Sea surface ship formation preset time output feedback control method with multiple quantization mechanisms

Abstract

The application discloses a sea surface ship formation preset time output feedback control method with multiple quantization mechanisms, and comprises the following steps: establishing a sea surface ship formation system model, using a fuzzy logic system to approximately process unknown nonlinear functions in the sea surface ship formation system model; constructing a fuzzy state observer to process unmeasurable states, and introducing state quantization and input quantization mechanisms; using dynamic surface technology and introducing a second-order filter to process the discontinuity of a virtual control signal, and then constructing a Lyapunov function; combining backstepping technology, designing an adaptive law and a preset time quantization controller, and the output state of the sea surface ship formation system converges to a desired precision range within a preset time. On the basis of guaranteeing system stability, the application improves control precision, effectively reduces communication overhead through state quantization and input quantization mechanisms, and ensures that the sea surface ship formation system can still stably and reliably operate under complex environments.

Description

Technical Field

[0001] This invention relates to the field of maritime vessel formation control, and in particular to a maritime vessel formation preset time output feedback control method with multiple quantization mechanisms. Background Technology

[0002] Surface vessel formation systems are a typical type of nonlinear, unstable dynamic system. Their control objective is to coordinate the movements of multiple vessels to maintain their relative positions and headings while simultaneously accomplishing collaborative tasks. Surface vessel formation systems are widely used in various fields, including automatic control, marine monitoring, transportation, military exercises, and unmanned surface vehicles (USVs). In these applications, the control methods for surface vessel formation systems can improve the system's dynamic response speed, reduce control errors, and enhance its robustness, enabling stable operation in complex environments. These control methods can also effectively cope with environmental disturbances, sea state changes, and mutual interference between vessels, ensuring the system's reliability and accuracy.

[0003] In recent years, with the rapid development of intelligent control, fuzzy logic, adaptive control, and other fields, the control technology of maritime vessel formation systems has gradually evolved towards higher precision, stronger real-time performance, and better anti-interference capabilities. In particular, methods such as preset time control, quantization control, and observer-based intelligent control have made maritime vessel formation systems a key development direction in the field of automatic control for applications with stringent requirements for high precision and high dynamic response.

[0004] The preset time quantization control in a surface vessel formation system aims to design an efficient control strategy to ensure stable operation of the system within a predetermined time and achieve the desired accuracy requirements. The goal of this method is to stabilize the system state within a finite time and ensure that the system output accurately tracks the reference signal, thereby guaranteeing the stability of the closed-loop system throughout the entire process.

[0005] Currently, various control algorithms have been applied to surface vessel formation systems, commonly including classical PID control, fuzzy control, sliding mode control, and adaptive control. However, existing technologies still face the following challenges:

[0006] First, traditional control methods exhibit poor robustness in dealing with complex nonlinear systems, external disturbances, and unmodeled dynamics, making it difficult to ensure stable convergence of the system within a finite time. For example, classical PID control and sliding mode control methods typically rely on precise mathematical models. However, in practical applications, due to uncertainties in system parameters, nonlinear characteristics, and external disturbances, the effectiveness of these control methods is often unreliable, and may even lead to system oscillations or instability. In high-dynamic control tasks, these methods struggle to guarantee that the system achieves the expected accuracy within a specified time, thus limiting their application scope.

[0007] Secondly, traditional control methods often rely on high-precision state measurements and frequent data transmissions, which can easily increase communication burdens and lead to network congestion, thus affecting control accuracy and real-time performance. Furthermore, in multivariable coupled systems, these control methods may introduce singularity problems. Many control algorithms require continuous and accurate state feedback, but in practical applications, limitations in sensor accuracy, data transmission bandwidth, and computing resources mean that frequent data acquisition and transmission can lead to network latency or data loss, significantly impacting system performance. Simultaneously, in multivariable coupled systems, some control methods may exhibit singularities during the solution process, meaning that in certain situations, the control law may fail to be realized or become infinitely large, causing the system to malfunction or its control effectiveness to deteriorate significantly. These problems greatly limit the application effectiveness of traditional control methods in complex environments. Summary of the Invention

