Fixed-time optimal containment control method and system for underactuated unmanned surface vehicle system

Abstract

The application provides a fixed-time optimal containment control method and system for an underactuated multi-unmanned surface vehicle system, comprising: using an auxiliary variable method to perform coordinate transformation on an underactuated multi-unmanned surface vehicle system model to establish a multi-unmanned surface vehicle system model; constructing an inclusion error system and a constraint condition of the inclusion error of the underactuated multi-unmanned surface vehicle system; combining a preset performance control method to construct an inclusion error conversion mechanism to obtain a dynamic equation of the inclusion error system; designing an optimal cost function based on the dynamic equation of the inclusion error system; and based on a reinforcement learning algorithm, using an identification-execution-evaluation learning network to solve a coupled HJB equation to obtain a fixed-time optimal containment controller, so that the optimal cost function of the inclusion error under the constraint condition is optimal. The application guarantees that the underactuated multi-unmanned surface vehicle system with the preset performance realizes the fixed-time containment control at a minimum cost, and the upper limit of the rest time is irrelevant to the initial state of the underactuated unmanned surface vehicle system.

Description

Technical Field

[0001] This invention relates to the field of under-steering unmanned surface vessel (USV) technology, and in particular to a fixed-time optimal control method and system for an under-steering multi-USV system. Background Technology

[0002] The widespread application of multi-unmanned surface vessel (MSV) systems in environmental monitoring, search and rescue, and collaborative transportation has drawn significant attention from researchers to the study of their distributed cooperative control strategies. Distributed cooperative control methods based on local information interaction to achieve global mission objectives have demonstrated significant advantages in improving the efficiency of mission execution in complex marine scenarios. Among these, inclusion control, a special type of distributed cooperative control method, aims to guide the follower states to converge within the convex hull formed by multiple leaders. The inclusion control problem of MSV systems has become a research hotspot in the field of MSV system control, but it still faces several key technical challenges that urgently need to be addressed.

[0003] The primary technical challenge stems from the inherent characteristics of unmanned surface vessel (USV) systems. During navigation, USV systems are inevitably affected by uncertainties in model dynamics. Furthermore, the underactuated nature of USVs results in a control input dimension lower than the motion degrees of freedom, creating nonholonomic constraints. These coupled characteristics easily lead to instability in the control system; therefore, designing an inclusive control law suitable for underactuated USV systems is a crucial fundamental issue.

[0004] Secondly, multi-unmanned surface vessel (USV) systems often face significant energy consumption issues during complex mission execution. Designing control strategies that minimize performance indices based on optimal control theory frameworks has become an important approach to improving system efficiency. Reinforcement learning methods, through iterative training by integrating system state, environmental information, and neighboring vessel interaction data, have demonstrated potential for solving such optimization problems. Specifically, the identification-execution-evaluation architecture provides a theoretical framework for optimal control of systems with unknown dynamics by constructing an identification network to approximate the unknown system dynamics, an execution network to approximate the optimal strategy, and an evaluation network to estimate the value function. How to construct an optimal inclusive control method for underactuated multi-USV systems within this architecture is the first technical problem this invention aims to solve.

[0005] Furthermore, practical applications place higher demands on the system's convergence speed and stability. Compared to finite-time cooperative control, fixed-time cooperative control offers advantages such as faster convergence rate, stronger robustness, and convergence time independent of the initial state. Although research on finite-time inclusion control for underactuated multi-unmanned surface vessel systems has achieved some progress, a systematic solution for fixed-time optimal inclusion control of underactuated systems is still lacking, constituting the second technical challenge.

[0006] On the other hand, existing research mostly focuses on the steady-state performance of the system, and has shortcomings in transient process control. Preset performance control methods, by introducing dynamic performance functions to constrain the error evolution trajectory, provide a new approach to simultaneously ensure the steady-state and transient performance of the system. However, existing preset performance control methods are difficult to meet the synergistic requirements of fixed-time control and performance optimization. Therefore, how to construct an optimal inclusive control method that combines preset performance constraints and fixed-time convergence characteristics has become the third key technical problem that urgently needs to be solved in this invention. Summary of the Invention

[0007] The purpose of this invention is to provide a fixed-time optimal control method and system for underdriven multi-unmanned surface vessel systems to solve the problems in the background art.

