Unmanned surface vehicle neural network command filter backstepping control method and system considering input saturation
By employing a neural network command filtering backstepping control method, combined with backstepping and anti-saturation algorithms, the error problem caused by input saturation in unmanned surface vessel trajectory tracking was solved, achieving high-precision and robust trajectory tracking control.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- QINGDAO UNIV
- Filing Date
- 2024-01-30
- Publication Date
- 2026-07-21
AI Technical Summary
The trajectory tracking control of unmanned surface vessels suffers from excessive error due to input saturation. Traditional backstepping methods are computationally complex and fail to effectively handle unknown nonlinearities, resulting in computational explosion and insufficient control accuracy.
A neural network command filtering backstepping control method is adopted, which combines command filtering technology and backstepping method to design an unmanned surface vessel neural network command filtering backstepping controller that considers input saturation. The RBF neural network is used to approximate internal uncertainties, and an anti-saturation algorithm is introduced to constrain the control input.
It improves control accuracy, reduces system steady-state error, enhances control performance, strengthens controller robustness, avoids computational complexity and excessive control input, and achieves high-precision trajectory tracking control.
Smart Images
Figure CN117724347B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of unmanned surface vessel trajectory tracking and control technology, and specifically relates to an unmanned surface vessel neural network command filtering backstepping control method and system that considers input saturation. Background Technology
[0002] Unmanned surface vessels (USVs) are important tools for developing marine resources and safeguarding maritime rights, with significant applications in production and military fields. Compared to traditional manned marine vehicles, USVs can operate in more dangerous waters without concerns about operator safety, and they are more adaptable and can be deployed over a wider range. However, as a coupled and highly uncertain unmanned maritime system, USVs need to navigate and operate in complex sea conditions and environments. Therefore, to ensure that USVs can complete their predetermined tasks as required, they need to possess high-precision maneuverability and adaptive capabilities, which presents a significant challenge to their high-precision trajectory tracking and control.
[0003] Furthermore, due to the physical limitations of the actuators, the unmanned surface vessel (USV) control system inevitably suffers from input saturation. Ignoring input saturation leads to errors between the desired input signal and the actual output signal. Therefore, input saturation is a significant challenge for USV trajectory tracking control. In addition, traditional backstepping methods require repeated differentiation and design of virtual control laws during controller design, directly resulting in excessive computational load and computational explosion. Moreover, these methods require strictly known system parameters and lack the means to handle the widespread unknown nonlinearities present in real-world applications. Summary of the Invention
[0004] To address the technical problem of excessive errors caused by input saturation in current unmanned surface vessel (USV) systems, this invention proposes a neural network command filtering backstepping control method for USVs that considers input saturation, in order to achieve trajectory tracking control of USV systems. To achieve the above objective, this invention adopts the following technical solution:
[0005] A neural network command filtering backstepping control method for unmanned surface vessels considering input saturation includes the following steps:
[0006] Step 1. Establish an unmanned surface vessel model under input saturation conditions and simplify it;
[0007] Step 2. Design backstepping control for the obtained unmanned surface vessel model and construct a neural network command filter backstepping controller for the unmanned surface vessel that considers input saturation;
[0008] Step 3. Track and control the unmanned surface vessel (USV) based on the unmanned surface vessel's neural network command filter backstepping controller.
[0009] Furthermore, based on the unmanned surface vessel (USV) neural network command filtering backstepping control method considering input saturation, this invention also proposes an USV neural network command filtering backstepping control system considering input saturation, which adopts the following technical solution:
[0010] A neural network command filtering backstepping control system for unmanned surface vessels considering input saturation includes:
[0011] The model building module is used to build unmanned surface vessels under input saturation conditions and perform simplification processing;
[0012] The controller design module is used to perform backstepping control design on the obtained unmanned surface vessel model and construct an unmanned surface vessel neural network command filter backstepping controller that considers input saturation.
[0013] And a tracking control module, which uses a neural network command filter backstepping controller for tracking and controlling the unmanned surface vessel.
[0014] Furthermore, based on the aforementioned unmanned surface vessel neural network command filtering backstepping control method considering input saturation, this invention also proposes a computer device comprising a memory and one or more processors.
