Finite time distributed formation method for unmanned surface vehicle swarm system

Abstract

The application provides a finite time distributed formation method of unmanned surface vehicle cluster system, which can not only guarantee that the unmanned surface vehicle system reaches the expected formation mode in finite time, but also ensure that the system speed and formation error always meet the time-varying constraint requirements during the whole operation period, and the method comprises the following steps: establishing a three-degree-of-freedom unmanned surface vehicle kinematics and dynamics model; approximating the saturation constraint of the system by using a smooth function, and combining a fault model to establish a new system dynamics model subjected to driver faults and saturation constraints; designing a virtual control law, also known as a kinematics guide law; designing a parameterized lane speed of a virtual leader; designing a finite time distributed formation controller; and designing an uncertain compensation adaptive law. According to the needs of the user, the time-varying formation mode and the time-varying constraint function can be designed, the formation form of the multiple unmanned surface vehicles is dynamically adjusted, and meanwhile, it is ensured that the speed and formation tracking error always do not deviate from the specified constraint set.

Description

TECHNICAL FIELD

[0001] The present application relates to a finite time formation control method of unmanned surface vehicle system, in particular to a finite time distributed formation method of unmanned surface vehicle cluster system considering speed constraint, cooperative formation error constraint and input saturation constraint. BACKGROUND

[0002] In recent years, the formation control problem of multi-unmanned surface vehicle (USV) system has attracted extensive attention due to its higher efficiency and performance in completing complex tasks such as environmental monitoring, coastal surveillance and rescue than a single vessel. It is of great significance to develop a distributed formation control strategy based on finite time stability to enhance the robustness of multi-USV system and improve its efficiency in completing tasks.

[0003] In actual operation scenarios, unmanned surface vehicle systems usually face various system constraints including speed constraints, input or output constraints and tracking error constraints due to their performance specifications and requirements. If these constraints are ignored, the transient performance of the system may not meet the requirements, and even the system may be damaged. However, due to the lack of a unified and effective nonlinear control method to handle constrained signals, existing finite time formation control methods for unmanned vehicle cluster systems (N. Gu, D. Wang, Z. H. Peng, and L. Liu, “Observer-based finite-time control for distributed path maneuvering of underactuated unmanned surface vehicles with collision avoidance and connectivity preservation,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 51, no. 8, pp.5105-5115, Aug. 2021.) only design distributed controllers for non-constrained scenarios, and cannot deal with the problem of system variable constraints, lacking practical value.

[0004] Furthermore, existing control methods that focus on system constraints (BJ Guerreiro, C. Silvestre, R. Cunha, and A. Pascoal, “Trajectory tracking nonlinear model predictive control for autonomous surface craft,” IEEE Trans. Control Syst. Technol., vol. 22, no. 6, pp. 2160-2175, Nov. 2014.) and (ZH Peng, J. Wang, and D. Wang, “Distributed maneuvering of autonomous surface vehicles based on neurodynamic optimization and fuzzy approximation,” IEEE Trans. Control Syst. Technol., vol. 26, no. 3, pp. 1083-1090, Mar. 2017.) only consider the control of unmanned surface vessel systems with a single input constraint or velocity constraint, and the constraint signal is within a constant constraint range and can only achieve asymptotic stability of the system that converges in infinite time. However, in actual complex ocean formation missions, the constraints on system speed, input, and other requirements are usually variable.

[0005] Real-world unmanned surface vessel (USV) systems often face multiple uncertainties from both internal and external sources, numerous time-varying constraints, and complex mission requirements. Furthermore, they may encounter even more complex marine environments during mission execution, increasing the risk of malfunctions. Therefore, designing a robust, well-constrained, and fast-converging effective formation control algorithm is crucial for promoting the safe and efficient operation of multiple USV systems. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention proposes a finite-time distributed formation method for unmanned surface vessel swarm systems that considers multiple constraints. The specific steps are as follows:

[0007] Step 1: Consider from A network of unmanned surface vessel systems, of which the first The unmanned surface vessel was modeled using both geodetic coordinate systems and hull coordinate systems, resulting in the following kinematic and dynamic models:

[0008] (1),

[0009] Formula (1) represents the first An unmanned surface vessel system, in which: It is the first Location information of an unmanned surface vessel in a geodetic coordinate system and heading angle The vector formed by these elements, where the superscript T indicates the transpose of the vector or matrix. Representing vectors The derivative with respect to time, It is a velocity vector in the ship's coordinate system composed of surge, roll, and yaw velocities. These represent forward velocity, drift velocity, and yaw rate, respectively. It is an unknown bounded disturbance vector caused by wind, waves, and swells. These represent unknown bounded disturbances in different velocity directions; It is driven by the following faults and saturation constraints. These represent the driving forces in the three velocity directions,

[0010] (2),

[0011] Formula (2) represents the fault model, where Represents the loss efficiency matrix. These represent the loss efficiency factors in different driving force directions, and satisfy the following conditions: , Representing an unknown bounded additive fault, the saturated input vector It is determined by the saturation function defined below.