[0008] The technical solution for achieving the objective of this invention is as follows:

[0009] A fixed-time optimal inclusion control method for an underactuated multi-unmanned surface vessel system includes:

[0010] Step 1: Use the auxiliary variable method to perform coordinate transformation on the underactuated multi-unmanned surface vessel system model to establish the multi-unmanned surface vessel system model;

[0011] Step 2: Construct the error-inclusive system and the error-inclusive constraints for the underactuated multi-unmanned surface vessel system;

[0012] Step 3: Combine the preset performance control method to construct a dynamic equation that includes an error conversion mechanism, and obtain the dynamic equation of the error system.

[0013] Step 4: Based on the dynamic equations of the system including the error, design the optimal cost function;

[0014] Step 5: Based on the reinforcement learning algorithm, the coupled Hamilton-Jacobi-Bellman equations of the multi-unmanned surface vessel system are solved using the identification-execution-evaluation learning network to obtain the fixed-time optimal inclusion controller, so that the inclusion error is optimal under the constraint conditions.

[0015] A fixed-time optimal inclusion control system for an underactuated multi-unmanned surface vessel system includes:

[0016] A model building unit for underactuated multi-unmanned surface vessel (USV) system is established by using the auxiliary variable method to transform the coordinates of the underactuated USV system model.

[0017] The system includes error system and constraint construction units, and constructs the error system and constraint conditions of the underdriven multi-unmanned surface vessel system.

[0018] A dynamic equation construction unit containing the error system is used, combined with a preset performance control method, to construct a dynamic equation containing the error conversion mechanism, thereby obtaining the dynamic equation containing the error system.

[0019] The optimal cost function design unit designs the optimal cost function based on the dynamic equations of the system containing errors.

[0020] The controller design unit, based on reinforcement learning algorithms, uses an identification-execution-evaluation learning network to solve the coupled Hamilton-Jacobi-Bellman equations of the multi-unmanned surface vessel system, and obtains the fixed-time optimal inclusion controller, which optimizes the inclusion error under the constraints.

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0022] In practical applications, for an underactuated multi-unmanned surface vessel system with any initial state, the fixed-time optimal inclusion control method for underactuated multi-unmanned surface vessel systems proposed in this invention can make the state of the followers in the system converge to the convex hull region formed by multiple leaders within a fixed time, and can estimate the resting time required to achieve inclusion control.

[0023] In practical applications, for underactuated multi-unmanned surface vessel systems with preset performance, the control method proposed in this invention can ensure that the transient and steady-state performance, including errors, of the system is simultaneously satisfied.

[0024] This invention designs a fixed-time control strategy based on an identification-execution-evaluation learning structure using reinforcement learning methods, enabling the system to complete control tasks while minimizing energy consumption, thus achieving a balance between performance and energy consumption. Attached Figure Description

[0025] Figure 1 This is a flowchart illustrating the complete technical solution of this invention patent;

[0026] Figure 2 This is the communication network of the underdriven multi-unmanned surface vessel system in the embodiment;

[0027] Figure 3 The example shows the trajectory curve of the under-drive unmanned surface vessel system.

[0028] Figure 4 The example includes an error variation curve;

[0029] Figure 5 Example τ ui Change trajectory diagram;

[0030] Figure 6 Example τ ri Change trajectory diagram;

[0031] Figure 7 Neural network weights for example and Change curve. Detailed Implementation

[0032] Combination Figure 1 This invention provides a fixed-time optimal inclusion control method for an underdriven multi-unmanned surface vessel system, comprising the following steps:

[0033] Step 1: Establish a model of the understeerable multi-unmanned surface vessel system

[0034] Consider an underactuated multi-unmanned surface vessel (USV) system consisting of M followers and NM (N > M) leaders. The model of the i-th underactuated following USV is described as follows:

[0035]