[0015] The memory stores executable code, and when the processor executes the executable code, it implements the steps of the above-mentioned unmanned surface vessel neural network command filtering backstepping control method considering input saturation.
[0016] Furthermore, based on the aforementioned unmanned surface vessel (USV) neural network command filtering backstepping control method considering input saturation, this invention also proposes a computer-readable storage medium storing a program thereon. When executed by a processor, this program is used to implement the steps of the aforementioned USV neural network command filtering backstepping control method considering input saturation.
[0017] The present invention has the following advantages:
[0018] As described above, this invention discloses a neural network command filtering backstepping control method for unmanned surface vessels (USVs) that considers input saturation. This method combines command filtering technology with backstepping during controller design, solving the "computation explosion" problem and eliminating the impact of filtering errors, thus improving system accuracy. This invention incorporates internal system uncertainties into the controller design, using an RBF neural network to approximate both internal uncertainties and external disturbances, further reducing the system's steady-state error and improving control performance. This invention introduces an anti-saturation algorithm into the USV system, constraining the system's control input, improving the controller's robustness, and making the controller better suited for practical applications. Attached Figure Description
[0019] Figure 1 The flowchart illustrates a neural network command filtering backstepping control method for unmanned surface vessels considering input saturation, as described in an embodiment of the present invention.
[0020] Figure 2 This is a schematic diagram of the overall structure of the controller designed in this embodiment of the invention.
[0021] Figure 3 This is a comparison chart of trajectory tracking curves using the control method of this invention and the fuzzy control method.
[0022] Figure 4 This is a tracking error curve diagram of the three degrees of freedom using the control method of this invention.
[0023] Figure 5 This is a longitudinal error comparison curve between the control method of this invention and the fuzzy control method.
[0024] Figure 6 This is a horizontal error comparison curve between the control method of this invention and the fuzzy control method.
[0025] Figure 7 This is a comparison curve of the heading error using the control method of this invention and the fuzzy control method.
[0026] Figure 8 This is a control input curve diagram using the control method of the present invention.
[0027] Figure 9 This is a virtual control law curve diagram using the control method of this invention. Detailed Implementation
[0028] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:
[0029] Example 1
[0030] This embodiment addresses the technical problem of excessive errors caused by input saturation in current unmanned surface vessel (USV) systems by proposing a neural network command filtering backstepping control method that considers input saturation for trajectory tracking control of USV systems. Specifically, in the controller design, this invention combines command filtering technology with backstepping, solving the "computation explosion" problem and eliminating the impact of filtering errors, thereby improving system accuracy. Furthermore, this invention incorporates internal uncertainties into the controller design, using an RBF neural network to approximate both internal uncertainties and external disturbances, further reducing the system's steady-state error and improving control performance.
[0031] In addition, this invention introduces an anti-saturation algorithm into the system to constrain the system's control input, limiting the rudder and propulsion control inputs to a certain range, thereby improving the system's control effect and avoiding excessive system complexity. This enhances the robustness of the controller and makes it better suited for practical applications.
[0032] like Figure 1 As shown, the neural network command filtering backstepping control method for unmanned surface vessels with input saturation includes the following steps:
[0033] Step 1. Considering the input saturation situation in the actual application of unmanned surface vessels, an unmanned surface vessel model is established. The unmanned surface vessel model is simplified according to the actual application scenario, so that it is close to the actual application situation and easy to design and derive.
[0034] Assuming the unmanned surface vessel has a uniform mass distribution and is symmetrical from left to right, and its center of gravity and center of buoyancy coincide on the Z-plane, to simplify the model and facilitate calculations, only the three degrees of freedom of the unmanned vessel—swell, roll, and yaw—are considered. Its dynamic model on the horizontal plane is then:
[0035]
[0036] in Let x, y, be the position vector in the ground coordinate system. Let represent the lateral distance, longitudinal distance, and bow angle of the unmanned surface vessel, respectively, and υ = (u, v, r). T Let be the velocity vector in the body coordinate system, where u, v, and r represent the linear velocity and y-direction angular velocity, respectively; J(η) is the coordinate transformation matrix, M is the inertia matrix, C(υ) is the Coriolis centripetal force matrix, D(υ) is the damping matrix, τ is the control input vector, and vector b = (b1, b2, b3). T Disturbed by unknown external winds and waves.