[0008] The purpose of this invention is to provide a preset time output feedback control method for maritime vessel formations with multiple quantization mechanisms. While ensuring system stability, it improves control accuracy and effectively reduces communication overhead through state quantization and input quantization mechanisms, ensuring that the maritime vessel formation system can still operate stably and reliably in complex environments.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] A method for preset time output feedback control of surface vessel formations with multiple quantization mechanisms includes the following steps:

[0011] Step 1: Establish a maritime vessel formation system model and use a fuzzy logic system to approximate the unknown nonlinear functions in the maritime vessel formation system model.

[0012] Step 2: Construct a fuzzy state observer to handle unmeasurable states, and introduce state quantization and input quantization mechanisms.

[0013] Step 3: Dynamic surface technique is used and a second-order filter is introduced to handle the discontinuity problem of the virtual control signal, and then the Lyapunov function is constructed.

[0014] Step 4: Combining the backstepping technique, design an adaptive law and a preset time quantization controller so that the output state of the sea vessel formation system converges to the desired accuracy range within a preset time.

[0015] Furthermore, in step 1, the surface vessel formation system consists of four agents and two leaders, and its model equations are as follows:

[0016]

[0017] Where i represents the i-th unmanned surface vessel on the ocean surface, i = 1, 2, 3, 4, t represents time, and C i (ν i ) indicates that it depends on the velocity ν i Coriolis force matrix, D i (ν i ) indicates that it depends on the velocity ν i The damping matrix; χ i Represents the longitudinal position coordinates of the ship. Indicates the ship's lateral position coordinates; This represents the longitudinal position coordinate χ that depends on the ship. i And the ship's lateral position coordinates Position vector; ψ i It is the yaw angle vector. Represents the longitudinal, lateral, and yaw velocity vectors; u i =[u ωi ,u νi ,u ri ] T It is the control input vector, where Indicates longitudinal propulsion. Indicates lateral thrust. Indicates yaw control torque; d i (t) represents an unknown perturbation, g i (η i ,ν i ) represents the dependence on the position vector η i and velocity ν i Uncertain hydrodynamic coefficients Represents the inertia matrix. The representation depends on the yaw angle vector ψ i A rotation matrix of is represented as:

[0018]

[0019] The model equation (1) of the surface vessel formation system can be rewritten as a state-space expression:

[0020]

[0021] Where, x i,1 Indicates location information, x i,2 Indicates speed information; f i,1 (x) and f i,2 (x) represents a state-dependent nonlinear function, defined as follows: The rotational inertia matrix is ​​defined as follows: R i Represents the rotation matrix; gi Indicates an uncertain hydrodynamic coefficient; The damping matrix after rotation is defined as follows: The rotated Coriolis force matrix is ​​defined as follows: C i This represents the original Coriolis force matrix, describing the effects of non-inertial forces; d i,j (t) represents the time-varying external disturbance term, which is defined here as d i,j (t) = 2sin(t);

[0022] Two leaders were selected as:

[0023]

[0024] Furthermore, in step 1, a fuzzy logic system (FLS) is used to approximate the unknown nonlinear function f in the surface ship formation system model. i,j (x);

[0025] The fuzzy logic system is represented as:

[0026]

[0027] in, It is the membership function of the output variable. These are fuzzy basis functions used to approximate unknown nonlinear functions;

[0028] By defining the fuzzy basis function φ l The fuzzy logic system is represented as:

[0029]

[0030] By introducing the parameter vector ξ = [ξ1, ξ2, ..., ξ] N ] T The fuzzy logic system is represented as:

[0031] y(x)=ξ T φ(x) (6)

[0032] This allows for the approximate handling of the unknown nonlinear function f in the robot dynamics model. i,j (x), where i = 1, 2, j = 1, 2.

