A method for flow-aware heterogeneous uuvs pre-scheduled time formation switching control in a restricted environment

Abstract

This invention discloses a pre-time formation switching control method for heterogeneous UUVs in confined environments based on mobility perception. The method includes: establishing a heterogeneous UUV formation switching system model; modeling the confined area as a time-varying curve virtual pipeline and defining a mobility index as the trigger for formation switching; constructing a data-driven neural network to approximate uncertainties and disturbances; designing a pre-defined time restraint controller for the actual root leader; generating a reference trajectory from the virtual root leader; and determining the leader formation's position and velocity based on the actual root leader information; designing a pre-defined time affine switching observer to observe the desired state of followers; and designing a full-state pre-time controller by combining a unified obstacle function and a neural network, ultimately achieving formation switching control. This invention integrates core technologies such as mobility perception, pre-time control, a unified obstacle function, and data-driven neural networks to construct a complete heterogeneous UUV formation switching control scheme, achieving comprehensive improvements in environmental adaptability, control accuracy, convergence performance, operational safety, and formation cooperative robustness.

Description

Technical Field

[0001] This invention relates to the field of cooperative control and autonomous navigation technology for underwater unmanned systems, and in particular to a predetermined time formation switching control method for heterogeneous UUVs based on mobility perception in confined environments. Background Technology

[0002] With the increasing complexity of marine resource development, scientific research, and environmental monitoring tasks, multi-unmanned underwater vehicle (UUV) systems have become a research hotspot due to their higher operational efficiency and robustness. These systems need to perform collaborative operations in complex, dynamic, and spatially constrained marine environments (such as subsea pipeline inspection, canyon terrain exploration, and traversing dense reef areas). In these tasks, UUVs not only need to maintain a predetermined formation to cooperate, but also must adapt in real time to changes in the geometry of the environmental passageway (such as width fluctuations and curvature changes), and strictly ensure that the position, velocity, and other states of each UUV remain within time-varying constraints determined by environmental boundaries and safety regulations to avoid collisions. Therefore, designing a robust collaborative controller that can simultaneously handle time-varying state constraints, achieve predetermined time convergence, and adaptively adjust the formation configuration according to the difficulty of environmental passage is a key technical problem that urgently needs to be solved for practical engineering applications in this field.

[0003] To address the aforementioned issues, existing technologies primarily focus on several aspects. In formation architecture, the leader-follower structure is widely used, where the leader's trajectory is set, and followers maintain relative configurations via a communication network to achieve formation. To ensure navigational safety, methods such as obstacle Lyapunov functions or model predictive control are often employed to handle state constraints. To overcome unknown disturbances and nonlinearities in the system model, neural networks and fuzzy systems are introduced into the controller for online compensation. To improve system convergence speed, finite-time control and fixed-time control methods have been proposed, enabling the system state to stabilize within a finite time. Regarding formation deformation, existing solutions mostly achieve this by switching preset formation patterns or adjusting connection weights in the communication topology.

[0004] However, existing technical solutions still face significant limitations in practical applications. First, in handling state constraints, mainstream methods such as logarithmic barrier Lyapunov functions have relatively strict design conditions, usually requiring constant or symmetric constraint boundaries. Furthermore, the control system exhibits overly sensitive responses when the state approaches the lower boundary, leading to complex controller design and insufficient adaptability in asymmetric, time-varying constraint scenarios. Second, regarding convergence performance, traditional methods mostly achieve asymptotic convergence, while the convergence time of finite-time or fixed-time control either depends on the unpredictable initial state or has a complex and difficult-to-adjust upper bound expression, making it impossible to accurately and intuitively preset the convergence time according to task requirements. Finally, in terms of adaptive formation adjustment, existing strategies lack a quantifiable decision-making basis directly related to the "difficulty of traversing" the environment, often relying on simple threshold-triggered switching. This results in inaccurate matching of formation scaling with environmental changes, and the switching process may produce trajectory jumps or oscillations, affecting the smooth operation and safety of the entire cluster. Summary of the Invention

[0005] This invention provides a method for pre-time formation switching control of heterogeneous UUVs based on mobility awareness in confined environments to overcome the above-mentioned technical problems.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: A method for scheduled grouping and handover control of heterogeneous UUVs based on liquidity awareness in a constrained environment, comprising the following steps: S1. Establish a switching system model for heterogeneous unmanned underwater vehicle formations, wherein the heterogeneous unmanned underwater vehicle formations include a virtual root leader, an actual root leader, a leader formation, and a follower formation. S2. Model the restricted operating area as a time-varying curve virtual pipeline, and define the cross-section and flow index of the time-varying curve virtual pipeline, thereby providing a trigger basis for the formation switching of heterogeneous unmanned underwater vehicles. S3. Establish a data-driven neural network for approaching uncertainty and disturbance; design a predefined time-restraint controller for the actual root leader based on the switching system model, time-varying curve virtual pipeline and data-driven neural network. S4. A reference trajectory is generated through the virtual root leader, the actual root leader performs environmental perception, and generates the actual root leader's running trajectory based on the reference trajectory and the predefined time restraint controller; the leader formation determines the formation position and speed information of the leader formation according to the environmental perception information sent by the actual root leader and the running trajectory. S5. Based on the preset affine formation topology switching rules between the leader formation and the follower formation, and the formation position and velocity information of the leader formation, design a predefined time affine switching observer. The predefined time affine switching observer is used to observe the desired position and velocity information of the follower formation. S6. A leader-follower full-state pre-time controller based on a unified obstacle function and data-driven neural network design. S7. Based on the predefined time affine switching observer and leader-follower full-state predetermined time controller, realize the switching control of heterogeneous unmanned underwater vehicle formation.

