A method and system for optimal backstepping control of unmanned surface vessel (USV) formations

Abstract

This disclosure provides a method and system for optimal backstepping control of unmanned surface vessels (USVs) in a specified performance context, relating to the field of optimal backstepping control technology for USVs. The method includes: establishing a dynamic model of multiple USVs; using a disturbance observer and a neural network identifier to compensate for external disturbances and unknown nonlinear terms in the dynamic model; constructing an optimal virtual controller by introducing a first-order integral filter to calculate the derivative of the optimal virtual control, thereby constructing an optimal actual controller; designing a monotonic tube boundary function using the characteristics of a hyperbolic cosecant function; and performing formation control using the virtual controller and the actual controller, employing a continuous control law and the monotonic tube boundary function to maintain synchronization between the position of the following USVs and the desired trajectory of the leader USV under external disturbance conditions. This invention utilizes a disturbance observer estimator to detect time-varying external disturbances and uses a neural network to approximate the unknown parameters of the dynamic model, employing the monotonic tube boundary function to allow the formation error to evolve within a specified region.

Description

Technical Field

[0001] This disclosure relates to the field of optimal backstepping control technology for unmanned surface vessels (USVs), specifically to a method and system for optimal backstepping control of specified performance for USV formations. Background Technology

[0002] With continuous technological advancements, unmanned systems have experienced rapid development. Unmanned surface vessels (USVs), as an important branch of unmanned systems, have naturally become a hot research focus in this field. Currently, USV technology is in a phase of rapid development, with technological integration and innovation being its main trends. In the future, USVs will become more intelligent and autonomous, capable of performing tasks in more complex and challenging marine environments. Simultaneously, the application areas of USVs will continue to expand, extending from traditional marine monitoring and surveys to cargo transportation, seabed mineral resource exploration, and offshore wind farm maintenance, among other fields. The rapid development of technology means that the application of a single USV is insufficient to meet the needs of marine exploration engineering; therefore, utilizing multiple USVs simultaneously to perform tasks in marine engineering is inevitable.

[0003] When unmanned surface vessels (USVs) perform various tasks such as marine monitoring, resource exploration, and maritime rescue, they are often affected by external disturbances and other uncertainties, which places increasingly higher demands on their control performance. During mission execution, the convergence speed and transient performance of formation errors are extremely important; therefore, predefined performance control has received widespread attention in engineering applications. In this context, it is worth noting that monotonic boundary performance functions improve the convergence speed and performance of predefined performance control methods while reducing chattering. Furthermore, a disturbance observer is used to estimate external disturbances, which are then incorporated into the optimal group control law to compensate for these disturbances. Simultaneously, an adaptive control method is employed to achieve precise control of the USV and realize an ideal motion trajectory.

[0004] Currently, there are few research schemes for optimal formation control based on specified performance. At the same time, factors such as harsh environment, limited resources, and equipment wear and tear of unmanned surface vessels can affect the control performance of the system and have a certain impact on the completion of the control task, resulting in poor optimal control performance of existing unmanned surface vessel formations. Summary of the Invention

[0005] To address the aforementioned issues, this disclosure proposes a specified performance optimal backstepping control method and system for unmanned surface vessel (USV) formations. It utilizes a disturbance observation estimator for time-varying external disturbances, approximates the unknown parameters of the dynamic model using a neural network, and employs a monotonic tube boundary function to allow the formation error to evolve within a specified region.

[0006] According to some embodiments, the present disclosure adopts the following technical solutions:

[0007] A specified performance optimal backstepping control method for unmanned surface vessel (USV) formations includes:

[0008] Considering external disturbances, a dynamic model of the multiple unmanned surface vessels to be controlled is established, and a disturbance observer and a neural network identifier are used to compensate for external disturbances and unknown nonlinear terms in the dynamic model.

[0009] Based on the dynamic model, an optimal virtual controller is constructed. The derivative of the optimal virtual control is calculated by introducing a first-order integral filter, and then the optimal actual controller is constructed.

[0010] Based on the dynamic model, and utilizing the characteristics of the hyperbolic cosecant function, a monotonic tube boundary function is designed to limit the formation error of the unmanned surface vessel within the specified performance range.

