Ship heading control method considering asymmetric full-state constraints and intelligent approximation

Abstract

This invention discloses a ship heading control method considering asymmetric full-state constraints and intelligent approximation. The method includes: constructing a first asymmetric constraint that the heading error must satisfy and a second asymmetric constraint that the bow turning angular velocity tracking error must satisfy; obtaining compensation tracking error based on the finite-time auxiliary system state variables and the inner-loop logarithmic transformation function to design a nonlinear integral sliding surface; obtaining the actual control input containing system uncertainties and external disturbances from the nonlinear integral sliding surface; approximating the system uncertainties using a radial basis function neural network to obtain estimated values ​​of the system uncertainties; constructing a parameter adaptive law for compensating for external disturbances; and obtaining a control law for ship heading control based on the parameter adaptive law and the estimated values ​​of the system uncertainties. This invention solves the problem of existing methods failing to meet the accuracy and efficiency requirements of ship heading control.

Description

Technical Field

[0001] This invention relates to the field of ship heading control technology, and in particular to a ship heading control method that considers asymmetric full-state constraints and intelligent approximation. Background Technology

[0002] With the rapid development of intelligent shipping and unmanned vessel technologies, high-precision and robust course-keeping control has become a crucial element in ensuring the autonomous and safe navigation of ships. In the actual marine environment, ships are constantly affected by complex time-varying disturbances such as wind, waves, and currents, and their dynamic characteristics exhibit significant nonlinearity, coupling, and parameter uncertainty. Currently, PID control or traditional sliding mode control are commonly used in engineering, but these methods generally suffer from slow adjustment speed, significant overshoot, and large steady-state errors when facing strong disturbances and model perturbations. In recent years, nonlinear control strategies based on the backstepping method have been widely applied in ship course control. However, existing technologies still have the following significant drawbacks when implemented in practical engineering: (1) The full-state constrained characteristics of safe navigation are ignored: Most existing heading control schemes only focus on the tracking error control of the heading angle () and do not effectively constrain the yaw rate. When faced with a sudden large-angle turning command, the ship is very likely to generate an excessive transient yaw rate, which will not only lead to increased ship roll, but may even cause serious accidents such as capsizing that endanger navigation safety.

[0003] (2) Risk of system instability caused by actuator saturation: Actual ship actuators have strict physical limits. Most existing control algorithms assume that the control input is unconstrained. Once the calculated control command exceeds the physical limit of the steering gear, it will cause control input saturation, which in turn leads to integral saturation, causing system oscillation, slower convergence speed or even instability.

[0004] (3) The inherent "differential explosion" defect of backstepping: Traditional backstepping control requires repeated analytical differentiation of the virtual control law during the design process. This calculation method is extremely cumbersome and will lead to the "differential explosion" problem; at the same time, the complex analytical derivatives are very easy to amplify the measurement noise of the sensor in practical engineering applications, which seriously reduces the robustness of the control system. Although some studies have introduced dynamic surface control for smoothing, the convergence time of traditional filters depends on the initial state and cannot guarantee the rapid elimination of filtering errors within a specific time, resulting in a large phase lag.

[0005] (4) Coupling problem between unknown model and strong disturbance: The complex nonlinear hydrodynamic damping of ships is difficult to model accurately, and the disturbance of the marine environment is highly time-varying. Existing methods still face challenges in simultaneously achieving dynamic compensation for disturbance and fitting of model uncertainty terms, which easily leads to the coupling of fitting error and disturbance error. Summary of the Invention

[0006] This invention provides a ship heading control method that considers asymmetric full-state constraints and intelligent approximation to overcome the above-mentioned technical problems.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows: A ship heading control method considering asymmetric full-state constraints and intelligent approximation includes the following steps: S1: Obtain a responsive ship mathematical model that takes into account input saturation; S2: Define the heading tracking error based on the responsive ship mathematical model; based on the heading tracking error, obtain the first asymmetric constraint that the heading error must satisfy according to a preset performance function based on exponential decay; design an outer-loop logarithmic error transformation function based on the first asymmetric constraint to construct a virtual control law; filter the virtual control law based on the designed filter dynamic equation to obtain a filtered signal; define the bow turning angular velocity tracking error based on the filtered signal; based on the bow turning angular velocity tracking error, obtain the second asymmetric constraint that the bow turning angular velocity tracking error must satisfy according to a novel smoothing performance function based on hyperbolic tangent; design an inner-loop logarithmic transformation function based on the second asymmetric constraint. S3: Construct the state variables of the finite-time auxiliary system, and obtain the compensation tracking error based on the state variables of the finite-time auxiliary system and the inner-loop logarithmic transformation function; design a nonlinear integral sliding surface based on the compensation tracking error; obtain the actual control input containing the system uncertainty terms of the ship model and the external disturbances it receives based on the nonlinear integral sliding surface; S4: Approximate the system uncertainty terms using a radial basis function neural network to obtain estimated values ​​of the system uncertainty terms; construct a parameter adaptive law for compensating for external disturbances; based on the parameter adaptive law and the estimated values ​​of the system uncertainty terms, combine the actual control input obtained in S3 to obtain a control law for ship heading control, so as to realize ship heading control considering asymmetric full-state constraints and intelligent approximation.