[0033] Furthermore, in step 2, a fuzzy state observer is used to handle unmeasurable states. The fuzzy state observer is designed as follows:

[0034]

[0035] in, For the estimated variables of the true state, s = 1, 2; Represents the fuzzy basis function vector; g i,s The observer gain represents the state and is used to adjust the strength of the error feedback; This represents the observed value output by the system; y i This represents the actual output value of the system; for The estimated value; Represents the optimal fuzzy modeling parameter vector corresponding to the state; in definition u i This indicates a control input.

[0036] Furthermore, in step 2, state quantization and input quantization mechanisms are introduced to reduce communication overhead. The quantizer is defined as follows:

[0037]

[0038] Where x is a state variable or its observed value, This represents the quantized value, where q indicates that the variable x is quantized, μ>0 is the length of the quantization interval, and Q... k These are quantized values, and Q1 = μ, Q k+1 =Q k +μ; quantization error z x =xx q satisfy

[0039] Furthermore, in step 3, the system state x will be considered. i,j System output status y i,r Virtual control signal α i,s and filtered signal To construct dynamic surfaces:

[0040]

[0041] Where, x i,1 and x j,1 Represents the actual state variable, j represents the index number of the dynamic surface; y j,r Indicates system output; a i,j It is the connection weight, representing the strength of edges in the network topology; z i,1 This represents the consistency error between the state variables and the reference trajectory; Represents the estimated value of the state variable; Indicates the filtered signal; z i,2 This represents the error in the state change and the filtered signal; α represents the error between the filtered signal and the virtual control function. i,1It is a virtual control function; the filtered signal Smoothing is achieved using a second-order low-pass filter to avoid discontinuities;

[0042] The dynamic equation of the filter is as follows:

[0043]

[0044] Among them, a i,1,1 and a i,1,2 These are the damping coefficient and natural frequency of the filter, respectively. Final filtering error for And there are

[0045] Furthermore, in step 3, when constructing the Lyapunov function, a Lyapunov function of the following form is selected:

[0046]

[0047] Among them, P i It is a positive definite matrix. It is an estimation error. For the target value The estimate, It is the target value The estimation error, To The estimated value.

[0048] Furthermore, in step 3, the virtual control signal is designed as follows:

[0049]

[0050] Among them, z i,1 This represents the consistency error between the state variables and the reference trajectory; a i,j This represents the connection weights between nodes in the communication topology, reflecting the existence and strength of edges in the network structure; j represents the index number. This represents a positive adaptive gain parameter; η satisfies 0 < η < 1 and is used to control the growth rate of the nonlinear feedback term. Represents a positive design parameter, where T d Indicates the preset convergence time; represents a positive design parameter; tanh represents the hyperbolic tangent function, used to avoid singularity problems; This represents a positive smoothing factor to prevent the tanh function from saturating due to excessively large inputs; and Represents the transpose of the fuzzy modeling parameter vector; and Represents the basis function vector of a fuzzy system; The first derivative of the reference trajectory; and Represents the observed value of the state variable.

[0051] Furthermore, in step 4, the adaptive law is designed as follows:

[0052]

[0053] in, It is the derivative of the fuzzy parameter estimate, representing its update rate; Indicates a positive adaptive gain parameter; l i,1 l i,2 and l i Indicates adaptive parameters;

[0054] The preset time quantization controller is designed as follows:

[0055]

[0056] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0057] First, by introducing a preset time stability criterion, this invention ensures that all state variables of the surface vessel formation system converge stably to a predetermined accuracy range within a finite time. Compared with traditional asymptotic stability control methods, this invention overcomes the limitation of convergence time's dependence on initial conditions and control parameters, enabling the control task to be completed within a set time, ensuring strict time constraints, and thus improving the system's dynamic performance and response speed. This characteristic is particularly important for scenarios with high requirements for accuracy and response speed.