[0037]
[0038] Where, m 11 m 22 m 33 These are the components of the inertia matrix on the three coordinate axes; d 11 d 22 d 33 b1, b2, and b3 are the damping torques acting on the hull, respectively; b1, b2, and b3 are the disturbance torques acting on the hull in the three degrees of freedom, respectively.
[0039] Then the model of formula (1) simplifies to:
[0040]
[0041] Where τu τ v τ r These represent the longitudinal control input, lateral control input, and steering control input acting on the system, respectively.
[0042] For formula (2), the control input is affected by saturation nonlinearity, and the saturation of the control input is described as follows:
[0043]
[0044] Where, τ u τ is the longitudinal control input acting on the system. ud For control signals, τ umax and τ umin Let τ be an unknown saturation constant. u =τ umax or τ u =τ umin There will be a point that is not differentiable, so equation (3) is rewritten.
[0045]
[0046] Combining equations (3) and (4), we obtain τ u =sat(τ ud )=S(τ ud )+d(τ ud ), and there are:
[0047] |d(τ ud )|=|sat(τ ud )-S(τ ud )|≤max{τ umax (1-tanh(1)),τ umin (tanh(1)-1)}=χ;where χ is a positive number, and by the mean value theorem, there exists λ such that S(τ) ud )=S(τ ud0 )+S τdλ (τ ud -τ ud0 ), 0 < λ < 1.
[0048]
[0049] When τ ud0 =0, S(τ) ud ) = S τdλ τ ud At that time, there were:
[0050] τ u =S τdλ τ ud +d(τ ud (5)
[0051] Where, 0 < S τdλ ≤1,|d(τ) ud )|≤χ.
[0052] The input saturated nonlinear function affects the lateral control input τ v and steering control input τ r The same applies.
[0053] In summary, the control objective is to design a control law τ = (τ) based on formula (2). u ,τ v ,τ r ) T In the presence of unknown disturbances and input saturation nonlinearity, the system tracking signal should be able to follow the target signal x. d .
[0054] Step 2. Design backstepping control for the obtained unmanned surface vessel model and construct a neural network command filter backstepping controller that considers input saturation.
[0055] In designing the controller, this invention combines command filtering technology with backstepping to solve the computational explosion problem and eliminate the influence of filtering errors, thereby improving the accuracy of the system.
[0056] Furthermore, this invention incorporates internal uncertainties into the controller design, using an RBF neural network to approximate both internal uncertainties and external disturbances, thereby reducing the system's steady-state error and improving control performance.
[0057] In addition, the present invention also considers introducing the anti-saturation algorithm described by formulas (3)-(5) into the unmanned surface vessel system, which constrains the control input of the system, improves the robustness of the controller, and makes the controller better meet the needs of actual use.
[0058] Define the command filter as follows:
[0059]
[0060] in, Let α be the output signal of the command filter, α be the input signal of the command filter, and ξ be the filter compensation signal; if at any time t > 0, we have Where ρ1 and ρ2 are both positive numbers; at the same time Then for any κ > 0, there exists ω n >0, satisfies Both are bounded.
[0061] The error transformation is defined as follows: z1 = x1 - x dz2 = x2 - x 1,c , v1=z1-ξ1, v2=z2-ξ2.
[0062] Where, x d For a given desired trajectory, x 1,c ξ1 and ξ2 are the output signals of the command filter, and z1, z2, v1, and v2 are the error variables in the system.