[0008] Furthermore, the responsive ship mathematical model described in S1 is as follows:

[0009]

[0010] In the formula: and These represent the ship's heading angle and turning angular velocity, respectively. g and These represent the system uncertainty and the external disturbances experienced by the ship model, respectively. This indicates the input rudder angle that is subject to saturation limitations; Represents the cyclicity index; Indicates the following index; Indicates the upper bound of the control input; Indicates the lower bound of the control input; Indicates the actual control input; express The first derivative.

[0011] Furthermore, step S2 specifically includes the following steps: S21: Based on the responsive ship mathematical model, the heading tracking error is defined as:

[0012] In the formula: Indicates heading tracking error; Indicates the desired heading angle; S22: Design a preset performance function based on exponential decay as follows:

[0013] In the formula: , , Indicates a pre-designed positive parameter; This represents a preset performance function based on exponential decay. express The abbreviated form; S23: Based on the heading tracking error and a preset performance function based on exponential decay, the first asymmetric constraint that the heading error must satisfy is:

[0014] In the formula: , This indicates a positive parameter designed based on a preset range of constraints; S24: Design the outer loop logarithmic error transformation function based on the first asymmetric constraint. for:

[0015] S25: Based on outer loop logarithmic error transformation function The virtual control law is constructed as follows:

[0016] In the formula: Represents a virtual control law; express The first derivative; express The first derivative; Indicates control gain; S26: Based on the designed filter dynamic equation, the virtual control law is filtered to obtain the filtered signal; and the filter dynamic equation is:

[0017] In the formula: Indicates the filtered signal; express The first derivative; Indicates the filter tracking error; Represents the filter gain constant and ; Denotes the fractional power parameter that guarantees convergence in a fixed time and ; S27: Define the steering angular velocity tracking error based on the filtered signal. for:

[0018] S28: Design a novel smoothing performance function based on hyperbolic tangent for:

[0019] In the formula: , Indicates a pre-designed positive parameter; Based on the bow angular velocity tracking error and a novel smoothing performance function based on hyperbolic tangent, the second asymmetric constraint that the bow angular velocity tracking error must satisfy is:

[0020] In the formula: , This indicates a positive parameter designed based on a preset range of constraints; express The abbreviated form; S29: Design the inner loop logarithmic transformation function based on the second asymmetric constraint. for: .

[0021] Furthermore, step S3 specifically includes the following steps: S31: Construct the state variables of the finite-time auxiliary system, and the corresponding expression is:

[0022]

[0023] In the formula: Indicates the dissipation gain of the auxiliary system and ; Denotes a fractional power that is guaranteed to converge in finite time. ; Indicates input saturation error and ; Representing the state variables of a finite-time auxiliary system The first derivative; This represents the nonlinear transformation partial derivative of BLF; S32: Obtain the compensation tracking error based on the state variables of the finite-time auxiliary system and the inner-loop logarithmic transformation function. for:

[0024] S33: Based on the aforementioned compensation tracking error, the nonlinear integral sliding surface is designed as follows:

[0025] In the formula: Indicates the design parameters of the sliding surface and ; express The abbreviated form; S34: The actual control input, including the system uncertainties of the ship model and the external disturbances it experiences, is obtained based on the nonlinear integral sliding surface:

[0026] In the formula: Indicates design constants; Indicates external interference The upper bound and satisfying ; express The abbreviated form; Represents the reaching law gain and ; Indicate design parameters and .

[0027] Furthermore, step S4 specifically includes the following steps: S41: Approximate the system uncertainty terms using a radial basis function neural network to obtain the estimated values ​​of the system uncertainty terms. Its expression is:

[0028]

[0029]

[0030] In the formula: The weights of a radial basis function neural network The ideal network weights; Represents the space of real numbers; Represents the Gaussian function; express Estimating network weights; Indicates the approximation error; This represents the adaptive law of weights; Indicate design parameters and ; S42: The adaptive law for compensating for external disturbances is constructed as follows:

[0031] In the formula: Indicate design parameters and ; express The prior estimate; express The estimated value; express The first derivative; S43: Based on the parameter adaptive law and the estimated value of the system uncertainty, combined with the actual control input obtained in S3, the control law for ship heading control is obtained as follows:

[0032] Based on the control law for ship heading control, ship heading control considering asymmetric full-state constraints and intelligent approximation is achieved.

