A robust data-driven autopilot control method for ship's preset performance course keeping

Abstract

The embodiment discloses a robust data-driven preset performance course keeping control method for a ship, obtains an unconstrained transformed error according to a ship course tracking error and a preset performance envelope obtained based on a predetermined time performance function; simultaneously, obtains a pseudo partial derivative estimation value of a course measurement value by adopting a PPD criterion according to the course measurement value, further obtains a compensated transformed error, then adopts a closed-loop gain shaping algorithm to obtain a command rudder angle, further obtains a constrained actual rudder angle, and realizes the course keeping control based on the preset performance of the ship. The application does not need a hydrodynamic model, and can be controlled on-line only by relying on the course and the rudder angle input and output data. The bandwidth, the damping and the robust characteristics can be set according to indexes by the closed-loop gain shaping, and the course keeping control and the robustness can be realized even in the case that the ship dynamics is unknown or seriously uncertain.

Description

Technical Field

[0001] This invention relates to the field of ship control technology, and in particular to a robust data-driven method for maintaining a ship's preset performance course. Background Technology

[0002] In recent years, with the continuous development of technology, maritime traffic density has been increasing, posing a significant challenge to navigation safety. Analysis of recent research reveals that the most important control method for ensuring navigation safety is currently preset performance control. However, this relies on tracking errors to maintain the ship's course, which is a fundamental control task in autonomous navigation and intelligent maritime systems. Its control performance directly affects navigation safety, steering energy consumption, steering gear wear, and the feasibility of higher-level tasks (such as path tracking, collision avoidance, and formation control). However, real-world ship systems exhibit significant nonlinearity, strong coupling, time-varying characteristics, and underactuation, and are constantly affected by external disturbances such as wind, waves, and currents, making accurate mechanistic-based models difficult to obtain or maintain long-term effectiveness.

[0003] Traditional heading-keeping control often employs model-driven or structured methods such as PID, LQR, and sliding mode control. These methods are effective when the model is relatively accurate and the disturbance is controllable. However, when model mismatch, parameter perturbations, or unknown strong disturbances exist, the control quality may deteriorate significantly, even leading to large overshoot, oscillations, or instability. Robust control (e.g., H∞) can be designed within an uncertainty framework, but it typically requires an explicit description of the uncertainty and involves a complex solution process, resulting in high engineering implementation costs.

[0004] To reduce reliance on precise models, data-driven control methods have gained attention in recent years. Among them, Model-Free Adaptive Control (MFAC) achieves control design that relies solely on input-output data through dynamic linearization and online estimation of pseudo-partial derivatives (PPD), offering advantages such as low computational cost and ease of implementation. However, existing MFAC-like methods often struggle to explicitly shape closed-loop frequency domain metrics (bandwidth, damping, robustness margin, noise suppression), leading to performance tuning that is empirically dependent and lacks interpretability. On the other hand, Closed-Loop Gain Shaping Algorithm (CGSA) can achieve structured design of frequency domain performance by specifying the desired closed-loop transfer function, offering advantages such as clear physical meaning and intuitive design process. However, traditional CGSA relies on nominal models and is difficult to apply directly to completely unknown objects.

[0005] In addition, there are two other key requirements in engineering applications: (1) The heading error needs to meet the preset transient / steady-state constraints and preferably reach the constraint boundary within a pre-specified time. (2) The servo motor has input constraints such as saturation of servo angle amplitude and servo angle rate. If the controller does not consider these constraints, it will lead to problems such as performance degradation and increased overshoot.

[0006] Therefore, there is an urgent need for a new course-keeping control method that can explicitly shape closed-loop performance, satisfy predetermined time error constraints, and adapt to rudder input saturation without requiring a ship hydrodynamic model. The method restricts the actual trajectory to converge near the desired trajectory; however, if the desired trajectory cannot be obtained in advance, the use of this control method will be limited. Ensuring a rapid convergence rate of speed tracking error under constrained control input is also a hot topic in the field of control. Therefore, researching a control method that enables ships to track a reference trajectory faster and more safely when the desired trajectory is unknown in advance is of great significance. Summary of the Invention

[0007] This invention discloses a robust data-driven method for maintaining the course of a ship's preset performance, in order to overcome the aforementioned technical problems.