[0063]
[0064] Step 2.1. Select the Lyapunov function:
[0065]
[0066] Differentiating equation (7) with respect to time, we get:
[0067]
[0068] Select the virtual control law α1 and the filter error compensation error signal respectively:
[0069]
[0070]
[0071] In the formula, k1 is a constant greater than zero. Substituting formulas (9) and (10) into formula (8), we get:
[0072]
[0073] Step 2.2. Select the Lyapunov function:
[0074]
[0075] in, Let the inverse of the coordinate transformation matrix be denoted by the matrix. Taking the derivative of equation (12) with respect to time, we get:
[0076]
[0077] Where, C(v)=C k (v)+C u (v), C k (v) and D k (v) is the known part of C(v) and D(v), and D(v) = D k (v)+D u (v), C u (v) and D u (v) is the unknown part of C(v) and D(v), therefore:
[0078]
[0079] make
[0080] Substituting equation (15) into equation (14), we get:
[0081]
[0082] The following is obtained by approximation using an RBF neural network:
[0083] F(z) = [f1(z), f2(z), f3(z)] T (17)
[0084] f i (z)=W i *T S(z)+ε i (18)
[0085] Where i = 1, 2, 3, W i * Let S(z) be the ideal weight vector of the neural network, and let S(z) represent the basis function vector. Let ε be the input vector. i Let be the estimation error of the neural network; from Young's inequality, we get:
[0086]
[0087] Where l1 represents the parameter in Young's inequality; from the characteristics of the input saturation function, τ = S τ τ d +d, 0 < b 11 <S τ ≤1, |d|≤D, b 11 Let be a constant, d represent the nonlinear part of the input saturation function, and S τ This represents the linear part of the saturation function.
[0088] Let the law of real control be:
[0089]
[0090] in, Indicates design parameters, This represents the estimated value of θ; at this point, we obtain:
[0091] v2 T τ=v2 T S τ τ d +v2 T d (21)
[0092] Similarly, by Young's inequality, we get:
[0093]
[0094] therefore:
[0095]
[0096] Among them, ||W i * || indicates W i * The norm of .
[0097] Step 2.3. Let To represent the estimated value of θ, we choose the Lyapunov function:
[0098]
[0099] Differentiating with respect to time, we get:
[0100]
[0101] definition Where k3 > 0.
[0102] The Lyapunov function of the controller and the command filter error compensation signal are selected for derivation, and the stability analysis of the unmanned surface vessel control system controlled by the unmanned surface vessel neural network command filter backstepping controller is carried out.
[0103] Step I. First, prove the boundedness of the command filter error compensation signal:
[0104] Choose the Lyapunov function as shown below:
[0105]
[0106] Differentiating with respect to time, we get:
[0107]
[0108] From the command filter correlation theorem in equation (6), we know that |x 1,c -α|≤κ, obtained from Young's inequality:
[0109]
[0110] Substituting equation (28) into equation (27), we get:
[0111]
[0112] Where α' = min{2k1-2,1}, Therefore, we can conclude that:
[0113]
[0114] Therefore, the compensation error signal is bounded.
[0115] Step II. Prove the stability of the system:
[0116] Choose the Lyapunov function:
[0117] V = V3 (31)
[0118] Differentiating with respect to time, we get:
[0119]
[0120] Where, a = min{k1,k2-1,b} 11 k3},
[0121] Therefore, we can conclude that:
[0122]
[0123] Where V(0) represents the initial value of V(t); according to equations (7), (12), (23), and (26), we obtain:
[0124]
[0125] From equations (28) and (29), we get:
[0126]
[0127] Therefore, there is
[0128] From equations (30) and (32), we know that v i ξ i Since θ is bounded, i = 1, 2, and z1 = v1 + ξ1, z1 is also bounded; and since v1 = z1 - ξ1 and z1 = x1 - x d Therefore, x1 is bounded, and from equation (9), we know that α is the sum of z1 and z1. The relevant function indicates that α is bounded; and because |x 1,c -α|≤κ holds true, therefore x 1,c Bounded, associating z² = x² - x 1,c v2 = z2 - ξ2, therefore x2 is bounded.
[0129] From equation (20), we know that τ d It is related to v2 and θ, therefore τ d If a system is bounded, then the system as a whole is stable.
[0130] Step 3. Track and control the unmanned surface vessel (USV) based on the unmanned surface vessel's neural network command filter backstepping controller.
[0131] like Figure 2 A schematic diagram of the overall system consisting of a command filter, an unmanned surface vessel (USV) neural network command filter backstepping control, a neural network, and the USV system is shown. The control process of the method of the present invention is as follows: A virtual control law is designed for the position vector of the USV system, and then sent to the command filter. The command filter generates an error compensation signal, which, together with the unknown nonlinearity approximated by the neural network, is sent to the controller to generate a control signal. After anti-input saturation processing, the control signal enters the USV system to control the propulsion and steering devices of the USV and compares it with the given desired trajectory. The difference is sent back to the controller as a feedback signal until its value converges to near the origin.