[0033] This invention provides a ship heading control method that considers asymmetric full-state constraints and intelligent approximation, with the following advantages: (1) In view of the safety problems that ships are prone to dangerous yaw rate and limited navigation space during large-angle turns, the present invention introduces a first asymmetric constraint that the heading error must satisfy and a second asymmetric constraint that the bow turning rate tracking error must satisfy, respectively, for the kinematic outer loop of the heading angle and the dynamic inner loop of the yaw rate. This achieves strict full-state constraints on the heading tracking error and the bow turning rate, effectively avoids dangerous angular velocity overshoot, and ensures that the actual motion state of the ship always operates within the preset safety boundary.

[0034] (2) To address the "differential explosion" problem in traditional backstepping methods and the integral saturation problem caused by the physical limiting of actual servo motors, this invention introduces fixed-time dynamic surface control technology. This involves obtaining smooth virtual control commands (virtual control laws) through the constructed filter dynamic equations to reduce phase lag in command tracking and ensure fixed-time convergence. Simultaneously, a nonlinear integral sliding surface with sinusoidal modification terms and finite-time auxiliary system state variables are designed to precisely counteract the nonlinear error impact generated by the actuator when the input is saturated, resulting in smoother control output and significantly reducing mechanical fatigue.

[0035] (3) In response to the problems of unknown complex hydrodynamic models of ships and disturbances from variable marine environments, this invention uses radial basis neural networks to approximate the nonlinear uncertainties of the ship model online, and designs a parameter adaptive law with correction terms to dynamically estimate the upper bound of time-varying external disturbances. The estimated values ​​of the two are fed back to the design process of the controller for collaborative feedforward compensation to construct a control law for ship heading control. Thus, the model perturbation and external disturbances are accurately decoupled without the need for precise model parameters. Attached Figure Description

[0036] 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.

[0037] Figure 1 The flowchart shows the ship heading control method of the present invention, which considers asymmetric full-state constraints and intelligent approximation. Figure 2 This is a schematic diagram of the basic framework of the method described in this embodiment; Figure 3 This is a graph showing the change of the ship's heading over time in this embodiment; Figure 4 This is a graph showing the change in ship heading tracking error over time in this embodiment; Figure 5 This is a graph showing the angular velocity tracking of the bow in this embodiment; Figure 6 This is a diagram showing the tracking error of the bow angular velocity in this embodiment; Figure 7 This is a graph showing the change in rudder angle in this embodiment; Figure 8 This is a diagram showing the convergence error of the fixed-time filter in this embodiment; Figure 9 This is a curve showing the actual lateral position of the ship in this embodiment; Figure 10This is a fitting graph of the nonlinear terms of the model in this embodiment. Detailed Implementation

[0038] 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.

[0039] This embodiment provides a ship heading control method that considers asymmetric full-state constraints and intelligent approximation, such as... Figure 1 As shown, the specific steps include: S1: Obtain a responsive ship mathematical model that takes into account input saturation; Specifically, the responsive ship mathematical model is as follows: (1) (2) In the formula: and These represent the ship's heading angle and turning angular velocity, respectively. g and These represent the system uncertainty and the external disturbances experienced by the ship model, respectively. This indicates the input rudder angle that is subject to saturation limitations; Represents the cyclicity index; Indicates the following index; Indicates the upper bound of the control input; Indicates the lower bound of the control input; Indicates the actual control input; express The first derivative.

[0040] This embodiment also includes preliminary knowledge: 1) Lemma Lemma 1: For any For a value greater than 0, the following inequalities exist: (3) In the formula: For any variable, It can be any number.

[0041] Lemma 2: For any definition on a compact set Continuous smooth function on ,have (4) In the formula: To approximate the error, for all There exists a vector >0, and satisfy ; The weight vector under ideal conditions is usually difficult to obtain and is an unknown variable, so it needs to be estimated. for Transpose of; Let be a Gaussian function, and its expression is shown in equation (5).

[0042] (5) In the formula: , where is the number of network nodes; The input center vector; is the standard deviation of the Gaussian function.

[0043] Lemma 3: Consider a dynamic system ,in For the state of the system, It is the equilibrium point of the system if a Lyapunov function exists. If equation (6) is satisfied, then the system is actually fixed-time stable, and the settling time is... satisfy ;in, , , , , , . (6) Lemma 4: If , , , , ,and Then there exists an inequality: (7) 2) Assumption Assumption 1: External disturbances experienced by the ship It is a time-varying perturbation, bounded with an unknown limit, and has a first derivative. Assumption 2: The ship's desired course It is smooth and has first and second derivatives.

