Global finite-time ship trajectory tracking control method considering input-output constraints

Abstract

The application discloses a global finite time ship trajectory tracking control method considering input and output limitations, S1: a mathematical model of an underactuated ship is established; S2: a trajectory tracking error is obtained based on an actual trajectory and an expected trajectory, a new error is obtained by limiting the trajectory tracking error, and an expected longitudinal velocity and an expected transverse velocity are designed based on the new error; S3: a first finite time sliding mode surface and a second finite time sliding mode surface are designed; S4: a longitudinal control force and a bow shaking control moment are designed; S5: the finite time sliding mode surface is adjusted to convergence through the longitudinal control force and the bow shaking control moment, and then the trajectory tracking error is converged, and finally, the ship trajectory tracking is realized. Under the condition of considering input limitation, the mathematical model of the underactuated ship is established, under the condition of considering output limitation, the trajectory tracking error is limited, so that the transient and steady state performances are ensured, the sailing trajectory is within the preset range, and the ship sailing safety is ensured.

Description

Technical Field

[0001] This invention relates to the field of ship trajectory control technology, and in particular to a global finite-time ship trajectory tracking control method that takes into account input and output limitations. Background Technology

[0002] Over the past two decades, with the widespread application of underactuated vessels in environmental surveying, marine sampling, and maritime rescue, the tracking and control of underactuated vessels has received increasing attention in the fields of control engineering and marine engineering. To accomplish these tasks, precise vessel control and improved control performance are typically required. However, the lack of lateral control input, the time-varying nature of external disturbances, and the presence of model uncertainties significantly complicate precise vessel control. Current control methods, which fail to consider input / output constraints, do not reflect real-world control conditions, resulting in insufficient control accuracy. Furthermore, the lack of consideration for accelerating error convergence leads to slower convergence rates, impacting navigation safety. Therefore, effectively accelerating error convergence while considering input / output constraints, effectively resisting unknown disturbances, and improving the vessel's trajectory tracking rate and accuracy are urgent problems to be solved. Summary of the Invention

[0003] This invention provides a global finite-time ship trajectory tracking control method that considers input and output constraints, in order to overcome the technical problems of existing technologies that do not consider input and output constraints, do not conform to actual control conditions, and result in insufficient control accuracy. At the same time, they do not consider accelerating the error convergence rate, which leads to a slower error convergence rate and affects navigation safety.

[0004] To achieve the above objectives, the technical solution of the present invention is as follows:

[0005] A global finite-time ship trajectory tracking control method considering input and output constraints, comprising the following steps:

[0006] S1: Establish a mathematical model for an underactuated ship, considering the input constraints.

[0007] S2: The trajectory tracking error is obtained based on the actual trajectory and the desired trajectory of the underactuated ship mathematical model.

[0008] Then, considering the output constraints, the trajectory tracking error is constrained by combining the preset performance function and the obstacle Lyapunov function to obtain a new error. Based on the new error, the desired longitudinal velocity and desired lateral velocity are designed.

[0009] S3: design the first linear anti-windup compensator and the second linear anti-windup compensator, combine the finite time convergence theory, and design the first finite time sliding mode surface based on the actual longitudinal velocity of the underactuated ship mathematical model, the expected longitudinal velocity, and the first state variable in the first linear anti-windup compensator; design the second finite time sliding mode surface based on the actual lateral velocity of the underactuated ship mathematical model, the expected lateral velocity, and the second state variable in the second linear anti-windup compensator;

[0010] S4: design the first disturbance observer and the second disturbance observer, obtain the first total disturbance estimation value based on the first disturbance observer, and obtain the second total disturbance estimation value based on the second disturbance observer; design the longitudinal control force based on the first finite time sliding mode surface and the first total disturbance estimation value; design the bow yaw control torque based on the second finite time sliding mode surface and the second total disturbance estimation value;

[0011] S5: adjust the first finite time sliding mode surface and the second finite time sliding mode surface through the longitudinal control force and the bow yaw control torque, make the first finite time sliding mode surface and the second finite time sliding mode surface converge, and then make the trajectory tracking error converge, so as to finally realize the ship trajectory tracking.

