Fixed time optimal inclusion control method and system of under-driven multi-unmanned ship system

Abstract

The invention provides a fixed time optimal inclusion control method and system for an under-actuated multi-unmanned ship system, and the method comprises the steps: carrying out the coordinate change of an under-actuated multi-unmanned ship system model through an auxiliary variable method, and building a multi-unmanned ship system model; constructing an error-containing system of the under-driven multi-unmanned ship system and constraint conditions of the error-containing system; in combination with a preset performance control method, an error-containing conversion mechanism is constructed, and a kinetic equation of an error-containing system is obtained; designing an optimal cost function based on a kinetic equation containing an error system; and on the basis of a reinforcement learning algorithm, an identification-execution-evaluation learning network is utilized to solve a coupling HJB equation, a fixed time optimal inclusion controller is obtained, and an optimal cost function of inclusion errors under constraint conditions is enabled to be optimal. According to the method, it is ensured that the under-driven multi-unmanned-ship system with the preset performance achieves fixed time inclusion control with the minimum cost, and the upper limit of the rest time is irrelevant to the initial state of the under-driven unmanned ship system.

Description

Technical Field

[0001] The present invention relates to the technical field of under-actuated unmanned boats, and in particular to a fixed-time optimal inclusion control method and system for an under-actuated multiple unmanned boat system. Background Art

[0002] The widespread application of multi-unmanned vehicle systems in environmental monitoring, search and rescue, and coordinated transportation has attracted widespread attention from researchers in the field of distributed cooperative control strategies. Distributed cooperative control methods that achieve global mission objectives based on local information interaction have shown significant advantages in improving the efficiency of task execution in complex ocean scenarios. Among them, inclusion control, as a special distributed cooperative control method, has the core goal of guiding the follower state to converge to the convex hull formed by multiple leaders. The inclusion control problem of multi-unmanned vehicle systems has become a research hotspot in the field of multi-unmanned vehicle system control, but it still faces several key technical challenges that need to be solved.

[0003] The primary technical challenge stems from the inherent characteristics of UAV systems. During navigation, they are inevitably affected by model dynamics uncertainties. Furthermore, the underactuated nature of the system results in control input dimensions being lower than the degrees of freedom of motion, resulting in nonholonomic constraints. The coupled effects of these characteristics can easily lead to control system instability, making the design of inclusive control laws suitable for underactuated UAV systems a key fundamental issue.

[0004] Secondly, in the process of executing complex tasks, multi-unmanned boat systems often face significant energy consumption problems. Designing a control strategy that minimizes performance indicators based on the optimal control theory framework has become an important way to improve system performance. Reinforcement learning methods perform training iterations by integrating system status, environmental information, and neighboring boat interaction data, showing the potential to solve such optimization problems. Among them, the identification-execution-evaluation architecture provides a theoretical framework for optimal control of systems with unknown system dynamics by constructing an identification network to approximate the unknown dynamics of the system, an execution network to approximate the optimal strategy, and an evaluation network to estimate the value function. How to construct the optimal inclusive control method for under-driven multi-unmanned boat systems under this architecture is the first technical problem that the present invention needs to solve.

[0005] Furthermore, practical application scenarios place higher demands on system convergence speed and stability. Compared to finite-time cooperative control, fixed-time cooperative control offers advantages such as faster convergence rate, greater robustness, and independence of convergence time from the initial state. While research on finite-time inclusive control for underactuated multi-unmanned vehicle systems has achieved initial success, a systematic solution for optimal fixed-time inclusive control of underactuated systems remains lacking, presenting a second technical challenge.

[0006] On the other hand, existing research focuses on the steady-state performance of the system and is insufficient in transient process control. The preset performance control method introduces a dynamic performance function to constrain the error evolution trajectory, providing a new approach for simultaneously ensuring the steady-state and transient performance of the system. However, existing preset performance control methods are difficult to meet the synergistic needs of fixed-time control and performance optimization. Therefore, how to construct an optimal inclusive control method that combines preset performance constraints with fixed-time convergence characteristics has become the third key technical problem to be solved in this invention. Summary of the Invention

[0007] The object of the present invention is to provide a fixed-time optimal inclusion control method and system for an underdriven multiple unmanned vehicle system to solve the problems in the background technology.

