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

Abstract

The invention discloses a sea surface ship formation preset time output feedback control method with multiple quantization mechanisms, and the method comprises the following steps: building a sea surface ship formation system model, and carrying out the approximate processing of an unknown nonlinear function in the sea surface ship formation system model through a fuzzy logic system; a fuzzy state observer is constructed to process an unmeasurable state, and in addition, a state quantization mechanism and an input quantization mechanism are introduced; a dynamic surface technology is adopted and a second-order filter is introduced to process a discontinuous problem of a virtual control signal so as to construct a Lyapunov function; in combination with a backstepping method technology, an adaptive law and a preset time quantization controller are designed, and the output state of the sea surface ship formation system is converged to an expected precision range within a preset time. On the basis of guaranteeing the stability of the system, the control precision is improved, the communication overhead is effectively reduced through a state quantization and input quantization mechanism, and it is ensured that the sea surface ship formation system can still operate stably and reliably in a complex environment.

Description

Technical Field

[0001] The present invention relates to the field of surface ship formation control, in particular to a surface ship formation preset time output feedback control method with multiple quantization mechanisms. Background Art

[0002] A surface vessel formation system is a typical nonlinear, unstable dynamic system whose control objective is to coordinate the motion of multiple vessels so that they can complete collaborative tasks while maintaining their relative positions and headings. Surface vessel formation systems are widely used in fields such as automatic control, ocean monitoring, transportation, military exercises, and unmanned surface vehicles (USVs). In these applications, control methods for surface vessel formation systems can improve the system's dynamic response speed, reduce control errors, and enhance the system's robustness, enabling it to maintain stable operation in complex environments. These control methods can also effectively respond to environmental disturbances, changes in sea conditions, and mutual interference between vessels, ensuring system reliability and accuracy.

[0003] In recent years, with the rapid development of intelligent control, fuzzy logic, and adaptive control, control technology for surface ship formation systems has gradually evolved toward high precision, strong real-time performance, and excellent anti-interference capabilities. In particular, methods such as preset time control, quantitative control, and observer-based intelligent control have made surface ship formation systems a key development direction in the field of automatic control for applications that require high precision and high dynamic response.

[0004] Preset-time quantization control in surface vessel formation systems aims to design an efficient control strategy to ensure the system operates stably within a predetermined timeframe and achieves the desired accuracy. This approach aims to stabilize the system state within a finite timeframe and ensure that the system output accurately tracks the reference signal, thereby maintaining the stability of the closed-loop system throughout the entire process.

[0005] Currently, a variety of control algorithms have been applied to surface ship formation systems, including classic PID control, fuzzy control, sliding mode control, and adaptive control. However, existing technologies still face the following challenges:

[0006] First, traditional control methods have poor robustness when 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, classic PID control and sliding mode control methods typically rely on precise mathematical models. However, in practical applications, due to the uncertainty of system parameters, nonlinear characteristics, and external disturbances, the effectiveness of these control methods is often not guaranteed and may even cause the system to oscillate or become unstable. In highly dynamic control tasks, these methods struggle to ensure that the system achieves the expected accuracy within the specified time, thus limiting their scope of application.

[0007] Second, traditional control methods often rely on high-precision state measurements and frequent data transmission, which can easily increase the communication burden and may cause network congestion, thereby affecting the accuracy and real-time performance of control. In addition, in multivariable coupled systems, these control methods may cause singularity problems. Many control algorithms require continuous and accurate state feedback, but in practical applications, due to limitations in sensor accuracy, data transmission bandwidth, and computing resources, frequent data acquisition and transmission may lead to network delays or data loss, significantly affecting system performance. At the same time, in multivariable coupled systems, some control methods may encounter singularities during the solution process. In other words, in some cases, the control law cannot be implemented or becomes infinite, resulting in the system not being able to operate normally or a significant decrease in control effectiveness. These problems greatly limit the application effect of traditional control methods in complex environments. Summary of the Invention

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

[0009] To achieve the above object, the present invention adopts the following technical solutions:

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

[0011] Step 1: Establish a surface ship formation system model and use a fuzzy logic system to approximate the unknown nonlinear functions in the surface ship 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 technology is used and a second-order filter is introduced to deal with the discontinuity problem of the virtual control signal, thereby constructing the Lyapunov function.

[0014] Step 4: Combined with the backstepping technique, an adaptive law and a preset time quantization controller are designed so that the output state of the surface ship formation system converges to the desired accuracy range within the preset time.

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

[0016]

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

[0018]

[0019] The model equation (1) of the surface ship formation system is rewritten as a state space expression:

[0020]

[0021] Among them, x i,1 Indicates location information, x i,2 Indicates speed information; f i,1 (x) and f i,2 (x) represents the state-related nonlinear function, which is defined as Represents the inertia matrix after rotation, defined as R i represents the rotation matrix; g irepresents the uncertain hydrodynamic coefficient; represents the damping matrix after rotation, defined as represents the rotated Coriolis force matrix, defined as C i represents the original Coriolis force matrix, describing the influence of non-inertial forces; d i,j (t) represents the time-varying external disturbance term, which is defined as d i,j (t) = 2sin(t);

[0022] Two leaders were chosen:

[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 expressed as:

[0026]

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

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

[0029]

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

[0031] y(x)=ξ T φ(x) (6)

[0032] Thus, the unknown nonlinear function f in the robot dynamics model can be approximated. i,j (x), where i = 1, 2, j = 1, 2.