[0008] To achieve the above objectives, the technical solution of the present invention is as follows: A robust data-driven method for maintaining the course of a ship's preset performance includes the following steps: S1: Construct the ship's heading tracking error based on the ship's desired heading command and the ship's heading measurement value; S2: Construct a preset performance function for a predetermined time to obtain the preset performance envelope; S3: Obtain the error after unconstrained transformation based on the ship's heading tracking error and the preset performance envelope; S4: Based on the heading measurement value, use the PPD criterion to obtain the pseudo-partial derivative estimate of the heading measurement value; S5: Obtain the input mismatch of the ship to construct a compensated dynamic system, and then obtain the compensated transformation error based on the error after the unconstrained transformation. S6: Based on the pseudo-partial derivative estimate of the heading measurement and the compensated transformation error, the closed-loop gain shaping algorithm is used to obtain the command rudder angle; S7: Based on the commanded rudder angle, obtain the constrained actual rudder angle to achieve course-keeping control based on the ship's preset performance.

[0009] Furthermore, the preset performance function for the predetermined time is expressed as follows:

[0010] In the formula: Preset performance envelope; This is for processing the preset performance envelope; For residual boundaries; For natural index; This represents the number of simulation steps. This is for simulating step size; For the scheduled time; The predetermined number of steps is obtained by dividing the predetermined time by the step size.

[0011] Furthermore, the formula used to obtain the error after unconstrained transformation is as follows:

[0012]

[0013] In the formula: This represents the error after unconstrained transformation. This is the normalized error; For heading tracking error; This is the preset performance envelope.

[0014] Furthermore, the method used to obtain the pseudo-partial derivative estimate of the heading measurement is as follows: First, the differences in heading and rudder angle are obtained using the following formulas:

[0015]

[0016] In the formula: For the course change Step and The difference between steps; This is the heading measurement value; For the rudder angle change Step and The difference between steps; For the first The actual rudder angle of the step; This is the sequence number of the sampling step; Then, a PPD estimation criterion is constructed to obtain the pseudo-partial derivative estimate of the heading measurement value. The formula used is as follows:

[0017] In the formula: For the first The pseudo-partial derivative estimate of the heading measurement values ​​for each sampling step; Step size factor ; As a smoothing factor, .

[0018] Furthermore, S5 includes: S51: The input mismatch of the vessel is obtained as follows:

[0019] In the formula: Input mismatch for the vessel; The ideal output rudder angle for the controller; This is the actual rudder angle; S52: Construct a compensated dynamic system, as follows:

[0020] In the formula: The compensation value for input saturation; This is for simulating step size; The attenuation coefficient is... ; Input mismatch for the vessel; S53: The transformation error after compensation is as follows:

[0021] In the formula: This is the compensated transformation error; To compensate for the gain.

[0022] Furthermore, S6 includes: S61: Obtain the pseudo-partial derivative estimate based on the heading measurement value, and obtain the discrete-form model transfer function, as shown below:

[0023] In the formula: The transfer function for the discrete-form model; It is the discrete transformation factor; For regularization terms used to avoid division by zero, ; S62: Constructing the desired closed-loop complementary sensitivity function:

[0024] In the formula: It is a continuous desired closed-loop complementary sensitivity function; These are parameters used to determine the desired closed-loop bandwidth. ; These are parameters used for damping and robustness shaping. ; It is the Laplace factor; For order; Will Its discretization yields:

[0025]

[0026] In the formula: The desired closed-loop complementary sensitivity function after discretization; The molecular formula for the desired closed-loop complementary sensitivity function after discretization; This is the denominator of the discretized desired closed-loop complementary sensitivity function; It is the difference between the denominator and the numerator. in,

[0027] In the formula: All are transfer function coefficients;

[0028] S63: Based on the discrete-form model transfer function and the closed-loop gain shaping algorithm, the supplementary sensitivity function is equivalent to the system's closed-loop transfer function, as shown below:

[0029] In the formula: This is the transfer function form of the controller. in:

[0030]

[0031] In the formula: for Control input after discrete transformation; for Error after discrete transformation; For regularization terms used to avoid division by zero; Taking the inverse discrete transformation, we get:

[0032] In the formula: To command the rudder angle; The control at the current time step is obtained by using the backward difference approximation: .