[0008] The technical solution for achieving the purpose of the present invention is:

[0009] A fixed-time optimal inclusion control method for an underdriven multi-unmanned vehicle system, comprising:

[0010] Step 1: Use the auxiliary variable method to change the coordinates of the underactuated multi-unmanned vehicle system model and establish the multi-unmanned vehicle system model;

[0011] Step 2: Construct the error-inclusive system and error-inclusive constraint conditions of the underactuated multi-unmanned vehicle system;

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

[0013] Step 4: Design the optimal cost function based on the dynamic equation containing the error system;

[0014] In step 5, based on the reinforcement learning algorithm, the identification-execution-evaluation learning network is used to solve the coupled Hamilton-Jacobi-Bellman equations of the multi-UAV system and obtain the fixed-time optimal inclusion controller to optimize the optimal cost function of the inclusion error under the constraints.

[0015] A fixed-time optimal inclusion control system for an underdriven multi-unmanned vehicle system, comprising:

[0016] The underactuated multi-unmanned boat system model building unit uses the auxiliary variable method to change the coordinates of the underactuated multi-unmanned boat system model and establish the multi-unmanned boat system model;

[0017] Contains error system and constraint condition construction unit, constructs the error system and error constraint conditions of the under-actuated multi-unmanned vehicle system;

[0018] A dynamic equation construction unit including an error system, combined with a preset performance control method, constructs an error conversion mechanism to obtain a dynamic equation including an error system;

[0019] The optimal cost function design unit designs the optimal cost function based on the dynamic equation containing the error system;

[0020] The controller design unit, based on the reinforcement learning algorithm, uses the identification-execution-evaluation learning network to solve the coupled Hamilton-Jacobi-Bellman equations of the multi-unmanned vehicle system and obtains the fixed-time optimal inclusion controller to optimize the optimal cost function of the inclusion error under the constraints.

[0021] Compared with the prior art, the present invention has the following beneficial effects:

[0022] In practical applications, for an underactuated multi-UAV system with any initial state, the fixed-time optimal inclusion control method for the underactuated multi-UAV system 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 also estimate the dwell time required to achieve inclusion control.

[0023] In practical applications, for the special requirements of convergence speed and overshoot during the control process of an underactuated multi-unmanned vehicle system with preset performance, the control method proposed in this invention can ensure that both the transient performance and steady-state performance of the system including errors are met.

[0024] The present invention designs a fixed-time control strategy through an identification-execution-evaluation learning structure based on a reinforcement learning method, so that the system can complete the control tasks while consuming the minimum energy, thus achieving a balance between performance and energy consumption. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 This is a complete technical solution flow chart for this patent;

[0026] Figure 2 A communication network for an underdriven multi-unmanned boat system;

[0027] Figure 3 This is the trajectory curve of the underdriven unmanned boat system in the embodiment;

[0028] Figure 4 For the embodiment including error variation curve;

[0029] Figure 5 For example, ui Change trajectory diagram;

[0030] Figure 6 For example, ri Change trajectory diagram;

[0031] Figure 7 Neural network weights for example and Change curve. DETAILED DESCRIPTION

[0032] Combine Figure 1 The present invention provides a fixed-time optimal inclusion control method for an underdriven multi-unmanned vehicle system, comprising the steps of:

[0033] Step 1: Establish an under-actuated multi-UAV system model

[0034] Consider a group of underactuated multi-UAV systems consisting of M followers and NM (N>M) leaders. The model of the i-th underactuated follower UAV is described as

[0035]