[0036] in Let x represent the position vector of the i-th unmanned surface vessel in geodetic coordinates. i and y i Indicates northward and eastward positions, ψ i ∈[0,2π] is the heading angle. Let u represent the velocity vector of the i-th unmanned surface vessel in the hull coordinate system. i , r i These represent the longitudinal velocity, lateral velocity, and bow roll angular velocity, respectively. τ represents the control input vector. ui ,τ ri R represents the longitudinal control force and the yaw control force, respectively. i (ψ i M i C i D i Let represent the rotation matrix, inertia matrix, Coriolis centripetal force matrix, and hydrodynamic damping matrix, respectively, in the following forms:

[0037]

[0038] Since system (1) is an underactuated system, a vector controller is introduced to better design the optimal controller. The above mathematical model of the unmanned surface vessel can be rewritten as:

[0039]

[0040] in For an unknown nonlinear function, ω i and control input τ i The relationship between them can be given as follows:

[0041] The position coordinates of the leader unmanned surface vessel are designed as follows: make The convex hull region formed by all leaders can then be represented as:

[0042] in and These represent the communication connection matrix between the following unmanned surface vessels (USVs) and the communication connection matrix between the following USV and the leader USV, respectively.

[0043] Step 2: Constructing an error-inclusive system for the underactuated multi-unmanned surface vessel system

[0044] Based on the underactuated multi-unmanned surface vessel (USV) system model in step 1, the inclusion error between the i-th follower USV and the leader USV is defined as:

[0045]

[0046] in a ij a represents the elements of the adjacency matrix of the unmanned surface vessel. ij >0 indicates that following unmanned surface vessel i can obtain information from unmanned surface vessel j; otherwise, a ij =0, Let N i For the set of unmanned surface vessels connected to the i-th following unmanned surface vessel, Define the Laplace matrix as Assuming that leaders cannot exchange information, but followers can, and each follower UAV has at least one neighbor. Therefore, the Laplace matrix corresponding to the communication topology of the underdriven multi-UAV system can be expressed as:

[0047]

[0048] in This indicates the information exchange between the following unmanned surface vessels. It represents the information exchange between the leader and followers of a formation.

[0049] To ensure that transient and steady-state performance, including errors, is confined within a predefined region, the constraints including errors are designed as follows:

[0050]

[0051] The upper and lower constraint boundaries can be represented as follows:

[0052]

[0053] z ip (t)=( z ip,0 - z ip,∞ )exp(-π ip t)+ z ip,∞ ,

[0054] 0 < z ip, ∞< z ip,0 , π ip It is a constant greater than zero. These are the initial values ​​of the upper constraint boundary. It is the convergence value of the upper constraint boundary. z ip,0 These are the initial values ​​of the lower constraint boundary. z ip,∞ It is the convergence value of the lower constraint boundary.

[0055] Step 3: Construct a mechanism that includes error transformation

[0056] In order to establish z ip (t) and upper and lower bounds - z ip (t), The relationship between the two, defining the error as...

[0057]

[0058] Among them, g ip It's a conversion error. It is a transformation function that satisfies the following conditions: 1) -λ ip <Y ip <1;2) 3) 4) If g ip =0,

[0059] Y ip =0. Select the conversion function as

[0060]

[0061] in Substituting the above equation into (5), we get

[0062]

[0063] ln(·) represents the natural logarithm function.

[0064] The dynamic equation for calculating the error is: in Let g i =[g ix ,g iy ,g iψ ] T ,l i =diag[l ix ,l iy ,l iψ ], Then, It can be rewritten as:

[0065]

[0066] Define the filtering tracking error as

[0067]

[0068] in μ i =diag[μ i1 ,μ i2 ,μ i3 ], μ ir >0 is a constant, r = 1, 2, 3. Combining systems (1), (2), and (8), the dynamic equation of the error system can be expressed as follows:

[0069]

[0070] in

[0071]

[0072] in It is a 0-compact set. Since the system's acceleration is difficult to obtain in most cases, F... i (G i ) is an unknown function.

[0073] Step 4: Design a fixed-time optimal controller

[0074] Based on the error system (8), the optimal cost function is defined.

[0075]

[0076] in Represents the optimal control input, Ψ(Ω) i ) represents the set of permissible control strategies.

[0077] Based on (8) and (9), and combined with optimal control theory, the Hamilton-Jacobi-Bellman equation is defined as follows:

[0078]

[0079] yes Relative to e i The gradient. By solving The general form of optimal control can be obtained as follows: To achieve optimal control at a fixed time, one can... Designed for

[0080]

[0081] in α i >0, k i >0, β i >0 represents the constant to be designed.