[0012] Further, in S1, under the condition of considering input limitation, the underactuated ship mathematical model is established as follows:

[0013] (3)

[0014] wherein

[0015] (4)

[0016] wherein, are the forward displacement, lateral displacement, and bow angle of the ship, respectively; are the longitudinal velocity, lateral velocity, and bow yaw angular velocity of the ship in the appendage coordinate system, respectively; is the actual ship longitudinal control force considering the limitation, is the actual bow yaw control torque considering the limitation; are inertia parameters, respectively; are hydrodynamic parameters, respectively; , , are uncertain terms of the ship model, respectively; are external unknown disturbances, respectively; is the upper limit of the control input; is the ideal longitudinal control force, is the ideal bow yaw control torque; is the difference between the actual longitudinal control force and the ideal longitudinal control force, is the difference between the actual bow yaw control torque and the ideal bow yaw control torque.

[0017] Furthermore, in S2, the trajectory tracking error is obtained based on the actual trajectory and the desired trajectory of the underactuated ship mathematical model. Then, considering output constraints, the trajectory tracking error is constrained by a preset performance function and a barrier Lyapunov function to obtain a new error. The process of designing the desired longitudinal velocity and desired lateral velocity based on the new error is as follows:

[0018] S21: The trajectory tracking error, obtained from the actual trajectory and the desired trajectory of the underactuated ship mathematical model, is expressed as:

[0019] (3)

[0020] In the formula, and These are the vertical and horizontal coordinates of the ship's desired trajectory, respectively. and These are the longitudinal trajectory tracking error and the lateral trajectory tracking error, respectively. These are the ship's forward displacement and lateral drift displacement, respectively, i.e., the output.

[0021] S22: Considering the output constraints, the trajectory tracking error is limited by combining a preset performance function and an obstacle Lyapunov function, resulting in a new error expression as follows:

[0022] (4)

[0023] (5)

[0024] (6)

[0025] In the formula, , All of these are positive parameters that need to be designed; , , All are positive parameters that need to be designed;

[0026] S23: The expected longitudinal velocity and expected lateral velocity based on the new error design are expressed as follows:

[0027] (7).

[0028] Furthermore, in S3, the first linear anti-saturation compensator is designed as follows:

[0029] (twenty one)

[0030] Actual longitudinal velocity based on underactuated ship mathematical model Desired longitudinal velocity and the first state variable in the first linear anti-saturation compensator The process of designing the first finite-time sliding surface is as follows:

[0031] make

[0032] (twenty two)

[0033] The first finite-time sliding surface of the design As shown in equation (23):

[0034] (twenty three)

[0035] In the formula, , All are positive parameters that need to be designed; This is the first state variable;

[0036] Differentiating equation (23) and combining it with equations (1) and (22), we can obtain:

[0037] (twenty four)

[0038] The designed second linear anti-saturation compensator is represented as follows:

[0039] (25)

[0040] In the formula, It is the second state variable;

[0041] Based on actual lateral velocity Desired lateral velocity and the second state variable in the second linear anti-saturation compensator The process of designing the second finite-time sliding surface is as follows:

[0042] make

[0043] (26)

[0044] The second finite-time sliding surface designed As shown in equation (27):

[0045] (27)

[0046] make

[0047] (28)

[0048] but

[0049] (29)

[0050] Utilizing dynamic surface techniques and introducing new variables As The output of the first-order low-pass filter, thereby avoiding interference with the output of the filter. f The problem of differential explosion arises from differentiation, and the expression for the dynamic surface technique is as follows:

[0051] (30)

[0052] In the formula, For design parameters, and >0;

[0053] Differentiating equation (27) and combining it with equations (1) and (26), we can obtain:

[0054] (31)

[0055] In the formula, , All of these are positive parameters that need to be designed.