[0007] Furthermore, in S1, the specific steps for establishing a formation switching system model for heterogeneous unmanned underwater vehicles include: S11. Establish the underlying communication topology of the formation switching system for heterogeneous unmanned underwater vehicles: Define a directed graph Node set does not change over time edge set It does not change over time. ,in, arrive It is a virtual root leader. It is the actual root leader. arrive He is a leader. arrive It is a follower, total number of nodes , Indicates the number of virtual root leaders. Indicates the number of followers. This indicates the number of leaders, where 1 represents the actual number of root leaders. S12. Design a discrete switching mechanism for a formation switching system of heterogeneous unmanned underwater vehicles: Set switching signal The switching signal is based on the flow rate. Select the activity configuration level, which is represented as: (1) in, It is a pre-set flowability threshold. ; For each level Set the stress matrix , is represented as: (2) in, It is a scaling stress weight. , It is a level scaling factor, For fixed edge The basic weights, ; The stress matrix reflects the hierarchical communication architecture and is represented as: (3) in, Represents 2*2 d The identity matrix, d For dimension; block , , , It is constant, and only varies with... The change alters the size of its non-zero elements without altering its sparsity pattern; Each element in the array is a non-negative number and the sum of all elements is 1. S13. Establish a dynamic model of the formation switching system for heterogeneous unmanned underwater vehicles. The specific steps are as follows: Assume that all unmanned underwater vehicles have a common 3-DOF dynamic structure. For the third... j An unmanned underwater vehicle Its generalized dynamic model is: (4) in, This is the position state vector, representing the position values ​​in the longitudinal, lateral, and yaw degrees of freedom. velocity vector It includes the corresponding velocity and planar position coordinates in the Earth's fixed coordinate system. Planar velocity components , and These represent the yaw angle and yaw rate, respectively. This represents typical dynamic characteristics, including the Coriolis effect, damping effect, and gravitational effect. Indicating model uncertainty and ocean current disturbance The sum, Indicates control gain, control input , It is a configuration-related transformation matrix. , The definition of is: (5) Assuming control gain and satisfy , , , Therefore, the dynamic model of the actual root leader is transformed into: (6) in, , , , , , , , Let be the rotation matrix of the actual root leader in the y-plane. ; The required yaw angles and positions for the leader and followers are set as follows: , , The expected yaw angle for the actual root leader is: , in, The direction of the cross section to be defined; Set up a virtual leader Following a pre-set reference trajectory, Its expression is: , in, This indicates the desired position of the virtual leader. , It is a transformation matrix. , Let be the rotation matrix of the virtual root leader in the y-plane. , ; In a heterogeneous unmanned underwater vehicle (UUV) formation, all real UUVs are subject to time-varying full-state output constraints, and the position of each UUV is... and speed Both are subject to lower and upper limits: , in, and These represent the position and velocity limits, respectively. S14. Define a two-dimensional affine coordinate system between the leader and followers, expressed as: (7) Among them, nominal configuration Affine transformation matrix that changes with time , transform vector ; and These are the ideal trajectories for leaders and followers, respectively, which satisfy environmental constraints. And for all All are true. and It is the boundary of a restricted region, and is continuously differentiable and has finite curvature.

[0008] Furthermore, in S2, the specific steps for modeling the restricted operating region as a time-varying curve virtual pipe and defining the cross-section and flow index of the time-varying curve virtual pipe are as follows: S21, When the actual root leader position When defining the cross section for: , And it satisfies the orthogonality condition: (8) in, It is the generating curve exist The unit tangent vector at that point; Determine the direction of the cross section based on the unit normal vector: (9) in, Is with The perpendicular unit normal vector, and They are Projection onto the X and Y axes of the global coordinate system; S22. Define liquidity indicators: pass The navigation capability of the time-varying curve virtual pipeline is quantified, and its standardized form is as follows: (10) in, , This indicates the average width of the TVT. , Indicates the generated curve arc length, , It is the local pipe width at time s. Indicates the time period from arrive Total control force required to traverse CORs. , , , and These represent baseline thrust, curvature penalty, width variation, and trajectory deviation adaptation, respectively. It is the set starting point of the dynamic sliding window; in, (11) in, To generate the curvature of the curve. It is the actual quality of the leader. The conductor is perpendicular to velocity in the direction, , , and These are the influence coefficients obtained through experimental calibration.

[0009] Furthermore, in S3, the specific steps for establishing the data-driven neural network are as follows: The ideal approximate expression for a data-driven neural network is defined as follows: , The corresponding estimate for the data-driven neural network is: (12) in, It is to satisfy Ideal weights, , yes The estimated value, , It is an activation function. , , This represents the input to the data-driven neural network. and They are the first The center and width of each node, , ; Configure data stack ,when k When =1, the data stack is in time interval Internally, it forms a time-varying, possessing A sequence of timestamps, whose timestamps are as follows: And the sequence length is ,based on Construct a vector containing past activation vectors Historical data stack , is represented as: (13) in, It is a positive weighting coefficient. It is to satisfy The estimation error, It is a bounded positive number.

[0010] Furthermore, in S3, the specific steps for designing a predefined time-restraint controller for the actual root leader based on the aforementioned switching system model, time-varying curve virtual pipeline, and data-driven neural network include: The envelope position error and velocity error are defined based on the relative state between the actual root leader and the virtual root leader: (14) Construct a sliding surface, its expression is: ; Differentiating with respect to the sliding surface, we get: (15) To approximate the uncertainty term Using data-driven neural networks ,in It is the ideal and appropriate weight, satisfying ; express The estimated value, and yes Error, input of data-driven neural network Represented as: (16) Based on the above design, the predefined time-restraint controller for the actual root leader is represented as follows: (17) The controller gain estimation of the predefined time-determination controller and the weight adaptation law of the data-driven neural network are defined as follows: (18) (19) Among them, the positive definite diagonal parameter matrix The estimated value of the controller gain , The error in the controller gain estimation; , , , This is a predefined time point for system convergence.

[0011] Furthermore, in S4, the specific steps for the leader formation to determine its formation position and speed information based on the environmental perception information and trajectory sent by the actual root leader include: The leader formation is based on the discrete switching mechanism and the liquidity indicator sent by the actual root leader. Query Table 1 to determine the current discrete configuration level. ; Table 1: Discrete Configuration Levels Based on Flowability

[0012] The leader formation uses the actual trajectory of the root leader as the global reference, combining the nominal formation configuration in the two-dimensional affine coordinate system between the leader and followers, as well as the body coordinate system. By scaling factor Generate the first The basic expected trajectory of a leader is: , ; Among them, scaling offset ,and ; During the scaling transition between leader and follower formations, the leader formation is based on the current configuration level. Compared to the previous configuration level The switching logic is calculated using the following formula:

[0013] A leader's smooth reference trajectory That is, the first The target formation position for each leader: (20) Wherein, the transfer function The expression is , For continuous conversion time, when hour, ; By taking the time derivative of the smoothed reference trajectory, the corresponding velocity information can be obtained, and the leader formation position and velocity information can be determined.