[0132] Furthermore, to verify the effectiveness of the control method proposed in this invention, the unmanned surface vessel system was simulated and verified using the method of this invention in the MATLAB / Simulink environment. The simulation parameters were selected as follows:
[0133] m 11 =200kg,m 22 =250kg,m 33 =100kg·m 2 ,d 11 =70kg / s,d 22 =100kg / m,d 33 =50kg·m 2 .
[0134] The expected trajectory is:
[0135] The initial positions of the USV are x(0) = 0, y(0) = 0. Simulation time t = 200s, expected initial position:
[0136] x d (0)=0,y d (0) = 0,
[0137] Select control parameters k3 = (250, 200, 200) T k4 = 28.
[0138] Simulation results are as follows Figures 3-9 As shown, where:
[0139] Figure 3This figure illustrates the tracking of the desired trajectory by the unmanned surface vessel on a horizontal plane. As can be seen from the figure, both the method proposed in this invention and the fuzzy control method can achieve the tracking of the desired trajectory.
[0140] Figure 4 The error tracking curves of the proposed method in the three coordinate axes are depicted. Figures 5 to 7 The figures show a comparison of the errors of the two methods across the three degrees of freedom. The comparison demonstrates that the method of this invention offers significant improvements in accuracy and response speed compared to the fuzzy control method, with a smaller maximum error and faster convergence speed.
[0141] Figure 8 As can be seen from this figure, after considering the input saturation nonlinearity, the control signal is effectively limited to a reasonable range, avoiding excessive control input from entering the system.
[0142] Figure 9 For the virtual control law curve, from Figure 9 The changes in the virtual control law across the three degrees of freedom can be observed. Here, the virtual control law α is a three-dimensional column vector, and α1, α2, and α3 are the three components of α.
[0143] The simulation results above show that the unmanned surface vessel neural network command filtering backstepping control method designed in this invention can achieve trajectory tracking control of unmanned surface vessels with high accuracy when considering input saturation.
[0144] This embodiment addresses the trajectory tracking control problem of an unmanned surface vessel system with input saturation and unknown nonlinearity. It proposes an adaptive trajectory tracking control method based on command filtering and backstepping. This method utilizes a radial basis function neural network to approximate the unknown dynamics of the system, requiring only three adaptive laws, thus reducing system complexity. The control law is designed based on the backstepping method. Furthermore, by introducing a command filter and its compensation mechanism, the computational complexity problem is solved, the influence of filtering errors is eliminated, and the control accuracy of the system is improved. This method effectively tracks the desired trajectory with high control accuracy and fast convergence speed, while limiting the control input within a certain range, further improving the control performance.
[0145] Example 2
[0146] This embodiment 2 describes an unmanned surface vessel (USV) neural network command filtering backstepping control system that considers input saturation. This system is based on the same inventive concept as the USV neural network command filtering backstepping control method that considers input saturation in embodiment 1.
[0147] Specifically, the unmanned surface vessel neural network command filtering backstepping control system considering input saturation includes:
[0148] The model building module is used to build unmanned surface vessels (USVs) models to take into account the input saturation situation in actual applications, and to simplify the USV models according to actual application scenarios.
[0149] The controller design module is used to perform backstepping control design on the obtained unmanned surface vessel model and construct an unmanned surface vessel neural network command filter backstepping controller that considers input saturation.
[0150] And a tracking control module, which uses a neural network command filter backstepping controller to track and control the unmanned surface vessel.
[0151] In a preferred embodiment, the unmanned surface vessel neural network command filtering backstepping control system further includes:
[0152] The stability analysis module is used to select the command filter error compensation signal and the Lyapunov function of the controller for derivation, and to perform stability analysis on the designed unmanned surface vessel neural network command filter backstepping controller considering input saturation.
[0153] It should be noted that the implementation process of the functions and roles of each functional module in the unmanned surface vessel neural network command filtering backstepping control system of this embodiment is detailed in the implementation process of the corresponding steps in the method of the above embodiment 1, and will not be repeated here.
[0154] Example 3
[0155] This embodiment 3 describes a computer device for implementing the steps of the unmanned surface vessel neural network command filtering backstepping control method considering input saturation described in embodiment 1 above.