[0056] Furthermore, in S4, the first disturbance observer is designed as shown in equation (32):

[0057] (32)

[0058] In the formula, Positive design parameters For the state variables of the first disturbance observer; , for The estimated value;

[0059] The process of designing the longitudinal control force based on the first finite-time sliding mode surface and the first total disturbance estimate is as follows:

[0060] Combining equations (21), (24), and (32), Designed as follows:

[0061] (33)

[0062] In the formula, , All design parameters are positive;

[0063] The design of the second perturbation observer is shown in equation (34):

[0064] (34)

[0065] In the formula, Positive design parameters For the state variables of the second perturbation observer, , for The estimated value;

[0066] The process of designing the yaw control torque based on the second finite-time sliding surface and the second total disturbance estimate is as follows:

[0067] Combining equations (25), (31), and (34), Designed as follows:

[0068] (35)

[0069] (36)

[0070] In the formula, , All are positive design parameters.

[0071] Beneficial effects: This invention establishes an underactuated ship mathematical model under input constraints. Based on the actual and desired trajectories of the underactuated ship mathematical model, the trajectory tracking error is obtained. Then, considering output constraints, the trajectory tracking error is limited by a preset performance function and a barrier Lyapunov function, thereby ensuring its transient and steady-state performance and keeping the navigation trajectory within a pre-set range, ensuring ship navigation safety. A first and second disturbance observer are designed to observe the total disturbance formed by internal and external disturbances and incorporate it into the design of the longitudinal control force and yaw control torque to counteract the disturbance's influence. For the problem of slow convergence speed, a first and second finite-time sliding surface are designed using finite-time convergence theory to achieve global finite-time convergence, ensuring that the error converges in finite time whether in the approach or sliding phase. Attached Figure Description

[0072] 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.

[0073] Figure 1 This is a flowchart of a global finite-time ship trajectory tracking control method considering input and output limitations in this invention;

[0074] Figure 2 This is a flowchart illustrating the design of a global finite-time ship trajectory tracking control method considering input and output limitations, as described in this invention.

[0075] Figure 3This is a comparison diagram of the expected trajectory and actual trajectory of the ship in the plane in an embodiment of the present invention;

[0076] Figure 4 This is a comparison diagram of the effects of lateral position error in embodiments of the present invention;

[0077] Figure 5 This is a comparison diagram of the effects of longitudinal position error in embodiments of the present invention;

[0078] Figure 6 This is a comparison diagram of lateral velocity errors in an embodiment of the present invention;

[0079] Figure 7 This is a comparison diagram of longitudinal velocity errors in an embodiment of the present invention;

[0080] Figure 8 This is a graph showing the longitudinal control force input in an embodiment of the present invention;

[0081] Figure 9 This is a graph showing the input torque of the bow roll control in an embodiment of the present invention.

[0082] Figure 10 This is a graph showing the disturbance observer estimation curve in an embodiment of the present invention. Detailed Implementation

[0083] 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.

[0084] Ships navigating at sea face various internal and external disturbances. External disturbances typically include drift, speed changes, and rolling caused by wind, waves, and currents. Internal disturbances arise from model uncertainties caused by changes in ship parameters due to cargo loading and unloading, fuel consumption, and food intake. Therefore, both internal and external disturbances must be considered when designing ship controllers. Furthermore, enabling ships to quickly track a reference trajectory from any initial position has always been a key research area in ship motion control. However, increasing the convergence rate inevitably leads to a larger control input. Due to the inherent characteristics of ship actuators, there are certain limits to the control input. Therefore, input constraints must be considered when designing ship controllers; otherwise, the design will be unrealistic. In addition to the above considerations, when a ship performs a specific task, it often needs to accurately track a reference trajectory, requiring the ship to exhibit good transient and steady-state performance under the control of the controller.

[0085] Based on the above, this embodiment provides a global finite-time ship trajectory tracking control method that considers input and output constraints, such as... Figure 1 and Figure 2 As shown, the specific steps include:

[0086] S1: Establish a mathematical model for an underactuated ship, considering the input constraints.

[0087] S2: The trajectory tracking error is obtained based on the actual trajectory and the desired trajectory of the underactuated ship mathematical model.

[0088] Then, considering the output constraints, the trajectory tracking error is constrained by combining the preset performance function and the obstacle Lyapunov function to obtain a new error. Based on the new error, the desired longitudinal velocity and desired lateral velocity are designed.