[0014] Furthermore, in S5, the predefined time-based affine switching observer, designed based on the preset affine formation topology switching rules between the leader and follower formations, and the formation position and velocity information of the leader formation, is as follows: (twenty one) Among them, design parameters ; and The first I The position and velocity error of each follower are jointly defined by the leader's formation position and velocity information and the affine formation topology switching rules, as shown in the following formula: (twenty two) In the formula, and To switch levels The varying stress weights and diagonal matrix are directly determined by the pre-defined leader-follower affine formation topology switching rules. and The first Estimated position and velocity of each follower; The first in The diagonal elements represent the in-degree of the node, i.e. ; and The first i The first follower and the first J The rotation matrix of the leaders in the xy plane.

[0015] Furthermore, in S6, the specific steps for designing a leader-follower full-state predetermined time controller based on a unified obstacle function and data-driven neural network are as follows: S61: Define a unified barrier function, for the... For an underwater unmanned vehicle, By using a unified obstacle function, position and velocity information are combined. Mapping to unconstrained variables, represented as: (twenty three) in, It is a gain that can be positively adjusted; The inverse function is: (twenty four) In the formula, System state constraint variables ; right Differentiation yields: , in, , ,and: (25) Based on the generalized dynamics model of the follower, the system state of the heterogeneous unmanned underwater vehicle formation, which is subject to time-varying full-state output constraints, is transformed into the following unconstrained standard form: (26) in, , and ; Based on the above, the tracking error signal is defined as follows: (27) Among them, the virtual control law to be designed A new reference signal Defined as The ideal trajectory of leaders and followers is defined as follows: ; S62. Design a virtual control law based on the tracking error signal, including: Tracking error signal Differentiate the equation and substitute it into formula (25) to obtain the error dynamic equation: (28) in, The ideal output format for data-driven neural networks, Using data-driven neural networks to Approximation; data-driven neural network input , To approach Ideal weights, The approximation error is bounded. A virtual control law is designed based on the aforementioned error dynamic equation. , is represented as: (29) in, The adaptive weight update law is: (30) in, For ideal weights The estimated value, All are positive definite design parameters; learning terms are based on historical data. ; S63. Design a leader-follower neural network output estimator: Design a leader-follower neural network output estimator for estimating the output of a data-driven neural network, in the following form: (31) Among them, the estimation error , To control the gain The estimated value, Used to approximate position dynamics , These are weight estimates; It is a 3-order identity matrix; S64. Based on the virtual control law and the leader-follower neural network output estimator, design a leader-follower full-state predetermined time controller as follows: (32) The corresponding adaptive law for parameters is: (33) in, In order to approach The designed data-driven neural network learning term; , .

[0016] Beneficial effects: This invention integrates core technologies such as mobility sensing, predetermined time control, unified obstacle function, and data-driven neural network to construct a complete heterogeneous UUV formation switching control scheme. Compared with existing technologies, it achieves comprehensive improvements in environmental adaptability, control accuracy, convergence performance, operational safety, and formation coordination robustness, as detailed below: (1) The restricted operating area is modeled as a time-varying curve virtual pipeline, and a flow quantification index is defined as the core trigger basis for formation switching. This enables heterogeneous UUV formations to automatically and smoothly complete formation scaling and communication topology weight adjustment according to the difficulty of environmental passage, avoiding the trajectory jump and oscillation problems of traditional switching strategies. This ensures that the formation always passes safely in the optimal configuration in the restricted environment with fluctuating pipeline width and curvature, greatly improving the formation's adaptability to dynamic restricted environments. (2) In the design of the actual root leader predefined time restraint controller, the predefined time affine switching observer, and the leader and follower full-state predetermined time controller, a predetermined time stabilization mechanism is systematically integrated. By constructing a dedicated predetermined time convergence feedback term, the tracking error and observation error of the system can converge to the desired compact set within the time limit set by the user and independent of the initial state. Compared with traditional asymptotic convergence, finite time control or fixed time control, this invention can directly and explicitly give the upper limit of the convergence time through a small number of parameters, realizing the active planning and precise control of the formation response time, greatly improving the speed and controllability of formation switching and trajectory tracking, and meeting the stringent real-time requirements of underwater missions; (3) By using data-driven neural networks, the impact of disturbances and uncertainties on control accuracy in complex underwater environments is effectively solved, enabling the formation to maintain high-precision trajectory tracking and formation even in the presence of unknown disturbances, with smaller steady-state errors and faster convergence speed. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of a predetermined time formation switching control method for heterogeneous UUVs based on mobility perception in a confined environment, as described in this invention. Figure 2 This is the overall control framework diagram of the switching system model in this embodiment of the invention; Figure 3 This is a schematic diagram of the internal structure of CORs in an embodiment of the present invention; Figure 4 This is a schematic diagram of the internal hierarchical structure of the TVT in an embodiment of the present invention; Figure 5 As described in the embodiments of the present invention Type and Two types of communication topology diagrams; Figure 6 This is a switching signal diagram in an embodiment of the present invention; Figure 7 This is a two-dimensional trajectory diagram of the underwater unmanned vehicle in an embodiment of the present invention; Figure 8 In this embodiment of the invention, tracking is performed in the X direction, while simultaneously... Comparison of results with set boundary constraints; Figure 9 In this embodiment of the invention, tracking is performed in the Y direction, while simultaneously... Comparison of results with set boundary constraints; Figure 10 This is a comparison diagram of the speed trajectories of the leader and followers under constrained conditions in an embodiment of the present invention; Figure 11 This is a virtual controller under constraints in an embodiment of the present invention. A comparison chart of the evolution of [the species / organization]. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] This embodiment provides a method for pre-time formation switching control of heterogeneous UUVs based on mobility awareness in a constrained environment, such as... Figure 1 and Figure 2 As shown, the specific steps include: S1. Establish a switching system model for heterogeneous unmanned underwater vehicle formations, wherein the heterogeneous unmanned underwater vehicle formations include a virtual root leader, a real root leader (UUV), leader formations (Leader UUVs), and follower formations (Followers UUVs). In a specific embodiment, the specific steps in S1 for establishing a formation switching system model for heterogeneous unmanned underwater vehicles include: S11. Establish the underlying communication topology of the formation switching system for heterogeneous unmanned underwater vehicles: To ensure reliability, the underlying communication topology is designed to be fixed. Specifically, a directed graph is defined. Node set does not change over time edge set It does not change over time. ,in, arrive It is a virtual root leader. It is the actual root leader. arrive He is a leader. arrive It is a follower, total number of nodes , Indicates the number of virtual root leaders. Indicates the number of followers. This indicates the number of leaders, where 1 represents the actual number of root leaders. Specifically, to adapt to changes in pipe width and achieve formation scaling, the formation switching system for heterogeneous unmanned underwater vehicles has a discrete switching mechanism that adjusts the control strategy. This is achieved by adjusting the stress weights applied to the fixed communication link.