[0156] The computer device includes memory and one or more processors.
[0157] The memory stores executable code, which, when executed by the processor, implements the steps of a neural network command filtering backstepping control method for unmanned surface vessels that takes into account input saturation.
[0158] In this embodiment, the computer device can be any device or apparatus with data processing capabilities, and will not be described in detail here.
[0159] Example 4
[0160] This embodiment 4 describes a computer-readable storage medium for implementing the steps of the unmanned surface vessel neural network command filtering backstepping control method considering input saturation described in embodiment 1 above.
[0161] The computer-readable storage medium in this embodiment 4 stores a program that, when executed by a processor, is used to implement the steps of the unmanned surface vessel neural network command filtering backstepping control method considering input saturation.
[0162] The computer-readable storage medium can be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc.
[0163] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.
Claims
1. A neural network command filtering backstepping control method for unmanned surface vessels considering input saturation, characterized in that, Includes the following steps: Step 1. Establish an unmanned surface vessel model under input saturation conditions and simplify it; Step 2. Design backstepping control for the unmanned surface vessel model obtained in Step 1, and construct a neural network command filter backstepping controller for the unmanned surface vessel that considers input saturation; Step 3. Perform tracking control on the unmanned surface vessel (USV) based on the unmanned surface vessel's neural network command filter backstepping controller; Step 1 specifically involves: Assuming the unmanned surface vessel has a uniform mass distribution and is symmetrical from left to right, and its center of gravity and center of buoyancy coincide on the Z-plane, to simplify the model and facilitate calculations, only the three degrees of freedom of the unmanned vessel—swell, roll, and yaw—are considered. Its dynamic model on the horizontal plane is then: (1) in, This is the position vector in the ground coordinate system. , , These represent the unmanned surface vessel's lateral distance, longitudinal distance, and bow angle, respectively. Let be the velocity vector in the body coordinate system. , , They represent in , Linear velocity and angular velocity of bow roll in the direction of travel; This is the coordinate transformation matrix. The inertia matrix, The Coriolis centripetal force matrix, Here is the damping matrix. To control the input vector, the vector Disturbed by unknown external winds and waves; ， ， ， ； in, , , These are the components of the inertia matrix on the three coordinate axes; , , These are the damping moments acting on the hull; , , These represent the disturbance torques experienced in the three degrees of freedom; Then the model of formula (1) simplifies to: (2) in , , These represent the longitudinal control input, lateral control input, and steering control input acting on the system, respectively. For formula (2), the control input is affected by saturation nonlinearity, and the saturation of the control input is described as follows: (3) in, As the longitudinal control input acting on the system, For control signals, and For an unknown saturation constant, when or There will be a point where it is not differentiable, so equation (3) is rewritten. (4) Combining equations (3) and (4), we obtain And there are: ;in, For a positive number, by the Mean Value Theorem, there exists ,make , ; ； when , At that time, there were: (5) in, , ; Input saturated nonlinear function for lateral control input and steering control input The same applies; In summary, the control objective of the controller is to design a control law based on formula (2). In the presence of unknown disturbances and input saturation nonlinearity, the system's tracking signal can follow the target signal. ; Step 2 specifically involves: Define the command filter as follows: (6) in, , The output signal of the command filter. The input signal for the command filter. This represents the filtered compensation signal; if in any There are moments when , ,in and All are positive numbers; at the same time , Then for any All exist ,satisfy , , , Both are bounded; Define the following error transformation: , , , ; in, Given the desired trajectory, and This is the signal for filtering error compensation. , , , All of these are error variables in the system; ； Step 2.
1. Select the Lyapunov function: (7) Differentiating equation (7) with respect to time, we get: (8) The virtual control law and the filter error compensation error signal are selected as follows: (9) (10) In the formula For a constant greater than zero, substituting equations (9) and (10) into equation (8) yields: (11) Step 2.