[0011] By using a virtual controller and a physical controller, continuous control law and monotonic tube boundary function are used for formation control, and the position of the following unmanned surface vessel is kept synchronized with the desired trajectory of the leader unmanned surface vessel under external disturbances.

[0012] According to some embodiments, the present disclosure adopts the following technical solutions:

[0013] A specified performance optimal backstepping control system for unmanned surface vessel (USV) formations includes:

[0014] The model building module is configured to: establish a dynamic model of the multiple unmanned surface vessels to be controlled under the condition of considering external disturbances, and use a disturbance observer and a neural network identifier to compensate for external disturbances and unknown nonlinear terms in the dynamic model;

[0015] The controller construction module is configured to: construct the optimal virtual controller based on the dynamic model, calculate the derivative of the optimal virtual control by introducing a first-order integral filter, and then construct the optimal actual controller.

[0016] The boundary design module is configured to: design a monotonic tube boundary function based on the dynamic model and utilizing the characteristics of the hyperbolic cosecant function to limit the formation error of the unmanned surface vessel within the specified performance range;

[0017] The formation control module is configured to perform formation control using a continuous control law and a monotonic tube boundary function through a virtual controller and a physical controller, thereby controlling the position of the following unmanned surface vessel to remain synchronized with the desired trajectory of the leader unmanned surface vessel under external disturbances.

[0018] According to some embodiments, the present disclosure adopts the following technical solutions:

[0019] A computer program product includes a computer program that, when executed by a processor, implements the aforementioned optimal backstepping control method for unmanned surface vessel formations.

[0020] According to some embodiments, the present disclosure adopts the following technical solutions:

[0021] A non-transitory computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement the aforementioned optimal performance backstepping control method for unmanned surface vessel formations.

[0022] According to some embodiments, the present disclosure adopts the following technical solutions:

[0023] An electronic device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to perform a specified performance optimal backstepping control method for unmanned surface vessel formations.

[0024] Compared with the prior art, the beneficial effects of this disclosure are as follows:

[0025] 1. The technical solution of this invention designs a predefined time performance function—a monotonic tube boundary function. Compared with the standard boundary function in the form of an exponential function, the monotonic tube boundary function not only effectively constrains the overshoot of formation errors and reduces chattering, allowing the formation error to converge to a neighborhood of the origin within a predetermined time, but also maintains the monotonicity of the function under parameter variations, achieving an ideal formation trajectory. Under the framework of backstepping optimality, a new formation control strategy is obtained, which can minimize energy consumption and ensure the evolution of formation error within a given region.

[0026] 2. Since the X and Y axes are coupled in the coordinate systems of two consecutive unmanned surface vessels, the Hamilton-Jacobi-Bellman equations are designed jointly, and two optimal virtual controllers are obtained simultaneously. The reinforcement learning algorithm utilizes the negative gradient of the simple positive definite function of the partial derivative of the Hamilton-Jacobi-Bellman equations to greatly simplify the optimal control and achieve optimal formation control. Attached Figure Description

[0027] The accompanying drawings, which form part of this disclosure, are used to provide a further understanding of this disclosure. The illustrative embodiments of this disclosure and their descriptions are used to explain this disclosure and do not constitute an undue limitation of this disclosure.

[0028] Figure 1 This is the leader-follower formation diagram of Example 1.

[0029] Figure 2 This is the phase plane trajectory of five unmanned surface vessels in Example 1 and its snapshot.

[0030] Figure 3 This refers to the line-of-sight error of two consecutive unmanned surface vessels and the monotonic tube boundary function in Example 1.

[0031] Figure 4 It is the angular error of two consecutive unmanned surface vessels and the monotonic tube boundary function of Example 1.

[0032] Figure 5 It is the control input for surge force, sway force and yaw moment in Example 1.

[0033] Figure 6 This is Example 1, which describes the disturbances and estimations of surge force, sway force, and yaw moment.

[0034] Figure 7 This is the weight convergence curve of the actor-critic network in Example 1.

[0035] Figure 8 This is the weight convergence curve of the actor-critic network in Example 1. Detailed Implementation

[0036] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.

[0037] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of this disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains.