[0082] Due to F i (G i )and Given an unknown continuous function, and combining radial basis function neural network approximation techniques, the following two functions were constructed to approximate F. i (G i )and

[0083]

[0084] in and These are the ideal weights, and n1 and n2 are the number of neurons. Φ Fi and Φ i It is the Gaussian function vector. ε Fi and ε i Represents the approximation error, satisfying

[0085] Due to ideal weights and The unknown function F is used to update the controller online in subsequent analyses to obtain a usable optimal controller. After using the identification network, the unknown function F... i (G i ) can be approximated as

[0086]

[0087] Updated by the following adaptive update law:

[0088]

[0089] Where δ Fi ,φ i1 and φ i2 It is a positive number greater than zero to be designed. Substituting (14) into (8), we get in This is the optimal controller to be designed next. Next, an evaluation network will be used to assess the control performance.

[0090]

[0091] in express The estimated value, The evaluation network weights are updated according to the following equation:

[0092]

[0093] Where v ci ξ is a constant to be designed. i >0, Let be the identity matrix. Then, an optimal controller is designed using an execution neural network, which is given by the following equation:

[0094]

[0095] in express The estimated value, α i and β i It is a control parameter to be designed that is greater than zero. The weights of the neural network are updated according to the following update rules.

[0096]

[0097] Where ξ i >0, 4v ci >2v ai >1 is a constant that needs to be designed.

[0098] Substituting (16) and (18) into (10), we obtain the approximate Hamilton-Jacobi-Bellman (HJB) equation as follows:

[0099]

[0100] Among them, Γ(e i ) is defined as The Bellman error is defined as... Based on the above analysis, the controller Expected to be achieved Typically, the solution to the HJB equation is unique; therefore, if If true, then it is equivalent to

[0101] Based on the above analysis, the positive function is chosen as... Then, based on The derivative of Ξ(t) and the adaptive update laws (17) and (19) can be calculated as follows:

[0102] From the above analysis, it can be seen that the designed adaptive update laws (17) and (19) can eventually achieve Ξ(t) = 0, which means that Established.

[0103] Control input It is designed for system (8), and the control input for dynamic system (2) is...

[0104] Step 6: Verify the effectiveness of the fixed-time optimal controller.

[0105] Consider a set of underactuated multi-unmanned surface vessel (USV) systems. Under a reinforcement learning strategy with an identification-execution-evaluation structure, if the learned parameters satisfy 4v... ai >4v ci >2v ai >1, the control parameter satisfies α i >0, β i >0, Under the influence of the identification update law (15), the execution of the network weight update law (19), the evaluation of the network update law (17), and the fixed-time optimal inclusion controller (18), systems (1) and (2) can achieve the following objectives:

[0106] 1) Includes error z ip ,i=1,...,M,p=x,y,ψ, satisfying the transient and steady-state performance requirements in (4); 2) all error signals in the system are bounded within a fixed time; 3) the follower's output η i It can converge to a group of multiple leaders η within a fixed time T at minimum cost. kd The formed convex hull η c Within, i=1,...,M, k=M+1,...,N, d=x,y,ψ,

[0107] Proof: Consider the following Lyapunov function

[0108]

[0109] in These represent the approximation errors for identifying, evaluating, and executing the neural network, respectively. Calculate V. i The derivative of has

[0110]

[0111] Based on Young's inequality, we obtain the following inequality:

[0112]

[0113] Furthermore, according to the definition, the following formula can be obtained:

[0114]

[0115] Where w = a, c. Furthermore, for the other terms in (20) related to the adaptive law, the following inequality holds: in

[0116] Substitute (20) and (21) into (19), and combine with condition 4v ci >2v ai >1, achievable

[0117]

[0118] in For the last two terms in (22), we have Established, express The largest (smallest) eigenvalue. Furthermore, based on the inequality... and v ai >v ci ,have It holds true. Construct a positive definite function. Q i The derivative of (t) is calculated as follows: Therefore, for and Established. Furthermore, due to and If the boundary is defined, the following inequalities hold:

[0119]