[0012] (3),

[0013] subscripts in the formula , These represent the actual control inputs in the three velocity directions, respectively. as well as These are two known constant bounds for a saturated function; definition This represents the actual control input vector to be designed; furthermore... Represents a known nonlinear function, where Describe the centripetal matrix of the Coriolis force and satisfy , and Represents a known function matrix. The mass matrix represents an unknown real vector composed of parameters that cannot be precisely measured in the system's nonlinear suppression matrix. It is a positive definite symmetric matrix and satisfies ,matrix Represents the transition matrix and has the following definition

[0014] ,

[0015] Setting initial state of unmanned surface vehicle system where denote the function values of the three quantities at the initial time; setting the parameterized path of the virtual leader as , denote the parameterized trajectories of the forward position, the lateral position and the yaw angle direction respectively, denote the set path parameters; setting the desired convergence speed of the parameterized path as , the desired formation trajectory of the th unmanned surface vehicle is , .

[0016] Step 2: estimating the saturation function defined in equation (3) by using a nonlinear smooth function :

[0017] (4),

[0018] Thus, according to the Lagrange mean value theorem, the following approximate relationship is obtained:

[0019] (5),

[0020] Equation (5) represents a function approximation model, in which denotes the approximation error and its absolute value has an upper bound value ; the symbol denotes the derivative of the function with respect to the variable , i.e. it satisfies , where , is a weight coefficient to be selected and satisfies , is a real number to be selected; in addition, the function value of the derivative satisfies , where is a known positive constant.

[0021] Define a diagonal matrix , where denote the derivatives of the nonlinear smooth function in equation (4); define the total error vector , where ​respectively represent the estimation error of the saturation function in three control force directions; then, combined with the fault model (2), the saturation input vector and the saturation function approximation model (5), the first unmanned surface vehicle system (1) is rewritten as follows:

[0022] (6),

[0023] In the formula: denotes the inverse matrix of matrix , represents the total external uncertainty of the system and is a bounded vector, that is norm satisfies , where denotes the unknown external disturbance bound.

[0024] Step 3: Define the cooperative formation tracking error vector and the virtual error coordinate transformation respectively

[0025] (7),

[0026] In the formula: represents the weight of the adjacency matrix between the th agent and the th agent, specifically, indicates that there is a connection relationship between agent and agent , otherwise it represents no communication relationship; represents the connection relationship between the agent and the virtual leader, equal to 1 represents a connection relationship, otherwise represents no connection relationship, , respectively represent the position information vector of the th and the th unmanned surface vehicle, denotes the kinematic guidance law to be designed, also known as the virtual control law, denotes the transpose of matrix in formula (1);

[0027] Step 4: Given the system formation error and the speed variable constraint requirement

[0028] ,

[0029] In the formula respectively represent the given error variable norm and the speed variable norm The constraint functions are all defined as monotonically decreasing functions with the following finite-time performance:

[0030] (8),

[0031] In the formula: , as well as All are given positive integers. Indicates time, finite time .

[0032] Step 5: Design the virtual control law

[0033] (9),

[0034] In the formula: , and These are the positive control parameters to be designed. It is a positive number to be designed. , They represent The derivative with respect to time, express right The partial derivatives; for convenience, simplified notation is used. Represents the constraint function term And control the nonlinear term Defined as the following piecewise function

[0035] (10)

[0036] in It is a pre-given small positive parameter, the process coefficient. , .

[0037] Step 6: Define , yes The derivative with respect to time, Representing the desired reference channel, the channel rate of the virtual leader is designed using the filtered gradient method.