[0036] in represents the position vector of the i-th unmanned boat in the geodetic coordinates, x i and y i Indicates the north position and the east position, ψ i ∈[0,2π] is the heading angle, represents the velocity vector of the i-th unmanned boat in the hull coordinate, u i , r i denote the longitudinal velocity, lateral velocity and yaw angular velocity respectively, represents the control input vector, τ ui ,τ ri They represent the longitudinal control force and the yaw control force respectively, R i (ψ i ), M i , C i , D i They represent the rotation matrix, inertia matrix, Coriolis centripetal force matrix and hydrodynamic damping matrix respectively, and are in the following form:

[0037]

[0038] Since system (1) is an underactuated system, in order to better design the optimal controller, the vector The above unmanned boat mathematical model can be rewritten as:

[0039]

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

[0041] The position coordinates of the leader unmanned boat are designed to be make Then the convex hull area formed by all leaders can be expressed as

[0042] in and They represent the communication connection matrix between the following unmanned boats and the communication connection matrix between the following unmanned boats and the leading unmanned boat respectively.

[0043] Step 2: Construct an error-inclusive system for the underactuated multi-UAV system

[0044] Based on the under-driven multi-UAV system model in step 1, the inclusion error between the i-th follower UAV and the leader UAV is defined as

[0045]

[0046] in a ij Represents the element of the adjacency matrix following the unmanned boat, a ij > 0 means that the following unmanned boat i can obtain information from unmanned boat j; otherwise a ij =0, Let N i is the set of unmanned boats connected to the i-th following unmanned boat, Define the Laplacian matrix as Assume that leaders cannot exchange information with each other, followers can exchange information with each other, and each follower UAV has at least one neighbor. Based on this, the Laplace matrix corresponding to the communication topology of the underdriven multi-UAV system can be expressed as:

[0047]

[0048] in Indicates the information interaction between following unmanned boats, Represents the information exchange between the formation leader and followers.

[0049] In order to ensure that the transient and steady-state performance including errors can be limited to the predefined region, the design error constraints are as follows:

[0050]

[0051] The upper and lower constraint boundaries can be expressed as

[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 is a constant greater than zero, is the initial value of the upper constraint boundary, is the convergence value of the upper constraint boundary, z ip,0 is the initial value of the lower constraint bound, z ip,∞ is the convergence value of the lower constraint bound.

[0055] Step 3: Construct an error conversion mechanism

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

[0057]

[0058] Among them, g ip is the conversion error, is a transfer 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 formula 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, can be rewritten as:

[0065]

[0066] Define the filtered 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 is a 0 compact set. Since the acceleration of the system is difficult to obtain in most cases, F i (G i ) is an unknown function.

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

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

[0075]

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

[0077] According to (8) and (9), and combined with optimal control theory, the Hamilton-Jacobi-Bellman equation is defined as

[0078]

[0079] yes Relative to e i The gradient of The general form of optimal control can be obtained as In order to achieve fixed time optimal control, Designed for

[0080]

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

[0082] Because F i (G i )and It is an unknown continuous function. Combining the radial basis function neural network approximation technology, the following two functions are constructed to approximate F i (G i )and

[0083]

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

[0085] Due to the ideal weight and is unknown. In order to obtain the optimal controller available, the controller is updated online using the identification-execution-evaluation structure in subsequent analysis. 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 is a positive number greater than zero to be designed. Substituting (14) into (8), we get in is the optimal controller to be designed next. Next, the evaluation network is used to evaluate the control performance.

[0090]

[0091] in express The estimated value of represents the evaluation network weight, and its update rule is given by the following equation:

[0092]

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

[0094]

[0095] in express The estimated value of α i and β i is the control parameter to be designed that is greater than zero. is the weight of the neural network, which is updated by the following update rule

[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 Expectation fulfillment In general, the solution of the HJB equation is unique, so if If established, it is equivalent to

[0101] According to the above analysis, the positive function is selected as Then, based on The derivative of Ξ(t) and the adaptive update laws (17) and (19) can be calculated as