[0038] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this disclosure. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0039] Example 1

[0040] One embodiment of this disclosure provides a specified performance optimal backstepping control method for unmanned surface vessel (USV) formations, comprising:

[0041] Step S1: Under the condition of considering external disturbances, establish the dynamic model of the multiple unmanned surface vessels to be controlled, and use the disturbance observer and neural network identifier to compensate for the external disturbances and unknown nonlinear terms of the dynamic model.

[0042] Step S2: Based on the dynamic model, construct the optimal virtual controller. Calculate the derivative of the optimal virtual control by introducing a first-order integral filter, and then construct the optimal actual controller.

[0043] Step S3: Based on the dynamic model, and utilizing the characteristics of the hyperbolic cosecant function, design a monotonic tube boundary function to limit the formation error of the unmanned surface vessel within the specified performance range.

[0044] Step S4: Using a virtual controller and a physical controller, continuous control law and monotonic tube boundary function are used for formation control to keep the position of the following unmanned surface vessel synchronized with the desired trajectory of the leader unmanned surface vessel under external disturbances.

[0045] As one embodiment, this disclosure provides a specified performance optimal backstepping control method for unmanned surface vessel (USV) formations. This method utilizes a disturbance observation estimator to detect time-varying external disturbances and a neural network to approximate unknown parameters. It employs an improved specified performance function to allow the formation error to evolve within a specified region. The specific implementation process is as follows:

[0046] Step 1:

[0047] Consider N fully actuated unmanned surface vessels (USVs). The kinematic model of the i-th USV is given by the following equation:

[0048]

[0049] Where, x i It is the position of the oscillation, y i It is the position of the sway, ψ i It's the bow roll angle, u i It is the oscillation linear velocity, v i It is the sway linear velocity, r i It is the bow roll rate.

[0050] Let η i =[x i ,y i ,ψ i ] T and ν i =[u i ,v i ,r i ] T Then the dynamic model of the i-th unmanned surface vessel is:

[0051]

[0052] in, It is the inertia matrix, C(ν) i ) is the total Coriolis and centripetal acceleration matrix, τ i =[τ ui ,τ vi,τ ri ] T It is the control input, τ wi =[τ wui ,τ wvi ,τ wri ] T It is an external disturbance, D(ν) i ) is the damping matrix.

[0053] A leader-follower formation, such as Figure 1 As shown, it includes the leader unmanned surface vessel i-1 and the follower unmanned surface vessels i, i = 1,...,N, where ψ i It's the bow roll angle, u i It is the oscillation linear velocity, v i It is the sway linear velocity, r i It is the bow roll angular velocity, (x i ,y i () indicates the location of the unmanned surface vessel. It is the angle between two consecutive unmanned surface vessels, d i It refers to the line-of-sight range between two consecutive unmanned surface vessels.

[0054] Define the angle and line-of-sight range between two consecutive unmanned surface vessels as:

[0055]

[0056] We can conclude that:

[0057]

[0058] Where, x i-1 It is the pitching position of the (i-1)th unmanned surface vessel, y i-1 It is the sway position of the (i-1)th unmanned surface vessel.

[0059] An external disturbance is estimated using a disturbance observer, and then the disturbance observer is incorporated into the dynamic model to compensate for the external disturbance. Furthermore, the unknown nonlinear term D(ν) in the dynamic model is addressed. i )ν i Approximation is performed using a neural network identifier, specifically:

[0060]

[0061] in, S represents the weights of the neural network. i (Z i ) represents the basis function vector, ε i This indicates the approximation error.

[0062] The disturbance observer takes the following form:

[0063]

[0064] in, It is the inertia matrix, C(ν) i ) is the total Coriolis and centripetal acceleration matrix, τ i =[τ ui ,τ vi ,τ ri ] T It is the control input, τ di For the total disturbance, ν i =[u i ,v i ,r i ] T Indicates speed, express The error, It is a state variable, C di =diag[C d1i C d2i C d3i ]>0 is the design parameter.

[0065] Step 2:

[0066] Below is the formation error e ji The definition of j = d and ψ indicates that formation error includes line-of-sight error and angle error.

[0067] e di (t)=d i (t)-d i,des

[0068] e ψi (t)=ψ i-1 (t)-ψ i (t)

[0069] Where, d i,des This represents the expected distance between two consecutive unmanned surface vessels.