[0033] Furthermore, the formula used to obtain the actual rudder angle after constraints is as follows:

[0034] In the formula: This is the actual rudder angle after constraints; For constraint functions; This is the maximum rudder angle value; This represents the maximum rate of change of the rudder angle; To command the rudder angle; in,

[0035] In the formula: To dynamically set the execution limit, For dynamic execution lower bound: .

[0036] Furthermore, the heading tracking error is constructed as follows:

[0037] In the formula: For heading tracking error; For the desired course instruction; This is the heading measurement value.

[0038] Beneficial effects: The present invention provides a robust data-driven ship preset performance heading control method, which obtains the unconstrained transformation error based on the ship's heading tracking error and the preset performance envelope obtained based on a predetermined time performance function; simultaneously, based on the heading measurement value, the pseudo-partial derivative estimate of the heading measurement value is obtained using the PPD criterion, and then the compensated transformation error is obtained; then, a closed-loop gain shaping algorithm is used to obtain the command rudder angle, and then the constrained actual rudder angle is obtained, so as to realize heading control based on the ship's preset performance. This invention eliminates the need for a hydrodynamic model, enabling online control solely based on heading and rudder angle input / output data. It introduces designable closed-loop frequency domain performance in data-driven / model-free control, achieving pre-defined dynamic qualities. Through closed-loop gain shaping, bandwidth, damping, and robustness characteristics can be tuned to specific parameters, allowing explicit shaping of closed-loop performance. Even under conditions of unknown or severely uncertain ship dynamics, it can still achieve heading-keeping control with robustness. Errors are strictly limited to a preset performance envelope and converge to a given residual boundary within a pre-specified time. In environments with strong disturbances and noise, the heading tracking error strictly meets preset performance constraints and converges to a given error interval within a pre-specified time, ensuring predetermined time error constraints. Furthermore, through an input saturation compensation mechanism, under rudder angle amplitude and rate saturation constraints, it avoids controller performance degradation, achieving input constraint compensation and implementable control, significantly reducing performance degradation caused by saturation. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0040] Figure 1 This is a flowchart of the robust data-driven ship preset performance heading maintenance control method of the present invention; Figure 2This is a schematic diagram of the basic framework of the ship preset performance heading maintenance control method in this embodiment of the invention; Figure 3 This is a schematic diagram illustrating the heading-keeping performance of different control strategies in embodiments of the present invention; Figure 4 This is a schematic diagram of the bow angular velocity response under different control strategies in embodiments of the present invention; Figure 5 This is a schematic diagram of the control input (rudder angle) response under different control strategies in embodiments of the present invention; Figure 6 This is a schematic diagram illustrating the evolution of tracking error under a preset performance limit in an embodiment of the present invention; Figure 7 This is a schematic diagram illustrating the evolution of the PPD estimate in an embodiment of the present invention. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0042] This embodiment introduces a robust data-driven method for ship preset performance heading maintenance control, including the following steps: Figure 1 As shown: In this embodiment, firstly, the control period is... The discrete sampling system performs sampling and variable initialization. The sampled variables include: heading measurements. Actual rudder angle (Actual output after servo limiting / speed limiting); Desired heading command Initialize control-related variables, including: initial values ​​of pseudo-partial derivative (PPD) estimates. Preset performance boundary parameters , scheduled time parameters Gain shaping parameters Input compensation parameters Wait, and set the rudder angle amplitude. With rate constraints .

[0043] S1: Construct the ship's heading tracking error based on the ship's desired heading command and the ship's heading measurement. This serves as the basis for generating error constraints and control laws.