[0120] Combining the above inequalities, It can be further deduced as

[0121]

[0122] in,

[0123]

[0124] Consider the entire Lyapunov function as Calculated

[0125]

[0126] in

[0127] Based on the above analysis, it can be inferred that e i It can converge to a neighborhood near the origin within a fixed time, i.e., g i Its derivative It is bounded. At the same time, it can be inferred that g... i , and It can converge to the neighborhood near the origin within a fixed time. According to the error transformation mechanism (5), it can be known that the error z is included. ip ,i=1,...,M,p=x,y,ψ is also bounded. Therefore, in (4) The condition is met, which means that the specified preset performance can be achieved even with errors. Furthermore, from (3), it can be seen that the system output η i It is bounded.

[0128] make Then, there are in therefore, The convex hull formed by all leader states is represented as follows:

[0129] Because it contains z i The boundedness of error, conditional Established, among which Representation matrix The minimum singular value. Therefore, the output η of all following unmanned surface vessels. i The i = 1, ..., M can eventually converge to a group of multiple leader unmanned surface vessels η. kd The convex hull η formed by k = M+1,...,N c Inside.

[0130] Based on step 5, the effectiveness of the fixed-time optimal inclusion control protocol can be demonstrated.

[0131] The method described in this invention solves the following technical problems:

[0132] (1) Based on reinforcement learning algorithm, an optimal control system is designed using the identification-execution-evaluation learning structure. The identification neural network is used to approximate the unknown dynamics of the system, the execution neural network generates the optimal control law by interacting with the external environment, and the evaluation neural network evaluates the value of the control strategy and generates reinforcement signals to the execution neural network to promote the improvement of subsequent behavior.

[0133] (2) By designing a performance index function containing power terms, we can ensure that the underdriven unmanned surface vessel system achieves the control objective in a fixed time with minimal cost and obtains a resting time estimate independent of the initial state of the unmanned surface vessel.

[0134] (3) By combining the preset performance control method with the inclusion error transformation, a transformation error dynamic model is constructed. Under this framework, the system can not only achieve the fixed-time inclusion control optimization objective, but also constrain the transient response overshoot and steady-state tracking accuracy of the system within the preset performance envelope range through the design of the preset performance function.

[0135] In summary, this invention innovatively proposes a fixed-time optimal inclusion control method for underactuated multi-unmanned surface vessel (MSV) systems with preset performance. First, an auxiliary variable method is used to perform coordinate transformation on the underactuated MSV system. Then, based on the preset performance control method, the transient and steady-state performance of the system are constrained, and the inclusion error is transformed. Finally, utilizing the identification-execution-evaluation learning structure in reinforcement learning, a fixed-time optimal inclusion controller is designed to ensure that the underactuated MSV system with preset performance achieves fixed-time inclusion control at minimum cost, and the upper limit of the resting time is independent of the initial state of the underactuated MSV system.

[0136] The present invention also provides a fixed-time optimal inclusion control system for an underdriven multi-unmanned surface vessel system, comprising:

[0137] A model building unit for underactuated multi-unmanned surface vessel (USV) system is established by using the auxiliary variable method to transform the coordinates of the underactuated USV system model.

[0138] The system includes error system and constraint construction units, and constructs the error system and constraint conditions of the underdriven multi-unmanned surface vessel system.

[0139] A dynamic equation construction unit containing the error system is used, combined with a preset performance control method, to construct a dynamic equation containing the error conversion mechanism, thereby obtaining the dynamic equation containing the error system.

[0140] The optimal cost function design unit designs the optimal cost function based on the dynamic equations of the system containing errors.

[0141] The controller design unit uses an identification-execution-evaluation learning network to solve the coupled Hamilton-Jacobi-Bellman equations of the multi-unmanned surface vessel system, thereby obtaining a fixed-time optimal inclusion controller that optimizes the inclusion error under the constraints.