[0021] S12. Design a discrete switching mechanism for a formation switching system of heterogeneous unmanned underwater vehicles: Set switching signal The switching signal is based on the flow rate. Select the activity configuration level, which is represented as: (1) in, It is a pre-set flowability threshold. ; For each level Set the stress matrix , is represented as: (2) in, It is a scaling stress weight. , It is a level scaling factor, For fixed edge The basic weights, ; The stress matrix exhibits a block-like structure, reflecting a hierarchical communication architecture, and is represented as follows: (3) in, Represents 2*2 d The identity matrix, where d is the dimension; block , , , It is constant, and only varies with... The size of its non-zero elements can be changed by the change of its sparsity pattern, without changing its sparsity pattern, thereby enabling the expansion of the structure within a fixed network topology. Specifically, this embodiment assumes that, Each element in the array is a non-negative number and the sum of all elements is 1.

[0022] S13. Establish a dynamic model of the formation switching system for heterogeneous unmanned underwater vehicles. The specific steps are as follows: All unmanned underwater vehicles are assumed to have a common 3-DOF dynamic structure, and their heterogeneity is reflected in their different physical parameters and control objectives. For the... j An unmanned underwater vehicle Its generalized dynamic model is: (4) in, This is the position state vector, representing the position values ​​in the longitudinal, lateral, and yaw degrees of freedom. velocity vector It includes the corresponding velocity and planar position coordinates in the Earth's fixed coordinate system. Planar velocity components , and These represent the yaw angle and yaw rate, respectively. This represents typical dynamic characteristics, including the Coriolis effect, damping effect, and gravitational effect. Indicating model uncertainty and ocean current disturbance The sum, Indicates control gain, control input , It is a configuration-related transformation matrix. , The definition of is: (5) Assuming control gain and satisfy , , , For the actual root leader, its responsibility is to provide global motion references and execute control measures. Therefore, the dynamic model of the actual root leader is transformed into: (6) in, , , , , , , , Let be the rotation matrix of the actual root leader in the y-plane. ; The required yaw angles and positions for the leader and followers are set as follows: (7) (8) The expected yaw angle for the actual root leader is: (9) in, The direction of the cross section to be defined; Set up a virtual leader Following a pre-set reference trajectory, Its expression is: (10) in, This indicates the desired position of the virtual leader. , It is a transformation matrix. , Let be the rotation matrix of the virtual root leader in the y-plane. , ; Specifically, in this embodiment, the virtual root leader provides a global reference path for the entire heterogeneous unmanned underwater vehicle (UUV) formation switching system. The leadership layer, guided by the actual root leader, must maintain a prescribed formation within constrained operational regions (CORs), with the entire leader and followers positioned directly behind the actual root leader. Simultaneously, all real UUVs in the heterogeneous UUV formation are subject to time-varying full-state output constraints to ensure operational safety within the constrained areas. Specifically, the position of each UUV... and speed Both are subject to lower and upper limits: (11) in, and These represent the position and velocity limits, respectively, which are determined by the geometry and dynamic characteristics of the controlled object.

[0023] S14. Define a two-dimensional affine coordinate system between the leader and followers, expressed as: (12) Among them, nominal configuration Affine transformation matrix that changes with time , transform vector ; and These are the ideal trajectories for leaders and followers, respectively, which satisfy environmental constraints. And for all All are true, of which this embodiment is true. and It is the boundary of a restricted region, and is continuously differentiable and has finite curvature.

[0024] S2. Model the restricted operating area as a time-varying curve virtual pipe (TVT) and define the cross-section and flow index of the TVT, thereby providing a trigger basis for the formation switching of heterogeneous unmanned underwater vehicles. Specifically, in this embodiment, CORs are modeled as a time-varying curved virtual pipeline. It provides navigation guidance and spatial constraints for underwater unmanned vehicles. In S2, the specific steps for modeling the restricted operating area as a time-varying curve virtual pipe and defining the cross-section and flow indices of the time-varying curve virtual pipe are as follows: S21, such as Figure 3 and Figure 4 As shown, when the actual root leader position When defining the cross section for: (13) And it satisfies the orthogonality condition: (14) in, It is the generating curve exist The unit tangent vector at that point; Determine the direction of the cross section based on the unit normal vector: (15) in, Is with The perpendicular unit normal vector, and They are Projection onto the X and Y axes of the global coordinate system; S22. Define liquidity indicators: pass The navigation capability of the time-varying curve virtual pipeline is quantified, and its standardized form is as follows: (16) in, , This indicates the average width of the TVT. , Indicates the generated curve arc length, , It is the local pipe width at time s. Indicates the time period from arrive Total control force required to traverse CORs. , , , and These represent baseline thrust, curvature penalty, width variation, and trajectory deviation adaptation, respectively. It is the set starting point of the dynamic sliding window; in, (17) in, To generate the curvature of the curve. It is the actual quality of the leader. The conductor is perpendicular to velocity in the direction, , , and These are the influence coefficients obtained through experimental calibration.

[0025] Specifically, this embodiment assumes the cross-section of the TVT. Wide enough so that it can be scaled by the scaling factor Within a defined minimum physical size, a convoy of heterogeneous unmanned underwater vehicles is allowed to pass through. It is assumed that the distance between the actual root leader and the following leader-follower convoy is large enough to allow them sufficient time to adapt to changes in the width of the restricted operating area.