[0102] From the above analysis, we can conclude that the designed adaptive update laws (17) and (19) can eventually achieve Ξ(t) = 0, which means 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 inclusion controller

[0105] Consider a group of underactuated multi-unmanned boat systems. Under the reinforcement learning strategy of identification-execution-evaluation structure, if the learning parameters satisfy 4v ai >4v ci >2v ai >1, the control parameter satisfies α i >0, β i >0, Then, under the action of the identification update law (15), the execution network weight update law (19), the evaluation network update law (17), and the fixed-time optimal inclusion controller (18), systems (1) and (2) can achieve the following goals:

[0106] 1) Including 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 output η of the follower i It can converge to a cluster with multiple leaders η at the minimum cost within a fixed time T. kd The convex hull η formed c Within, i=1,...,M, k=M+1,...,N, d=x,y,ψ,

[0107] Proof: Consider the following Lyapunov function

[0108]

[0109] in Represent the approximate errors of identification, evaluation and execution of neural network respectively. Calculate V i The derivative of

[0110]

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

[0112]

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

[0114]

[0115] Where w = a,c. In addition, for other terms related to the adaptive law in (20), the following inequalities exist: in

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

[0117]

[0118] in For the last two terms in (22), we have Established, express The maximum (minimum) eigenvalue of . In addition, based on the inequality and v ai >v ci ,have Established. Construct a positive definite function Q i The derivative of (t) is calculated as Therefore, for and In addition, due to and is bounded, the following inequality holds:

[0119]

[0120] Combined with 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] According to the above analysis, it can be inferred that e i It can converge to the area near the origin within a fixed time, that is, g i Its derivative is bounded. At the same time, it can be inferred that g i , and It can converge to the area near the origin within a fixed time. According to the error conversion mechanism (5), it can be seen that the error z ip ,i=1,...,M,p=x,y,ψ is also bounded. Therefore, in (4) The condition is established, which means that the specified preset performance can be achieved by including the error. In addition, from (3), it can be seen that the system output η i It is bounded.

[0128] make Then, there is in therefore, Among them, the convex hull formed by all leader states is expressed as

[0129] Since it contains z i Boundedness of error, conditional Established, of which Representation matrix Therefore, the output η of all the unmanned boats is i ,i=1,...,M can eventually converge to a system consisting of multiple leading unmanned boatsη kd , k=M+1,...,N, the convex hull η formed c Inside.

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

[0131] The method of the present invention solves the following technical problems:

[0132] (1) Based on the reinforcement learning algorithm, the optimal inclusive controller is designed using the identification-execution-evaluation learning structure, in which 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 assesses 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 indicator function containing a power term, it is ensured that the underdriven unmanned vehicle system achieves the control target within a fixed time at the minimum cost, and an estimated value of the rest time that is independent of the initial state of the unmanned vehicle can be obtained.

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

[0135] In summary, the present invention innovatively proposes a fixed-time optimal inclusion control method for an under-actuated multi-unmanned vehicle system with preset performance. First, the coordinate transformation of the under-actuated multi-unmanned vehicle system is performed using the auxiliary variable method. Then, based on the preset performance control method, the transient performance and steady-state performance of the system are restricted, and the inclusion error is converted. Finally, the identification-execution-evaluation learning structure in reinforcement learning is used to design a fixed-time optimal inclusion controller to ensure that the under-actuated multi-unmanned vehicle system with preset performance can achieve fixed-time inclusion control at the minimum cost, and the upper limit of the rest time is independent of the initial state of the under-actuated unmanned vehicle system.

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

[0137] The underactuated multi-unmanned boat system model building unit uses the auxiliary variable method to change the coordinates of the underactuated multi-unmanned boat system model and establish the multi-unmanned boat system model;

[0138] Contains error system and constraint condition construction unit, constructs the error system and error constraint conditions of the under-actuated multi-unmanned vehicle system;

[0139] A dynamic equation construction unit including an error system, combined with a preset performance control method, constructs an error conversion mechanism to obtain a dynamic equation including an error system;

[0140] The optimal cost function design unit designs the optimal cost function based on the dynamic equation containing the error system;

[0141] The controller design unit uses an identification-execution-evaluation learning network to solve the coupled Hamilton-Jacobi-Bellman equations of the multi-UAV system and obtains a fixed-time optimal inclusion controller that optimizes the optimal cost function of the inclusion error under the constraints.