[0070] Using the initial value properties of the hyperbolic cosecant function, a set of feasible monotonic tube boundary functions was designed:

[0071]

[0072] Where 12 = col(1,1), j = d, ψ, and

[0073]

[0074] Where T_c>0 is the time constant, It is the formation error e ji The convergence rate, The initial value represents the pre-selected boundary.

[0075] Step 3:

[0076] To establish the formation error e ji With monotonic tube boundary function and b ji Inspired by traditional exponential performance specification techniques, the relationship between these parameters is illustrated by the following error transformation function:

[0077]

[0078] Among them, z ji It is the transformation error, T(z) ji The following conditions must be met:

[0079]

[0080] Let e ji =T(z) ji ),get

[0081]

[0082] Differentiate both sides of the above equation

[0083]

[0084] in,

[0085] Based on the previous description, we can conclude that:

[0086]

[0087] Then we have:

[0088]

[0089] Step 4: Design the optimal controller by combining backstepping techniques and reinforcement learning algorithms:

[0090] Based on the given kinematic and dynamic models of the unmanned surface vessel, design the optimal virtual controller and the optimal actual controller, respectively.

[0091] (1) Optimal Virtual Controller

[0092] Establish the optimal performance index function for the unmanned surface vessel's position:

[0093]

[0094] Where, α 1i ,α 2i It is a virtual controller. It is the optimal virtual controller. It is the cost function, Ω di It is a compact set containing the origin, Φ(Ω) di ) is the allowable control set.

[0095] Differentiating both sides of the above formula, we obtain the Hamilton-Jacobi-Bellman (HJB) equation as follows:

[0096]

[0097] By solving Get with unknown parameters The optimal virtual controller is shown below:

[0098]

[0099] Will Decomposed into:

[0100]

[0101] in, and These are positive design parameters.

[0102] Therefore, the optimal virtual controller can be expressed as:

[0103]

[0104] Due to V NNdi Since V is an unknown continuous function, its value can be estimated within the compact set Ω using a neural network. NNdi Represented as:

[0105]

[0106] in Represents the ideal weight. Denotes the basis function vector, ε di (z di ) is the approximation error.

[0107] A reinforcement learning algorithm based on an actor-critic network is used to process the unknown parameters. By approximating the optimal virtual controller, we can obtain:

[0108]

[0109] in, yes Approximate value, yes The estimated value, neural network Approaching Unknown dynamics within, These are estimates of the ideal critic network weights, in a neural network. Approaching Unknown dynamics within, It is an estimate of the ideal actor's weight. Represents a basis function vector.

[0110] Based on the above formula, the approximate HJB function is obtained as follows:

[0111]

[0112] The Bellman residual is defined as follows:

[0113]

[0114] Establish the optimal performance index function for the angle of the unmanned surface vessel:

[0115]

[0116] Among them, Ω ψi It is a compact set containing the origin, Φ(Ω) ψi α is the permissible control set. 3i It is a virtual controller. It is the optimal virtual controller. It is the cost function.

[0117] Differentiating both sides of the above formula, we obtain the Hamilton-Jacobi-Bellman (HJB) equation as follows:

[0118]

[0119] By solving Get with unknown parameters The optimal virtual controller is shown below:

[0120]

[0121] Will Decomposed into:

[0122]

[0123] in, and These are design parameters.

[0124] Therefore, the optimal virtual controller can be expressed as

[0125]

[0126] Due to VNNψi Since V is an unknown continuous function, its value is estimated within the compact set Ω using a neural network. NNψi Represented as:

[0127]

[0128] in Represents the weights of the neural network. Denotes the basis function vector, ε ψi (z ψi ) is the approximation error.

[0129] A reinforcement learning algorithm based on an actor-critic network is used to process the unknown parameters. By approximating the optimal virtual controller, we can obtain:

[0130]

[0131] in, yes Approximate value, yes The estimated value, neural network Approach Unknown dynamics within, These are estimates of the ideal critic network weights, in a neural network. Approach Unknown dynamics within, It is an estimate of the ideal actor network weights. Represents a basis function vector.