[0044] S2: Define the heading tracking error based on the responsive ship mathematical model; based on the heading tracking error, obtain the first asymmetric constraint that the heading error must satisfy according to a preset performance function based on exponential decay; design an outer-loop logarithmic error transformation function based on the first asymmetric constraint to construct a virtual control law; filter the virtual control law based on the designed filter dynamic equation to obtain a filtered signal; define the bow turning angular velocity tracking error based on the filtered signal; based on the bow turning angular velocity tracking error, obtain the second asymmetric constraint that the bow turning angular velocity tracking error must satisfy according to a novel smoothing performance function based on hyperbolic tangent; design an inner-loop logarithmic transformation function based on the second asymmetric constraint. The specific steps include: S21: Based on the responsive ship mathematical model, the heading tracking error is defined as: (8) In the formula: Indicates heading tracking error; Indicates the desired heading angle; Differentiating both sides of equation (8), we can obtain: (9) S22: Design a preset performance function based on exponential decay as follows: (10) In the formula: , , Indicates a pre-designed positive parameter; This represents a preset performance function based on exponential decay. express The abbreviated form; S23: Based on the heading tracking error and a preset performance function based on exponential decay, the first asymmetric constraint that the heading error must satisfy is: (11) In the formula: , This indicates a positive parameter designed based on a preset range of constraints; S24: In order to transform the constrained error into an unconstrained system, an outer-loop logarithmic error transformation function is designed based on the first asymmetric constraint. for: (12) Differentiating equation (12) yields: (13) S25: From equations (9) and (12), it can be seen that in order to make Achieving convergence, i.e., based on the outer-loop logarithmic error transformation function The virtual control law is constructed as follows: (14) In the formula: Represents a virtual control law; express The first derivative; express The first derivative; Indicates control gain; S26: Based on the designed filter dynamic equation, the virtual control law is filtered to obtain the filtered signal; and the filter dynamic equation is: (15) In the formula: Indicates the filtered signal; express The first derivative; Indicates the filter tracking error; Represents the filter gain constant and ; Denotes the fractional power parameter that guarantees convergence in a fixed time and In this embodiment, the backstepping control design... It is the key intermediate variable connecting the outer loop kinematics and the inner loop dynamics, and the original virtual control law generated by the outer loop design. Typically, these terms contain complex algebraic terms, and directly taking their analytical derivatives can lead to a serious "differential explosion" problem and easily amplify sensor noise; therefore, the fixed-time filter shown in equation (15) is introduced. Perform smoothing; Replaced the original As the actual tracking command for the inner loop bow angular velocity control, it avoids the complex analytical differentiation process; According to Lemma 3, the final formula for solving the fixed-time convergence upper bound of the filter is: (16) From equation (15), we can know that when When it approaches 0, it can be simplified to: (17) Design the Lyapunov function as follows: (18) Differentiating equation (18) and substituting equation (17) into it, we can obtain: (19) From equation (19), we can know that According to Lyapunov's stability theorem, assuming the turning angular velocity perfectly tracks the virtual control command, the outer-loop kinematic system is asymptotically stable, and the heading tracking error... It can always remain within the preset asymmetric boundary.

[0045] S27: Define the steering angular velocity tracking error based on the filtered signal. for: (20) S28: To mitigate control chattering at the initial moment, a novel smoothing performance function based on hyperbolic tangent is designed. for: (twenty one) In the formula: , Indicates a pre-designed positive parameter; Based on the bow angular velocity tracking error and a novel smoothing performance function based on hyperbolic tangent, the second asymmetric constraint that the bow angular velocity tracking error must satisfy is: (twenty two) In the formula: , This indicates a positive parameter designed based on a preset range of constraints; express The abbreviated form; S29: Design the inner loop logarithmic transformation function based on the second asymmetric constraint. for: (twenty three) Differentiating equation (23) yields: (twenty four) In the formula: The nonlinear transformation partial derivative of BLF is expressed as follows: This is used to map saturation error to the conversion error space for accurate compensation; S3: Construct the state variables of the finite-time auxiliary system, and obtain the compensation tracking error based on the state variables of the finite-time auxiliary system and the inner-loop logarithmic transformation function; design a nonlinear integral sliding surface based on the compensation tracking error; obtain the actual control input containing the system uncertainty terms of the ship model and the external disturbances it receives based on the nonlinear integral sliding surface; The specific steps include: S31: To compensate for the nonlinear error caused by input saturation, the state variables of the finite-time auxiliary system are constructed, and their corresponding expressions are as follows: (25) In the formula: Indicates the dissipation gain of the auxiliary system and ; Denotes a fractional power that is guaranteed to converge in finite time. ; Indicates input saturation error and ; Representing the state variables of a finite-time auxiliary system The first derivative; S32: Obtain the compensation tracking error based on the state variables of the finite-time auxiliary system and the inner-loop logarithmic transformation function. for: (26) S33: To eliminate steady-state errors and further improve the robustness of the system, the nonlinear integral sliding surface is designed based on the aforementioned compensation tracking error as follows: (27) In the formula: Indicates the design parameters of the sliding surface and ; express The simplified form; taking the derivative of equation (28) yields: (28) To ensure that the system state reaches and remains on the sliding surface, the following reaching law is selected: (29) S34: The actual control input, including the system uncertainties of the ship model and the external disturbances it experiences, is obtained based on the nonlinear integral sliding surface: (30) In the formula: Indicates design constants; Indicates external interference The upper bound and satisfying ; express The abbreviated form; Represents the reaching law gain and ; This indicates the design parameters, i.e., the boundary layer thickness. .

