Regulated performance optimal backstepping control method and system for unmanned ship formation

Abstract

The invention provides a stipulated performance optimal backstepping control method and system for an unmanned ship formation, and relates to the technical field of unmanned ship optimal backstepping control, and the method comprises the steps: building a dynamic model of multiple unmanned ships, and compensating the external interference and unknown nonlinear terms of the dynamic model through a disturbance observer and a neural network identifier; an optimal virtual controller is constructed, a derivative of optimal virtual control is calculated by introducing a first-order integral filter, and then an optimal actual controller is constructed; designing a monotonic tube boundary function by utilizing the characteristics of a hyperbolic cosecant function; formation control is carried out through a virtual controller and an actual controller by using a continuous control law and a monotone control boundary function, and the position of the following unmanned surface vehicle is controlled to be synchronous with the expected trajectory of the leading unmanned surface vehicle under the condition of external disturbance; according to the method, the disturbance observation estimator is used for time-varying external disturbance, a neural network is used for approximating unknown parameters of a dynamic model, and a monotone pipe boundary function is used for enabling formation errors to evolve in a specified area.

Description

Technical Field

[0001] The present disclosure relates to the technical field of optimal backstepping control for unmanned boats, and in particular to a method and system for optimal backstepping control of specified performance for an unmanned boat formation. Background Art

[0002] With the continuous advancement of technology, unmanned systems have experienced rapid development. As an important branch of the unmanned system field, unmanned boats have naturally become a hot focus of research in this field. At present, unmanned boat technology is in a rapid development stage, and technological integration and innovation are its main trends. In the future, unmanned boats will be more intelligent and autonomous, and will be able to perform tasks in more complex and harsher marine environments. At the same time, the application areas of unmanned boats will continue to expand, from traditional fields such as marine monitoring and marine surveys to cargo transportation, seabed mineral resource exploration, offshore wind farm maintenance and other fields. The rapid development of science and technology has made the application of a single unmanned boat insufficient to meet the needs of marine exploration projects. Therefore, it is inevitable to use multiple unmanned boats to perform work tasks simultaneously in marine engineering.

[0003] When unmanned boats perform various tasks such as ocean monitoring, resource exploration, and maritime rescue in the ocean, they are often affected by uncertain factors such as external interference, which puts higher and higher requirements on the control performance of unmanned boats. When performing tasks, the convergence speed and transient performance of the formation error are extremely important, so the prescribed performance control has received extensive attention in engineering applications. In this case, it is worth pointing out that the monotonic tube boundary performance function improves the convergence speed and performance of the prescribed performance control method, while also reducing jitter; and uses a disturbance observer to estimate the external disturbance, and then introduces the disturbance observer into the optimal group control law to compensate for the external disturbance; at the same time, the purpose of precision control of the unmanned boat is achieved through an adaptive control method to achieve an ideal motion trajectory.

[0004] At present, 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 loss of unmanned boats will 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 boat formations. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a specified performance optimal backstepping control method and system for unmanned boat formation, which utilizes the disturbance observation estimator to estimate the time-varying external disturbance, and uses a neural network to approximate the unknown parameters of the dynamic model, and uses the monotonic tube boundary function to make the formation error evolve within a specified area.

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

[0007] A prescribed performance optimal backstepping control method for an unmanned boat formation, comprising:

[0008] Under the condition of external disturbance, the dynamic model of the multi-unmanned boat to be controlled is established, and the disturbance observer and neural network identifier are used to compensate for the external disturbance and unknown nonlinear terms of the dynamic model.

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

[0010] Based on the dynamic model, the monotone boundary function is designed by using the characteristics of the hyperbolic cosecant function to limit the formation error of the unmanned boats within the specified performance range.

[0011] Through virtual controller and actual controller, continuous control law and monotonic pipe boundary function are used to perform formation control, and the position of the follower unmanned boat is controlled to keep synchronization with the desired trajectory of the leading unmanned boat under external disturbance.