[0142] Example

[0143] Consider a multi-unmanned surface vessel (USV) system consisting of a group of CyberShipII underdriven USVs to verify the correctness of the theoretical analysis. The communication network between the USVs is as follows: Figure 2 As shown, nodes F1-F4 represent 4 following unmanned surface vessels (USVs), and nodes L5-L7 represent 3 leader USVs. The main parameters of the CyberShipII USV are: m 11i =25.8, m 22i =33.8, m 23i =1.9048, m 33i =2.76, c 13i =-m 22i v i -m 23i r i c 23i =m 11i u i , d 22i =0.805‖r i +36.2823 i +0.8612, d 23i =3.450‖r i +0.845 v i ||-0.1079, d 32i =-0.13‖r i -5.0437 v i ||-0.1052, d 33i =0.75‖r i -0.08v i +1.9.

[0144] The initial position vectors and velocity vectors of the four following unmanned surface vessels are η1(0) = [-5.2, -3.5, 1]. T η2(0) = [-5, -1.8, 1.7] T η3(0)=[-5.2,3,0.9] T η4(0) = [-5, 5.8, 0.7] T v i (0) = [0,0,0] T Let i = 1, 2, 3, 4. The expected trajectories of the three leader unmanned surface vessels are given by the following formula:

[0145]

[0146] in t1 = 12s, t2 = 24s. The performance function is chosen as follows: z ix (t)=(8-0.55)exp(-0.08t)+0.55, z iy (t)=(8-0.65)exp(-0.07t)+0.65, z iψ (t)=(8-0.65)exp(-0.06t)+0.65. To achieve the fixed-time control objective, the parameters can be selected as follows: α1=diag[1.01,1.01,0.85], α2=diag[1.5,1.5,1.5], α3=diag[1.5,1.11,0.5], α4=diag[1,1,0.5], β1=diag[0.25,1.25,0.225], β2=diag[1.53,0.445,0.33], β3=diag[0.25,1.25,0.225], β2=diag[1.53,0.445,0.33], β3=diag[0.25,1.25,0.225], β3=diag[0.25,1.25,0.225], β2 ... g[1.12,0.82,0.5], β4=diag[0.13,0.43,0.13], k1=diag[8.85,7.75,9.9], k2=diag[8.75,10. 2,9.95], k3=diag[8.55,8.45,8.99], k4=diag[5.75,5.75,7.15], μ1=μ2=μ3=μ4=diag[1,1,1].

[0147] The execution and evaluation networks are approximated using an RBF neural network, with 9 neurons evenly distributed in the range [-4, 4] and a width of 1. The evaluation network weights are... The initial value is chosen as Execute network weights The initial value is chosen as The recognition neural network has 5 neurons, which are evenly distributed in the range [-4, 4], with a width of 2. The initial weight values ​​are chosen as follows. The learning rate parameter is set to θ Fi =0.1, φ1=0.6, φ2=0.3, v ci =2.5,v ai =3, ξ=0.1.

[0148] Using the given controller parameters and initial values, the simulation results of the underactuated unmanned surface vessel are as follows: Figure 3-7 As shown. Figure 3The phase plane trajectories of four followers and three leaders are depicted. Figure 3 It can be seen that the trajectories of the four following unmanned surface vessels can converge into the convex hull formed by the trajectory of the leader unmanned surface vessel. Figure 4 The system's trajectory variation curve, including the error, is described by... Figure 4 It can be seen that the included error can converge to a small neighborhood near the origin within a fixed time and remain within the preset boundary range. Figure 5 and Figure 6 The control input τ is displayed respectively. ui and τ ri The trajectory change curve. Figure 7 The curves showing the changes in the weight matrices of the identification network, execution network, and evaluation network are displayed. Experimental results demonstrate that this invention can guarantee fixed-time optimal containment control for underdriven multi-unmanned surface vessels (USVs).

[0149] The above description is merely a further embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope disclosed in the present invention, based on the technical solution and concept of the present invention, shall fall within the scope of protection of the present invention.