[0026] Specifically, this embodiment constructs a dynamic formation switching strategy centered on the quantitative assessment of environmental "fluidity." This strategy enables formation configuration and communication weights to intelligently match the real-time environmental passage difficulty. Through the generation of smooth transition trajectories, it ensures the continuity and smoothness of the formation scaling and switching process, significantly improving the overall collaborative efficiency and operational robustness of UUVs in dynamically constrained environments. Simultaneously, a quantitative "fluidity" index is defined, comprehensively considering factors such as average pipeline width and control energy required for navigation, and multiple discrete configuration levels are defined based on this index. When a change in fluidity triggers a level switch, the switching system can automatically generate a continuous expected transition trajectory between the old and new configurations using a smooth exponential transfer function, achieving smooth and unobtrusive adaptive adjustment of formation size according to the "width" or "narrowness" of the environment.

[0027] S3. Establish a data-driven neural network for approximating uncertainties and disturbances to improve approximation accuracy and provide an approximation tool for the subsequent design of an adaptive controller; design a predefined time-restraint controller for the actual root leader based on the switching system model, the time-varying curve virtual pipeline, and the data-driven neural network; in a specific embodiment, the specific steps in S3 for establishing the data-driven neural network for approximating uncertainties and disturbances are as follows: The ideal approximate expression for a data-driven neural network is defined as follows: (18) The corresponding estimate for the data-driven neural network is: (19) in, It is to satisfy Ideal weights, , yes The estimated value, , It is an activation function. , , This represents the input to the data-driven neural network. and They are the first The center and width of each node, , ; Configure data stack ,when k When =1, the data stack is in time interval Internally, it forms a time-varying, possessing A sequence of timestamps, whose timestamps are as follows: And the sequence length is ,based on Construct a vector containing past activation vectors Historical data stack , is represented as: (20) in, It is a positive weighting coefficient. It is to satisfy The estimation error, It is a bounded positive number.

[0028] In a specific embodiment, the predefined time restraint controller ensures the safe navigation of the actual root leader within the CORs by following the envelope structure defined by the virtual root leader and dynamically responding to environmental boundaries. In S3, the specific steps for designing the predefined time restraint controller for the actual root leader based on the switching system model, the time-varying curve virtual pipeline, and the data-driven neural network include: The envelope position error and velocity error are defined based on the relative state between the actual root leader and the virtual root leader: (twenty one) To facilitate the design of a predefined time-determination controller, a sliding surface is constructed, whose expression is: ; Differentiating with respect to the sliding surface, we get: (twenty two) To approximate the uncertainty term Using data-driven neural networks ,in It is the ideal and appropriate weight, satisfying ; express The estimated value, and yes Error, input of data-driven neural network Represented as: (twenty three) Based on the above design, the predefined time-restraint controller for the actual root leader is represented as follows: (twenty four) The controller gain estimation of the predefined time-determination controller and the weight adaptation law of the data-driven neural network are defined as follows: (25) (26) Among them, the positive definite diagonal parameter matrix The estimated value of the controller gain , The error in the controller gain estimation; , , , This is a predefined time point for system convergence.

[0029] S4. A reference trajectory is generated through the virtual root leader, the actual root leader performs environmental perception, and generates the actual root leader's running trajectory based on the reference trajectory and the predefined time restraint controller; the leader formation determines the formation position and speed information of the leader formation according to the environmental perception information sent by the actual root leader and the running trajectory. Specifically, the virtual root leader generates a reference trajectory. Designed along the boundary of the restricted area, the virtual root leader forms an envelope aligned with the restricted area, providing trajectory guidance for the actual root leader. When the actual root leader detects a contraction in the restricted operating area through topology evaluation, the predefined time-delay controller triggers formation contraction control: converging the actual root leader's trajectory towards the pipeline centerline within a predefined time, while providing a benchmark for subsequent leader formation trajectory scaling, preventing formation overshoot. When an expansion of the restricted operating area is detected, the predefined time-delay controller triggers formation expansion control: adjusting the actual root leader's trajectory within a predefined time, providing space for leader formation deployment and ensuring formation passage efficiency. When the pipeline width is stable, the predefined time-delay controller maintains formation hold control, ensuring the actual root leader navigates stably along the pipeline centerline, providing a stable navigation benchmark for the entire formation.

[0030] In a specific embodiment, the actual root leader obtains the time-varying curve virtual pipeline status of the restricted operating area through environmental perception, including pipeline width and flow indicators. The information is then sent to the leader formation. In S4, the specific steps for the leader formation to determine its formation position and speed information based on the environmental perception information and trajectory sent by the actual root leader include: The leader formation is based on the discrete switching mechanism and the liquidity indicator sent by the actual root leader. Query Table 1 to determine the current discrete configuration level. Among them, different levels Different formation sizes, communication topologies, and weight matrices are designed to adapt to different widths of restricted operating areas; Table 1: Discrete Configuration Levels Based on Flowability

[0031] The actual root leader will determine its own operational trajectory The heading angle is sent to the leader formation, which uses the actual trajectory of the leader as the global reference, combined with the nominal formation configuration in the two-dimensional affine coordinate system between the leader and followers and the body coordinate system. By scaling factor Generate the first The basic expected trajectory of a leader is: , (27) Among them, scaling offset ,and This ensures that the higher the configuration level and the smaller the formation size, the better it can adapt to the shrinking of the pipeline width.

[0032] During the scaling transition between leader and follower formations, to avoid abrupt trajectory changes, the leader formation is based on the current configuration level. Compared to the previous configuration level The switching logic is calculated using the following formula: A leader's smooth reference trajectory That is, the first The target formation position for each leader: (28) Wherein, the transfer function It ensures smooth scaling between different configuration levels, and its expression is: , For continuous conversion time, when hour, ; By taking the time derivative of the smoothed reference trajectory, the corresponding velocity information can be obtained, and the leader formation position and velocity information can be determined.

[0033] S5. Based on the preset affine formation topology switching rules between the leader formation and the follower formation, and the formation position and velocity information of the leader formation, design a predefined time affine switching observer. The predefined time affine switching observer is used to observe the desired position and velocity information of the follower formation. In a specific embodiment, to achieve distributed, fast, and accurate estimation of the leader's position and velocity state by followers, and to adapt to hierarchical switching of the communication topology, a predefined time-based affine switching observer based on the switching stress matrix is ​​designed. In S5, the predefined time-based affine switching observer, designed based on the preset affine formation topology switching rules between the leader formation and follower formations, and the formation position and velocity information of the leader formation, is as follows: (29) Among them, design parameters ; and The first I The position and velocity error of each follower are jointly defined by the leader's formation position and velocity information and the affine formation topology switching rules, as shown in the following formula: (30) In the formula, and To switch levels The varying stress weights and diagonal matrix are directly determined by the pre-defined leader-follower affine formation topology switching rules. and The first Estimated position and velocity of each follower; The first in The diagonal elements represent the in-degree of the node, i.e. ; and The first i The first follower and the first J A rotation matrix for the leader in the xy plane is used to transform the body coordinate system state of the followers and the leader into the global coordinate system state.