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

[0013] A specified performance optimal backstepping control system for an unmanned boat formation, comprising:

[0014] The model building module is configured to: establish a dynamic model of the multi-unmanned boat to be controlled under external disturbance conditions, and compensate for the external disturbance and unknown nonlinear terms of the dynamic model by using a disturbance observer and a neural network identifier;

[0015] The controller construction module is configured to: construct an 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 an optimal actual controller;

[0016] The boundary design module is configured to: design a monotone pipe boundary function based on the dynamic model and using the characteristics of the hyperbolic cosecant function to limit the formation error of the unmanned boats within the specified performance range;

[0017] The formation control module is configured to: perform formation control through a virtual controller and an actual controller using a continuous control law and a monotonic pipe boundary function, and control the position of the follower unmanned boat to keep synchronization with the desired trajectory of the leading unmanned boat 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, and when the computer program is executed by a processor, the computer program implements the specified performance optimal backstepping control method for an unmanned boat formation.

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

[0021] A non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by a processor, a specified performance optimal backstepping control method for an unmanned boat formation is implemented.

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

[0023] An electronic device comprises: 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 so that the electronic device executes the specified performance optimal backstepping control method for an unmanned boat formation.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] 1. The technical solution of the present invention designs a performance function of a predefined time - the monotonic tube boundary. 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 the formation error and reduces the jitter, so that the formation error converges to a neighborhood of the origin within a predetermined time, but also maintains the monotonicity of the function in the presence of parameter changes, thereby achieving an ideal formation trajectory. Under the framework of backstepping optimization, a new formation control strategy is obtained, which can minimize the energy consumption and ensure that the formation error evolves within a given area.

[0026] 2. Since the X-axis and Y-axis in the coordinate systems of two consecutive unmanned boats are coupled together, the Hamilton-Jacobi-Bellman equations are jointly designed, and then two optimal virtual controllers are obtained at the same time. The reinforcement learning algorithm uses the negative gradient of a simple positive definite function of the partial derivatives of the Hamilton-Jacobi-Bellman equations to greatly simplify the optimal control and achieve optimal formation control. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The accompanying drawings constituting a part of the present disclosure are used to provide a further understanding of the present disclosure. The illustrative embodiments of the present disclosure and their descriptions are used to explain the present disclosure and do not constitute an improper limitation on the present disclosure.

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

[0029] Figure 2 1 is the phase plane trajectory of the five unmanned boats and their snapshots in Example 1.

[0030] Figure 3 It is the sight range error of two consecutive unmanned boats and the monotonic tube boundary function in Example 1.

[0031] Figure 4 It is the angle error of two consecutive unmanned boats and the monotonic tube boundary function in Example 1.

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

[0033] Figure 6 The disturbances of surge force, sway force and yaw moment and their estimation in Example 1.

[0034] Figure 7 It is a weight convergence curve diagram of the actor-critic network of Example 1.

[0035] Figure 8 It is a weight convergence curve diagram of the actor-critic network of Example 1. DETAILED DESCRIPTION

[0036] The present disclosure is further described below in conjunction with the accompanying drawings and embodiments.

[0037] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present disclosure belongs.

[0038] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present disclosure. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0039] Example 1

[0040] In one embodiment of the present disclosure, a method for optimal backstepping control of a specified performance for an unmanned boat formation is provided, comprising:

[0041] Step S1: Under the condition of external disturbance, a dynamic model of the multi-unmanned boat to be controlled is established, and the external disturbance and unknown nonlinear terms of the dynamic model are compensated by using a disturbance observer and a neural network identifier;

[0042] Step S2: Based on the dynamic model, an optimal virtual controller is constructed, and the derivative of the optimal virtual control is calculated by introducing a first-order integral filter, thereby constructing an optimal actual controller;

[0043] Step S3: Based on the dynamic model, using the characteristics of the hyperbolic cosecant function, a monotone pipe boundary function is designed to limit the formation error of the unmanned boats within a specified performance range;

[0044] Step S4: Through the virtual controller and the actual controller, the formation control is performed using the continuous control law and the monotonic tube boundary function, and the position of the follower unmanned boat is controlled to be synchronized with the desired trajectory of the leading unmanned boat under external disturbance.