[0132] Based on the above formula, the approximate HJB function is obtained as follows:

[0133]

[0134] The Bellman residual is defined as follows:

[0135]

[0136] To avoid redundant differentiation in virtual control, dynamic surface control technology is used. A first-order integral filter is introduced to calculate the derivative of the optimal virtual control, thereby preventing the so-called complexity problem in subsequent steps. Specifically:

[0137] let α is obtained through a first-order filter. fi :

[0138]

[0139] Where, μi =diag[μ 1i ,μ 2i ,μ 3i [] is the time constant. It is the optimal virtual control input vector, α fi =[α f1i ,α f2i ,α f3i ] T It is the filtered virtual control input vector.

[0140] therefore, The derivative is:

[0141]

[0142] in, Bounded.

[0143] (2) Optimal practical controller

[0144] The optimal performance index function is established as follows:

[0145]

[0146] in, τ i It is the actual controller. It is the optimal practical controller. It is the cost function.

[0147] The corresponding Hamiltonian-Jacobi-Bellman (HJB) equations can then be obtained. as follows:

[0148]

[0149] Similar to the construction of the optimal virtual controller, an approximate optimal real-world controller is obtained by employing a reinforcement learning algorithm:

[0150]

[0151] in, yes The estimated value, neural network Used for approximation Unknown dynamics within, This represents an estimate of the ideal weights for the actor network. It is a basis function vector.

[0152] In the approximation process using a reinforcement learning algorithm based on an execution-critic network, an adaptive update rate for the weights of the execution-critic network is designed using a stability determination method based on gradient descent and Lyapunov function stability theory.

[0153]

[0154] in, and These are the design parameters of the critic network. and These are the design parameters of the actor network, σ. i It is a design constant. It is an identity matrix.

[0155] To demonstrate the feasibility, effectiveness, and correctness of this example, the following simulation example is performed:

[0156] In this simulation experiment, an optimal controller based on reinforcement learning was designed for an unmanned surface vessel (USV) formation system with external disturbances. This controller not only enables the USV formation to track the reference trajectory of the unmanned surface vessel, but also improves the tracking accuracy and transient performance of the system.

[0157] In the optimal controller design process, the system model parameters are set as follows:

[0158] First, the system model parameters are given: the mass of the unmanned surface vessel is 23.8 kg; the length is 1.255 m; and the external disturbance is τ. wi =[-11+4sin(0.02t),-3+2cos(0.02t),2-5sin(0.02t)] T The reference trajectory is as follows:

[0159]

[0160] Among them, t c >0 and t′=0.02(tt) c The required monotonic tube boundary function form is: and b di =b ψi =b=0.4q-1.6, where,

[0161] In the process of optimal controller design, the critic network and And actor networks and Both contain 27 neurons and have a width of 0.1; neural networks and The center points are uniformly distributed on [-1.2, 1.2]; neural network and The center point is evenly distributed on [-1.2,1.2]×[-1.2,1.2]×[-1.2,1.2].

[0162] The initial weights of the neural network are: i = 1, ..., 5. The initial condition is δ. 21 (0)=δ 22 (0) = [0.1, 0.1, 0.1] T and δ 2ι (0) = [0.5, 0.5, 0.5] T ι=2,...,5; The initial positions and angles of these five unmanned surface vessels are η1(0)=[0.2,5,0.2] T η2(0)=[0.3,10,0.3] T η3(0)=[0.4,15,0.4] T η4(0)=[0.5,20,0.5] T And η5(0)=[0.6,25,0.6] T And the initial velocity is ν i (0) = [0,0,0] T , i = 1, ..., 5.

[0163] The system design parameters are as follows:

[0164] C 2i =diag[33,33,30],C di =diag[33,33,29] and μ li =0.01.

[0165] Using MATLAB software, the control method of this embodiment is applied to... Figure 1 The simulation of the multiple unmanned surface vessels shown is performed, and the simulation results are as follows. Figures 2-8 As shown, Figure 2 The trajectories of the five vehicles at 0s, 45s, 120s, 230s, 360s, and 500s, along with their snapshots, are given. Figure 3 This embodiment represents the line-of-sight error between two consecutive unmanned surface vessels and the monotonic tube boundary function. Figure 4 This embodiment includes the angular error of two consecutive unmanned surface vessels and the monotonic tube boundary function. Figure 3 and Figure 4 It can be seen that both the line-of-sight error and the angle error evolve within the specified area and converge at a time of 2.7 seconds. Figure 5 It is the control input for surge force, sway force, and yaw moment; Figure 6 It includes disturbances such as surge force, sway force, and yaw moment, and their estimation. Figure 7 and Figure 8 The graphs show the convergence curves of the neural network weights. As can be seen from the graphs, each weight in the actor and critic networks eventually tends to stabilize and converge. Therefore, the designed reinforcement learning neural network control scheme can effectively achieve an accurate approximation of the designed optimal controller and has a good convergence effect. In summary, all signals in the system are uniformly bounded, and the simulation results prove the effectiveness of the proposed optimal control scheme.