[0058] Secondly, this invention employs a multi-quantization mechanism to quantize state information and system inputs during the control process, thereby effectively reducing data transmission volume, lowering the demand for communication bandwidth, and minimizing the negative impact of quantization errors on control performance. Furthermore, by combining a fuzzy logic system and a fuzzy state observer, this invention can effectively compensate for unknown nonlinear dynamics in the system and estimate unmeasurable states, improving the system's anti-interference capability and adaptability. This enables the system to maintain stable and reliable operation in complex environments with significant modeling uncertainties and external disturbances. This characteristic is particularly important in resource-constrained distributed control systems and multi-machine cooperative control applications.

[0059] Third, this invention effectively avoids control singularities and improves the system's feasibility. Traditional backstepping control can lead to control singularities in certain situations, affecting the controller's feasibility and stability. This invention avoids the "differential explosion" problem common in backstepping by incorporating a second-order command filter, and constructs the control law without relying on state derivatives. Furthermore, the introduction of the filter further smooths the control signal, reduces the impact on the actuator, and improves the system's performance in practical applications.

[0060] Fourth, this invention enhances the system's adaptability and improves its ability to cope with complex environments. Due to the strong nonlinearity and instability of surface vessel formation systems, practical applications may face external disturbances and modeling uncertainties. By introducing an adaptive quantization control scheme, this invention can dynamically adjust the control gain and compensate for quantization errors, thereby meeting the control requirements under different environments. The designed control scheme can ensure stable convergence of the system within a preset time under different initial conditions and system parameter variations, providing solid technical support for the intelligent control and high-precision execution of surface vessel formation systems. Attached Figure Description

[0061] Figure 1 This is a schematic diagram of a network system for a pre-set time output feedback control method for surface vessel formations with multiple quantification mechanisms.

[0062] Figure 2 This is a performance curve of trajectory tracking for a surface vessel formation system;

[0063] Figure 3 It is a diagram of the state variables and quantification process of a surface vessel formation system;

[0064] Figure 4 It is a graph comparing the state variables and observed values ​​of a surface vessel formation system;

[0065] Figure 5 This is a control input response curve diagram of a surface vessel formation system;

[0066] Figure 6 This is a curve showing the trajectory tracking error of a surface vessel formation system under different design parameters. Detailed Implementation

[0067] The invention will now be further explained with reference to the accompanying drawings.

[0068] like Figure 1 As shown, the pre-set time output feedback control method for surface vessel formations with multiple quantization mechanisms of the present invention includes the following steps:

[0069] Step 1: Establish a maritime vessel formation system model and use a fuzzy logic system to approximate the unknown nonlinear functions in the maritime vessel formation system model.

[0070] The surface vessel formation system consists of four agents and two leaders, and its model equations are as follows:

[0071]

[0072] Where i represents the i-th unmanned surface vessel on the ocean surface, i = 1, 2, 3, 4, t represents time, and C i (ν i ) indicates that it depends on the velocity ν i Coriolis force matrix, D i (ν i ) indicates that it depends on the velocity ν i The damping matrix; χ i Represents the longitudinal position coordinates of the ship. Indicates the ship's lateral position coordinates; This represents the longitudinal position coordinate χ that depends on the ship. i And the ship's lateral position coordinates Position vector; ψ i It is the yaw angle vector. Represents the longitudinal, lateral, and yaw velocity vectors; u i =[u ωi ,u νi ,u ri ] T It is the control input vector, where Indicates longitudinal propulsion. Indicates lateral thrust. Indicates yaw control torque; d i (t) represents an unknown perturbation, g i (η i ,ν i ) represents the dependence on the position vector η i and velocity ν i Uncertain hydrodynamic coefficients Represents the inertia matrix. The representation depends on the yaw angle vector ψ i A rotation matrix of is represented as:

[0073]

[0074] The model equation (1) of the surface vessel formation system can be rewritten as a state-space expression:

[0075]