[0089] S3: Design the first linear anti-saturation compensator and the second linear anti-saturation compensator. Combining the finite-time convergence theory, design the first finite-time sliding surface based on the actual longitudinal velocity, the desired longitudinal velocity, and the first state variable in the first linear anti-saturation compensator of the underactuated ship mathematical model; design the second finite-time sliding surface based on the actual lateral velocity, the desired lateral velocity, and the second state variable in the second linear anti-saturation compensator of the underactuated ship mathematical model.

[0090] S4: Design a first disturbance observer and a second disturbance observer; obtain a first total disturbance estimate based on the first disturbance observer and a second total disturbance estimate based on the second disturbance observer; design longitudinal control force based on the first finite-time sliding surface and the first total disturbance estimate; design yaw control torque based on the second finite-time sliding surface and the second total disturbance estimate.

[0091] S5: By adjusting the first finite-time sliding surface and the second finite-time sliding surface through the longitudinal control force and the yaw control torque, the first finite-time sliding surface and the second finite-time sliding surface converge, thereby reducing the trajectory tracking error and ultimately achieving ship trajectory tracking.

[0092] In a specific embodiment, in S1, considering the input constraints, the established mathematical model of the underactuated ship is as follows:

[0093] (5)

[0094] in

[0095] (6)

[0096] In the formula, These are the ship's forward displacement, lateral drift displacement, and heading angle, respectively. These are the ship's longitudinal velocity, lateral velocity, and bow roll rate in the attached coordinate system, respectively. To account for the actual longitudinal control force of the ship after the restrictions, To account for the actual bow roll control torque after the limitations; These are the inertial parameters; These are the hydrodynamic parameters; , , These are the uncertainties in the ship model; These are unknown external disturbances; To control the upper bound of the input, i.e. the maximum allowed input value, in this embodiment, by... Limit the input, thereby restricting the input to below the maximum value; For ideal longitudinal control force, For ideal bow roll control torque; This is the difference between the actual longitudinal control force and the ideal longitudinal control force. This is the difference between the actual yaw control torque and the ideal yaw control torque.

[0097] In a specific embodiment, in S2, the trajectory tracking error is obtained based on the actual trajectory and the desired trajectory of the underactuated ship mathematical model. Then, considering output constraints, the trajectory tracking error is constrained by a preset performance function and an obstacle Lyapunov function to obtain a new error. The process of designing the desired longitudinal velocity and desired lateral velocity based on the new error is as follows:

[0098] S21: The trajectory tracking error, obtained from the actual trajectory and the desired trajectory of the underactuated ship mathematical model, is expressed as:

[0099] (3)

[0100] In the formula, and These are the vertical and horizontal coordinates of the ship's desired trajectory, respectively. and These are the longitudinal trajectory tracking error and the lateral trajectory tracking error, respectively.

[0101] Specifically, in this embodiment, we assume the ship's desired trajectory. It is smooth and has first and second derivatives.

[0102] S22: Considering the output constraints, the trajectory tracking error is limited by combining a preset performance function and an obstacle Lyapunov function, resulting in a new error expression as follows:

[0103] (4)

[0104] (5)

[0105] (6)

[0106] In the formula, , All of these are positive parameters that need to be designed; , , All are positive parameters that need to be designed;

[0107] Specifically, in formula (3), x This is the output; in this embodiment, it is obtained by analyzing the trajectory tracking error. Restrictions were imposed, and because It is bounded, thus enabling control over the output. x Restrictions.

[0108] S23: The expected longitudinal velocity and expected lateral velocity based on the new error design are expressed as follows:

[0109] (7)

[0110] In this embodiment, since it is necessary to limit the output, according to equation (4), if and If convergence can be achieved, then and Bounded, if and If it is bounded, then , If the new error converges, then the output constraint can be satisfied.

[0111] Differentiating equation (4) yields:

[0112] (8)

[0113] According to equation (8), if we want to make and If all tend to 0, then and Designed as follows:

[0114] (9)

[0115] In the formula, , , , All are positive parameters that need to be designed;

[0116] Combining equations (1), (3), and (9), we can obtain:

[0117] (10)

[0118] when tending to , tending to At that time, that is and When all terms tend to 0, equation (8) can be simplified to:

[0119] (11)

[0120] In this embodiment, Lemma 1 is given: For any For a value greater than 0, the following inequalities exist:

[0121] (12)

[0122] In the formula, It can be any variable.