[0142] Example

[0143] Consider a multi-UAV system consisting of a group of CyberShipII underdriven UAVs to verify the correctness of the theoretical analysis. The communication network between the UAVs is as follows: Figure 2 As shown in the figure, nodes F1-F4 represent 4 follower unmanned boats, and nodes L5-L7 represent 3 leading unmanned boats. The main parameters of CyberShipII unmanned boat 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‖v 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 ‖-0.08‖v i ‖+1.9.

[0144] The initial position vectors and velocity vectors of the four following unmanned boats 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 , i = 1, 2, 3, 4. The expected trajectories of the three leading unmanned boats are given by the following formula:

[0145]

[0146] in t1=12s, t2=24s. The performance function is selected as 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. In order to achieve the fixed time control target, the parameters can be selected as 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[1.5,1.11,0.5], 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 network and evaluation network are approximated based on RBF neural network, with 9 neurons, which are evenly distributed in [-4, 4] and a width of 1. Evaluation network weight The initial value is selected as Execution network weights The initial value is selected as The number of neurons in the identification neural network is 5, the neurons are evenly distributed in [-4, 4], the width is 2, and the initial value of the weight is selected as 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 controller parameters and initial values given above, the simulation results of the underactuated unmanned vehicle are as follows: Figure 3-7 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 follower UAVs can converge into the convex hull formed by the trajectory of the leading UAV. Figure 4 Describes the trajectory change curve of the system including the error, which is Figure 4 It can be seen that the inclusion error can converge to a small neighborhood near the origin in a fixed time and remain within the preset boundary range. Figure 5 and Figure 6 The control input τ is shown respectively ui and τ ri The trajectory change curve diagram. Figure 7 The curves of the weight matrices of the identification network, execution network, and evaluation network are shown. The experimental effect diagram shows that the present invention can ensure the fixed-time optimal inclusion control of the under-actuated multi-unmanned vehicle system.

[0149] The above is only a further embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes based on the technical solutions and concepts of the present invention within the scope disclosed by the present invention, which fall within the scope of protection of the present invention.

Claims

1. A fixed-time optimal inclusion control method for an underactuated multi-unmanned vehicle system, characterized in that: include: Step 1: Use the auxiliary variable method to change the coordinates of the underactuated multi-unmanned vehicle system model and establish the multi-unmanned vehicle system model; Step 2: Construct the error-inclusive system and error-inclusive constraint conditions of the underactuated multi-unmanned vehicle system; Step 3: Combine the preset performance control method to construct an error conversion mechanism and obtain the dynamic equation of the error system; Step 4: Design the optimal cost function based on the dynamic equation containing the error system; In step 5, based on the reinforcement learning algorithm, the identification-execution-evaluation learning network is used to solve the coupled Hamilton-Jacobi-Bellman equations of the multi-UAV system and obtain the fixed-time optimal inclusion controller to optimize the optimal cost function under the inclusion error constraint.

2. The fixed-time optimal containment control method for an underactuated multi-unmanned vehicle system according to claim 1, characterized in that: The multi-unmanned boat system model includes: The model of the i-th following unmanned boat system is: in, represents the velocity vector of the i-th unmanned boat in the hull coordinate, u i ,θ i ,r i denote the longitudinal velocity, lateral velocity and yaw angular velocity respectively, represents the position vector of the i-th unmanned boat in the geodetic coordinates, x i and y i Indicates the north position and the east position, ψ i ∈[0,2π] is the heading angle, is an unknown nonlinear function, R i (ψ i ), M i 、C i 、D i denote the rotation matrix, inertia matrix, Rioli centripetal force matrix and hydrodynamic damping matrix respectively, ω i is an auxiliary variable, M is the number of followers; The model of the leader unmanned boat is: the position coordinates of the leader unmanned boat are designed as The convex hull area formed by all leaders is expressed as in, and They represent the communication connection matrix between the following unmanned boats and the communication connection matrix between the following unmanned boats and the leading unmanned boat, respectively, and N is the total number of unmanned boats.