[0076] Where, x i,1Indicates location information, x i,2 Indicates speed information; f i,1 (x) and f i,2 (x) represents a state-dependent nonlinear function, defined as follows: The rotational inertia matrix is ​​defined as follows: R i Represents the rotation matrix; g i Indicates an uncertain hydrodynamic coefficient; The damping matrix after rotation is defined as follows: The rotated Coriolis force matrix is ​​defined as follows: C i This represents the original Coriolis force matrix, describing the effects of non-inertial forces; d i,j (t) represents the time-varying external disturbance term, which is defined here as d i,j (t) = 2sin(t);

[0077] Two leaders were selected as:

[0078]

[0079] In this study, a fuzzy logic system (FLS) is used to approximate the unknown nonlinear function f in the model of a surface ship formation system. i,j (x);

[0080] The fuzzy logic system is represented as:

[0081]

[0082] in, It is the membership function of the output variable. These are fuzzy basis functions used to approximate unknown nonlinear functions;

[0083] By defining the fuzzy basis function φ l The fuzzy logic system is represented as:

[0084]

[0085] By introducing the parameter vector ξ = [ξ1, ξ2, ..., ξ] N ] T The fuzzy logic system is represented as:

[0086] y(x)=ξ T φ(x) (6)

[0087] This allows for the approximate handling of the unknown nonlinear function f in the robot dynamics model. i,j (x), where i = 1, 2, j = 1, 2.

[0088] Step 2: Construct a fuzzy state observer to handle unmeasurable states, and introduce state quantization and input quantization mechanisms.

[0089] Among them, a fuzzy state observer is used to handle unmeasurable states. The fuzzy state observer is designed as follows:

[0090]

[0091] in, For the estimated variables of the true state, s = 1, 2; Represents the fuzzy basis function vector; g i,s The observer gain represents the state and is used to adjust the strength of the error feedback; This represents the observed value output by the system; y i This represents the actual output value of the system; for The estimated value; Represents the optimal fuzzy modeling parameter vector corresponding to the state; in definition u i This indicates a control input.

[0092] Among them, state quantization and input quantization mechanisms are introduced to reduce communication burden. The quantizer is defined as follows:

[0093]

[0094] Where x is a state variable or its observed value, This represents the quantized value, where q indicates that the variable x is quantized, μ>0 is the length of the quantization interval, and Q... k These are quantized values, and Q1 = μ, Q k+1 =Q k +μ; quantization error z x =xx q satisfy

[0095] In addition, a second-order filter was introduced to address the discontinuity of the virtual control signal, ensuring the smoothness and stability of the signal and thus optimizing the performance of the sea vessel formation control.

[0096] Step 3: Dynamic surface technique is used and a second-order filter is introduced to handle the discontinuity problem of the virtual control signal, and then the Lyapunov function is constructed.

[0097] Will target system state x i,j System output status y i,r Virtual control signal α i,s and filtered signal To construct dynamic surfaces:

[0098]

[0099] Where, x i,1 and x j,1 Represents the actual state variable, j represents the index number of the dynamic surface; y j,r Indicates system output; a i,j It is the connection weight, representing the strength of edges in the network topology; z i,1 This represents the consistency error between the state variables and the reference trajectory; Represents the estimated value of the state variable; Indicates the filtered signal; z i,2 This represents the error in the state change and the filtered signal; α represents the error between the filtered signal and the virtual control function. i,1 It is a virtual control function; the filtered signal Smoothing is achieved using a second-order low-pass filter to avoid discontinuities;

[0100] The dynamic equation of the filter is as follows:

[0101]

[0102] Among them, a i,1,1 and a i,1,2 These are the damping coefficient and natural frequency of the filter, respectively. Final filtering error for And there are

[0103] When constructing the Lyapunov function, the following form of Lyapunov function is chosen:

[0104]

[0105] Among them, P i It is a positive definite matrix. It is an estimation error. For the target value The estimate, It is the target value The estimation error, To The estimated value.

