Unmanned ship cluster steering consistency control method based on dynamic regression expansion and fusion mechanism

Abstract

The invention relates to an unmanned ship cluster steering consistency control method based on a dynamic regression expansion and fusion mechanism. The method comprises the following steps: constructing an actual unmanned ship steering control physical model; constructing a multi-agent following unmanned ship directed network with parameter uncertainty and a leader unmanned ship model; constructing a multi-agent directed graph; building a virtual reference model, designing a control protocol, and achieving the tracking of the virtual reference model to the leader unmanned ship; designing a control law of the following agent, and realizing tracking of the virtual reference model by the following unmanned ship; and designing an unknown parameter identifier, estimating an unknown parameter matrix of the following agent, and realizing unmanned ship cluster steering consistency cycle control. According to the method, the problems of following precision reduction and stability analysis difficulty caused by directed information flow propagation due to uncertainty of hydrodynamic parameter change, wave flow disturbance and the like in a traditional method are solved, and uncertain unmanned ship leader following consistency control is realized under directed communication topology.

Description

Technical Field

[0001] This invention relates to the field of unmanned swarm system control technology, and in particular to a method for unmanned surface vessel swarm steering consistency control based on a dynamic regression expansion mechanism. Background Technology

[0002] With the development of intelligent and networked technologies, unmanned surface vessel (USV) swarms are increasingly being used in maritime patrol and search and rescue missions. Cooperative control of USVs requires each vessel to start from different initial headings and angular velocities, update its status through neighborhood information exchange, and gradually form the desired formation and steering consistency to adapt to complex sea conditions and mission requirements.

[0003] In engineering, leader-follower consistency is a common organizational approach: the leader unmanned surface vessel (USV) provides a reference trajectory, while the following USVs coordinate their following based on local information. However, maritime communication often involves directed information flow and asymmetrical coupling, making control design and stability analysis more challenging. Furthermore, the heading dynamics of USVs are affected by variations in hydrodynamic parameters, wave and current disturbances, and actuator efficiency degradation, resulting in matching uncertainties in the input channel and potentially leading to decreased following accuracy. Therefore, it is necessary to study adaptive cooperative control methods for USV swarms under directed communication topologies, enabling online identification and compensation of uncertainties and achieving leader-follower consistency under distributed conditions. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a swarm steering consistency control method for unmanned surface vessels (USVs) based on a dynamic regression expansion mechanism. This method solves the problems of decreased following accuracy and difficulty in stability analysis caused by uncertainties such as changes in hydrodynamic parameters and wave flow disturbances propagating through directed information flow in traditional methods. It achieves leader-follower consistency control of unmanned surface vessels under a directed communication topology.

[0005] To achieve the above technical objectives, this invention provides the following technical solution: a method for unmanned surface vessel swarm steering consistency control based on a dynamic regression expansion mechanism, comprising the following steps: S1. Construct a physical model for the steering control of an actual unmanned surface vessel; S2. Using the following unmanned surface vessel (USV) as the following agent and the leading USV as the leading agent, a multi-agent directed network for following USVs and a leading USV model with parameter uncertainty are constructed based on the actual physical model of USV steering control. S3. Construct a multi-agent directed graph based on follower agents and leader agents to describe the communication relationships between agents; S4. Construct a virtual reference model containing control protocols based on a multi-agent directed network for following unmanned surface vessels. Design control protocols based on the leader unmanned surface vessel model and the multi-agent directed graph. Update the reference state of the virtual reference model so that the virtual reference model can track the leader unmanned surface vessel. S5. Based on the control protocol and virtual reference model, design the control law of the following agent, solve the control input of the following agent, and enable the following unmanned surface vessel to track the virtual reference model; S6. Design an unknown parameter identifier and estimate the unknown parameter matrix of the following agent by combining the control input of the following agent calculated in step S5. S7. Obtain the current system state of the following unmanned surface vessel (USV), combine the unknown parameter matrix of the following agent estimated by the unknown parameter identifier, update the control input of the following agent according to the control law designed in step S5, perform the following USV control, and then use the unknown parameter identifier designed in step S6 to estimate the new unknown parameter matrix again to achieve consistent cyclic control of the USV cluster turning.

[0006] Optionally, in step S1, the physical model for the actual unmanned surface vessel's steering control is described by the following equations: ; in, Indicates the status of the unmanned surface vessel (USV) system, including the USV's heading angle. angular velocity of unmanned surface vessel , For the heading angle of the unmanned surface vessel The first time derivative; Status of unmanned surface vessel system The first-order time derivative describes the state of the unmanned surface vessel system. Dynamic changes over time; , These are the time constant and the rudder effectiveness coefficient, respectively. This is the rudder angle command; Time is the independent variable; For the nonlinear function of the actual unmanned surface vessel steering control physical model, it is defined as: , This indicates unknown or uncertain hydrodynamics.

[0007] Optionally, in step S2, the multi-agent directed network following the unmanned surface vessel with parameter uncertainty is described by the following equation: ; in, Indicates following agent The system status, i.e., numbered as The system status of the following unmanned surface vessel, including its heading angle and angular velocity; Indicates following agent Control input; Represents the system state matrix; Represents the control input matrix; Time is the independent variable; System status about The first derivative describes the system state. Dynamic changes over time; Let be a nonlinear function describing the parameter uncertainty of a directed network for multi-agent following an unmanned surface vessel, which satisfies the following linear parameterization condition: ; in, Represents intelligent agents The unknown parameter matrix; Represents the regression function; Indicates the transpose operation; In step S2, the leader unmanned surface vessel model is described by the following equation: ; in, To lead the system status of the unmanned surface vessel (USV), responsible for planning the route to follow the USV. for about The first derivative describes Dynamic changes over time.

[0008] Optionally, in step S3, constructing a multi-agent directed graph based on the following agent and the leader agent includes: S31. Construct a directed graph of following agents, with the following agents as nodes and the communication states between following agents as edges; the direction of the directed edges of the following agent directed graph is the direction of information transmission between following agents. S32. Constructing the traction matrix between the leader agent and the follower agents. ,in This indicates the construction of a diagonal matrix. Representing the leader agent and the follower agent The communication status between them Represents nodes in a directed graph that follow the agent. The system state of the leading agent can be obtained directly; otherwise... , This represents the total number of following agents, i.e., the total number of nodes in the directed graph of following agents; S33. The leader agent is connected to the follower agents in a directed graph through a traction matrix, forming a multi-agent directed graph. The multi-agent directed graph has at least one support tree with the leader agent as the root node; In the multi-agent directed graph, each node can obtain the system state of any of its incoming neighbor nodes.