[0034] Specifically, considering the basic assumptions made by the follower model and S1, if the signal is switched... Average stay time satisfy Then, the predefined time-affine switching observer can guarantee that the observation error exponent can converge to a bounded region under any switching sequence.

[0035] S6. A leader-follower full-state pre-time controller based on a unified obstacle function and data-driven neural network design. In a specific embodiment, the specific steps in S6 for designing a leader-follower full-state predetermined time controller based on a unified obstacle function and a data-driven neural network are as follows: S61: Define a unified barrier function (UBF) for the th For an underwater unmanned vehicle, By using a unified obstacle function, position and velocity information are combined. Mapping to unconstrained variables, represented as: (31) in, It is a gain that can be positively adjusted; The inverse function is: (32) In the formula, System state constraint variables ; right Differentiation yields: (33) in, , ,and: (34) Based on the generalized dynamics model of the follower, the system state of the heterogeneous unmanned underwater vehicle formation, which is subject to time-varying full-state output constraints, is transformed into the following unconstrained standard form: (35) in, , and ; Specifically, this embodiment proposes a barrier function processing method with relaxed design conditions and unified transformation. Combined with online learning of neural networks driven by historical data, it achieves strict and smooth control over time-varying, asymmetric full-state constraints, significantly improving the versatility and adaptability of the constraint control method in complex underwater environments. UBF only requires the upper and lower bounds of the state to satisfy simple size relationships and has symmetrical response characteristics near the constraint boundaries, effectively avoiding the sensitivity imbalance problem at the boundaries of traditional methods.

[0036] Based on the above, the tracking error signal is defined as follows: (36) Among them, the virtual control law to be designed A new reference signal Defined as The ideal trajectory for leaders and followers is defined as follows: ; S62. Design a virtual control law based on the tracking error signal, including: Tracking error signal Differentiate the equation and substitute it into formula (26) to obtain the error dynamic equation: (37) Among them, the uncertain nonlinear terms existing in the online approximation and compensation system are formed by dynamic deep neural networks (DDNN); The ideal output format for data-driven neural networks, Using data-driven neural networks to Approximation; data-driven neural network input , To approach Ideal weights, The approximation error is bounded. A virtual control law is designed based on the aforementioned error dynamic equation. , is represented as: (38) in, The adaptive weight update law is: (39) in, For ideal weights The estimated value, All are positive definite design parameters; learning terms are based on historical data. It is used to improve approximation accuracy and convergence speed; S63. Design a leader-follower neural network output estimator: This embodiment addresses the speed state. For problems that cannot be directly used for feedback, data-driven neural network estimation is employed. To further improve accuracy, a leader-follower neural network output estimator is designed to estimate the output of the data-driven neural network, in the following form: (40) Among them, the estimation error , To control the gain The estimated value, Used to approximate position dynamics , These are weight estimates; It is a 3-order identity matrix; S64. Based on the virtual control law and the leader-follower neural network output estimator, design a leader-follower full-state predetermined time controller as follows: (41) The corresponding adaptive law for parameters is: (42) in, In order to approach The designed data-driven neural network learning term; , .

[0037] S7. Based on the predefined time affine switching observer and leader-follower full-state predetermined time controller, realize the switching control of heterogeneous unmanned underwater vehicle formation.

[0038] Specifically, this embodiment systematically integrates a predetermined time stabilization mechanism into key components such as the controller and state estimator. This ensures that both the tracking and observation errors of the entire system converge to the desired compact set within a user-preset time limit independent of the initial state, endowing the formation control system with accurate and predictable fast transient performance. In the design of the virtual control law, final control law, and neural network state estimator, a feedback term with predetermined time convergence characteristics is creatively constructed. Theoretical analysis proves that the upper limit of the system's convergence time can be directly and explicitly given by the designer using a few parameters, thereby achieving proactive planning and precise control of the system's response time.

[0039] This embodiment constructs a series of numerical simulations to verify the effectiveness of the proposed flow-aware-based, time-based formation switching control method for heterogeneous UUVs in confined environments. The underwater unmanned vehicle formation consists of two virtual root leaders, one actual root leader, four leaders, and four followers, all modeled as underwater unmanned vehicles with three degrees of freedom. The overall control architecture of the underwater unmanned vehicle formation system is as follows: Figure 3 As shown, the directional communication topology is as follows: Figure 4 As shown. The virtual root leaders are designated as pentagons "V1" to "V2", and the actual root leaders are pentagons "r". Leaders "1" to "4" are represented by green circles, and followers "1" to "4" are represented by orange circles. For stress switching, this embodiment selects as follows... Figure 5 shown and Two types, switching signals such as Figure 6 As shown. Translation nominal configuration. And the initial positions of leaders and followers As shown in the following equation, the parameters are set as follows: the initial yaw angle and speed are both set to zero.

[0040] ; ; The controller and adaptive algorithm parameters are set as follows: , , .set up Other parameter selections are as follows: ; ; For ease of understanding, the virtual leader's trajectory is designed to coincide with the boundaries of the CORs. For performance comparison, the following controller will be evaluated: the Leader-Follower Full-State Predetermined Time Controller proposed in this embodiment (…). PT ), with the same parameters, using UBF fixed-time controller ( FT ) and fixed-time controllers using UBF ( FT U ).