[0106] The virtual control signal is designed as follows:

[0107]

[0108] Among them, z i,1This represents the consistency error between the state variables and the reference trajectory; a i,j This represents the connection weights between nodes in the communication topology, reflecting the existence and strength of edges in the network structure; j represents the index number. This represents a positive adaptive gain parameter; η satisfies 0 < η < 1 and is used to control the growth rate of the nonlinear feedback term. Represents a positive design parameter, where T d Indicates the preset convergence time; represents a positive design parameter; tanh represents the hyperbolic tangent function, used to avoid singularity problems; This represents a positive smoothing factor to prevent the tanh function from saturating due to excessively large inputs; and Represents the transpose of the fuzzy modeling parameter vector; and Represents the basis function vector of a fuzzy system; The first derivative of the reference trajectory; and Represents the observed value of the state variable.

[0109] Step 4: Combining the backstepping technique, design an adaptive law and a preset time quantization controller so that the output state of the sea vessel formation system converges to the desired accuracy range within a preset time.

[0110] The adaptive law is designed as follows:

[0111]

[0112] in, and It is the derivative of the fuzzy parameter estimate, representing its update rate; Indicates a positive adaptive gain parameter; l i,1 l i,2 and l i Indicates adaptive parameters;

[0113] The preset time quantization controller is designed as follows:

[0114]

[0115] Simulation results are as follows Figure 2-6 As shown, the effectiveness of the preset time output feedback control method for a surface vessel formation system with multiple quantization mechanisms is verified. Among them, Figure 2 The trajectory tracking performance of a surface vessel formation system was demonstrated, showing that the proposed method can effectively achieve multiple quantization control objectives within a preset time and ensure that the system outputs an accurate tracking reference signal. Subsequently, Figure 3The study further demonstrates the state variables of a maritime vessel formation system and their corresponding quantification process, reflecting the impact of multiple quantification mechanisms on system operation. Figure 4 The comparison between the state variables and their observed values ​​is shown, verifying the effectiveness of the fuzzy state observer in estimating unmeasurable states. Figure 5 This presents the system's control input response, revealing the dynamic characteristics of the control signal within a preset time control framework. Finally, Figure 6 The study demonstrated the trajectory tracking error under different design parameters, further verifying the control scheme's ability to guarantee system accuracy and its robustness under different parameter configurations.

[0116] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for preset time output feedback control of surface vessel formations with multiple quantization mechanisms, characterized in that: Includes the following steps: Step 1: Establish a maritime vessel formation system model and use a fuzzy logic system to approximate the unknown nonlinear functions in the maritime vessel formation system model. A surface vessel formation system consists of four agents and two leaders, and its model equations are as follows: （1） in, Representing the An unmanned surface vessel on the ocean surface. , Represents time, Indicates speed dependence Coriolis force matrix Indicates speed dependence The damping matrix; Represents the longitudinal position coordinates of the ship. Indicates the ship's lateral position coordinates; Represents the longitudinal position coordinates dependent on the ship. And the ship's lateral position coordinates The position vector; It is the yaw angle vector. Represents the longitudinal, lateral, and yaw velocity vectors; It is the control input vector, where Indicates longitudinal propulsion. Indicates lateral thrust. Indicates the yaw control torque; It represents an unknown disturbance. The representation depends on the position vector. and speed Uncertain hydrodynamic coefficients Represents the inertia matrix. This indicates that the yaw angle vector is dependent on the yaw angle vector. A rotation matrix of is represented as: ； The model equation (1) of the surface vessel formation system can be rewritten as a state-space expression: （2） in, Indicates location information, Indicates speed information; and The nonlinear functions representing state-dependent functions are defined as follows: , ； The rotational inertia matrix is ​​defined as follows: , Represents the rotation matrix; Indicates an uncertain hydrodynamic coefficient; The damping matrix after rotation is defined as follows: ; The rotated Coriolis force matrix is ​​defined as follows: , This represents the original Coriolis force matrix, describing the effects of non-inertial forces; The time-varying external disturbance term is defined here as ; Two leaders were selected as: （3）； Step 2: Construct a fuzzy state observer to handle unmeasurable states, and introduce state quantization and input quantization mechanisms. A quantizer is defined as: （8） in, For state variables or their observed values, This represents the quantized value, where Represents the variable Quantify, The length of the quantization interval, It is a quantized value, and Quantization error satisfy ; Step 3: Dynamic surface technique is used and a second-order filter is introduced to handle the discontinuity problem of the virtual control signal, and then the Lyapunov function is constructed. Step 4: Combining the backstepping technique, design an adaptive law and a preset time quantization controller so that the output state of the sea vessel formation system converges to the desired accuracy range within a preset time. The adaptive law is designed as follows: （13） in, , and It is the derivative of the fuzzy parameter estimate, representing its update rate; Indicates a positive adaptive gain parameter; , and Indicates adaptive parameters; The preset time quantization controller is designed as follows: （14）。 2. The method for preset time output feedback control of surface vessel formations with multiple quantization mechanisms according to claim 1, characterized in that: In step 1, a fuzzy logic system (FLS) is used to approximate the unknown nonlinear function in the surface ship formation system model. ; The fuzzy logic system is represented as: （4） in, , It is the membership function of the output variable. These are fuzzy basis functions used to approximate unknown nonlinear functions; By defining fuzzy basis functions The fuzzy logic system is represented as: （5） By introducing parameter vectors The fuzzy logic system is represented as: （6） This allows for the approximate handling of unknown nonlinear functions in robot dynamics models. ,in .