[0045] As an embodiment, the present invention discloses a method for optimal backstepping control of prescribed performance for unmanned boat formation, which uses a disturbance observation estimator to estimate time-varying external disturbances, and uses a neural network to approximate unknown parameters, and uses an improved prescribed performance function to make the formation error evolve within a prescribed area. The specific implementation process is as follows:

[0046] Step 1:

[0047] Considering N fully driven unmanned boats, the kinematic model of the i-th unmanned boat is given by:

[0048]

[0049] Among them, x i is the vertical position, y i is the sway position, ψ i is the heading angle, u i is the longitudinal velocity, v i is the lateral velocity, r i is the yaw angular velocity.

[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 boat is:

[0051]

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

[0053] A leader-follower formation architecture, such as Figure 1 As shown, it includes the leader unmanned boat i-1 and the follower unmanned boat i, i = 1, ..., N, where ψ i is the heading angle, u i is the longitudinal velocity, v i is the lateral velocity, r i is the yaw angular velocity, (x i ,y i ) represents the position of the unmanned boat, is the angle between two consecutive unmanned boats, d i It is the visual range between two consecutive unmanned boats.

[0054] The angle and sight range between two consecutive unmanned boats are defined as:

[0055]

[0056] It can be concluded that:

[0057]

[0058] Among them, x i-1 is the longitudinal position of the i-1th unmanned boat, y i-1 is the lateral swing position of the i-1th unmanned boat.

[0059] The disturbance observer is used to estimate the external disturbance, and then the disturbance observer is introduced into the dynamic model to compensate for the external disturbance. i ) i Approximation is performed through a neural network identifier, specifically:

[0060]

[0061] in, represents the neural network weight, S i (Z i ) represents the basis function vector, ε i Represents the approximation error.

[0062] The disturbance observer has the following form:

[0063]

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

[0065] Step 2:

[0066] The following is the formation error e ji ,j=d,ψ definition, the formation error includes the sight range 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] Among them, d i,des Represents the expected distance between two consecutive unmanned boats.

[0070] Using the initial value property of the hyperbolic cosecant function, a set of feasible monotone tube boundary functions are designed:

[0071]

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

[0073]

[0074] Where T_c>0 is the time constant, is the formation error e ji The convergence rate of is the initial value representing the preselected boundary.

[0075] Step 3:

[0076] In order to establish the formation error e ji With the monotonic tube boundary function and b ji Inspired by the traditional exponential form of the prescribed performance technology, the error conversion function is introduced as follows:

[0077]

[0078] Among them, z ji is the conversion error, T(z ji ) satisfies the following:

[0079]

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

[0081]

[0082] Take the derivative of both sides of the above equation

[0083]

[0084] in,

[0085] From the previous description we can get:

[0086]

[0087] Then we have:

[0088]

[0089] Step 4: Combine backstepping techniques and reinforcement learning algorithms to design the optimal controller:

[0090] According to the given kinematic model and dynamic model of the unmanned boat, the optimal virtual controller and the optimal actual controller are designed respectively.

[0091] (1) Optimal virtual controller

[0092] Establish the optimal performance index function for the position of the unmanned boat:

[0093]

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

[0095] The Hamilton Jacobi Bellman (HJB) equation is obtained by derivatizing both sides of the above formula as follows:

[0096]

[0097] By solving Get with unknown parameters The optimal virtual controller is as follows:

[0098]

[0099] Will This breaks down into:

[0100]

[0101] in, and is a positive design parameter.

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

[0103]

[0104] Since V NNdi is an unknown continuous function, so we use a neural network to estimate its value in a compact set Ω, then V NNdi It is expressed as:

[0105]

[0106] in represents the ideal weight, represents the basis function vector, ε di (z di ) is the approximate error.

[0107] The reinforcement learning algorithm based on the actor-critic network is used to respectively Approximating with the optimal virtual controller yields:

[0108]

[0109] in, yes The approximate value of yes The estimated value of the neural network Approach Unknown dynamics in is an estimate of the weights of the ideal critic network, the neural network Approach Unknown dynamics in is an estimate of the ideal actor weight, represents the basis function vector.