[0044] Preferably, the heading tracking error is constructed as follows:

[0045] In the formula: For heading tracking error; For the desired course instruction; This is the heading measurement value; S2: Construct a preset performance function (PT-PPF) for a predetermined time to obtain the preset performance envelope. So that it will be at the scheduled time From initial value Smooth shrinkage to residual limit and at the scheduled time After holding This achieves error evolution constraints: .

[0046] Preferably, the preset performance function for the predetermined time is expressed as follows:

[0047] In the formula: Preset performance envelope; This is for processing the preset performance envelope; For residual boundaries; For natural index; This represents the number of simulation steps. This is for simulating step size; For the scheduled time; The predetermined number of steps is obtained by dividing the predetermined time by the step size; S3: Obtain the error after unconstrained transformation based on the ship's heading tracking error and the preset performance envelope. This achieves error normalization and unconstrained transformation, thus transforming the "constrained error control problem" into a "problem of controlling transformation error". "The problem of unconstrained regulation." When When bounded, it can guarantee That is, the error strictly meets the preset performance constraints.

[0048] Preferably, the formula used to obtain the error after unconstrained transformation is as follows:

[0049]

[0050] In the formula: This represents the error after unconstrained transformation. This is the normalized error; For heading tracking error; This is the preset performance envelope.

[0051] S4: Based on heading measurements The PPD criterion is used to obtain the pseudo-partial derivative estimate of the heading measurement. This enables an online PPD estimation and reset mechanism.

[0052] Preferably, the method used to obtain the pseudo-partial derivative estimate of the heading measurement is as follows: First, the differences in heading and rudder angle are obtained using the following formulas:

[0053]

[0054] In the formula: For the course change Step and The difference between steps; This is the heading measurement value; For the rudder angle change Step and The difference between steps; For the first The actual rudder angle of the step; This is the sequence number of the sampling step; Then, a PPD estimation criterion is constructed to obtain the pseudo-partial derivative estimate of the heading measurement value. The formula used is as follows:

[0055] In the formula: For the first The pseudo-partial derivative estimate of the heading measurement values ​​for each sampling step; Step size factor ; As a smoothing factor, .

[0056] Specifically, to avoid numerical instability caused by excessively small input variations or estimations crossing zeros, a reset rule is set: when Less than the threshold or Approaching zero or sign abnormality ( When ), Reset to initial value .

[0057] S5: Obtain the input mismatch of the ship to construct a compensated dynamic system, and then obtain the compensated transformation error. ; Preferably, S5 includes: S51: Define the ideal output rudder angle of the controller (before amplitude and speed limits are set) as The actual output of the servo motor is The input mismatch of the ship is obtained as follows:

[0058] In the formula: Input mismatch for the vessel; The ideal output rudder angle for the controller; This is the actual rudder angle; S52: Construct a compensated dynamic system, as follows:

[0059] In the formula: The compensation value for input saturation; This is for simulating step size; The attenuation coefficient is... ; Input mismatch for the vessel; S53: The transformation error after compensation is as follows:

[0060] In the formula: This is the compensated transformation error; To compensate for the gain, the controller is designed to have an inherent ability to suppress command-execution inconsistency, thereby mitigating the risk of performance degradation caused by saturation.

[0061] S6: Based on the pseudo-partial derivative estimate of the heading measurement and the compensated transformation error, the closed-loop gain shaping algorithm is used to obtain the command rudder angle; Preferably, S6 includes: S61: Obtain the pseudo-partial derivative estimate based on the heading measurement value, and obtain the discrete-form model transfer function, as shown below:

[0062] In the formula: The transfer function for the discrete-form model; It is the discrete transformation factor; For regularization terms used to avoid division by zero, ; S62: Constructing the desired closed-loop complementary sensitivity function:

[0063] In the formula: It is a continuous desired closed-loop complementary sensitivity function; These are parameters used to determine the desired closed-loop bandwidth. ; These are parameters used for damping and robustness shaping. ; It is the Laplace factor; For order; Will Its discretization yields:

[0064]

[0065] In the formula: The desired closed-loop complementary sensitivity function after discretization; The molecular formula for the desired closed-loop complementary sensitivity function after discretization; This is the denominator of the discretized desired closed-loop complementary sensitivity function; It is the difference between the denominator and the numerator. in,

[0066] In the formula: All are transfer function coefficients;

[0067] S63: Based on the discrete-form model transfer function and the closed-loop gain shaping algorithm, the supplementary sensitivity function is equivalent to the system's closed-loop transfer function, as shown below:

[0068] In the formula: This is the transfer function form of the controller. in:

[0069]

[0070] In the formula: for Control input after discrete transformation; for Error after discrete transformation; For regularization terms used to avoid division by zero; Taking the inverse discrete transformation, we get:

[0071] In the formula: To command the rudder angle; But in reality, we cannot predict. Therefore, the backward difference approximation is used to obtain the control at the current time step:

[0072] S7: Based on the commanded rudder angle, obtain the constrained actual rudder angle to achieve course-keeping control based on the ship's preset performance.

[0073] Preferably, the command rudder angle is... After servo amplitude / speed constraint operator Actual rudder angle after obtaining constraints:

[0074] In the formula: This is the actual rudder angle after constraints; For constraint functions; This is the maximum rudder angle value; This represents the maximum rate of change of the rudder angle; This is the command rudder angle. Among them... The constraint function can be expressed as:

[0075] In the formula: To dynamically set the execution limit, For dynamic execution lower bound: in: .

[0076] In this embodiment, after this step is completed, the actual rudder angle after constraint is determined. The process is repeated in a loop to achieve online closed-loop control.

[0077] This embodiment takes the course maintenance control of the "Yukun" vessel of Dalian Maritime University as an example: the verification example uses the MMG model as the simulation model.

[0078] Figure 2 This is the basic framework of this embodiment, shown in the figure. For the desired course instruction, This is the heading measurement value. This is the rudder angle constraint compensation value. This is the actual rudder angle. To command the rudder angle, and These are the heading difference component and the rudder angle difference component, respectively. This is a pseudo-partial derivative estimate. The framework states that: first, a performance envelope function with predetermined time convergence characteristics is designed to constrain the transient and steady-state performance of the heading tracking error. Through nonlinear error transformation, the constrained heading tracking error problem is transformed into an unconstrained transformed error stabilization problem. The online estimated PPD is used as the "instantaneous nominal model" gain required by the closed-loop gain shaping algorithm (CGSA). This algorithm, as a robust control method, effectively handles unmodeled dynamics and external disturbances. Using the compensated error signal as the control input, a recursive digital controller with specified closed-loop response characteristics is designed to calculate the ideal rudder angle command. The actual control command is generated and executed. The calculated ideal rudder angle command is processed through a saturation function simulating the physical limitations of the rudder, generating an actually executable rudder angle command, which is then applied to the ship's rudder system. Simultaneously, utilizing historical and current input (rudder angle) and output (heading angle) data of the ship, and based on the compact form dynamic linearization (CFDL) technique—which relies solely on input and output data without depending on a specific control model, exhibiting purely data-driven characteristics—a linearized data model capable of locally equivalently describing the ship's nonlinear dynamics is constructed. An estimation algorithm is designed to identify the key time-varying parameter of this model—the pseudo-partial derivative (PPD)—online. An auxiliary dynamic system is established to estimate in real time the deviation between the ideal control input and the actual executed input caused by rudder angle magnitude and rudder angle rate saturation. This deviation is incorporated into the adjustment of the transformed error, forming a compensated error signal to actively suppress integral saturation. A robust data-driven control law is then designed.

[0079] This simulation uses a 4th-order Runge-Kutta integrator with a sampling period of 0.1 seconds and a simulation duration of 1600 seconds. The comparison algorithms are Model-Free Adaptive Control (MFAC) and Robust Data-Driven Control (RDDC), with the desired heading set as follows:

[0080] Figures 3-7 The simulation results are presented, and the quantitative evaluation indicators are listed in Table 1.