3. The method for preset time output feedback control of surface vessel formations with multiple quantization mechanisms according to claim 1, characterized in that: In step 2, a fuzzy state observer is used to handle unmeasurable states. The fuzzy state observer is designed as follows: （7） in, For the variables estimated from the true state, s=1,2; Represents a fuzzy basis function vector; The observer gain represents the state and is used to adjust the strength of the error feedback; This represents the observed value output by the system; This represents the actual output value of the system; for The estimated value; Represents the optimal fuzzy modeling parameter vector corresponding to the state; ,in , , ,definition ; This indicates a control input.

4. The method for preset time output feedback control of surface vessel formations with multiple quantization mechanisms according to claim 1, characterized in that: In step 3, the system status will be considered. System output status Virtual control signals and filtered signal To construct dynamic surfaces: （9） in, and Represents the actual state variable. Indicates the index number of the dynamic surface; Indicates system output; It is the connection weight, which represents the strength of the edges in the network topology; This represents the consistency error between the state variables and the reference trajectory; Represents the estimated value of the state variable; Indicates the filtered signal; This represents the error in the state change and the filtered signal; This represents the error between the filtered signal and the virtual control function; It is a virtual control function; the filtered signal Smoothing is achieved using a second-order low-pass filter to avoid discontinuities; The dynamic equation of the filter is as follows: （10） in, and These are the damping coefficient and natural frequency of the filter, respectively. , ; final filtering error for And there are .

5. The method for preset time output feedback control of surface vessel formations with multiple quantization mechanisms according to claim 1, characterized in that: In step 3, when constructing the Lyapunov function, the following form of Lyapunov function is selected: （11） in, It is a positive definite matrix. It is an estimation error. For the target value The estimate, It is the target value The estimation error, To The estimated value.

6. The method for preset time output feedback control of surface vessel formations with multiple quantization mechanisms according to claim 1, characterized in that: In step 3, the virtual control signal is designed as follows: （12） in, This represents the consistency error between the state variables and the reference trajectory; This represents the connection weights between nodes in the communication topology, reflecting the existence and strength of edges in the network structure. Indicates the index number; Indicates a positive adaptive gain parameter; satisfy This is used to control the growth rate of the nonlinear feedback term; Represents positive design parameters, where Indicates the preset convergence time; Indicates a positive design parameter; This represents the hyperbolic tangent function, used to avoid singularity problems; Represents a positive smoothing factor to prevent... The function saturates due to excessive input. and Represents the transpose of the fuzzy modeling parameter vector; and Represents the basis function vector of a fuzzy system; The first derivative of the reference trajectory; and Represents the observed value of the state variable.

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