[0123] Lemma 2: Consider a system , ,in Let V be a continuous function. Suppose there exists a continuous Lyapunov function V: The following conditions can be satisfied: V is a positive definite function, and there exists a real number... , , , And an open-loop neighborhood near the origin satisfies Then the system is practically stable in finite time, and the stability time is... satisfy:

[0124]

[0125] in, For the system The initial value.

[0126] Construct the Lyapunov function as shown in equation (13) to prove... and It can achieve convergence:

[0127] (13)

[0128] Differentiating equation (13) and combining it with equation (11) and Lemma 1, we can obtain:

[0129] (14)

[0130] in

[0131] (15)

[0132] (16)

[0133] (17)

[0134] From Lemma 2, we know that It can achieve finite-time convergence, and the convergence time is... satisfy:

[0135] (18)

[0136] Differentiating and simplifying equation (7), we get:

[0137] (19).

[0138] In a specific embodiment, considering that in actual ship maneuvering, the output of the controller is often limited by the actuator, and excessive control input will cause the ship's propeller and rudder angle to fail to execute, this embodiment uses a linear anti-saturation compensator to handle input saturation in order to solve this problem. The general expression of the linear anti-saturation compensator is shown in equation (20):

[0139] (20)

[0140] In the formula, , For the parameters that need to be designed, These are the state variables of the compensator.

[0141] In a specific embodiment, based on the general expression of the linear anti-saturation compensator, in S3, the designed first linear anti-saturation compensator is expressed as:

[0142] (twenty one)

[0143] Actual longitudinal velocity based on underactuated ship mathematical model Desired longitudinal velocity and the first state variable in the first linear anti-saturation compensator The process of designing the first finite-time sliding surface is as follows:

[0144] make

[0145] (twenty two)

[0146] The first finite-time sliding surface of the design As shown in equation (23):

[0147] (twenty three)

[0148] In the formula, , All are positive parameters that need to be designed; The first state variable is used to eliminate nonlinear terms caused by input saturation. ;

[0149] Differentiating equation (23) and combining it with equations (1) and (22), we can obtain:

[0150] (twenty four)

[0151] The designed second linear anti-saturation compensator is represented as follows:

[0152] (25)

[0153] In the formula, The purpose of this second state variable is to eliminate nonlinear terms caused by input saturation. ;

[0154] Based on actual lateral velocity Desired lateral velocity and the second state variable in the second linear anti-saturation compensator The process of designing the second finite-time sliding surface is as follows:

[0155] make

[0156] (26)

[0157] The second finite-time sliding surface designed As shown in equation (27):

[0158] (27)

[0159] For ease of writing later,

[0160] (28)

[0161] but

[0162] (29)

[0163] Specifically, to avoid directly targeting Differential explosion occurs when performing differentiation. In this embodiment, dynamic surface techniques are used, and the output of a first-order filter can avoid this phenomenon. Direct differentiation introduces a new variable. As The output of the first-order low-pass filter, thereby avoiding interference with the output of the filter. fThe problem of differential explosion arises from differentiation, and the expression for the dynamic surface technique is as follows:

[0164] (30)

[0165] In the formula, For design parameters, and >0;

[0166] Differentiating equation (27) and combining it with equations (1) and (26), we can obtain:

[0167] (31)

[0168] In the formula, , All of these are positive parameters that need to be designed.

[0169] In this embodiment, it is assumed that the rates of change of both external disturbances and internal disturbances experienced by the ship are bounded and satisfy the following:

[0170]

[0171] in, All are greater than 0.

[0172] Based on the above assumptions, in a specific embodiment, the first disturbance observer designed in S4 is as shown in equation (32):

[0173] (32)

[0174] In the formula, Positive design parameters For the state variables of the first disturbance observer; , for The estimated value;

[0175] In this embodiment, the first disturbance observer is used to observe the total disturbance. Conduct observations and record these observations. Join The design process aims to compensate for the impact of disturbances;

[0176] The process of designing the longitudinal control force based on the first finite-time sliding mode surface and the first total disturbance estimate is as follows:

[0177] Combining equations (21), (24), and (32), Designed as follows:

[0178] (33)

[0179] In the formula, , All design parameters are positive;

[0180] The design of the second perturbation observer is shown in equation (34):

[0181] (34)

[0182] In the formula, Positive design parameters For the state variables of the second perturbation observer, , for Observed values;

[0183] The process of designing the yaw control torque based on the second finite-time sliding surface and the second total disturbance estimate is as follows:

[0184] Combining equations (25), (31), and (34), Designed as follows:

[0185] (35)

[0186] (36)

[0187] In the formula, , The design parameters are positive.