2. Select the Lyapunov function: (12) in, Let the inverse of the coordinate transformation matrix be denoted by the matrix. Taking the derivative of equation (12) with respect to time, we get: (13) in, , and for and The known part, , and For respectively and The unknown part, therefore: (14) make (15) Substituting equation (15) into equation (14), we get: (16) The following is obtained by approximation using an RBF neural network: (17) (18) in, , The ideal weight vector for the neural network. Represents a basis function vector. For the input vector, Let be the estimation error of the neural network; from Young's inequality, we get: (19) in, This represents the parameter in Young's inequality; based on the characteristics of the input saturation function, , , , It is a constant. This represents the nonlinear part of the input saturation function. Represents the linear part of the saturation function; Let the law of real control be: (20) in, Indicates design parameters, This represents the estimated value of θ; at this point, we obtain: (21) Similarly, by Young's inequality, we get: (22) therefore: (23) in, express The norm; Step 2.
3. Let , , express The estimated value is obtained by selecting the Lyapunov function: (24) Differentiating with respect to time, we get: (25) in, , .
2. The unmanned surface vessel neural network command filtering backstepping control method considering input saturation according to claim 1, characterized in that, In step 2, the command filtering technique is combined with the backstepping method when designing the controller to solve the problem of computational explosion and eliminate the impact of filtering error; the uncertainties inside the system are taken into account in the controller design, and the RBF neural network is used to approximate both internal uncertainties and external disturbances in order to reduce the steady-state error of the system.
3. The unmanned surface vessel neural network command filtering backstepping control method considering input saturation according to claim 1, characterized in that, In step 2, after constructing the unmanned surface vessel neural network command filter backstepping controller, the command filter error compensation signal and the Lyapunov function of the controller are selected for derivation, and the stability analysis of the unmanned surface vessel control system controlled by the unmanned surface vessel neural network command filter backstepping controller is performed.
4. The unmanned surface vessel neural network command filtering backstepping control method considering input saturation according to claim 1, characterized in that, In step 2, the specific steps of the stability analysis are as follows: Step I. First, prove the boundedness of the command filter error compensation signal; Choose the Lyapunov function as shown below: (26) Differentiating with respect to time, we get: (27) From the command filter correlation theorem in formula (6), we know that We obtain the following from Young's inequality: (28) Substituting equation (28) into equation (27), we get: (29) in , ; Therefore, we can conclude that: (30) Therefore, the compensation error signal is bounded; Step II. Prove the stability of the system: Choose the Lyapunov function: (31) Differentiating with respect to time, we get: (32) in, , Therefore, we can conclude that: (33) in, express The initial value is obtained according to equations (7), (12), (23), and (26): (34) From equations (28) and (29), we get: (35) Therefore, there is ; From equations (30) and (32), we know that , , Both are bounded. ,and ,therefore It is also bounded; and because , ,so It is bounded, as we know from equation (9). To and and The relevant functions, therefore we know Bounded; and because there is Established, therefore Bounded, Associative , get Bounded; From equation (20), we know that and and Related, therefore If a system is bounded, then the system as a whole is stable.
5. The unmanned surface vessel neural network command filtering backstepping control method considering input saturation according to claim 1, characterized in that, Step 3 specifically involves: A virtual control law is designed for the position vector of the unmanned surface vessel (USV) system. This law is then fed into a command filter, which generates an error compensation signal. This signal, along with an unknown nonlinearity approximated by a neural network, is fed into the USV's neural network command filter backstepping controller to generate a control signal. After anti-input saturation processing, the control signal enters the USV system to control its propulsion and steering mechanisms. The signal is compared with the given desired trajectory, and the difference is fed back to the controller as a feedback signal until the value converges to near the origin.
6. A neural network command filtering backstepping control system for implementing the unmanned surface vessel (USV) command filtering backstepping control method considering input saturation as described in claim 1, characterized in that, The unmanned surface vessel neural network command filtering backstepping control system considering input saturation includes: The model building module is used to build unmanned surface vessels under input saturation conditions and perform simplification processing; The controller design module is used to perform backstepping control design on the obtained unmanned surface vessel model and construct an unmanned surface vessel neural network command filter backstepping controller that considers input saturation. And a tracking control module, which uses a neural network command filter backstepping controller to track and control the unmanned surface vessel.
7. A computer device comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that, When the processor executes the executable code, it implements the steps of the unmanned surface vessel neural network command filtering backstepping control method considering input saturation as described in any one of claims 1 to 5.
8. A computer-readable storage medium having a program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the unmanned surface vessel neural network command filtering backstepping control method considering input saturation as described in any one of claims 1 to 5.