[0009] Optionally, in step S4, the virtual reference model containing the control protocol is described by the following equation: ; in, Indicates following agent Reference state, Indicates reference state The first-order time derivative describes the reference state. Dynamic changes over time; Indicates the control protocol; , Let represent the system state matrix and control input matrix of the multi-agent directed network following the unmanned surface vessel, respectively; the control protocol is described by the following equations: ; ; ; in, Represents the independent variable with respect to time. The adaptive gain is used to adjust the coupling weights between the following agents, and its initial value is... ; For adaptive gain about The first derivative of represents the adaptive gain. Update rate; For time as the independent variable The measured value of local consistency tracking error; Indicates the transpose operation; This represents the nodes in the directed graph of the following agent constructed in step S3. Its neighboring nodes Edge weights between them; Represents a node The corresponding following agent Reference state; To monitor the system status of unmanned surface vessels; Represents the gain matrix; Represents a node The set of incoming neighbor nodes; In step S5, the control law of the following agent is described by the following equation: ; ; ; in, Indicates following agent The system status, i.e., numbered as The system status of the following unmanned surface vessel, including its heading angle and angular velocity; Indicates following agent Control input; , These represent the following agents. Online adaptive compensation term and error feedback term; Indicates following agent For unknown parameter matrix The estimate; This represents the regression function.

[0010] Optionally, in step S6, designing the unknown parameter identifier includes the following steps: S61. Define the tracking error of the following agent on the virtual reference model, and calculate it as follows: ; in, Indicates following agent The tracking error of the virtual reference model, i.e., numbered The tracking error of the unmanned surface vessel to the virtual reference model; S62. Based on the multi-agent guided network for following the unmanned surface vessel, the virtual reference model, and the control law of the following agent designed in step S5, an error dynamic equation is established. The mathematical expression of the error dynamic equation is as follows: ; in, For tracking error The first-order time derivative describes the tracking error. Dynamic changes over time; S63, For online adaptive compensation items Regression function Tracking error Perform linear time-invariant filtering and output the corresponding smoothed signals, denoted as the online adaptive compensation term for smoothing. Smooth regression function Smoothing tracking error ; S64, Construction Identification Output , the unknown parameter matrix Rewrite it in linear regression form, and construct the filtered linear regression equation: ; in, , express The left inverse; S65. Establish a scalar equation for the filtered linear regression equation based on the dynamic regression factor expansion and fusion algorithm. S66. Design finite-time excitation conditions for the scalar equations established in step S65, and then solve for the unknown parameter matrix. Least squares estimation An unknown parameter identifier is constructed, which is described by the following equation: ; in Represents the independent variable with respect to time. The truncation function.

[0011] Optionally, in step S65, the step of establishing a scalar equation for the filtered linear regression equation based on the dynamic regression factor expansion and fusion algorithm includes: S651, Introducing Bounded Stability Operators The filtered linear regression equation is mapped to Given an infinite-norm bounded signal space, the dynamically extended regression equation is obtained as follows: ; in, ; ; , They represent respectively to , After bounded stable operators The processed regression output matrix, Indicates a stacking operation. Represents the first step used for linear time-invariant filtering. A linear time-invariant filter, This represents the total number of linear time-invariant filters. S652, multiply both sides of the dynamic extended regression equation by... From the adjoint matrix, the scalar equation is obtained as follows: ; in, ; ; This indicates finding the adjoint matrix. This indicates finding the determinant. This indicates the regression output matrix The intermediate output vector after adjoint matrix processing Represents the regression output matrix The determinant of .

[0012] Optionally, in step S66, the finite-time excitation conditions are designed based on the scalar equation established in step S65, and then the unknown parameter matrix is ​​solved. Least squares estimation ,include: S661, regarding the scalar equation in The finite-time incentive conditions are designed as follows: For following agents Given a constant , existence time and identify update gain Make: ; in, This represents the set of nodes in the directed graph of the following agent constructed in step S3. Represents the space of positive real numbers. Indicates the interval Internal to any time beg The integral; S662. Constructing the unknown parameter matrix Least squares estimation The dynamic update equation is solved to calculate the least squares estimate. The least squares estimation The dynamic update equation is defined as follows: ; in For least squares estimation The first-order time derivative describes the least squares estimation. Dynamic changes over time.

[0013] Optionally, in step S66, the truncation function is defined as: ; in, For the effect on Safety factor on ,make The value is always less than ; Represents the independent variable with respect to time. The attenuation coefficient, its initial value It is always greater than 0 and monotonically non-increasing. Its dynamic update equation is defined as follows: ; Attenuation coefficient about The first derivative describes the attenuation coefficient. Dynamic changes over time.

[0014] This invention also provides a swarm steering consistency control system based on a dynamic regression expansion mechanism, used to apply the aforementioned swarm steering consistency control method based on a dynamic regression expansion mechanism, comprising: The physical model building module is used to build a physical model for the steering control of actual unmanned surface vessels (USVs), a directed network for multi-agent following USVs, a leader USV model, a multi-agent directed graph, and a virtual reference model. The first-layer tracking module is used to design the control protocol, update the reference state of the virtual reference model, and enable the virtual reference model to track the leader unmanned surface vessel. The second-layer tracking module is used to design the control law of the following agent, solve the control input of the following agent, and enable the following unmanned surface vessel to track the virtual reference model. The unknown parameter identifier module is used to design the unknown parameter identifier and estimate the unknown parameter matrix of the following agent by combining the control input from the following agent from the second-layer tracking module. The unmanned surface vessel (USV) cyclic control module combines the estimation results of the unknown parameter matrix from the unknown parameter identifier module to enable the second-layer tracking module to update the control input of the following agent, perform following USV control, and then enable the unknown parameter identifier module to estimate a new unknown parameter matrix again, thereby realizing the consistent cyclic control of USV swarm steering.

[0015] By employing the above technical solution, this invention provides a method for controlling the steering consistency of unmanned surface vessel swarms based on a dynamic regression expansion mechanism, which has at least the following beneficial effects: (1) In view of the characteristics of the unmanned surface vessel’s maritime communication link quality fluctuation, topology connection strength unevenness and different hull maneuverability, the present invention introduces an online updated adaptive gain to realize the adaptive allocation of the cooperative control strength. When the sea state disturbance is enhanced or the communication connection is weakened, the adaptive gain can be automatically increased to strengthen the cooperative correction. When the tracking error is reduced and tends to be consistent, the adaptive gain gradually tends to be stable to avoid over-control and chattering. (2) By introducing a virtual reference model and designing a control protocol based on adaptive gain, the present invention enables the following unmanned surface vessel to achieve coordinated following of the state of the leader unmanned surface vessel by relying only on neighborhood information, thereby reducing the dependence on global information and centralized coordination and improving the applicability of the method in actual maritime communication-limited scenarios. (3) In response to uncertainties such as changes in hydrodynamic parameters and wave current disturbances, this invention combines regression functions and dynamic regression factor expansion and fusion parameter estimation methods to form a dynamic regression expansion and fusion mechanism, designs an unknown parameter identifier, and constructs an online adaptive compensation term to eliminate the influence of uncertainty, thereby significantly improving the system's following accuracy and steady-state consistency performance. At the same time, this invention designs an unknown parameter identifier based on the DREM algorithm, performs regression construction according to the uncertain hydrodynamic terms of the unmanned vessel's turning dynamics, and couples it with the distributed cooperative control closed loop to realize the real-time update of online parameter estimation-compensation-control. Thus, under the conditions of sea state disturbance and communication limitation, it can still suppress the influence of uncertainty and improve the convergence speed and steady-state accuracy of the cluster's turning consistency. (4) Through rigorous stability and convergence analysis, this invention proves that the proposed control strategy can achieve leader following consistency and parameter identification convergence under certain graph conditions and system stability conditions, thus theoretically ensuring the reliability and verifiability of the proposed method. (5) The present invention has a clear structure and clear implementation steps, which facilitates engineering deployment and can be extended to unmanned surface vessel clusters of different sizes and other second-order attitude / heading channel cooperative control scenarios. It has good versatility and engineering promotion value. Attached Figure Description