[0081] Table 1 Comparison of Quantitative Evaluation Indicators for Simulation Results of Different Algorithms

[0082] Where MAE is the mean absolute error, ITAE is the integral time absolute error, RMSE is the root mean square error, MIA is the mean integral absolute error, and MTV is the mean total variation.

[0083] like Figure 3As shown, the proposed PT-PPCRDDC provides a heading response closest to the commanded heading in all maneuver phases. This advantage is particularly pronounced during setpoint changes, with PT-PPCRDDC exhibiting shorter transient recovery times and smaller residual (steady-state) tracking bias compared to MFAC and the conventional RDDC. In contrast, MFAC and RDDC demonstrate more pronounced low-frequency drift in the mid-to-late stages, implying weaker suppression of environmental disturbances and model / parameter uncertainties under actuator constraints.

[0084] Figure 4 Furthermore, it is shown that the PT-PPCRDDC implements a more aggressive yaw rate adjustment during command transitions, characterized by rapid decay to a smaller neighborhood after concentrated rate fluctuations, consistent with finite-time performance control mechanisms. In contrast, while MFAC and RDDC have smaller rate injection amplitudes, they tend to retain larger post-maneuver oscillation components, consistent with their lower RMS and MAE values.

[0085] Figure 5 The illustrated control surface activity highlights the performance-operational force trade-offs resulting from enforcing strict transient specifications under conditions of limited control amplitude and speed. To meet the preset transient envelope, the PT-PPCRDDC employs more aggressive control surface actions. The enlarged view shows that without explicit compensation, the required control commands could approach or even exceed permissible limits; the introduced input constraint compensation reshapes / saturates the applied commands, thus maintaining feasibility. Therefore, the significant improvement in heading-tracking performance comes at the cost of increased control activity; however, the compensation mechanism ensures constraint compatibility and prevents unreasonable control angle deviations, which is crucial for practical servo applications.

[0086] Figure 6 The preset performance characteristics were directly verified. The PT-PPC RDDC tracking error was strictly limited to the predefined boundaries. Within a narrow neighborhood, the error quickly falls back to a smaller range after each setpoint change, while MFAC and RDDC exhibit larger deviations and wider steady-state error bands. This constrained error evolution is consistent with a significant reduction in MAE and, more importantly, ITAE, indicating that the proposed method not only limits peak deviation but also mitigates persistent small errors that would otherwise accumulate during long-term navigation.

[0087] Figure 7 The evolution of the PPD estimates is illustrated. All schemes maintain the PPD values ​​within a bounded range without divergence, indicating online adaptive stability. The PT-PPC RDDC scheme exhibits more pronounced transient changes near the maneuver time, but still within the bounded range, which is consistent with... Figures 3 to 4This is consistent with the stronger steering injection and constraint compensation interactions observed in [the study]. Importantly, these estimated transient changes do not affect closed-loop tracking and are consistent with [other factors]. Figure 5 It is compatible with strict error constraints and improved integral indicators.

[0088] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions 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 robust data-driven method for maintaining a ship's preset performance course, characterized in that, Includes the following steps: S1: Construct the ship's heading tracking error based on the ship's desired heading command and the ship's heading measurement value; S2: Construct a preset performance function for a predetermined time to obtain the preset performance envelope; S3: Obtain the error after unconstrained transformation based on the ship's heading tracking error and the preset performance envelope; S4: Based on the heading measurement value, use the PPD criterion to obtain the pseudo-partial derivative estimate of the heading measurement value; S5: Obtain the input mismatch of the ship to construct a compensated dynamic system, and then obtain the compensated transformation error based on the error after the unconstrained transformation. S6: Based on the pseudo-partial derivative estimate of the heading measurement and the compensated transformation error, the closed-loop gain shaping algorithm is used to obtain the command rudder angle; S7: Based on the commanded rudder angle, obtain the constrained actual rudder angle to achieve course-keeping control based on the ship's preset performance.