[0188] In this embodiment, to verify the stability of the designed controller, a Lyapunov function is defined as shown in equation (37):

[0189] (7)

[0190] In the formula, , .

[0191] Differentiating both sides of equation (37) and substituting them into equations (24), (33), (31), and (35), we get:

[0192] (8)

[0193] In equation (38),

[0194] (9)

[0195] because

[0196] (10)

[0197] Combining equations (32), (34), (39), and (40), equation (38) can be simplified to:

[0198] (11)

[0199] in

[0200] (12)

[0201] (13)

[0202] (14)

[0203] According to equation (41), we can obtain:

[0204] (15)

[0205] in, ,when At that time, there exists Therefore, according to Lemma 2, It can converge to the set region within a finite time. And time satisfy:

[0206] (16)

[0207] because Bounded, therefore In , , , Both are bounded, therefore , It also has boundaries, and because , Bounded, therefore , It is also bounded, thus ensuring that all error signals in the underactuated ship trajectory tracking control system are consistent and eventually bounded.

[0208] In this embodiment, the trajectory tracking error is... and Finite-time stability analysis is performed as follows:

[0209] because as well as Both are bounded, therefore and The derivatives are also bounded, and we assume they are all less than 1. ,but

[0210] (17)

[0211] The Lyapunov function is defined as follows, as shown in equation (48):

[0212] (18)

[0213] Differentiating equation (48) and combining it with equation (47), we get:

[0214] (19)

[0215] According to Lemma 1 and Young's inequality, equation (49) can be transformed into:

[0216] (20)

[0217] in

[0218] (twenty one)

[0219] (twenty two)

[0220] (twenty three)

[0221] According to Lemma 2, It can achieve finite-time convergence, and the time... satisfy:

[0222] (twenty four)

[0223] In summary, trajectory tracking error and Finite-time convergence can be achieved in both the approach phase and the sliding phase, thus achieving global finite-time convergence.

[0224] To verify the effectiveness of the method proposed in this invention, a computer simulation experiment was conducted using a Singapore Customs patrol boat named BAY CLASS as the simulation object. The boat is 38m long and has a mass of [missing information]. kg, other parameters are kg, kg, kg, kg / s, kg / s, kg / s.

[0225] To verify the effectiveness of the ship under the control strategy proposed in this invention, this simulation experiment was divided into two groups: the first group did not use a finite-time sliding surface and did not consider output limitations, specifically... and Sliding surface, control law, parameters , , , The adaptive laws are shown in equations (55), (56), (57) and (58); the second group is the effect of the control strategy of the present invention, the effect of the first group is set as the first group, and the effect of the second group is set as the second group.

[0226] (25)

[0227] (26)

[0228] (27)

[0229] (28)

[0230] To simulate sea conditions, the external time-varying disturbance is represented by equation (59):

[0231] (29)

[0232] Setting parameters , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , .

[0233] Set the uncertainty term of the model as , , Set input limit. , .

[0234] Set the expected trajectory of the sine wave as , The initial position and speed of the ship are selected as... .

[0235] Specifically, the simulation results are as follows: Figures 3 to 10 As shown, from Figure 3 As can be seen, under different control strategies, ships are able to complete trajectory tracking even when input is limited.