[0016] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a schematic diagram of the process for unmanned surface vessel (USV) swarm steering consistency loop control according to the present invention. Figure 2 This is a schematic diagram illustrating the communication process between unmanned surface vessels based on a multi-agent directed graph according to the present invention. Figure 3 The unknown parameter identification curves for each following unmanned surface vessel in the simulation experiment of this embodiment of the invention are shown below. Figure 4 This is a graph showing the adaptive gain changing over time in the simulation experiment of this embodiment of the invention; Figure 5 This is a graph showing the state-tracking curves of the leader and follower unmanned surface vessel (USVs) over time in the simulation experiment of this embodiment of the invention. Figure 6 This is a graph showing the change in state 2 of the leader unmanned surface vessel and the tracking unmanned surface vessel over time in the simulation experiment of this embodiment of the invention; Figure 7 This is a three-dimensional curve of the leader following state in the simulation experiment of this embodiment of the invention. Detailed Implementation

[0017] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This will allow for a full understanding of how the present application uses technical means to solve technical problems and achieve technical effects, and to facilitate its implementation.

[0018] Those skilled in the art will understand that all or part of the steps in the implementation of the methods of the embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0019] Please refer to Figures 1-7 This illustration demonstrates a specific implementation of this embodiment. This embodiment constructs a multi-agent directed network for following unmanned surface vessels (USVs) and a leader USV model, builds a multi-agent directed graph, introduces a virtual reference model and designs a control protocol to achieve tracking of the leader USV by the virtual reference model, designs control laws for the following agents to achieve tracking of the virtual reference model by the following USVs, designs an unknown parameter identifier to estimate the unknown parameter matrix of the following agents, and achieves consistent cyclic control of USV swarm steering. This solves the problems of decreased tracking accuracy and difficulty in stability analysis caused by uncertainties such as changes in hydrodynamic parameters and wave current disturbances propagating through directed information flow in traditional methods, and achieves consistent leader-follower control of uncertain USVs under a directed communication topology.

[0020] This embodiment proposes a method for unmanned surface vessel (USV) swarm steering consistency control based on a dynamic regression expansion mechanism. The method includes the following steps: S1. Construct a physical model for the actual steering control of unmanned surface vessels.

[0021] As a preferred embodiment of step S1, it specifically includes: Consider the following class of dynamic equations for the steering control of unmanned surface vessels: ;(Formula 1) in, For the unmanned surface vessel's heading angle, The unmanned surface vessel's angular velocity is its heading. For the heading angle of the unmanned surface vessel The first time derivative, Angular velocity of the unmanned surface vessel The first time derivative describes the heading angular velocity of the unmanned surface vessel. Dynamic changes over time For rudder angle command, , These are the time constant and the rudder effectiveness coefficient, respectively. For unknown and uncertain hydrodynamics (nonlinear damping, additional mass changes, etc.). The independent variable is time.

[0022] Equation 1 above can be rewritten in a unified form by adding a matching uncertainty term to the linear part, taking the unmanned surface vessel system state as an example. The following physical model of the actual unmanned surface vessel steering control is obtained: ;(Formula 2) in Status of unmanned surface vessel system The first-order time derivative describes the state of the unmanned surface vessel system. Dynamic changes over time; For the nonlinear function of the actual unmanned surface vessel steering control physical model, it is defined as: .

[0023] S2. Using the following unmanned surface vessel (USV) as the following agent and the leading USV as the leading agent, a multi-agent directed network for following USVs and a leading USV model are constructed based on the actual USV steering control physical model.

[0024] This embodiment considers containing For the purpose of facilitating derivation and explanation, the physical model of the actual unmanned surface vessel steering control described above can be abstracted into a multi-agent network to address the parameter identification and adaptive control of the following unmanned surface vessel.

[0025] As a preferred embodiment of step S2, it specifically includes: Consider a multi-agent directed network following an unmanned surface vessel with parameter uncertainties, described by the following equation: ;(Formula 3) in, Indicates following agent The system state is of length . The vector, i.e., the one numbered as The system status of the following unmanned surface vessel, including its heading angle and angular velocity; Indicates following agent The control input is a length of The vector, Represents the system state matrix. Represents the control input matrix. Represents the space of real numbers; System status about The first derivative describes the system state. Regarding the dynamic changes over time; in this invention and All are known constant matrices, and the matrix pairs It can be calmed down, and It has full rank.

[0026] Consider a leader unmanned surface vessel model of the following form: ;(Formula 4) in, To lead the system status of the unmanned surface vessel (USV), responsible for planning the route to follow the USV. for about The first derivative describes Dynamic changes over time.

[0027] In formula 3, For a multi-agent guided network of an unmanned surface vessel, a nonlinear function is used to describe the parameter uncertainty. Assumption 1 is constructed as follows: Assumption 1: For each agent ,function The following linear parameterization conditions must be met: ;(Formula 5) in, Indicates following agent The unknown parameter matrix, Representing the unknown parameter matrix The row dimension; Represents the regression function; This indicates the transpose operation.

[0028] S3. Construct a multi-agent directed graph based on follower agents and leader agents to describe the communication relationships between agents.

[0029] In step S2 The multi-agent guided network of following unmanned surface vessels, consisting of several following agents, can be described by a directed graph. As a preferred implementation of step S3, it specifically includes: S31. Construct a directed graph of following agents, using the following agents as nodes and the communication states between them as edges; the directed edges of the following agent directed graph represent the directions of information transmission between the following agents; the constructed directed graph of following agents is denoted as... ,in This represents the set of nodes in the directed graph that follows the agent. Represents the set of directed edges. For nodes to its neighbor node The directed edges between them, Represents the weighted adjacency matrix. For nodes Its neighboring nodes The edge weights between them, and ,node Called a node The incoming neighbor node, and correspondingly, the node Called a node Each node's outgoing neighbor nodes It can obtain the system state of any of its incoming neighbor nodes.

[0030] Define a directed graph of following agents. The Laplace matrix is To describe the impact of the leader unmanned surface vessel (USV) on the follower USV, a directed graph of the following agents is used. Laplace matrix It can be derived from the weighted adjacency matrix, and its mathematical representation is as follows: ;in Laplace matrix The off-diagonal elements in the text represent nodes. For nodes The coupling coefficient, Laplace matrix The diagonal elements in the text.