[0046] S4: Approximate the system uncertainty terms using a radial basis function neural network to obtain estimated values ​​of the system uncertainty terms; construct a parameter adaptive law to compensate for external disturbances; based on the parameter adaptive law and the estimated values ​​of the system uncertainty terms, combined with the actual control input obtained in S3, obtain a control law for ship heading control, so as to realize ship heading control considering asymmetric full-state constraints and intelligent approximation, specifically including the following steps: S41: Because of equation (30), which is the equivalent control law and Since all are unknown, the solution involves two steps: first, address the uncertainties in the model. The system's unknowns are approximated using a radial basis function neural network (RBF) control algorithm. Because RBF neural networks have strong learning capabilities, they can approximate arbitrary functions, avoiding tedious mathematical analysis and exhibiting fast convergence speed. In this embodiment, the system's uncertainties are approximated using a radial basis function neural network to obtain estimated values. : For ideal network weights To make the approximation error Minimum weight vector value Its expression is: (31) The ideal network weights in this embodiment are unattainable in practical applications, therefore, when calculating the network weights... The fitting process requires the use of The estimated value Thus obtain The estimated value Assume there exists a constant greater than zero. , making ,have to The expression is: (32) (33) In the formula: The weights of a radial basis function neural network The ideal network weights; Represents the space of real numbers; Represents the Gaussian function; express Estimating network weights; Indicates the approximation error; This represents the adaptive law of weights; Indicate design parameters and ; S42: The upper bound of the disturbance is estimated using a parameter adaptive law with a correction term to compensate for external disturbances. The parameter adaptive law with the correction term is used to construct the parameter adaptive law for compensating for external disturbances as follows: (34) In the formula: Indicate design parameters and ; express The prior estimate; express The estimated value; express The first derivative; S43: Based on the parameter adaptive law and the estimated value of the system uncertainty, combined with the actual control input obtained in S3, the control law for ship heading control is obtained as follows: (35) Based on the control law for ship heading control, ship heading control considering asymmetric full-state constraints and intelligent approximation is achieved.

[0047] This embodiment also includes: The Lyapunov function for a closed-loop system is designed as follows: (36) In the formula: For parameter estimation error; This represents the weight estimation error.

[0048] Differentiating equation (36) and substituting equations (25) to (35) into the equation and simplifying, we get: (37) because Using Young's inequality and the lemma in Lemma 1, we can define and shrink equation (37): Regarding external interference: (38) Because the preset performance control ensures that the system does not exceed the limits, There exists an upper bound. Therefore, this term is bounded.

[0049] Then consider the following inequality: (39) (40) (41) (42) Substitute the above inequality into equation (37) and discard the negative fixed term. and Finally obtained (43) In the formula: (44) As the sum of residual error bounds, it can be known from equation (43) that the system V 2 is stable, therefore V 2 variables s , , , It can also converge to a bounded region. Because s , There is a boundary, so r e , It is bounded. And because... , There is a boundary, so It also has boundaries. Because... , Bounded, therefore the weights of the RBF function It is also bounded. Therefore, all error signals in ship heading control are bounded.