Claims

1. A fixed-time optimal inclusion control method for an underactuated multi-unmanned surface vessel system, characterized in that, include: Step 1: Use the auxiliary variable method to perform coordinate transformation on the underactuated multi-unmanned surface vessel system model to establish the multi-unmanned surface vessel system model; Step 2: Construct the error-inclusive system and the error-inclusive constraints for the underactuated multi-unmanned surface vessel system; Step 3: Combine the preset performance control method to construct a dynamic equation that includes an error conversion mechanism, and obtain the dynamic equation of the error system. Step 4: Based on the dynamic equations of the system including the error, design the optimal cost function; Step 5: Based on the reinforcement learning algorithm, use the identification-execution-evaluation learning network to solve the coupled Hamilton-Jacobi-Bellman equation of the multi-unmanned surface vessel system, and obtain the fixed-time optimal controller to make the optimal cost function under the error constraint optimal. The multi-unmanned surface vessel system model includes: No. The model of a following unmanned surface vessel system is as follows: in, Indicates the first The velocity vector of an unmanned surface vessel in the hull coordinate system These represent the longitudinal velocity, lateral velocity, and bow roll angular velocity, respectively. Indicates the first The position vector of an unmanned surface vessel in geodetic coordinates. and Indicates the northward and eastward positions. For the heading angle, For an unknown nonlinear function, , , , These represent the rotation matrix, inertia matrix, Rioli centripetal force matrix, and hydrodynamic damping matrix, respectively. As an auxiliary variable, Number of followers; The leader unmanned surface vessel model is as follows: The position coordinates of the leader unmanned surface vessel are designed as follows: , The convex hull region formed by all leaders is represented as ,in, , , , and These represent the communication connection matrix between the following unmanned surface vessels (USVs) and the communication connection matrix between the following USVs and the leader USV, respectively, where N is the total number of USVs. The included error is: in, , This represents the elements of the adjacency matrix of the unmanned surface vessel (USV). This indicates following the unmanned surface vessel. From unmanned surface vessel Obtain information, otherwise, , Where N is the number of followers, and N is the total number of unmanned surface vessels; The constraints that include error are: in, For upper and lower constraint boundaries, It is a constant greater than zero. These are the initial values ​​of the upper constraint boundary. It is the convergence value of the upper constraint boundary. These are the initial values ​​of the lower constraint boundary. It is the convergence value of the lower constraint boundary. .

2. The fixed-time optimal inclusion control method for an underdriven multi-unmanned surface vessel system according to claim 1, characterized in that, The auxiliary variable , and control input The relationship between them is: , .

3. The fixed-time optimal inclusion control method for an underdriven multi-unmanned surface vessel system according to claim 1, characterized in that, The dynamic equation of the system including the error is: The parameters of the equation are: ， ， ， ， ， ， ， ， ， ， ， in, It is a compact set. It is an unknown function. It is a constant. This indicates the location coordinates of the leader's unmanned surface vessel. .

4. The fixed-time optimal inclusion control method for an underdriven multi-unmanned surface vessel system according to claim 3, characterized in that, The optimal cost function is: in, , , This represents the optimal control input. This represents the set of permissible control strategies.

5. A fixed-time optimal inclusion control method for an underdriven multi-unmanned surface vessel system according to claim 4, characterized in that, The identification update law, execution network weight update law, and evaluation network update law of the learning network are designed as follows: in, Indicates the identification parameters, , and It is a positive number greater than zero that is to be designed. It is the weights of the neural network. Indicates the evaluation of network weights, , , is the constant to be designed. It is an identity matrix.

6. The fixed-time optimal inclusion control method for an underdriven multi-unmanned surface vessel system according to claim 5, characterized in that, The fixed-time optimal controller is: in, and It is a control parameter to be designed that is greater than zero.

7. A fixed-time optimal control system for an underdriven multi-unmanned surface vessel system implementing the method of any one of claims 1-6, characterized in that, include: A model building unit for underactuated multi-unmanned surface vessel (USV) system is established by using the auxiliary variable method to transform the coordinates of the underactuated USV system model. The system includes error system and constraint construction units, and constructs the error system and constraint conditions of the underdriven multi-unmanned surface vessel system. A dynamic equation construction unit containing the error system is used, combined with a preset performance control method, to construct a dynamic equation containing the error conversion mechanism, thereby obtaining the dynamic equation containing the error system. The optimal cost function design unit designs the optimal cost function based on the dynamic equations of the system containing errors. The controller design unit, based on reinforcement learning algorithms, uses an identification-execution-evaluation learning network to solve the coupled Hamilton-Jacobi-Bellman equations of the multi-unmanned surface vessel system, and obtains the fixed-time optimal inclusion controller, which optimizes the inclusion error under the constraints.

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