[0031] S32. Construct the traction matrix between the leader agent and the follower agents; the constructed traction matrix is ​​denoted as... ,in Indicates that the parameter Place them sequentially on the main diagonal of the matrix to construct a diagonal matrix. Representing the leader agent and the follower agent The communication status between them Represents nodes in a directed graph that follow the agent. The system state of the leading agent can be obtained directly; otherwise... , This represents the total number of following agents, which is the total number of unmanned surface vessels following the drone, and also the total number of nodes in the directed graph of the following agents.

[0032] S33. The leader agent is connected to the follower agents in a directed graph via a traction matrix, forming a multi-agent directed graph. The Laplace moment of this multi-agent directed graph is then expressed as: The constructed multi-agent directed graph allows each node to obtain the system state of any of its incoming neighbor nodes.

[0033] Introducing some essential concepts: Represents a group The stacking, Indicates a stacking operation; Describes the bounded signal space of the infinite norm, if satisfy Then it is called ,in This indicates the calculation of the L2 norm. Represents the calculation of the infinite norm. Indicates in Within range Take the upper boundary, It means "infinity".

[0034] If a directed graph has a root node, and there exists a directed path from the root node to every other node in the graph, then the directed graph is said to contain a support tree. Assumption 2 for constructing multi-agent directed graphs is as follows: Assumption 2: The multi-agent directed graph contains a support tree with the leader agent as the root node.

[0035] Lemma 1: Under the condition that Assumption 2 holds, there exists a positive definite matrix. and a positive definite diagonal matrix This makes the following equation true: ;(Formula 6) The control problem of this invention can be described as: solving the distributed adaptive leader-follower consistency tracking problem in a directed network when multiple following unmanned surface vessels have uncertainties in their dynamic parameters, i.e., achieving: (Formula 7a) (Formula 7b) in Indicates "restricted by", Indicates following agent For unknown parameter matrix The estimated value, Representing time, it is an auxiliary variable used to construct the conditions. This indicates a search for the limit.

[0036] The process of realizing communication between unmanned surface vessels based on multi-agent directed graphs can be referred to... Figure 2 . Figure 2 In the text, Leader represents the leading unmanned surface vessel (USV), numbers 1-6 represent the following USVs numbered 1-6, and arrows indicate communication between the leading USV and the following USVs, as well as between the following USVs.

[0037] S4. Construct a virtual reference model containing a control protocol based on a multi-agent directed network for following unmanned surface vessels. Design a control protocol based on the leader unmanned surface vessel model and the multi-agent directed graph to update the reference state of the virtual reference model, enabling the virtual reference model to track the leader unmanned surface vessel.

[0038] Inspired by Model Reference Adaptive Control (MRAC), this invention constructs a virtual reference model to achieve hierarchical unmanned surface vessel tracking.

[0039] As a preferred embodiment of step S4, the specific process includes: A virtual reference model incorporating the control protocol is constructed, described by the following equations: ;(Formula 8) in, Indicates following agent Reference state, Indicates reference state The first-order time derivative describes the reference state. Dynamic changes over time; This indicates the control protocol.

[0040] Therefore, the leader-following consistency tracking problem can be decomposed into a two-layer tracking structure: the bottom layer is the tracking of the virtual reference model by each following agent (following unmanned surface vessel) based on MRAC, and the upper layer is the consistency tracking of the leader unmanned surface vessel by these virtual reference models.

[0041] The control protocol is designed and described by the following equations: ;(Formula 9) ;(Formula 10) ;(Formula 11) in, Represents the independent variable with respect to time. The adaptive gain is used to adjust the coupling weights between the following agents, and its initial value is... ; For adaptive gain about The first derivative of represents the adaptive gain. As the dynamic changes over time (i.e., the update rate) occur, Formula 10 becomes the update law for the adaptive gain. For time as the independent variable The measured value of local consistency tracking error; This represents the nodes in the directed graph of the following agent constructed in step S3. Its neighboring nodes Edge weights between them; Represents a node The corresponding following agent Reference state; Represents a node The set of incoming neighbor nodes, gain matrix Designed for ,in The positive definite matrix is ​​obtained by solving the following equation: ;(Formula 12) in Let be any symmetric positive definite matrix. It is an all-zero matrix. The solvability of Equation 12 is determined by matrix pairs. It is positively determined and ensure.

[0042] Control Protocol Measurement of local consistency tracking error With adaptive gain Co-generated, and From the current moment , as well as Therefore, it is calculated that , , All three evolved simultaneously.

[0043] This invention addresses the challenges of fluctuating communication link quality, uneven topology connectivity, and varying maneuverability among different unmanned surface vessels (USVs) by introducing an online-updated adaptive gain. This allows for adaptive allocation of cooperative control strength. When sea disturbances intensify or communication connections weaken, the adaptive gain automatically increases to enhance cooperative correction. As tracking errors decrease and become more consistent, the adaptive gain gradually stabilizes to avoid over-control and chattering. By introducing a virtual reference model and designing a control protocol based on adaptive gain, the following USV can achieve cooperative following of the leader USV's state solely based on neighborhood information. This reduces reliance on global information and centralized coordination, enhancing the method's applicability in real-world maritime communication-constrained scenarios.

[0044] S5. Based on the control protocol and virtual reference model, design the control law of the following agent, solve the control input of the following agent, and enable the following unmanned surface vessel to track the virtual reference model.

[0045] In a preferred embodiment of step S5, the control law of the intelligent agent is described by the following equation: ;(Formula 13) ;(Formula 14) ;(Formula 15) in, , These represent the following agents. Online adaptive compensation term and error feedback term; Indicates following agent For unknown parameter matrix The estimate. Because the constructed directed graph of the following agent was not used. Therefore, the control protocol formulas 9-11 and the control law formulas 13-15 are completely distributed.

[0046] S6. Design an unknown parameter identifier and estimate the unknown parameter matrix of the following agent by combining the control input of the following agent calculated in step S5.

[0047] To address the problem of identifying parameter uncertainties, a Dynamic Regressor Extension and Mixing (DREM) algorithm is considered to estimate the unknown parameter matrix, thereby achieving accurate identification of uncertain hydrodynamics of unmanned surface vessels. As a preferred embodiment of step S6, the design of the unknown parameter identifyr specifically includes the following process: S61. Define the tracking error of the following agent on the virtual reference model, and calculate it as follows: ; in, Indicates following agent The tracking error of the virtual reference model, i.e., numbered The tracking error of the unmanned surface vessel to the virtual reference model.

[0048] S62. Based on the multi-agent unmanned surface vessel (USV) following directed network, virtual reference model, and control law of the following agent designed in step S5, establish the error dynamic equation. Specifically, substituting equations 5, 8, and 13-15 into equation 3 yields: ;(Formula 16) Formula 16 is the aforementioned error dynamic equation, where, For tracking error The first-order time derivative describes the tracking error. Dynamic changes over time.