[0110] According to the above formula, the approximate HJB function is 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 boat:

[0115]

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

[0117] The Hamilton Jacobi Bellman (HJB) equation is obtained by derivatizing both sides of the above formula as follows:

[0118]

[0119] By solving Get with unknown parameters The optimal virtual controller is as follows:

[0120]

[0121] Will This breaks down into:

[0122]

[0123] in, and is a design parameter.

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

[0125]

[0126] Since VNNψi is an unknown continuous function, so a neural network is used to estimate its value in a compact set Ω. Then V NNψi It is expressed as:

[0127]

[0128] in represents the neural network weights, represents the basis function vector, ε ψi (z ψi ) is the approximate error.

[0129] The reinforcement learning algorithm based on the actor-critic network is used to respectively Approximating with the optimal virtual controller yields:

[0130]

[0131] in, yes The approximate value of yes The estimated value of the neural network Approach Unknown dynamics in is an estimate of the weights of the ideal critic network, the neural network Approach Unknown dynamics in is an estimate of the ideal actor network weights, represents the basis function vector.

[0132] According to the above formula, the approximate HJB function is as follows:

[0133]

[0134] The Bellman residual is defined as follows:

[0135]

[0136] In order to avoid repeated differentiation of virtual control, the dynamic surface control technology is used to calculate the derivative of the optimal virtual control by introducing a first-order integral filter, thereby preventing the so-called complexity problem in the subsequent steps, specifically:

[0137] let Through the first-order filter to get α fi :

[0138]

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

[0140] therefore, The derivative of is:

[0141]

[0142] in, Bounded.

[0143] (2) Optimal actual controller

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

[0145]

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

[0147] Next, we can get the corresponding Hamilton Jacobi Bellman (HJB) equation as follows:

[0148]

[0149] Similar to the construction method of the optimal virtual controller, the approximate optimal actual controller is obtained by using the reinforcement learning algorithm:

[0150]

[0151] in, yes The estimated value of the neural network For approximation Unknown dynamics in represents the estimated value of the ideal weight of the actor network, is the basis function vector.

[0152] In the process of approximation using the reinforcement learning algorithm based on the executive-critic network, a stability judgment method based on the gradient descent method and the Lyapunov function stability theory is used to design the adaptive update rate of the executive-critic network weights:

[0153]

[0154] in, and is the design parameter of the critic network, and is the design parameter of the actor network, σ i is the design constant, is the identity matrix.

[0155] In order to prove the feasibility, effectiveness and correctness of this example, the following simulation example is carried out:

[0156] In this simulation experiment, an optimal controller based on reinforcement learning was designed for an unmanned boat formation system with external disturbances, which enabled the unmanned boat formation to not only track the reference trajectory of Liang, but also improve 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 boat is 23.8 kg; the length is 1.255 m; 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 is of the form and b di =b ψi = b = 0.4q-1.6, where

[0161] In the optimal controller design process, the critic network and and actor networks and Both contain 27 neurons and have a width of 0.1; Neural Network and The center points of the neural network are evenly distributed on [-1.2, 1.2]; and The center points are 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 the five unmanned boats 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 design parameters of the system are:

[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 used to Figure 1 The multi-unmanned boats shown in the figure are modeled and simulated, and the simulation results are as follows Figure 2-Figure 8 As shown, Figure 2 The trajectories and snapshots of five vehicles at 0s, 45s, 120s, 230s, 360s and 500s are given; Figure 3 is the sight range error of two consecutive unmanned boats and the monotonic tube boundary function of this embodiment; Figure 4 is the angle error of two consecutive unmanned boats and the monotonic tube boundary function in this embodiment; Figure 3 and Figure 4 It can be seen that the sight range error and angle error evolve within the specified area and the convergence time is 2.7s; Figure 5 It is the control input for surge force, sway force and yaw moment; Figure 6 are the disturbances of surge force, sway force and yaw moment and their estimates; Figure 7 and Figure 8 These are all weight convergence curves of neural networks. It can be seen from the figure that each weight in the actor network and the critic network eventually tends to be stable and converged. Therefore, the designed reinforcement learning neural network control scheme can effectively achieve accurate approximation of the designed optimal controller and has a good convergence effect. In summary, all signals in the system are consistently and ultimately bounded, and the simulation results prove the effectiveness of the proposed optimal control scheme.