[0041] Specifically, the simulation results are as follows: Figure 7-11 As shown, a detailed analysis follows: Figure 7 The diagram demonstrates how a root leader guides leaders and followers to achieve a pre-defined arrangement, with the entire formation scaling smoothly when approaching narrow areas. As clearly seen in the magnified image, the method proposed in this embodiment achieves a pre-defined hexagonal formation. Figure 8 and Figure 9 With leaders A comparative analysis of the controller was conducted using an example. Simulation results show that UBF is effective for boundary functions. and There are no strict positive or negative requirements, from In terms of tracking performance in the X and Y directions, the method proposed in this embodiment outperforms the other two methods in terms of transient performance. Further magnification of the region shows that the method proposed in this embodiment has a faster convergence speed and a smaller steady-state error. FT It performs better than others. Furthermore, Figure 10 and Figure 11 The comparison verifies that the control method proposed in this embodiment relaxes the usual requirements for virtual control laws. The required restrictive feasibility conditions. It is not difficult to see that... PT The controller satisfies the full-state output constraints by providing a smooth control input. In summary, simulation results verify that the method proposed in this application is superior to traditional fixed-time controllers using UBF (Unified Filtering). FT / FT U It is superior in transient performance, control smoothness, and constraint satisfaction. The entire solution is simple in design and easy to implement in engineering, and can be widely adapted to the collaborative operation needs of heterogeneous UUVs in various restricted environments such as subsea pipeline inspection, canyon terrain exploration, and crossing dense reef areas.

[0042] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for pre-time formation switching control of heterogeneous UUVs based on mobility awareness in a confined environment, characterized in that, The specific steps include: S1. Establish a switching system model for heterogeneous unmanned underwater vehicle formations, wherein the heterogeneous unmanned underwater vehicle formations include a virtual root leader, an actual root leader, a leader formation, and a follower formation. S2. Model the restricted operating area as a time-varying curve virtual pipeline, and define the cross-section and flow index of the time-varying curve virtual pipeline, thereby providing a trigger basis for the formation switching of heterogeneous unmanned underwater vehicles. S3. Establish a data-driven neural network for approaching uncertainty and disturbance; design a predefined time-restraint controller for the actual root leader based on the switching system model, time-varying curve virtual pipeline and data-driven neural network. S4. A reference trajectory is generated through the virtual root leader, the actual root leader performs environmental perception, and generates the actual root leader's running trajectory based on the reference trajectory and the predefined time restraint controller; the leader formation determines the formation position and speed information of the leader formation according to the environmental perception information sent by the actual root leader and the running trajectory. S5. Based on the preset affine formation topology switching rules between the leader formation and the follower formation, and the formation position and velocity information of the leader formation, design a predefined time affine switching observer. The predefined time affine switching observer is used to observe the desired position and velocity information of the follower formation. S6. A leader-follower full-state pre-time controller based on a unified obstacle function and data-driven neural network design. S7. Based on the predefined time affine switching observer and leader-follower full-state predetermined time controller, realize the switching control of heterogeneous unmanned underwater vehicle formation.

2. The method for pre-time formation switching control of heterogeneous UUVs based on mobility awareness in a confined environment according to claim 1, characterized in that, In S1, the specific steps for establishing a formation switching system model for heterogeneous unmanned underwater vehicles include: S11. Establish the underlying communication topology of the formation switching system for heterogeneous unmanned underwater vehicles: Define a directed graph Node set does not change over time edge set It does not change over time. ,in, arrive It is a virtual root leader. It is the actual root leader. arrive He is a leader. arrive It is a follower, total number of nodes , Indicates the number of virtual root leaders. Indicates the number of followers. This indicates the number of leaders, where 1 represents the actual number of root leaders. S12. Design a discrete switching mechanism for a formation switching system of heterogeneous unmanned underwater vehicles: Set switching signal The switching signal is based on the flow rate. Select the activity configuration level, which is represented as: （1） in, It is a pre-set flowability threshold. ; For each level Set the stress matrix , is represented as: （2） in, It is a scaling stress weight. , It is a level scaling factor, For fixed edge The basic weights, ; The stress matrix reflects the hierarchical communication architecture and is represented as: （3） in, Represents 2*2 d The identity matrix, d For dimension; block , , , It is constant, and only varies with... The change alters the size of its non-zero elements without altering its sparsity pattern; Each element in the array is a non-negative number and the sum of all elements is 1. S13. Establish a dynamic model of the formation switching system for heterogeneous unmanned underwater vehicles. The specific steps are as follows: Assume that all unmanned underwater vehicles have a common 3-DOF dynamic structure. For the third... j An unmanned underwater vehicle Its generalized dynamic model is: （4） in, This is the position state vector, representing the position values ​​in the longitudinal, lateral, and yaw degrees of freedom. velocity vector It includes the corresponding velocity and planar position coordinates in the Earth's fixed coordinate system. Planar velocity components , and These represent the yaw angle and yaw rate, respectively. This represents typical dynamic characteristics, including the Coriolis effect, damping effect, and gravitational effect. Indicating model uncertainty and ocean current disturbance The sum, Indicates control gain, control input , It is a configuration-related transformation matrix. , The definition of is: （5） Assuming control gain and satisfy , , , Therefore, the dynamic model of the actual root leader is transformed into: （6） in, , , , , , , , Let be the rotation matrix of the actual root leader in the y-plane. ; The required yaw angles and positions for the leader and followers are set as follows: ， ， The expected yaw angle for the actual root leader is: ， in, The direction of the cross section to be defined; Set up a virtual leader Following a pre-set reference trajectory, Its expression is: ， in, This indicates the desired position of the virtual leader. , It is a transformation matrix. , Let be the rotation matrix of the virtual root leader in the y-plane. , ; In a heterogeneous unmanned underwater vehicle (UUV) formation, all real UUVs are subject to time-varying full-state output constraints, and the position of each UUV is... and speed Both are subject to lower and upper limits: ， in, and These represent the position and velocity limits, respectively. S14. Define a two-dimensional affine coordinate system between the leader and followers, expressed as: （7） Among them, nominal configuration Affine transformation matrix that changes with time , transform vector ; and These are the ideal trajectories for leaders and followers, respectively, which satisfy environmental constraints. And for all All are true. and It is the boundary of a restricted region, and is continuously differentiable and has finite curvature.

3. The method for pre-time formation switching control of heterogeneous UUVs based on mobility awareness in a confined environment according to claim 2, characterized in that, In S2, the specific steps for modeling the restricted operating region as a time-varying curve virtual pipe and defining the cross-section and flow index of the time-varying curve virtual pipe are as follows: S21, When the actual root leader position When defining the cross section for: ， And it satisfies the orthogonality condition: （8） in, It is the generating curve exist The unit tangent vector at that point; Determine the direction of the cross section based on the unit normal vector: （9） in, Is with The perpendicular unit normal vector, and They are Projection onto the X and Y axes of the global coordinate system; S22. Define liquidity indicators: pass The navigation capability of the time-varying curve virtual pipeline is quantified, and its standardized form is as follows: （10） in, , This indicates the average width of the TVT. , Indicates the generated curve arc length, , It is the local pipe width at time s. Indicates the time period from arrive Total control force required to traverse CORs. , , , and These represent baseline thrust, curvature penalty, width variation, and trajectory deviation adaptation, respectively. It is the set starting point of the dynamic sliding window; in, （11） in, To generate the curvature of the curve. It is the actual quality of the leader. The conductor is perpendicular to velocity in the direction, , , and These are the influence coefficients obtained through experimental calibration.