[0038] (11),

[0039] In the formula and These are the positive parameters to be designed;

[0040] Step 7: Design a nonlinear tracking differential observer to estimate the virtual control law of equation (9). time derivative

[0041] (12),

[0042] where denotes the estimate of , and denotes the estimate of , and denotes the time derivative of , and

[0043] and a given positive constant , the mathematical operator is defined as , where denotes the component of the vector , and denotes the sign function of , and denotes the absolute value of

[0044] Step 8: Design the finite-time control input vector for the

[0045] (13),

[0046] where and are the positive control parameters to be designed; for convenience, the simplified notation is used to represent the constraint function term , denotes the estimate signal of the unknown parameter , and denotes the estimate signal of the unknown external disturbance bound , and the nonlinear control function satisfies the following definition:

[0047] ,

[0048] where is a small positive parameter given in advance, and the process coefficient , . In addition, the hyperbolic tangent diagonal function matrix is defined as follows:

[0049]

[0050] where is the nonlinear cross function vector left-multiplied by the unit vector , and the obtained components, are three positive real numbers to be selected;

[0051] Step 9: design an adaptive update law to compensate for system uncertainties as

[0052] (14),

[0053] (15),

[0054] wherein: are normal numbers to be designed.

[0055] In one specific embodiment of the present application, in step 2, .

[0056] The finite-time distributed formation control scheme proposed in the present application not only ensures that the multi-agent achieves the desired formation mode in finite time, but also ensures that the speed and collaborative error vector is always within the specified constraint set under internal and external multi-source uncertainties, driver failures and multiple constraints. Compared with the prior art, the present application has the following advantages:

[0057] (1) For the case of multiple constraint variables, internal and external multi-source uncertainties and multiple constraints in the multi-unmanned surface vehicle system, step 4 establishes a monotonically decreasing function with finite-time performance as the upper bound of the constraint, which is more in line with the actual application requirements, but it is difficult to design a finite-time controller. Steps 5 and 8 handle the time-varying constraints by designing a virtual control law with a tangent barrier function and a control input, which can achieve finite-time distributed controller design under multiple time-varying constraint requirements and multiple uncertain coupling conditions.

[0058] (2) The present application introduces a smoothing function as an approximation of the saturation function in the control design, which not only handles the saturation constraint but also reduces the dynamic order of the system. In addition, the present application uses a nonlinear differential tracker to avoid solving the derivative of the virtual control law, thereby avoiding the computational complexity explosion problem of the traditional backstepping method. Therefore, the controller designed in the present application not only has the advantages of low complexity, strong robustness and fast convergence speed, but most importantly, it can ensure that the speed and formation error do not deviate from the specified constraint set during the entire operation period. BRIEF DESCRIPTION OF DRAWINGS

[0059] Figure 1 shows a schematic diagram of the overall control process;

[0060] Figure 2 shows a two-dimensional plan view of the motion trajectory of the multi-unmanned surface vehicle;

[0061] Figure 3A plot of a trajectory of operation showing a norm of a velocity variable;

[0062] Figure 4 A plot of a trajectory of operation showing a norm of a platoon error;

[0063] Figure 5 A plot of a trajectory of motion showing a norm of an adaptive law;

[0064] Figure 6 A plot of a trajectory of operation showing a norm of a system control input. DETAILED DESCRIPTION

[0065] The present application provides a kind of based on finite time stable unmanned surface vehicle cluster system finite time distributed platoon method, can guarantee that velocity and platoon error always do not deviate from specified time-varying constraint set under internal and external multi-source uncertainty, and in finite time form desired platoon mode.The technical idea of this method is as follows: first, using hyperbolic tangent function designs Lyapunov function to ensure the time-varying constraint requirement of system;Second, introduce nonlinear continuous smooth function to approximate system input saturation, and saturation error, system external disturbance and additive fault are regarded as total external uncertain factors of system;Subsequently, by means of adaptive compensation strategy iteration design virtual control law and actual control input, while introducing nonlinear differential tracker to avoid solving the derivative of virtual control law, so as to reduce the complexity of designed algorithm, finally form an effective finite time platoon control scheme to realize the desired system performance.

[0066] The specific steps of the method of the present application are as follows:

[0067] Step 1: consider a network composed of unmanned surface vehicle systems, wherein the first unmanned surface vehicle system, the second unmanned surface vehicle is modeled using the earth coordinate system and the ship coordinate system respectively, to obtain the following kinematic and dynamic models:

[0068] (1),

[0069] Formula (1) represents the first unmanned surface vehicle system, wherein: is the position information of the first unmanned surface vehicle in the earth coordinate system and the heading angle consisting of a vector, the upper index T represents the transpose of vector or matrix, represents the vector with respect to time, is the velocity vector composed of surge, sway and yaw velocity in the ship coordinate system, respectively represent the forward velocity, lateral velocity and yaw angle velocity; is the unknown bounded disturbance vector caused by wind, wave, and swell, denote unknown bounded disturbances in different velocity directions, respectively; is the driving force subject to the following fault and saturation constraints, denote driving forces in three velocity directions, respectively,