[0050] To ensure the stability of the closed-loop system, the design parameters must meet the following requirements. ; make (45) Equation (43) can be written as a standard differential inequality: (46) The method described in this embodiment addresses the aforementioned deficiencies in the prior art and aims to solve the following technical problems: (1) Solving the problem that the prior art cannot simultaneously consider both heading tracking and large-angle turning safety: The method described in this embodiment needs to solve how to simultaneously impose strict transient and steady-state constraints on the heading angle error and yaw rate of the ship, avoid dangerous yaw rate overshoot during large-angle turning, and thus ensure the absolute physical safety of the ship in the restricted navigation space. (2) Solving the problem of integral saturation and control oscillation caused by the physical constraints of the actuator: The method described in this embodiment needs to solve how to accurately offset the nonlinear impact of input saturation on system stability under the actual working conditions of fixed physical dead zones and amplitude limits of the servo motor, alleviate the mechanical fatigue of the actuator, and make the actual control output smoother. (3) Solving the problem of "differential explosion" and command tracking phase lag in backstep control: The present invention needs to solve how to obtain smooth virtual control commands and their derivatives without amplifying sensor measurement noise, and ensure that the filtering error can quickly converge to the minimum neighborhood within a fixed time without depending on the initial state. (4) Solving the problem of unknown model parameters and difficulty in accurately compensating for external disturbances under complex sea conditions: The method described in this embodiment needs to solve how to achieve online approximation of nonlinear perturbation terms and dynamically capture the upper bound of time-varying ocean disturbances in the absence of an accurate ship hydrodynamic model, so as to achieve accurate decoupling and feedforward compensation of model uncertainty and external disturbances, and improve the composite disturbance rejection accuracy of the closed-loop system.

[0051] Figure 2 The figure shows the basic framework of the method described in this embodiment. Indicates the ship's desired course; This refers to the ship's actual course and actual turning angular velocity; Indicates heading tracking error; This represents the heading tracking error after passing through the Lyapunov function constraint of the obstacle; Indicates the ship's desired bow turning angular velocity; This indicates the ship's actual speed in both the longitudinal and lateral directions; For virtual control law tracking error; For auxiliary system state variables; The tracking error of the virtual control law after limitation; Represents a nonlinear integral sliding surface; Input the ideal ship rudder angle; Due to external disturbances and neural network estimation error The upper bound of the composite perturbation. for The estimated value; These are the uncertainties in the model; For ideal weights in a neural network, for The estimated value. The specific process of the method described in this embodiment is as follows: first, the actual course of the ship is estimated. Obtain by limiting Regarding the desired course Obtain by limiting The actual course after restrictions With restrictions on the expected course The difference yields a new error. Through new errors Design the desired turning angular velocity. Then, by comparing the actual bow angular velocity with the desired bow angular velocity... The difference yields the virtual control law tracking error. Then to Obtain by limiting Combined with auxiliary variables Design ,according to Design of nonlinear sliding surfaces Finally, combined with the adaptive law , Design the rudder angle Make the sliding surface Once converged to near the stable region, the heading tracking error will be located on the sliding surface. Slide it up so that converges to , converges to This enables course tracking.

[0052] To verify the effectiveness of the ship's course-keeping controller, the method described in this embodiment uses the Dalian Maritime University's Yu Kun ship as a simulation ship model. After substituting the parameters, the ship's nonlinear mathematical model in equation (1) is used as the simulation model. The relevant ship parameters are shown in Table 1: Table 1. Main parameters of the "Yu Kun" ship

[0053] Ship Followability Index Cyclicality index Model parameters , The ship's initial heading is set to 2°; external time-varying disturbances. , change rudder angle Reference heading The controller parameters are: , , , , , , , , , Based on the constraint range of BLF on the bow angular velocity, the center point of the Gaussian kernel function... Take in Evenly distributed on top In the experiment, to verify the speed, accuracy, and stability of the method described in this embodiment, an unconstrained sliding mode control algorithm under the same conditions was used as a control group for comparative experiments. The method described in this embodiment is denoted as "AFSC," and the adaptive sliding mode control algorithm without full-state constraints is denoted as "ASMC." The controller parameters for both control algorithms were optimized to ensure the fairness of the comparative experiment. For the accuracy of ship heading maintenance and the response time of the system output, MAE and RMSE were used as evaluation indicators; RMSE is mainly used to measure the stability and robustness of the system's transient response. To fully verify the superiority of the method described in this embodiment, the above indicators were quantitatively calculated and compared for the heading angle error and the bow turning angular velocity error, respectively.

[0054] (47) In the formula: The end time; This is the start time; For reference only; Let t be the system state at time t. Figure 3 and Figure 4 These are, respectively, the ship's heading versus time curve and the ship's heading tracking error versus time curve, with the ship's initial heading and bow turning angular velocity being... .Depend on Figure 3 It can be seen that the controller designed by the method described in this embodiment is in Convergence had already been completed, while ASMC controller convergence takes more than ten seconds; according to Figure 4 It can be determined that the heading error convergence of the method described in this embodiment is superior to that of the ASMC controller. Evaluation metrics for the two algorithms were calculated using data generated from simulation experiments, as shown in Table 2: Table 2. Heading Tracking Evaluation Indicators

[0055] As can be seen from Table 2, in terms of heading tracking, AFSC improved MAE by 31.85% and RMSE by 5.87% compared to ASMC.