[0166] This embodiment uses backstepping and reinforcement learning technology as the design framework to propose a specified performance optimal formation control scheme based on reinforcement learning for an unmanned boat formation system with time-varying unknown disturbances. In order to ensure that the formation error accurately and stably converges to a near-zero state within a predetermined time range, a class of predefined performance boundary functions is adopted to greatly improve the formation accuracy. This embodiment solves the problem that the Hamilton-Jacobi-Bellman square equation is difficult to solve directly by utilizing the approximation ability of the reinforcement learning neural network to nonlinear functions and using the reinforcement learning algorithm to approximate the actual optimal controller, and designs an optimal controller that meets the control requirements, and adjusts the weights of the neural network through the adaptive law, so that the designed approximate optimal controller can approximate the actual optimal controller. The algorithm can be trained online and generate the optimal controller. The adaptive optimization algorithm introduced in this embodiment guides each unmanned boat to follow the previous unmanned boat, and no one falls behind. Finally, the proposed vehicle queue control method is verified by simulation examples to ensure the quality of all signals.

[0167] Example 2

[0168] In one embodiment of the present disclosure, a specified performance optimal backstepping control system for an unmanned boat formation is provided, comprising:

[0169] The model building module is configured to: establish a dynamic model of the multi-unmanned boat to be controlled under external disturbance conditions, and compensate for the external disturbance and unknown nonlinear terms of the dynamic model by using a disturbance observer and a neural network identifier;

[0170] The controller construction module is configured to: construct an 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 an optimal actual controller;

[0171] The boundary design module is configured to: design a monotone pipe boundary function based on the dynamic model and using the characteristics of the hyperbolic cosecant function to limit the formation error of the unmanned boats within the specified performance range;

[0172] The formation control module is configured to: perform formation control through a virtual controller and an actual controller using a continuous control law and a monotonic pipe boundary function, and control the position of the follower unmanned boat to keep synchronization with the desired trajectory of the leading unmanned boat under external disturbances.

[0173] Example 3

[0174] In one embodiment of the present disclosure, a computer program product is provided, including a computer program, and when the computer program is executed by a processor, the computer program implements the specified performance optimal backstepping control method for an unmanned boat formation.

[0175] Example 4

[0176] In one embodiment of the present disclosure, a non-transitory computer-readable storage medium is provided, wherein the non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by a processor, the specified performance optimal backstepping control method for an unmanned boat formation is implemented.

[0177] Example 5

[0178] In one embodiment of the present disclosure, an electronic device is provided, 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, so that the electronic device executes the specified performance optimal backstepping control method for an unmanned boat formation.

[0179] The present disclosure is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present disclosure. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0180] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0181] Although the above describes the specific implementation methods of the present disclosure in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present disclosure. Technical personnel in the relevant field should understand that on the basis of the technical solution of the present disclosure, various modifications or variations that can be made by those skilled in the art without creative work are still within the scope of protection of the present disclosure.

Claims

1. A method for optimal backstepping control of specified performance for unmanned boat formation, characterized in that: include: Under the condition of external disturbance, the dynamic model of the multi-unmanned boat to be controlled is established, and the disturbance observer and neural network identifier are used to compensate for the external disturbance and unknown nonlinear terms of the dynamic model. Based on the dynamic model, the optimal virtual controller is constructed, and the derivative of the optimal virtual control is calculated by introducing a first-order integral filter, thereby constructing the optimal actual controller; Based on the dynamic model, the monotone boundary function is designed by using the characteristics of the hyperbolic cosecant function to limit the formation error of the unmanned boats within the specified performance range. Through virtual controller and actual controller, continuous control law and monotonic pipe boundary function are used to perform formation control, and the position of the follower unmanned boat is controlled to keep synchronization with the desired trajectory of the leading unmanned boat under external disturbance.