[0070] (2),

[0071] Equation (2) represents the fault model, where represents the loss efficiency matrix, denote loss efficiency factors in different driving force directions, respectively, and satisfy , represents unknown bounded additive faults, and the saturation input vector is determined by the saturation function defined as

[0072] (3),

[0073] The subscript in the equation denotes actual control inputs in three velocity directions, respectively, and are two known constant bounds of the saturation function; define , which represents the actual control input vector to be designed; in addition, represents a known nonlinear function, where denotes the Coriolis centripetal matrix and satisfies , and denote known function matrices, denotes an unknown real vector composed of unmeasurable parameters in the system nonlinear suppression matrix, and the mass matrix is a positive definite symmetric matrix and satisfies , the matrix represents a transition matrix and has the following definition

[0074] ,

[0075] Set the initial state of the unmanned surface vehicle system as , where denote function values of three quantities at the initial time, respectively; set the parameterized path of the virtual leader as , denote parameterized trajectories in the forward position, lateral position, and yaw angle directions, respectively, denotes the set path parameter; set the desired convergence speed of the parameterized path as​ , No. The expected formation trajectory of the unmanned surface vessels is , .

[0076] Step 2: Utilize nonlinear smoothing functions The saturation function defined in equation (3) is estimated :

[0077] (4),

[0078] Therefore, based on the Lagrange mean-means theorem, the following approximate relationship is obtained:

[0079] (5),

[0080] Formula (5) represents the approximate model of the function, where Represents the approximation error and its absolute value Has an upper bound value ;symbol Representation function For variables The differentiation operation, that is, satisfying ,in

[0081] , The weighting coefficients to be selected and satisfying , For the real number to be selected; in addition, the derivative The function value satisfies ,in It is a known positive number.

[0082] Define a diagonal matrix ,in The nonlinear smooth function in equation (4) is expressed separately. The derivative; defining the total error vector. ,in These represent the estimation errors of the saturation function in the three control force directions, respectively; then, combined with the fault model (2), the saturation input vector... And the saturation function approximation model (5), the first The unmanned surface vessel system (1) is rewritten in the following form:

[0083] (6),

[0084] In the formula: Representation matrix The inverse matrix, is a bounded vector, i.e. The norm satisfies where denotes the unknown external disturbance bound.

[0085] Step 3: Define the cooperative formation tracking error vector and the virtual error coordinate transformation as

[0086] (7),

[0087] where denotes the weight of the adjacency matrix between the th agent and the th agent, specifically, denotes that there is a connection between agent and agent , otherwise it represents no communication relationship; denotes the connection relationship between the agent and the virtual leader, equal to 1 represents a connection relationship, otherwise it represents no connection relationship, , and respectively represent the position information vectors of the th and the th unmanned surface vehicle, denotes the kinematic guidance law to be designed, also known as the virtual control law, denotes the transpose of the matrix in equation (1);

[0088] Step 4: Give the system formation error and the constraint requirements of the speed variable

[0089] ,

[0090] where and respectively represent the constraint functions of the given error variable norm and the speed variable norm , which are defined as monotonically decreasing functions with the following finite time performance:

[0091] (8),

[0092] where , and are all given normal numbers, denotes time, and the finite time .

[0093] Step 5: Design the virtual control law

[0094] (9),

[0095] where: , and are positive control parameters to be designed, is a positive number to be designed, , denote derivative with respect to time, denote partial derivative with respect to ; for convenience, the simplified notation is used to represent the constraint function term , and the control nonlinear term is defined as the following piecewise function

[0096] (10),

[0097] where is a small positive parameter given in advance, and the process coefficient ,

[0098] Step 6: Define , is derivative with respect to time, denote the desired reference channel, and the filtered gradient method is used to design the virtual leader's channel rate

[0099] (11),

[0100] where and are positive parameters to be designed.