3. The fixed-time optimal containment control method for an underactuated multi-unmanned vehicle system according to claim 2, characterized in that: The auxiliary variable ω i and control input τ i The relationship between them is: m 11i , m 22i , m 33i , m 23i ∈M i .

4. The fixed-time optimal containment control method for an underactuated multi-unmanned vehicle system according to claim 2, characterized in that: The inclusion error is: in, a ij Represents the element of the adjacency matrix following the unmanned boat, a ij > 0, indicating that the following unmanned boat i can obtain information from unmanned boat j, otherwise, a ij =0, M is the number of followers, and N is the total number of unmanned boats.

5. The fixed-time optimal containment control method for an underactuated multi-unmanned vehicle system according to claim 4, characterized in that: The constraints that include the error are: in, are the upper and lower constraint boundaries, π ip is a constant greater than zero, is the initial value of the upper constraint boundary, is the convergence value of the upper constraint boundary, z ip,0 is the initial value of the lower constraint bound, z ip,∞ is the convergence value of the lower constraint bound, i=1,...,M,p=x,y,ψ.

6. The fixed-time optimal containment control method for an underactuated multi-unmanned vehicle system according to claim 2, characterized in that: The dynamic equation including the error system is: The parameters of the equation are: l i =diag[l ix ,l iy ,l iψ ],i=1,...,M,p=x,y,ψ, m i =diag[μ i1 ,m i2 ,m i3 ], r=1,2,3, in, is a compact set, F i (G i ) is an unknown function, μ ir >0 is a constant, represents the position coordinates of the leader unmanned boat, j=M+1,...,N.

7. The fixed-time optimal containment control method for an underactuated multi-unmanned vehicle system according to claim 6, characterized in that: The optimal cost function is: in, represents the optimal control input, Ψ(Ω i ) represents the set of admissible control strategies.

8. The fixed-time optimal containment control method for an underactuated multi-unmanned vehicle system according to claim 7, characterized in that: The identification update law of the learning network, the execution network weight update law, and the evaluation network update law are designed as follows: in, represents the identification parameter, δ Fi 、φ i1 and φ i2 is a positive number greater than zero to be designed, are the weights of the neural network, represents the evaluation network weight, ξ i >0,4v ci >2v ai >1, is the constant to be designed, is the identity matrix.

9. The fixed-time optimal containment control method for an under-actuated multi-unmanned vehicle system according to claim 8, characterized in that: The fixed time optimal inclusion controller is: Among them, α i and β i is the control parameter to be designed that is greater than zero.

10. A fixed-time optimal inclusion control system for an underactuated multi-unmanned vehicle system implementing the method according to any one of claims 1 to 9, characterized in that: include: The underactuated multi-unmanned boat system model building unit uses the auxiliary variable method to change the coordinates of the underactuated multi-unmanned boat system model and establish the multi-unmanned boat system model; Contains error system and constraint condition construction unit, constructs the error system and error constraint conditions of the under-actuated multi-unmanned vehicle system; A dynamic equation construction unit including an error system, combined with a preset performance control method, constructs an error conversion mechanism to obtain a dynamic equation including an error system; The optimal cost function design unit designs the optimal cost function based on the dynamic equation containing the error system; The controller design unit, based on the reinforcement learning algorithm, uses the identification-execution-evaluation learning network to solve the coupled Hamilton-Jacobi-Bellman equations of the multi-unmanned vehicle system and obtains the fixed-time optimal inclusion controller to optimize the optimal cost function of the inclusion error under the constraints.

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