[0049] From the matrix The full rank can be known It is invertible, therefore the matrix There exists a left inverse, denoted as In formula 16, multiply by the left... Further results can be obtained: . (Formula 17) S63, For online adaptive compensation items Regression function Tracking error Perform linear time-invariant filtering and output the corresponding smoothed signals, denoted as the online adaptive compensation term for smoothing. Smooth regression function Smoothing tracking error . Specifically: The formula for linear time-invariant filtering is as follows: ; in This represents a linear time-invariant filter. This represents the signal to be filtered. Indicates the filter gain. It represents the space of positive real numbers.

[0050] Based on the above formula for linear time-invariant filtering, the online adaptive compensation term... Regression function Tracking error The state-space equations for linear time-invariant filtering are constructed as follows: ; (Formula 18a) ;(Formula 18b) ;(Formula 19) in, , , These represent the smoothing online adaptive compensation term, the smoothing regression function, and the smoothing tracking error, respectively. The online adaptive compensation term... Regression function Tracking error The smoothed signal output after linear time-invariant filtering; , , They are respectively , , The first-order time derivatives of these three smoothed signals describe their dynamic changes over time. Formula 14 can then be written in the following form: ;(Formula 20) S64. Based on formula 20, let The filtered linear regression equation is constructed as follows: ;(Formula 21) in, Indicates the identification output; S65. Establish a scalar equation for the filtered linear regression equation based on the dynamic regression factor expansion and fusion algorithm. In step S65, the step of establishing a scalar equation for the filtered linear regression equation based on the dynamic regression factor expansion and fusion algorithm includes: S651, Introducing Bounded Stability Operators The filtered linear regression equation is then transferred from... Mapped to Infinite norm bounded signal space of dimension Dimensions here That is, the unknown parameter matrix mentioned above. By determining the row dimension, the dynamically extended regression equation is obtained as follows: ;(Formula 22) in: ; ; , They represent respectively to , After bounded stable operators The processed regression output matrix, at any given time, It is a square formation. ; Represents the first step used for linear time-invariant filtering. There are n linear time-invariant filters, and the total number of linear time-invariant filters is 1. ; S652. Multiply both sides of the dynamic extended regression equation (Equation 22) on the left. From the adjoint matrix, the scalar equation is obtained as follows: ;(Formula 23) in: ; ; This indicates finding the adjoint matrix. This indicates finding the determinant. This indicates the regression output matrix The intermediate output vector after adjoint matrix processing Represents the regression output matrix The determinant of .

[0051] S66. Design finite-time excitation conditions for the scalar equations established in step S65, and then solve for the unknown parameter matrix. Least squares estimation An unknown parameter identifier is constructed; specifically, the unknown parameter identifier is constructed using Equation 23, described by the following equation: ;(Formula 24) in Represents the independent variable with respect to time. The truncation function truncates the unknown parameter matrix when the finite-time excitation conditions are not met. The estimate is defined as follows: (Formula 25a) in, For the effect on Safety factor on ,make The value is always less than In the simulation experiment The initial value is set to 0.999; Represents the independent variable with respect to time. attenuation coefficient, attenuation coefficient initial value As incentives accumulate, the value decreases, remains positive and monotonically non-increasing, and its dynamic update equation is defined as follows: (Formula 25b) for about The first derivative describes Dynamic changes over time.

[0052] Safety factor in truncation function The settings prevent the denominator from being in the unknown parameter identifier If the value is too small, it will result in singular values, thus enhancing the stability of the values. The closer it is to 1, the smaller the margin, and the closer the estimate is. The smaller the value, the greater the margin, resulting in a more conservative and stable value.

[0053] In step S66, the finite-time excitation conditions are designed based on the scalar equation established in step S65, and then the unknown parameter matrix is ​​solved. Least squares estimation ,include: S661. Hypothesis 3 is constructed as follows: Assumption 3: For intelligent agents Given a constant , existence time and identify update gain Make: ;(Formula 26) in, This represents the set of nodes in the following directed graph constructed in step S3. Represents the space of positive real numbers. Indicates the interval Internal to any time beg The integral is the incentive energy.

[0054] Assumption 3 is the scalar equation in... The designed finite-time excitation condition ensures that the excitation energy reaches a lower bound within a finite time, thus enabling the parameter identification process... This allows the signal to shrink to a sufficiently small size within a finite time. This condition is weaker than the traditional duration-based excitation condition. Traditional parameter convergence often uses the duration-based excitation condition, which requires the signal to continuously satisfy a certain excitation intensity throughout the entire time domain. This condition is too stringent. In contrast, the finite-time excitation designed in this invention only requires the excitation to be strong enough within a certain finite time window, thereby ensuring that parameter estimation can be effectively advanced within a finite time.

[0055] S662. Constructing the unknown parameter matrix Least squares estimation The dynamic update equation is solved to calculate the least squares estimate. The least squares estimation The dynamic update equation is defined as follows: ;(Formula 27) in For least squares estimation The first-order time derivative describes the least squares estimation. Dynamic changes over time.

[0056] This invention addresses uncertainties such as changes in hydrodynamic parameters and wave and current disturbances by combining regression functions with dynamic regression factor expansion and fusion parameter estimation methods to form a dynamic regression expansion and fusion mechanism. It designs an unknown parameter identifier and constructs an online adaptive compensation term to eliminate the impact of uncertainties, thereby significantly improving the system's following accuracy and steady-state consistency performance. Furthermore, this invention designs an unknown parameter identifier based on the DREM algorithm, constructs a regression model according to the uncertain hydrodynamic terms of the unmanned surface vessel's turning dynamics, and couples it with a distributed cooperative control closed loop to achieve real-time updates of online parameter estimation, compensation, and control. This allows it to suppress the impact of uncertainties even under conditions of sea state disturbances and communication limitations, improving the convergence speed and steady-state accuracy of swarm turning consistency.

[0057] S7. Obtain the current system state of the following unmanned surface vessel (USV), combine the unknown parameter matrix of the following agent estimated by the unknown parameter identifier, update the control input of the following agent according to the control law designed in step S5, perform the following USV control, and then use the unknown parameter identifier designed in step S6 to estimate the new unknown parameter matrix again to achieve consistent cyclic control of the USV cluster turning.

[0058] This cyclic control process can be referred to Figure 1 The entire control framework is divided into two layers. The constructed multi-agent directed graph serves as the communication network for the leader-follower unmanned surface vessel, and a dynamic regression fusion mechanism is used to solve the unknown parameter matrix. In layer two, each virtual reference model (reference state)... , , ...) Combined with adaptive gain Measurement of local consistency tracking error Based on the leader-following unmanned surface vessel communication network, the leader unmanned surface vessel is tracked (system status). During the tracking process, the local consistency tracking error measurement value is obtained. And perform adaptive gain update In layer one, each unmanned surface vessel (system status) is followed. , , ...) Based on the designed control law ( , , ...), calculate the tracking error of the following agent on the virtual reference model. The system tracks a virtual reference model, and through this two-layer cyclic control, it ultimately achieves the tracking of the leader unmanned surface vessel (USV) by the following USV.