[0166] This embodiment proposes a performance-optimized formation control scheme based on reinforcement learning for unmanned surface vessel (USV) platooning systems with time-varying unknown disturbances, using backstepping recursion and reinforcement learning techniques as the design framework. To ensure that the formation error converges accurately and stably to near-zero within a predetermined time range, a predefined class of performance boundary functions is employed, significantly improving formation accuracy. This embodiment leverages the approximation capability of reinforcement learning neural networks for nonlinear functions, using reinforcement learning algorithms to approximate the actual optimal controller. This solves the problem of directly solving the Hamilton-Jacobi-Bellman square equations and designs an optimal controller that meets the control requirements. Furthermore, an adaptive law is used to adjust the weights of the neural network, enabling the designed approximate optimal controller to closely approximate the actual optimal controller. The algorithm can be trained online and generate the optimal controller. The adaptive optimization algorithm described in this embodiment guides each USV to follow the preceding USV without any vehicles falling behind. Finally, simulation examples verify that the proposed vehicle platooning control method ensures the quality of all signals.

[0167] Example 2

[0168] One embodiment of this disclosure provides a specified performance optimal backstepping control system for unmanned surface vessel (USV) formations, comprising:

[0169] The model building module is configured to: establish a dynamic model of the multiple unmanned surface vessels to be controlled under the condition of considering external disturbances, and use a disturbance observer and a neural network identifier to compensate for external disturbances and unknown nonlinear terms in the dynamic model;

[0170] The controller construction module is configured to: construct the optimal virtual controller based on the dynamic model, calculate the derivative of the optimal virtual control by introducing a first-order integral filter, and then construct the optimal actual controller.

[0171] The boundary design module is configured to: design a monotonic tube boundary function based on the dynamic model and utilizing the characteristics of the hyperbolic cosecant function to limit the formation error of the unmanned surface vessel within the specified performance range;

[0172] The formation control module is configured to perform formation control using a continuous control law and a monotonic tube boundary function through a virtual controller and a physical controller, thereby controlling the position of the following unmanned surface vessel to remain synchronized with the desired trajectory of the leader unmanned surface vessel under external disturbances.

[0173] Example 3

[0174] One embodiment of this disclosure provides a computer program product, including a computer program that, when executed by a processor, implements the aforementioned optimal backstepping control method for unmanned surface vessel formations.

[0175] Example 4

[0176] One embodiment of this disclosure provides a non-transitory computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the specified performance optimal backstepping control method for unmanned surface vessel formations.

[0177] Example 5

[0178] One embodiment of this disclosure provides an electronic device, including a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to perform the aforementioned optimal performance backstepping control method for unmanned surface vessel formations.

[0179] This disclosure is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0180] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0181] While the specific embodiments of this disclosure have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of this disclosure. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this disclosure are still within the scope of protection of this disclosure.

Claims

1. A method for optimal backstepping control of unmanned surface vessel (USV) formations, characterized in that, include: Considering external disturbances, a dynamic model of the multiple unmanned surface vessels to be controlled is established, and a disturbance observer and a neural network identifier are used to compensate for external disturbances and unknown nonlinear terms in the dynamic model. Based on the dynamic model, an optimal virtual controller is constructed. The derivative of the optimal virtual control is calculated by introducing a first-order integral filter, and then the optimal actual controller is constructed. Based on the dynamic model, and utilizing the characteristics of the hyperbolic cosecant function, a monotonic tube boundary function is designed to limit the formation error of the unmanned surface vessel within the specified performance range. By using a virtual controller and a physical controller, continuous control law and monotonic tube boundary function are used for formation control, and the position of the following unmanned surface vessel is kept synchronized with the desired trajectory of the leader unmanned surface vessel under external disturbances. The optimal virtual controller constructed is expressed by the formula: The optimal actual controller constructed is expressed by the formula: in, It is the optimal practical controller. , , , The angle between two consecutive unmanned surface vessels. It's the bow roll angle, a neural network. , , Approximation controllers , , , Unknown dynamics within, , , , It is a Gaussian radial basis function. , , These represent the estimated values ​​of the ideal weights for the actor network. Indicates the error coordinate transformation. Indicates speed, where, It is the oscillation linear velocity. It is the sway linear velocity. It is the bow roll rate.