[0236] First, from Figure 4 and Figure 5 It can be seen that under the second set of control strategies, the convergence rate of the ship's lateral and longitudinal position errors is faster than that of the first set, and it exhibits better transient and steady-state performance. Secondly, from... Figure 6 and Figure 7 It can be seen that the speed tracking error of the ship can converge to near 0 under the action of the two different control strategies, but from Figure 6 It can be seen that the first control strategy fluctuated around 115 seconds, while the second strategy showed almost no fluctuation. From... Figure 8 and Figure 9 As can be seen, the longitudinal control forces of the two control strategies are almost identical. However, when the control force is limited, the yaw control torque of the first group fluctuates drastically, while the second group remains almost unchanged, demonstrating the superiority of the control strategy of this invention. Finally, from... Figure 10 As can be seen from this, the disturbance observer can estimate the sum of external disturbances and uncertainties in the internal model relatively well. , This is incorporated into the controller design to compensate for the effects of disturbances and improve the tracking accuracy of the control method of this invention.

[0237] Based on the above comparative simulation results, the beneficial effects of this invention can be summarized in the following three points:

[0238] (1) For unknown external disturbances, ship model uncertainties and differential explosion problems, a disturbance observer is used to estimate the total disturbance formed by external disturbances and internal model uncertainties, and dynamic surface technology is used to solve the differential explosion problem.

[0239] (2) To address the convergence speed issue, a controller will be designed based on finite-time convergence theory, and a finite-time sliding surface will be used to achieve global finite-time convergence. First, by adding a finite-time term during the approach phase, the velocity tracking error will achieve finite-time convergence during this phase. Second, by using a finite-time sliding surface, when the error reaches or is near the sliding surface, the velocity error on the sliding surface will also achieve finite-time convergence during the sliding phase due to the special effect of the sliding surface. Simultaneously, to address the input saturation problem, this scheme employs a linear anti-saturation compensator to resolve the nonlinear terms caused by input saturation.

[0240] (3) To address the issue of ship navigation safety, the output is limited by combining a preset performance function and a barrier Lyapunov function, so that the system has good transient and steady-state performance and the navigation trajectory is always within the preset range.

[0241] The global finite-time ship trajectory tracking control method considering input-output constraints proposed in this invention effectively solves the problems of ships operating under unknown external disturbances, model uncertainties, and input-output constraints, thus accelerating the convergence rate of errors. Using Lyapunov theory, it is proven that all signals in the ship system are bounded, and the tracking error can converge within a finite time. Comparison with existing control strategies verifies that the proposed control strategy can achieve output constraints, keeping the navigation trajectory within pre-set limits, and achieving finite-time convergence in both the approach and sliding phases, thus achieving global finite-time convergence. Theoretical analysis and simulation results demonstrate the feasibility of the proposed global finite-time ship trajectory tracking control method considering input-output constraints.

[0242] 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 therein. Such 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 global finite-time ship trajectory tracking control method considering input-output constraints, characterized in that, The specific steps comprise: S1: establishing a mathematical model of the underactuated ship under the condition of considering input limitation; S2: obtaining a trajectory tracking error based on an actual trajectory and an expected trajectory of the mathematical model of the underactuated ship, and then limiting the trajectory tracking error by combining a preset performance function and a barrier Lyapunov function under the condition of considering output limitation, to obtain a new error, and designing an expected longitudinal velocity and an expected lateral velocity based on the new error; S3: designing a first linear anti-windup compensator and a second linear anti-windup compensator, combining a finite time convergence theory, and designing a first finite time sliding mode surface based on an actual longitudinal velocity, the expected longitudinal velocity and a first state variable in the first linear anti-windup compensator of the mathematical model of the underactuated ship, and designing a second finite time sliding mode surface based on an actual lateral velocity, the expected lateral velocity and a second state variable in the second linear anti-windup compensator of the mathematical model of the underactuated ship; S4: designing a first disturbance observer and a second disturbance observer, obtaining a first total disturbance estimation value based on the first disturbance observer, obtaining a second total disturbance estimation value based on the second disturbance observer, designing a longitudinal control force based on the first finite time sliding mode surface and the first total disturbance estimation value, and designing a bow-rolling control moment based on the second finite time sliding mode surface and the second total disturbance estimation value; S5: adjusting the first finite time sliding mode surface and the second finite time sliding mode surface through the longitudinal control force and the bow-rolling control moment, so that the first finite time sliding mode surface and the second finite time sliding mode surface converge, and then the trajectory tracking error converges, and finally the ship trajectory tracking is realized. In S1, the mathematical model of the underactuated ship established under the condition of considering input limitation is:

2. The global finite-time ship trajectory tracking control method considering input-output constraints according to claim 1, characterized in that, wherein (1) In S2, the trajectory tracking error is obtained based on an actual trajectory and an expected trajectory of the mathematical model of the underactuated ship, and then the trajectory tracking error is limited by combining a preset performance function and a barrier Lyapunov function under the condition of considering output limitation, to obtain a new error, and the process of designing an expected longitudinal velocity and an expected lateral velocity based on the new error is: (2) wherein, respectively denote the forward displacement, the cross drift displacement and the heading angle of the ship; respectively denote the longitudinal velocity, the lateral velocity and the yaw angular velocity of the ship in the body-fixed coordinate system; denote the actual longitudinal control force considering the constraints, denote the actual yaw control moment considering the constraints; respectively denote the inertia parameters; respectively denote the hydrodynamic parameters; , , respectively denote the uncertain terms of the ship model; respectively denote the external unknown disturbances; denote the upper bound of the control input; denote the ideal longitudinal control force, denote the ideal yaw control moment; denote the difference between the actual longitudinal control force and the ideal longitudinal control force, denote the difference between the actual yaw control moment and the ideal yaw control moment.

3. The global finite-time ship trajectory tracking control method considering input-output constraints according to claim 2, characterized in that, S21: the trajectory tracking error is obtained based on an actual trajectory and an expected trajectory of the mathematical model of the underactuated ship, and is expressed as: S22: the new error obtained by limiting the trajectory tracking error by combining a preset performance function and a barrier Lyapunov function under the condition of considering output limitation is expressed as: (3) wherein and are the longitudinal and lateral coordinates of the desired trajectory of the ship, respectively; and are the longitudinal and lateral trajectory tracking errors, respectively; are the forward displacement and the lateral drift displacement of the ship, i.e. the outputs. S23: the expected longitudinal velocity and the expected lateral velocity designed based on the new error are expressed as: (4) (5) (6) wherein , are positive parameters to be designed; , , are positive parameters to be designed; In S3, the first linear anti-windup compensator designed is expressed as: (7)。 4. The global finite-time ship trajectory tracking control method considering input-output constraints according to claim 3, characterized in that, Let (21) Actual longitudinal velocity based on a mathematical model of an underactuated ship , desired longitudinal velocity and a first state variable in a first linear anti-windup compensator The process of designing the first finite-time sliding surface is: Derivation is performed on formula (23), and formula (1) and formula (22) are combined to obtain: (22) A first finite-time sliding surface is designed As shown in equation (23): (23) wherein , are positive parameters to be designed; is the first state variable; The second linear anti-windup compensator designed is expressed as: (24) Let (25) In the formula, is a second state variable; based on the actual lateral velocity , the desired lateral velocity and the second state variable in the second linear antisaturation compensator The process of designing the second finite-time sliding surface is: Let (26) Second finite-time sliding surface As shown in equation (27): (27) Then (28) Derivation is performed on formula (27), and formula (1) and formula (26) are combined to obtain: (29) The dynamic surface control technique is used and a new variable is introduced The output of the first-order low-pass filter Thus, the problem of the derivative explosion caused by the derivation of f The expression of the dynamic surface control technique is as follows: (30) wherein is a design parameter, and > 0; In S4, the first disturbance observer designed is shown in formula (32): (31) wherein , are positive parameters to be designed.

5. The global finite-time ship trajectory tracking control method considering input-output constraints according to claim 4, characterized in that, The process of designing a longitudinal control force based on the first finite time sliding mode surface and the first total disturbance estimation value is: (32) wherein is a positive design parameter, is a state variable of the first disturbance observer; , is an estimate of is an estimate of The second disturbance observer designed is shown in formula (34): In conjunction with equations (21), (24) and (32), we have is designed as: (33) wherein , are positive design parameters; The process of designing a bow-rolling control moment based on the second finite time sliding mode surface and the second total disturbance estimation value is: (34) wherein is a positive design parameter, is a state variable of the second disturbance observer, , is an estimated value of . ​ In conjunction with equations (25), (31), and (34), we have is designed to be: (35) (36) wherein , are positive design parameters.

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