[0059] The effectiveness of the control method provided by this invention will be addressed by constructing and proving theorems.

[0060] Theorem 1: Under the condition that Assumptions 1-3 hold, by designing control protocols (Equations 9-11), control laws (Equations 13-15), and parameter identifiers (Equations 24-27), parameter identification (Equation 7a) and leader-follower consistency (Equation 7b) can be achieved by combining the virtual reference model (Equation 8).

[0061] The theorem proof can be divided into four parts. The first part proves that the unknown parameters are identified to achieve adaptive compensation; the second part proves that the following agent... The first part focuses on tracking the virtual reference model; the second part demonstrates how the virtual reference model tracks the leader unmanned surface vessel (USV); and the third part combines the first three parts to achieve consistency in the USV leader's following behavior.

[0062] 1) Parameter identification proof: Notice each following agent The following is an example: ;(Formula 28) so, It has a good definition. The least squares estimation error of the parameters is defined as follows: According to formulas 23 and 27, we can obtain: ;(Formula 29) in For scalar functions, matrices Updates can perform bitwise operations, where for The first-order time derivative. According to the definitions in Equations 25a and 25b and the principle of superposition for linear systems, we can obtain: ;(Formula 30) Based on least squares estimation error We can obtain: ;(Formula 31) Substituting formula 31 into formula 24, we get: ;(Formula 32) Under the condition that assumption 3 holds, we have Therefore: ;(Formula 33) It can be known that after a certain time... back( ), following the intelligent agent For unknown parameter matrix Online estimates It will converge precisely to its true value. .

[0063] 2) Proof of the agent's tracking of the virtual reference model: From the online adaptive compensation term (Equation 14), we can obtain that... back: ;(Formula 34) Substituting it into formula 16 yields: ;(Formula 35) For each following agent Consider candidate Lyapunov functions along Differentiate the direction and design using the gain matrix. We can obtain: ;(Formula 36) in for The first-order time derivative; because it exists , This represents the operation of finding the minimum eigenvalue of a matrix, where Representation matrix The smallest eigenvalue, therefore: ;(Formula 37) This means following the intelligent agent. Tracking error of virtual reference model exist The exponent converges to 0 after time 1.

[0064] 3) Virtual reference model proof of leader unmanned surface vessel tracking: The first The tracking error of the virtual reference model for the leader unmanned surface vessel is defined as follows: It can be written in the following global form: ;(Formula 38) Among them, global tracking error Global reference state Global leadership unmanned surface vessel system status , For elements all equal to 1 3D column vector, It represents the Kronecker product.

[0065] Starting from the adaptive gain law (Equation 10), its analytical solution is: ;(Formula 39) Among them, items For any Non-negative. Because of the initial conditions. , can be obtained .

[0066] Substituting the control protocol (Equation 9) into the virtual reference model (Equation 8), we get: ;(Formula 40) Its global form can be written as follows: ;(Formula 41) The global form of the adaptive gain It is a diagonal matrix containing the adaptive gains of each node. Representing the identity matrix, in Formula 11 Global form can be and express: ;(Formula 42) From Equation 39, we get It is a positive definite diagonal matrix, which can be obtained from Equation 42 according to the conditions in Assumption 2: ;(Formula 43) in , To reflect from arrive The positive constants of the lower and upper bounds of energy transfer. Differentiating equation 38, we get: ;(Formula 44) in express First-order time derivative; construct Lyapunov function as follows: ;(Formula 45) in Let be the diagonal matrix defined in Lemma 1. Solve from formula 12, , Let be a positive constant specified later. Taking the derivative of Equation 45, we get: ;(Formula 46) in for The first time derivative, Considering Formula 39 exist When the time is constant, we can obtain formula 10. Non-negative, combined with a positive definite diagonal matrix and , can be obtained When, the following inequality holds, . (Formula 47) Simplifying formula 46, we get: ;(Formula 48) According to Lemma 1 and Formula 12, Formula 48 can be rewritten as: ;(Formula 49) Using the adaptive gain law (Equation 10) and Equation 43, the last term on the right side of inequality 49 becomes as follows: ;(Formula 50) in , As defined in Formula 43, , ; , These are constants introduced artificially, due to , Since they are positive constants, any positive constant can be selected. and The value can then be set arbitrarily. and The value of satisfies the simplification requirements of Formula 50. Furthermore, because and It is a positive definite matrix, which can be obtained from the properties of the Kronecker product operator. , It is the identity matrix. This represents a positive constant. Therefore, there exists a positive constant in Formula 50. Make .

[0067] Based on the above inequality, Equation 49 becomes: ;(Formula 51) Let positive constants be given , They are respectively Maximum singularity sum The minimum singular value, and Defined by Lemma 1, the variables in Formula 50 are designed. Make it satisfy: ;(Formula 52) in for The maximum singular value, and the design constant. Large enough to satisfy From formula 51, we get: ;(Formula 53) The first inequality is... and We obtain the second inequality from Equation 52. From Equation 53, we can rewrite the last three terms on the right side of Equation 51 as follows: ;(Formula 54) Substituting formula 54 into formula 51, we get: ;(Formula 55) Thus guarantee It is bounded for any time. Boundedness means and Both are bounded, as can be seen from Formula 44. Bounded. Within the interval Integrating both sides of equation 55, we get: ;(Formula 56) Depend on and Given the boundedness, for any ,integral Bounded. According to Barbara's lemma, we know... , This represents a column vector of all zeros, thus proving that the virtual reference model can track the leader unmanned surface vessel.

[0068] 4) Proof of Unmanned Surface Vessel Leader-Follower Consistency: Review For any As has been proven above and Then we can get: ;(Formula 57) This clearly demonstrates that following the unmanned surface vessel (USV) is related to tracking the leader USV.

[0069] This invention demonstrates, through rigorous stability and convergence analysis, that the proposed control strategy can achieve leader-following consistency and parameter identification convergence under certain graph conditions and system stability conditions, thus theoretically ensuring the reliability and verifiability of the proposed method.

[0070] To enable researchers in the field to better understand the implementation of this invention, simulation experiments were conducted using Matlab software.

[0071] The specific information about the simulation software is as follows: Software Name: MATLAB; Version information: 25.1.0.2943329 (R2025a); License number: 968398; Operating system: Microsoft Windows 11 Home Version 10.0 (Build 26200); This invention is based on a class of dynamic equations concerning the steering control of unmanned surface vessels: ; The physical model for the steering control of an actual unmanned surface vessel is modeled as follows: ; Pick , The value is 1. Function Satisfy linear parameterization conditions .

[0072] ; in, Represents the unknown parameter matrix Set the actual value; retrieve the gain matrix. , Adaptive gain Selected from; , These represent the calculations for sine and cosine, respectively.