2. The optimal backstepping control method for unmanned surface vessel formations as described in claim 1, characterized in that, The dynamic model is constructed based on the kinematic model of the unmanned surface vessel, specifically as follows: No. The kinematic model of an unmanned surface vessel is expressed by the following formula: in, It is the position of the oscillation. It is a horizontal position. It's the bow roll angle. It is the oscillation linear velocity. It is the sway linear velocity. It is the bow roll angular velocity; make and Then the first The dynamic model of the unmanned surface vessel is as follows: in, It is the inertia matrix. It is the total Coriolis and centripetal acceleration matrix. It is a control input. It is an external disturbance. It is the damping matrix.

3. The optimal backstepping control method for unmanned surface vessel formations as described in claim 1, characterized in that, The method of using a perturbation observer and a neural network identifier to compensate for external disturbances and unknown nonlinear terms in the dynamic model specifically includes: in, Represents the weights of the neural network. Represents a basis function vector. Indicates the approximation error; The disturbance observer takes the following form: in, It is the inertia matrix. It is the total Coriolis and centripetal acceleration matrix. It is a control input. For the total disturbance, Indicates speed, express The error, It is a state variable. These are design parameters.

4. The optimal backstepping control method for unmanned surface vessel formations as described in claim 1, characterized in that, The optimal virtual controller and the optimal actual controller are constructed using a combination of backstepping techniques and reinforcement learning algorithms, and the steps are as follows: Establish the optimal performance index function; Taking the derivative of both sides of the optimal performance index function, we obtain the Hamilton-Jacobi-Bellman equation. Based on the Hamilton-Jacobi-Bellman equation, the optimal controller with unknown parameters is obtained by solving the equation. By using a reinforcement learning algorithm based on an actor-critic network, and guided by the optimal performance index function, the unknown parameters in the optimal controller are approximated to obtain the final optimal virtual controller and the optimal actual controller.

5. The optimal backstepping control method for unmanned surface vessel formations as described in claim 1, characterized in that, The monotonic tube boundary function is as follows: in, , , , , It refers to the line-of-sight range between two consecutive unmanned surface vessels. It is the angle between two consecutive unmanned surface vessels and in, It is a time constant. It is formation error The convergence rate, The initial value represents the pre-selected boundary.

6. A specified performance optimal backstepping control system for unmanned surface vessel (USV) formations, characterized in that, The method for optimal backstepping control of unmanned surface vessel formations as described in any one of claims 1-5 includes: The model building module is configured to: establish a dynamic model of the multiple unmanned surface vessels to be controlled under the condition of considering external disturbances, and use a disturbance observer and a neural network identifier to compensate for external disturbances and unknown nonlinear terms in the dynamic model; The controller construction module is configured to: construct the optimal virtual controller based on the dynamic model, calculate the derivative of the optimal virtual control by introducing a first-order integral filter, and then construct the optimal actual controller. The boundary design module is configured to: design a monotonic tube boundary function based on the dynamic model and utilizing the characteristics of the hyperbolic cosecant function to limit the formation error of the unmanned surface vessel within the specified performance range; The formation control module is configured to perform formation control using a continuous control law and a monotonic tube boundary function through a virtual controller and a physical controller, thereby controlling the position of the following unmanned surface vessel to remain synchronized with the desired trajectory of the leader unmanned surface vessel under external disturbances.

7. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the optimal backstepping control method for unmanned surface vessel formations according to any one of claims 1-5.

8. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, which, when executed by a processor, implement a specified performance optimal backstepping control method for unmanned surface vessel formations as described in any one of claims 1-5.

9. An electronic device, characterized in that, include: The device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to perform a specified performance optimal backstepping control method for unmanned surface vessel formation as described in any one of claims 1-5.

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