corresponding calculation formula is shown in the following formula (1 - 18); where z e and ψ e are the ship position error and attitude error respectively.

8. A control system for implementing the ship trajectory tracking event-triggered control method according to any one of claims 1-7, characterized in that Including: The first data acquisition unit, which is used to determine the corresponding position error and attitude error of the ship based on the three - degree - of - freedom planar motion model of the ship; The first data design unit, which is used to design the first performance index and the corresponding first value function based on the position error and attitude error; The second data design unit, which is used to design the first negative gradient estimate, the optimal virtual control law and the online learning law corresponding to the first value function, and the optimal virtual control law and the online learning law are used to obtain the index value corresponding to the minimum first performance index; The second data acquisition unit, which is used to perform a reduced - order processing on the derivative of the optimal virtual control law based on the dynamic surface technology to obtain the corresponding dynamic reference signal, and then obtain the dynamic control error; The third data design unit, which is used to define the second performance index and the corresponding second value function based on the input - end event - triggered mechanism and the obtained dynamic control error; The fourth data design unit, which is used to design the second negative gradient estimate, the optimal control input and the optimal trigger error corresponding to the second value function; The first data judgment unit, which is used to judge whether the trigger rule is satisfied based on the design parameters of the fourth data design unit. If so, determine that the optimal control input is the control input estimate corresponding to the next trigger moment and continue to judge whether the navigation task is completed by the second data judgment unit. Otherwise, determine that the optimal control input is the control input estimate corresponding to the current trigger moment and continue to judge whether the navigation task is completed by the second data judgment unit; The second data judgment unit, which is used to change the ship's state and continue to judge whether the navigation task is completed. If not, re - confirm the current state of the ship and re - determine the corresponding position error and attitude error of the ship through the first data acquisition unit.

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