2. The robust data-driven ship preset performance heading maintenance control method according to claim 1, characterized in that, The preset performance function for the predetermined time is expressed as follows: In the formula: Preset performance envelope; This is for processing the preset performance envelope; For residual boundaries; For natural index; This represents the number of simulation steps. This is for simulating step size; For the scheduled time; The predetermined number of steps is obtained by dividing the predetermined time by the step size.

3. The robust data-driven ship preset performance heading maintenance control method according to claim 1, characterized in that, The formula used to obtain the error after unconstrained transformation is as follows: In the formula: This represents the error after unconstrained transformation. This is the normalized error; For heading tracking error; This is the preset performance envelope.

4. A robust data-driven ship preset performance heading maintenance control method according to claim 1, characterized in that, The method used to obtain the pseudo-partial derivative estimate of the heading measurement is as follows: First, the differences in heading and rudder angle are obtained using the following formulas: In the formula: For the course change Step and The difference between steps; This is the heading measurement value; For the rudder angle change Step and The difference between steps; For the first The actual rudder angle of the step; This is the sequence number of the sampling step; Then, a PPD estimation criterion is constructed to obtain the pseudo-partial derivative estimate of the heading measurement value. The formula used is as follows: In the formula: For the first The pseudo-partial derivative estimate of the heading measurement values ​​for each sampling step; Step size factor ; As a smoothing factor, .

5. A robust data-driven ship preset performance heading maintenance control method according to claim 1, characterized in that, S5 includes: S51: The input mismatch of the vessel is obtained as follows: In the formula: Input mismatch for the vessel; The ideal output rudder angle for the controller; This is the actual rudder angle; S52: Construct a compensated dynamic system, as follows: In the formula: The compensation value for input saturation; This is for simulating step size; The attenuation coefficient is... ; Input mismatch for the vessel; S53: The transformation error after compensation is as follows: In the formula: This is the compensated transformation error; To compensate for the gain.

6. A robust data-driven ship preset performance heading maintenance control method according to claim 1, characterized in that, S6 includes: S61: Obtain the pseudo-partial derivative estimate based on the heading measurement value, and obtain the discrete-form model transfer function, as shown below: In the formula: The transfer function for the discrete-form model; It is the discrete transformation factor; For regularization terms used to avoid division by zero, ; S62: Constructing the desired closed-loop complementary sensitivity function: In the formula: It is a continuous desired closed-loop complementary sensitivity function; These are parameters used to determine the desired closed-loop bandwidth. ; These are parameters used for damping and robustness shaping. ; It is the Laplace factor; For order; Will Its discretization yields: In the formula: The desired closed-loop complementary sensitivity function after discretization; The molecular formula for the desired closed-loop complementary sensitivity function after discretization; This is the denominator of the discretized desired closed-loop complementary sensitivity function; It is the difference between the denominator and the numerator. in, In the formula: All are transfer function coefficients; S63: Based on the discrete-form model transfer function and the closed-loop gain shaping algorithm, the supplementary sensitivity function is equivalent to the system's closed-loop transfer function, as shown below: In the formula: This is the transfer function form of the controller. in: In the formula: for Control input after discrete transformation; for Error after discrete transformation; For regularization terms used to avoid division by zero; Taking the inverse discrete transformation, we get: In the formula: To command the rudder angle; The control at the current time step is obtained by using the backward difference approximation: 。 7. A robust data-driven ship preset performance heading maintenance control method according to claim 1, characterized in that, The formula used to obtain the actual rudder angle after obtaining the constraints is as follows: In the formula: This is the actual rudder angle after constraints; For constraint functions; This represents the maximum rudder angle. This represents the maximum rate of change of the rudder angle; To command the rudder angle; in, In the formula: To dynamically set the execution limit, For dynamic execution lower bound: 。 8. A robust data-driven ship preset performance heading maintenance control method according to claim 1, characterized in that, The heading tracking error is constructed as follows: In the formula: For heading tracking error; For the desired course instruction; This is the heading measurement value.

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