2. A method for optimal backstepping control of specified performance for unmanned boat formation according to claim 1, characterized in that: The dynamic model is constructed based on the kinematic model of the unmanned boat, specifically: The kinematic model of the i-th unmanned boat is expressed as: Among them, x i is the vertical position, y i is the sway position, ψ i is the heading angle, u i is the longitudinal velocity, v i is the lateral velocity, r i is the yaw angular velocity; 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 boat is: in, is the inertia matrix, C(ν i ) is the total Coriolis and centripetal acceleration matrix, τ i =[τ ui ,τ vi ,τ ri ] T is the control input, τ wi =[τ wui ,τ wvi ,τ wri ] T is the external disturbance, D(ν i ) is the damping matrix.

3. The method for optimal backstepping control of specified performance for unmanned boat formation according to claim 1, characterized in that: The use of the disturbance observer and the neural network identifier to compensate for the external disturbance and unknown nonlinear terms of the dynamic model is specifically as follows: in, represents the neural network weight, S i (Z i ) represents the basis function vector, ε i Represents the approximation error. The disturbance observer has the following form: in, is the inertia matrix, C(ν i ) is the total Coriolis and centripetal acceleration matrix, τ i =[τ ui ,τ vi ,τ ri ] T is the control input, τ di is the total disturbance, ν i =[u i ,v i ,r i ] T Indicates speed, express The error, is the state variable, C di =diag[C d1i ,C d2i ,C d3i ]>0 is the design parameter.

4. The method for optimal backstepping control of specified performance for unmanned boat formation according to claim 1, characterized in that: The optimal virtual controller and the optimal actual controller are constructed by combining backstepping technology and reinforcement learning algorithm, and the steps are as follows: Establish optimal performance indicator function; By 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 solved; Through the reinforcement learning algorithm based on the actor-critic network, under the guidance of the optimal performance indicator function, the unknown parameters in the optimal controller are approximated to obtain the final optimal virtual controller and optimal actual controller.

5. The method for optimal backstepping control of specified performance for unmanned boat formation according to claim 1, characterized in that: The optimal virtual controller constructed is expressed as: The optimal actual controller constructed is expressed as: in, is the optimal actual controller, is the angle between two consecutive unmanned boats, Neural Networks Approximation Unknown dynamics in S i is a Gaussian radial basis function, They respectively represent the estimated values ​​of the ideal weights of the actor network.

6. The method for optimal backstepping control of specified performance for unmanned boat formation according to claim 1, characterized in that: The monotone tube boundary function is as follows: Among them, 12 = col(1,1), j = d,ψ, and Where T_c>0 is the time constant, is the formation error e ji The convergence rate of is the initial value representing the preselected boundary.

7. A specified performance optimal backstepping control system for an unmanned boat formation, characterized in that: include: The model building module is configured to: establish a dynamic model of the multi-unmanned boat to be controlled under external disturbance conditions, and compensate for the external disturbance and unknown nonlinear terms of the dynamic model by using a disturbance observer and a neural network identifier; The controller construction module is configured to: construct an 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 an optimal actual controller; The boundary design module is configured to: design a monotone pipe boundary function based on the dynamic model and using the characteristics of the hyperbolic cosecant function to limit the formation error of the unmanned boats within the specified performance range; The formation control module is configured to: perform formation control through a virtual controller and an actual controller using a continuous control law and a monotonic pipe boundary function, and control the position of the follower unmanned boat to keep synchronization with the desired trajectory of the leading unmanned boat under external disturbances.

8. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the specified performance optimal backstepping control method for an unmanned boat formation as described in any one of claims 1 to 6 is implemented.

9. A non-transitory computer-readable storage medium, characterized in that: The non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by the processor, a specified performance optimal backstepping control method for an unmanned boat formation as described in any one of claims 1-6 is implemented.

10. An electronic device, characterized in that: include: 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 so that the electronic device executes a specified performance optimal backstepping control method for an unmanned boat formation as described in any one of claims 1-6.

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