4. The method for pre-time formation switching control of heterogeneous UUVs based on mobility awareness in a confined environment according to claim 3, characterized in that, In S3, the specific steps for establishing the data-driven neural network are as follows: The ideal approximate expression for a data-driven neural network is defined as follows: ， The corresponding estimate for the data-driven neural network is: （12） in, It is to satisfy Ideal weights, , yes The estimated value, , It is an activation function. , , This represents the input to the data-driven neural network. and They are the first The center and width of each node, , ; Configure data stack ,when k When =1, the data stack is in time interval Internally, it forms a time-varying, possessing A sequence of timestamps, whose timestamps are as follows: And the sequence length is ,based on Construct a vector containing past activation vectors Historical data stack , is represented as: （13） in, It is a positive weighting coefficient. It is to satisfy The estimation error, It is a bounded positive number.

5. The method for pre-time formation switching control of heterogeneous UUVs based on mobility awareness in a confined environment according to claim 4, characterized in that, In S3, the specific steps for designing a predefined time-restraint controller for the actual root leader based on the switching system model, the time-varying curve virtual pipeline, and the data-driven neural network include: The envelope position error and velocity error are defined based on the relative state between the actual root leader and the virtual root leader: （14） Construct a sliding surface, its expression is: ; Differentiating with respect to the sliding surface, we get: （15） To approximate the uncertainty term Using data-driven neural networks ,in It is the ideal and appropriate weight, satisfying ; express The estimated value, and yes Error, input of data-driven neural network Represented as: （16） Based on the above design, the predefined time-restraint controller for the actual root leader is represented as follows: （17） The controller gain estimation of the predefined time-determination controller and the weight adaptation law of the data-driven neural network are defined as follows: （18） （19） Among them, the positive definite diagonal parameter matrix The estimated value of the controller gain , The error in the controller gain estimation; , , , This is a predefined time point for system convergence.

6. The method for pre-time formation switching control of heterogeneous UUVs based on mobility awareness in a confined environment according to claim 5, characterized in that, In S4, the specific steps for the leader formation to determine its formation position and speed information based on the environmental perception information and trajectory sent by the actual root leader include: The leader formation is based on the discrete switching mechanism and the liquidity indicator sent by the actual root leader. Query Table 1 to determine the current discrete configuration level. ; Table 1: Discrete Configuration Levels Based on Flowability The leader formation uses the actual trajectory of the root leader as the global reference, combining the nominal formation configuration in the two-dimensional affine coordinate system between the leader and followers, as well as the body coordinate system. By scaling factor Generate the first The basic expected trajectory of a leader is: ， ； Among them, scaling offset ,and ; During the scaling transition between leader and follower formations, the leader formation is based on the current configuration level. Compared to the previous configuration level The switching logic is calculated using the following formula: A leader's smooth reference trajectory That is, the first The target formation position for each leader: （20） Wherein, the transfer function The expression is , For continuous conversion time, when hour, ; By taking the time derivative of the smoothed reference trajectory, the corresponding velocity information can be obtained, and the leader formation position and velocity information can be determined.

7. The method for pre-time formation switching control of heterogeneous UUVs based on mobility awareness in a confined environment according to claim 6, characterized in that, In S5, the predefined time-based affine switching observer, designed based on the preset affine formation topology switching rules between the leader and follower formations, and the formation position and velocity information of the leader formation, is as follows: （21） Among them, design parameters ; and The first I The position and velocity error of each follower are jointly defined by the leader's formation position and velocity information and the affine formation topology switching rules, as shown in the following formula: （22） In the formula, and To switch levels The varying stress weights and diagonal matrix are directly determined by the pre-defined leader-follower affine formation topology switching rules. and The first Estimated position and velocity of each follower; The first in The diagonal elements represent the in-degree of the node, i.e. ; and The first i The first follower and the first J The rotation matrix of the leaders in the xy plane.

8. The method for pre-time formation switching control of heterogeneous UUVs based on mobility awareness in a confined environment according to claim 7, characterized in that, In S6, the specific steps for designing a leader-follower full-state pre-time controller based on a unified obstacle function and data-driven neural network are as follows: S61: Define a unified barrier function, for the... For an underwater unmanned vehicle, By using a unified obstacle function, position and velocity information are combined. Mapping to unconstrained variables, represented as: （23） in, It is a gain that can be positively adjusted; The inverse function is: （24） In the formula, System state constraint variables ; right Differentiation yields: ， in, , ,and: （25） Based on the generalized dynamics model of the follower, the system state of the heterogeneous unmanned underwater vehicle formation, which is subject to time-varying full-state output constraints, is transformed into the following unconstrained standard form: （26） in, , and ; Based on the above, the tracking error signal is defined as follows: （27） Among them, the virtual control law to be designed A new reference signal Defined as The ideal trajectory of leaders and followers is defined as follows: ; S62. Design a virtual control law based on the tracking error signal, including: Tracking error signal Differentiate the equation and substitute it into formula (25) to obtain the error dynamic equation: （28） in, The ideal output format for data-driven neural networks, Using data-driven neural networks to Approximation; data-driven neural network input , To approach Ideal weights, The approximation error is bounded. A virtual control law is designed based on the aforementioned error dynamic equation. , is represented as: （29） in, The adaptive weight update law is: （30） in, For ideal weights The estimated value, All are positive definite design parameters; learning terms are based on historical data. ; S63. Design a leader-follower neural network output estimator: Design a leader-follower neural network output estimator for estimating the output of a data-driven neural network, in the following form: （31） Among them, the estimation error , To control the gain The estimated value, Used to approximate position dynamics , These are weight estimates; It is a 3-order identity matrix; S64. Based on the virtual control law and the leader-follower neural network output estimator, design a leader-follower full-state predetermined time controller as follows: （32） The corresponding adaptive law for parameters is: （33） in, In order to approach The designed data-driven neural network learning term; , .

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