[0101] Step 7: Design a nonlinear tracking differential observer to estimate the virtual control law derivative with respect to time

[0102] (12),

[0103] where: denote the estimate of , denote the estimate of , denote the derivative with respect to time of , denote a positive real parameter to be selected; in addition, for any vector

[0104] and given positive constant , define the mathematical operator where denotes the components of the vector denotes the sign function of denotes the absolute value of

[0105] Step 8: Design the finite-time control input vector for the

[0106] th unmanned surface vehicle system

[0107] where and are the positive control parameters to be designed; for convenience, the simplified notation is used to represent the constraint function term is used to represent the estimated signal of the unknown parameter is used to represent the estimated signal of the unknown external disturbance bound The nonlinear control function

[0108]

[0109] where is a small positive parameter given in advance, and the process coefficient In addition, the hyperbolic tangent diagonal function matrix is defined as follows:

[0110]

[0111] where is the component obtained by left-multiplying the nonlinear cross function vector by the unit vector

[0112] Step 9: Design the adaptive update law to compensate for system uncertainty as

[0113]

[0114]

[0115] where​​​​​​​​​​​​​​​ All are normal numbers to be designed. Specific embodiments

[0117] According to the specific implementation steps of the technical scheme of the present application, an embodiment is given as follows.

[0118] Step 1: Establish the unmanned surface vehicle system model as formula (1). Select a directed network composed of one virtual leader and five unmanned surface vehicles, and the adjacency matrix of the communication topology is defined as follows: , The remaining matrix elements are all 0. Set the initial position state of the five unmanned surface vehicle system respectively , , , and , define the parameterized path of the virtual leader as , and the desired formation mode , the given input saturation function parameter is , .

[0119] Step 2: Substitute the driver fault model (2) and the approximate model (4) of the saturation function into model (1) to obtain model (6).

[0120] Step 3: Define the cooperative formation error in formula (7) and the virtual control error .

[0121] Step 4: Select the time-varying constraint function in the form of formula (8), and the parameters in the constraint function are defined as and , .

[0122] Step 5: Design the virtual control law in the form of formula (9), and the parameters of the virtual controller are selected as .

[0123] Step 6: Design the virtual leader channel speed as formula (11) , and the partial parameters of the controller are selected as , and the desired virtual leader speed is selected as .

[0124] Step 7: Design the nonlinear tracking differential observer as formula (12) , .

[0125] Step 8: Design the finite-time control input vector in the form of equation (13), and select the partial parameters of the controller as .

[0126] Step 9: Design the adaptive laws of equations (14) and (15), and select the adaptive law parameters as ,

[0127] .

[0128] Figure 2 The two-dimensional plane graph of the motion trajectory formation of the unmanned surface vehicle system is shown, which shows that the desired time-varying formation mode has been formed. Figure 3 and Figure 4 are the running trajectories of the speed norm and the formation error norm, respectively, from Figure 3 and Figure 4 it can be seen that the speed and the formation error do not deviate from the given time-varying constraint set throughout the running. In addition, the formation error also converges to a small neighborhood of the origin eventually, that is, the proposed control algorithm can meet the constraint requirements of the system. Figure 5 It is shown that the parameter adaptive law and the external uncertainty adaptive law of the proposed method are bounded. From Figure 6 it can be seen that the saturated input and the driver fault input are bounded and have a relatively small range of values, that is, the proposed control method allows the system to be simultaneously subject to driver fault and saturation constraints. Under the conditions of internal and external multi-source uncertainty and multi-time-varying constraints, the time-varying formation performance of the system can be realized while meeting the constraint requirements, and the performance of the controller is maximized.