[0073] In this simulation experiment, one leader UAV (numbered 0) and six follower UAVs (numbered 1-6) were set up. The unknown parameter identification curves of each follower UAV can be referenced. Figure 3 , Figure 3 This demonstrates the effectiveness of the present invention in estimating the unknown parameter matrix based on the DREM algorithm, and achieves accurate identification of unknown hydrodynamics of unmanned surface vessels. Figure 3 W11-W01 indicates the following unmanned surface vessels 1-6 and the leader unmanned surface vessel 0. The first row of values ​​is identified. Letters W12-W02 represent the following unmanned surface vessels (USVs) 1-6 and the leader USV 0. The second row of values ​​is identified. Letters W13-W03 represent the following unmanned surface vessels (USVs) 1-6 and the leader USV 0. Identification of the third row value. Figure 3 The fact that the curve reaches a stable value over time means that the unknown parameter matrix... The estimate converged to the true value.

[0074] In the simulation experiment of this embodiment, adaptive gain The curve showing the change over time can be referenced. Figure 4 , Figure 4 The invention visually demonstrates the boundedness of the adaptive gain of its method, indicating that the method is stable and feasible, and automatically adjusts to an appropriate level.

[0075] In the simulation experiment of this embodiment, the steering motion of the unmanned surface vessel is in a second-order steering system, which is described by a two-dimensional state vector. This vector has two components, which are referred to as "state one" and "state two" to represent the first and second dimensions, respectively. These represent the differences between followers 1-6 and leader 0 in state 1, i.e., the tracking error in state 1; These represent the differences between followers 1-6 and leader 0 in state two, i.e., the tracking error in state two.

[0076] In the simulation experiment of this embodiment, the state-tracking error curves of the leader and follower unmanned surface vessels as a function of time can be referenced. Figure 5In the simulation experiment of this embodiment, the state-to-state tracking error curves of the leader and follower unmanned surface vessels as a function of time can be referenced. Figure 6 .

[0077] Figure 5 , Figure 6 This indicates that the designed control law and adaptive gain update law can bring the tracking error of the following unmanned surface vessel to zero.

[0078] In the simulation experiment of this embodiment, the three-dimensional curve of the leader's following state can be referenced. Figure 7 As time progresses, the state of the following unmanned surface vessel (USV) system and the state of the leader USV system become consistent. The coordinate axes x1 and x2 represent state one and state two, respectively.

[0079] This application also provides an embodiment of an unmanned surface vessel (USV) swarm steering consistency control system based on a dynamic regression expansion mechanism, used to apply the aforementioned USV swarm steering consistency control method based on a dynamic regression expansion mechanism, including: The physical model building module is used to build a physical model for the steering control of actual unmanned surface vessels (USVs), a directed network for multi-agent following USVs, a leader USV model, a multi-agent directed graph, and a virtual reference model. The first-layer tracking module is used to design the control protocol, update the reference state of the virtual reference model, and enable the virtual reference model to track the leader unmanned surface vessel. The second-layer tracking module is used to design the control law of the following agent, solve the control input of the following agent, and enable the following unmanned surface vessel to track the virtual reference model. The unknown parameter identifier module is used to design the unknown parameter identifier and estimate the unknown parameter matrix of the following agent by combining the control input from the following agent from the second-layer tracking module. The unmanned surface vessel (USV) cyclic control module combines the estimation results of the unknown parameter matrix from the unknown parameter identifier module to enable the second-layer tracking module to update the control input of the following agent, perform following USV control, and then enable the unknown parameter identifier module to estimate a new unknown parameter matrix again, thereby realizing the consistent cyclic control of USV swarm steering.

[0080] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0081] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus or device (such as a computer-based system, a processor-included system or other system that can fetch and execute instructions from, an instruction execution system, apparatus or device).

[0082] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for controlling the steering consistency of unmanned surface vessel (USV) swarms based on a dynamic regression expansion mechanism, characterized in that, include: S1. Construct a physical model for the steering control of an actual unmanned surface vessel; S2. Using the following unmanned surface vessel (USV) as the following agent and the leading USV as the leading agent, a multi-agent directed network for following USVs and a leading USV model with parameter uncertainty are constructed based on the actual physical model of USV steering control. S3. Construct a multi-agent directed graph based on follower agents and leader agents to describe the communication relationships between agents; S4. Construct a virtual reference model containing control protocols based on a multi-agent directed network for following unmanned surface vessels. Design control protocols based on the leader unmanned surface vessel model and the multi-agent directed graph. Update the reference state of the virtual reference model so that the virtual reference model can track the leader unmanned surface vessel. S5. Based on the control protocol and virtual reference model, design the control law of the following agent, solve the control input of the following agent, and enable the following unmanned surface vessel to track the virtual reference model; S6. Design an unknown parameter identifier and estimate the unknown parameter matrix of the following agent by combining the control input of the following agent calculated in step S5. S7. Obtain the current system state of the following unmanned surface vessel (USV), combine the unknown parameter matrix of the following agent estimated by the unknown parameter identifier, update the control input of the following agent according to the control law designed in step S5, perform the following USV control, and then use the unknown parameter identifier designed in step S6 to estimate the new unknown parameter matrix again to achieve consistent cyclic control of the USV cluster turning.

2. The unmanned surface vessel swarm steering consistency control method based on dynamic regression expansion mechanism according to claim 1, characterized in that: In step S1, the actual unmanned surface vessel steering control physical model is described by the following equations: ； in, Indicates the status of the unmanned surface vessel (USV) system, including the USV's heading angle. angular velocity of unmanned surface vessel , For the heading angle of the unmanned surface vessel The first time derivative; Status of unmanned surface vessel system The first-order time derivative describes the state of the unmanned surface vessel system. Dynamic changes over time; , These are the time constant and the rudder effectiveness coefficient, respectively. This is the rudder angle command; Time is the independent variable; For the nonlinear function of the actual unmanned surface vessel steering control physical model, it is defined as: , This indicates unknown or uncertain hydrodynamics.

3. The unmanned surface vessel swarm steering consistency control method based on dynamic regression expansion mechanism according to claim 1, characterized in that: In step S2, the multi-agent directed network following the unmanned surface vessel with parameter uncertainty is described by the following equation: ； in, Indicates following agent The system status, i.e., numbered as The system status of the following unmanned surface vessel, including its heading angle and angular velocity; Indicates following agent Control input; Represents the system state matrix; Represents the control input matrix; Time is the independent variable; System status about The first derivative describes the system state. Dynamic changes over time; Let be a nonlinear function describing the parameter uncertainty of a directed network for multi-agent following an unmanned surface vessel, which satisfies the following linear parameterization condition: ； in, Represents intelligent agents The unknown parameter matrix; Represents the regression function; Indicates the transpose operation; In step S2, the leader unmanned surface vessel model is described by the following equation: ； in, To lead the system status of the unmanned surface vessel (USV), responsible for planning the route to follow the USV. for about The first derivative describes Dynamic changes over time.