[0056] Figure 5 and Figure 6 This shows the bow angular velocity tracking curve and the bow angular velocity tracking error curve. (From...) Figure 5It can be seen that both the controller in this paper and the ASMC controller can track virtual angular velocities, but the convergence speed and tracking performance of the method described in this embodiment are significantly better than those of ASMC. Figure 6 The tracking error performance and convergence time are both better than ASMC. The evaluation indicators of the virtual control quantity are shown in Table 3. Table 3. Evaluation Indicators for Virtual Control Quantities

[0057] As can be seen from Table 3, in terms of virtual control law tracking, AFSC improves MAE by 50.77% and RMSE by 8.07% compared to ASMC.

[0058] Depend on Figure 7 It can be seen that the method described in this embodiment is smoother in the initial stage of control than ASMC without saturation compensation, but both are limited to within 35°. Figure 8 The figure shows the filter convergence error. Based on the selected fixed-time filter parameters, the upper limit of its absolute convergence time can be calculated using theoretical formulas. The filter error can converge rapidly, thus ensuring waveform smoothness while producing almost no hysteresis. Figure 9 This demonstrates that the designed adaptive parameter law successfully estimates the upper bound of the disturbance. Utilizing this upper bound, the controller can generate a sufficiently strong control input to counteract the disturbance in the worst-case scenario, thereby ensuring the stability and tracking accuracy of the closed-loop system. Figure 10 The figure shows a comparison of the online identification and fitting results of the nonlinear terms in the model based on the RBF neural network in a ship heading control system. As can be seen from the figure, there are slight local deviations in the fitting results due to the approximation error of the neural network, the coupling effect of external time-varying disturbances, and the instantaneous dynamics during the network weight update process. This deviation is controlled within a very small range, which verifies the effectiveness and stability of the algorithm. Overall, the RBF neural network involved in the method described in this embodiment can fit the nonlinear terms in the ship's nonlinear response mathematical model, providing accurate feedforward compensation information for the controller. In conclusion, the simulation experiment in this embodiment can verify the effectiveness and effect of the method described in this embodiment.

[0059] Through comparative simulation experiments with existing research, the method described in this embodiment demonstrates that the proposed composite robust heading control method based on asymmetric full-state constraints effectively solves the problem of absolute physical safety of ship navigation in complex and constrained sea conditions, and accelerates the smooth tracking rate of commands. Using Lyapunov stability theory, it is rigorously proven that all signals within the closed-loop system achieve semi-globally consistent eventual boundedness, and that the heading angle error and yaw rate remain strictly within the preset asymmetric limits throughout the entire control process. The designed fixed-time dynamic surface filter completely eliminates the "differential explosion" phenomenon, and the finite-time auxiliary system effectively handles the nonlinear terms caused by the physical saturation of the steering gear. Both theoretical analysis and comparative simulation results show that the method described in this embodiment not only greatly improves the accuracy and disturbance rejection stability of ship heading, but its effectiveness and feasibility for engineering applications are also fully verified.

[0060] 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 ship heading control method considering asymmetric full-state constraints and intelligent approximation, characterized in that, The specific steps include: S1: Obtain a responsive ship mathematical model that takes into account input saturation; S2: Define the heading tracking error according to the responsive ship mathematical model; based on the heading tracking error, obtain the first asymmetric constraint that the heading error must satisfy according to the preset performance function based on exponential decay; design an outer loop logarithmic error transformation function based on the first asymmetric constraint to construct a virtual control law; filter the virtual control law based on the designed filter dynamic equation to obtain the filtered signal; Define the bow angular velocity tracking error based on the filtered signal; based on the bow angular velocity tracking error, obtain the second asymmetric constraint that the bow angular velocity tracking error must satisfy according to a novel smoothing performance function based on hyperbolic tangent; design the inner loop logarithmic transformation function based on the second asymmetric constraint; S3: Construct the state variables of the finite-time auxiliary system, obtain the compensation tracking error based on the state variables of the finite-time auxiliary system and the inner-loop logarithmic transformation function; design a nonlinear integral sliding surface based on the compensation tracking error; The actual control input, including the system uncertainty terms of the ship model and the external disturbances it experiences, is obtained based on the nonlinear integral sliding surface. S4: Approximate the system uncertainty terms using a radial basis function neural network to obtain estimated values ​​of the system uncertainty terms; construct a parameter adaptive law for compensating for external disturbances; based on the parameter adaptive law and the estimated values ​​of the system uncertainty terms, combine the actual control input obtained in S3 to obtain a control law for ship heading control, so as to realize ship heading control considering asymmetric full-state constraints and intelligent approximation.