Claims

1. A finite-time distributed formation method for unmanned surface vehicle swarm system, characterized in that, The specific steps are as follows: Step 1: Consider a network consisting of unmanned surface vehicle systems, where the first unmanned surface vehicle is modeled in the Earth coordinate system and the second unmanned surface vehicle is modeled in the body coordinate system, resulting in the following kinematic and dynamic models: unmanned surface vehicle systems, where the first unmanned surface vehicle is modeled in the Earth coordinate system and the second unmanned surface vehicle is modeled in the body coordinate system, resulting in the following kinematic and dynamic models: （1）， Equation (1) represents the position of the unmanned surface vehicle system, where is the position of the unmanned surface vehicle in the earth coordinate system and the heading angle , the superscript T denotes the transpose of a vector or matrix, is the velocity vector of the vehicle in the body coordinate system , the derivative with respect to time, is the velocity vector of the vehicle in the body coordinate system , where is the unknown bounded disturbance vector caused by wind, wave and current, , where is the control input of the vehicle subject to the following fault and saturation constraints , where （2）， Equation (2) represents the fault model, where represents the loss efficiency matrix, represents the loss efficiency factor in different driving force directions, respectively, and satisfies , represents an unknown bounded additive fault, and the saturated input vector is determined by the saturation function defined as follows （3）， the subscripts in the formula , respectively represent the actual control input in three speed directions, and are two known constant bounds of saturation function; define , which represents the actual control input vector to be designed; in addition, represents a known nonlinear function, wherein , represents the Coriolis force centripetal matrix and satisfies , and represent known function matrices, represents an unknown real vector composed of non-accurately measured parameters in the system nonlinear suppression matrix, the mass matrix is a positive definite symmetric matrix and satisfies , the matrix represents a transition matrix and has the following definition ， Setting the initial state of an unmanned surface vehicle system wherein respectively denote the function values of the three quantities at the initial time instant; Setting the parameterized path of virtual leader as , respectively represent the parameterized trajectories of forward position, lateral drift position and yaw angle direction, represent the set path parameters; set the convergence speed of the parameterized path as , the desired formation trajectory of the unmanned surface vehicle is , ; Step 2: Utilizing a non-linear smoothing function Estimating the saturation function defined in equation (3) : （4）， Thus, according to the Lagrange mean value theorem, the following approximate relationship is obtained: （5） ， Equation (5) represents a function approximation model, where represents an approximation error and its absolute value has an upper bound value ; the symbol represents a function of a variable ; the derivative operation of the variable , that is, satisfies , is a weight coefficient to be selected and satisfies , is a real number to be selected; in addition, the function value of the derivative satisfies , where is a known normal number; Definition of diagonal matrix where denote the derivative of the nonlinear smooth function in equation (4); definition of total error vector where denote the saturation function estimation error in the three control force directions; afterwards, combining the fault model (2), the saturated input vector and the saturated function approximation model (5), the first unmanned surface vehicle system (1) is rewritten as follows: （6）， wherein: denotes the inverse matrix of the matrix represents the total external uncertainty of the system and is a bounded vector, i.e. the norm satisfies wherein denotes the unknown external disturbance bound;​ Step 3: Define the cooperative formation tracking error vector and the virtual error coordinate transformation for （7）， In the formula: represents the weight of the adjacency matrix between the first agent and the first agent, specifically, represents that the agent and the agent have a connection relationship, otherwise it represents no communication relationship; represents the connection relationship between the agent and the virtual leader, equals 1 to represent a connection relationship, otherwise it represents no connection relationship, , respectively represent the position information vector of the first and the first unmanned surface vehicle, represents the kinematic guidance law to be designed, also known as the virtual control law, represents the transpose of the matrix in formula (1); Step 4: Given the system formation error and the constraint requirements of the speed variable ， where respectively denote constraint functions for the given error variable norm and velocity variable norm which are defined as monotonically decreasing functions with the following finite time performance: （8）， wherein: , and are given positive numbers, denotes time, finite time ; Step 5: Design virtual control law （9）， where: , and are positive control parameters to be designed, is a positive number to be designed, , respectively denote derivative with respect to time, denotes partial derivative with respect to ; for convenience, the simplified notation stands for the constraint function term , and the control nonlinear term is defined in the form of the following piecewise function （10）， wherein is a predetermined small positive parameter, the process coefficient , ； Step 6: Definition , is derivative with respect to time, denotes the desired reference lane, the lane rate of the virtual leader is designed using the filtered gradient method （11）， In the formula and is a positive parameter to be designed; Step 7: Design a nonlinear tracking-differentiation observer to estimate the time derivative of the virtual control law (9) of the virtual control law (9) （12）， wherein: denotes an estimate of an estimate of an estimate of the time derivative of the time derivative of denotes a positive real parameter to be selected; furthermore, for any vector ; and given positive numbers , defining mathematical operator symbols where denotes the components of the vector denotes the sign function of denotes the absolute value of ;​​ Step 8: For the nth unmanned surface vehicle system design finite-time control input vector ​ （13）， In the formulae: and are the positive control parameters to be designed; For convenience, simplified notation is used represents a constraint function term , represents an unknown parameter of the estimated signal, represents an unknown external disturbance bound of the estimated signal, a nonlinear control function satisfies the following definition: ， wherein is a predetermined small positive parameter, the process coefficient , ; Furthermore, the hyperbolic tangent diagonal function matrix is defined as follows: where is a vector of nonlinear cross functions is a vector of nonlinear cross functions , and the components obtained by are three positive real numbers to be chosen Step 9: Design an adaptive update law to compensate for system uncertainties as follows （14）， （15）， In the formulae: are normal numbers to be designed.

2. The finite-time distributed formation method of the unmanned surface vehicle swarm system according to claim 1, wherein, In step 2, .

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