4. The unmanned surface vessel swarm steering consistency control method based on dynamic regression expansion mechanism according to claim 1, characterized in that: In step S3, the construction of a multi-agent directed graph based on the follower agent and the leader agent includes: S31. Construct a directed graph of following agents, with the following agents as nodes and the communication states between following agents as edges; the direction of the directed edges of the following agent directed graph is the direction of information transmission between following agents. S32. Constructing the traction matrix between the leader agent and the follower agents. ,in This indicates the construction of a diagonal matrix. Representing the leader agent and the follower agent The communication status between them Represents nodes in a directed graph that follow the agent. The system state of the leading agent can be obtained directly; otherwise... , This represents the total number of following agents, i.e., the total number of nodes in the directed graph of following agents; S33. The leader agent is connected to the follower agents in a directed graph through a traction matrix, forming a multi-agent directed graph. The multi-agent directed graph has at least one support tree with the leader agent as the root node; In the multi-agent directed graph, each node can obtain the system state of any of its incoming neighbor nodes.

5. The unmanned surface vessel swarm steering consistency control method based on dynamic regression expansion mechanism according to claim 4, characterized in that: In step S4, the virtual reference model containing the control protocol is described by the following equation: ； in, Indicates following agent Reference state, Indicates reference state The first-order time derivative describes the reference state. Dynamic changes over time; Indicates the control protocol; , Let represent the system state matrix and control input matrix of the multi-agent directed network following the unmanned surface vessel, respectively; the control protocol is described by the following equations: ； ； ； in, Represents the independent variable with respect to time. The adaptive gain is used to adjust the coupling weights between the following agents, and its initial value is... ; For adaptive gain about The first derivative of represents the adaptive gain. The update rate; For time as the independent variable The measured value of local consistency tracking error; Indicates the transpose operation; This represents the nodes in the directed graph of the following agent constructed in step S3. Its neighboring nodes Edge weights between them; Represents a node The corresponding following agent Reference state; To monitor the system status of unmanned surface vessels; Represents the gain matrix; Represents a node The set of incoming neighbor nodes; In step S5, the control law of the following agent is described by the following equation: ； ； ； in, Indicates following agent The system status, i.e., numbered as The system status of the following unmanned surface vessel, including its heading angle and angular velocity; Indicates following agent Control input; , These represent the following agents respectively. Online adaptive compensation term and error feedback term; Indicates following agent For unknown parameter matrix The estimate; This represents the regression function.

6. The unmanned surface vessel swarm steering consistency control method based on dynamic regression expansion mechanism according to claim 5, characterized in that: In step S6, the design of the unknown parameter identifier includes the following steps: S61. Define the tracking error of the following agent on the virtual reference model, and calculate it as follows: ； in, Indicates following agent The tracking error of the virtual reference model, i.e., numbered The tracking error of the unmanned surface vessel to the virtual reference model; S62. Based on the multi-agent guided network for following the unmanned surface vessel, the virtual reference model, and the control law of the following agent designed in step S5, an error dynamic equation is established. The mathematical expression of the error dynamic equation is as follows: ； in, For tracking error The first-order time derivative describes the tracking error. Dynamic changes over time; S63, For online adaptive compensation items Regression function Tracking error Perform linear time-invariant filtering and output the corresponding smoothed signals, denoted as the online adaptive compensation term for smoothing. Smooth regression function Smoothing tracking error ; S64, Construction Identification Output , the unknown parameter matrix Rewrite it in linear regression form, and construct the filtered linear regression equation: ； in, , express The left reverse; S65. Establish a scalar equation for the filtered linear regression equation based on the dynamic regression factor expansion and fusion algorithm. S66. Design finite-time excitation conditions for the scalar equations established in step S65, and then solve for the unknown parameter matrix. Least squares estimation An unknown parameter identifier is constructed, which is described by the following equation: ； in Represents the independent variable with respect to time. The truncation function.

7. The unmanned surface vessel swarm steering consistency control method based on dynamic regression expansion mechanism according to claim 6, characterized in that: In step S65, the step of establishing a scalar equation for the filtered linear regression equation based on the dynamic regression factor expansion and fusion algorithm includes: S651, Introducing Bounded Stability Operators The filtered linear regression equation is mapped to Given an infinite-norm bounded signal space, the dynamically extended regression equation is obtained as follows: ； in: ； ； , They represent respectively to , After bounded stable operators The processed regression output matrix, Indicates a stacking operation. Denotes the first step used for linear time-invariant filtering. A linear time-invariant filter, This represents the total number of linear time-invariant filters. S652, multiply both sides of the dynamic extended regression equation by... From the adjoint matrix, the scalar equation is obtained as follows: ； in, ； ； This indicates finding the adjoint matrix. This indicates finding the determinant. This indicates the regression output matrix The intermediate output vector after adjoint matrix processing Represents the regression output matrix The determinant of .

8. The unmanned surface vessel swarm steering consistency control method based on dynamic regression expansion mechanism according to claim 7, characterized in that: In step S66, the finite-time excitation conditions are designed based on the scalar equation established in step S65, and then the unknown parameter matrix is ​​solved. Least squares estimation ,include: S661, regarding the scalar equation in The finite-time incentive conditions are designed as follows: For following agents Given a constant Existence time and identify update gain Make: ； in, This represents the set of nodes in the directed graph of the following agent constructed in step S3. Represents the space of positive real numbers. Indicates the interval Internal to any time beg The integral; S662. Constructing the unknown parameter matrix Least squares estimation The dynamic update equation is solved to calculate the least squares estimate. The least squares estimation The dynamic update equation is defined as follows: ； in For least squares estimation The first-order time derivative describes the least squares estimation. Dynamic changes over time.

9. The unmanned surface vessel swarm steering consistency control method based on dynamic regression expansion mechanism according to claim 8, characterized in that: In step S66, the truncation function is defined as: ； in, For the effect on Safety factor on ,make The value is always less than ; Represents the independent variable with respect to time. The attenuation coefficient, its initial value It is always greater than 0 and monotonically non-increasing. Its dynamic update equation is defined as follows: ； Attenuation coefficient about The first derivative describes the attenuation coefficient. Dynamic changes over time.

10. A dynamic regression-based unmanned surface vessel (USV) swarm steering consistency control system, used to apply the dynamic regression-based unmanned surface vessel swarm steering consistency control method as described in any one of claims 1-9, characterized in that, include: The physical model building module is used to build a physical model for the steering control of actual unmanned surface vessels (USVs), a directed network for multi-agent following USVs, a leader USV model, a multi-agent directed graph, and a virtual reference model. The first-layer tracking module is used to design the control protocol, update the reference state of the virtual reference model, and enable the virtual reference model to track the leader unmanned surface vessel. The second-layer tracking module is used to design the control law of the following agent, solve the control input of the following agent, and enable the following unmanned surface vessel to track the virtual reference model. The unknown parameter identifier module is used to design the unknown parameter identifier and estimate the unknown parameter matrix of the following agent by combining the control input from the following agent from the second-layer tracking module. The unmanned surface vessel (USV) cyclic control module combines the estimation results of the unknown parameter matrix from the unknown parameter identifier module to enable the second-layer tracking module to update the control input of the following agent, perform following USV control, and then enable the unknown parameter identifier module to estimate a new unknown parameter matrix again, thereby realizing the consistent cyclic control of USV swarm steering.

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