2. The ship heading control method considering asymmetric full-state constraints and intelligent approximation according to claim 1, characterized in that, The responsive ship mathematical model described in S1 is: In the formula: and These represent the ship's heading angle and turning angular velocity, respectively. g and These represent the system uncertainty and the external disturbances experienced by the ship model, respectively. This indicates the input rudder angle that is subject to saturation limitations; Represents the cyclicity index; Indicates the following index; Indicates the upper bound of the control input; Indicates the lower bound of the control input; Indicates the actual control input; express The first derivative.

3. The ship heading control method considering asymmetric full-state constraints and intelligent approximation according to claim 2, characterized in that, S2 specifically includes the following steps: S21: Based on the responsive ship mathematical model, the heading tracking error is defined as: In the formula: Indicates heading tracking error; Indicates the desired heading angle; S22: Design a preset performance function based on exponential decay as follows: In the formula: , , Indicates a pre-designed positive parameter; This represents a preset performance function based on exponential decay. express The abbreviated form; S23: Based on the heading tracking error and a preset performance function based on exponential decay, the first asymmetric constraint that the heading error must satisfy is: In the formula: , This indicates a positive parameter designed based on a preset range of constraints; S24: Design the outer loop logarithmic error transformation function based on the first asymmetric constraint. for: S25: Based on outer loop logarithmic error transformation function The virtual control law is constructed as follows: In the formula: Represents a virtual control law; express The first derivative; express The first derivative; Indicates control gain; S26: Based on the designed filter dynamic equation, the virtual control law is filtered to obtain the filtered signal; and the filter dynamic equation is: In the formula: Indicates the filtered signal; express The first derivative; Indicates the filter tracking error; Represents the filter gain constant and ; Denotes the fractional power parameter that guarantees convergence in a fixed time and ; S27: Define the steering angular velocity tracking error based on the filtered signal. for: S28: Design a novel smoothing performance function based on hyperbolic tangent for: In the formula: , Indicates a pre-designed positive parameter; Based on the bow angular velocity tracking error and a novel smoothing performance function based on hyperbolic tangent, the second asymmetric constraint that the bow angular velocity tracking error must satisfy is: In the formula: , This indicates a positive parameter designed based on a preset range of constraints; express The abbreviated form; S29: Design the inner loop logarithmic transformation function based on the second asymmetric constraint. for: 。 4. The ship heading control method considering asymmetric full-state constraints and intelligent approximation according to claim 3, characterized in that, S3 specifically includes the following steps: S31: Construct the state variables of the finite-time auxiliary system, and the corresponding expression is: In the formula: Indicates the dissipation gain of the auxiliary system and ; Denotes a fractional power that is guaranteed to converge in finite time. ; Indicates input saturation error and ; Representing the state variables of a finite-time auxiliary system The first derivative; This represents the nonlinear transformation partial derivative of BLF; S32: Obtain the compensation tracking error based on the state variables of the finite-time auxiliary system and the inner-loop logarithmic transformation function. for: S33: Based on the aforementioned compensation tracking error, the nonlinear integral sliding surface is designed as follows: In the formula: Indicates the design parameters of the sliding surface and ; express The abbreviated form; S34: The actual control input, including the system uncertainties of the ship model and the external disturbances it experiences, is obtained based on the nonlinear integral sliding surface: In the formula: Indicates design constants; Indicates external interference The upper bound and satisfying ; express The abbreviated form; Represents the reaching law gain and ; Indicate design parameters and .

5. A ship heading control method considering asymmetric full-state constraints and intelligent approximation according to claim 4, characterized in that, S4 specifically includes the following steps: S41: Approximate the system uncertainty terms using a radial basis function neural network to obtain the estimated values ​​of the system uncertainty terms. Its expression is: In the formula: The weights of a radial basis function neural network The ideal network weights; Represent the space of real numbers; Represents the Gaussian function; express Estimating network weights; Indicates the approximation error; This represents the adaptive law of weights; Indicate design parameters and ; S42: The adaptive law for compensating for external disturbances is constructed as follows: In the formula: Indicate design parameters and ; express The prior estimate; express The estimated value; express The first derivative; S43: Based on the parameter adaptive law and the estimated value of the system uncertainty, combined with the actual control input obtained in S3, the control law for ship heading control is obtained as follows: Based on the control law for ship heading control, ship heading control considering asymmetric full-state constraints and intelligent approximation is achieved.

Images