[0033] Furthermore, in step 2, a fuzzy state observer is used to process the unmeasurable state, and the fuzzy state observer is designed as follows:

[0034]

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

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

[0037]

[0038] Where x is the state variable or its observed value, Represents the quantized value, where q represents the quantization of the variable x, μ>0 is the length of the quantization interval, Q k is the quantized value, 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 i,j , system output state y i,r , virtual control signal α i,s and filtered signal To construct a dynamic surface:

[0040]

[0041] Among them, 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 is the connection weight, which represents the strength of the edge in the network topology; z i,1 represents the consistency error between the state variables and the reference trajectory; represents the estimated value of the state variable; represents the filtered signal; z i,2 Represents the error between the state change and the filtered signal; represents the error between the filtered signal and the virtual control function; α i,1 is a virtual control function; the filtered signal Smoothing is performed through a second-order low-pass filter to avoid discontinuity;

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

[0043]

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

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

[0046]

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

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

[0049]

[0050] Among them, z i,1 represents the consistency error between the state variables and the reference trajectory; a i,j It represents the connection weight between nodes in the communication topology, reflecting the existence and strength of edges in the network structure, and j represents the index number; 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, which is used to avoid singularity problems; Represents a positive smoothing factor to prevent the tanh function from saturating due to excessive input; and Represents the transposed form of the fuzzy modeling parameter vector; and Represents the basis function vector of the fuzzy system; represents the first-order 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, is the derivative of the fuzzy parameter estimate, indicating its update speed; represents a positive adaptive gain parameter; l i,1 、l i,2 and l i represents the adaptive parameter;

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

[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, we ensure that all state variables of the surface ship formation system converge stably to a predetermined accuracy range within a finite time. Compared with traditional asymptotically stable control methods, this method overcomes the dependence of convergence time on initial conditions and control parameters. It can complete control tasks within a set time, ensuring strict time constraints, thereby improving the system's dynamic performance and response speed. This feature is particularly important in scenarios with high requirements for accuracy and response speed.

[0058] Second, the present invention adopts a multiple quantization mechanism to quantize state information and system inputs during the control process, thereby effectively reducing the amount of data transmission, lowering the demand for communication bandwidth, and reducing the negative impact of quantization errors on control performance. In addition, combined with a fuzzy logic system and a fuzzy state observer, the present invention can effectively compensate for unknown nonlinear dynamics in the system and estimate unmeasurable states, thereby improving the system's anti-interference ability and adaptability, enabling it to maintain stable and reliable operation in complex environments with large modeling uncertainties and external disturbances. This feature is particularly important in resource-limited distributed control systems and multi-machine collaborative control applications.

[0059] Third, the present invention effectively avoids control singularities and improves the feasibility of the system. Traditional backstepping control may cause control singularities in certain situations, affecting the feasibility and stability of the controller. By incorporating a second-order command filter, the present invention avoids the common "differential explosion" problem in backstepping and constructs a control law without relying on state derivatives. In addition, the introduction of the filter further smoothes the control signal, reduces the impact on the actuator, and improves the performance of the system in practical applications.

[0060] Fourth, the present invention enhances the system's adaptability and improves its ability to adapt to complex environments. Due to the strong nonlinearity and instability of surface ship formation systems, practical applications may face external interference and modeling uncertainty. By introducing an adaptive quantization control scheme, the present invention can dynamically adjust control gains and compensate for quantization errors, thereby meeting control requirements in diverse environments. The designed control scheme ensures stable system convergence within a preset timeframe under varying initial conditions and system parameter variations, providing solid technical support for the intelligent control and high-precision execution of surface ship formation systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 This is a schematic diagram of a network system for a preset time output feedback control method for a surface vessel formation with multiple quantization mechanisms;

[0062] Figure 2 It is a trajectory tracking performance curve of the surface ship formation system;

[0063] Figure 3 It is the state variables of the surface ship formation system and its quantitative process diagram;

[0064] Figure 4 It is a curve chart comparing the state variables and observation values of the surface ship formation system;

[0065] Figure 5 is the control input response curve of the surface ship formation system;

[0066] Figure 6 It is a trajectory tracking error curve of the surface ship formation system under different design parameters. DETAILED DESCRIPTION

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

[0068] like Figure 1 As shown, the preset time output feedback control method of a surface vessel formation with a multiple quantization mechanism of the present invention comprises the following steps:

[0069] Step 1: Establish a surface ship formation system model and use a fuzzy logic system to approximate the unknown nonlinear functions in the surface ship formation system model;

[0070] The surface ship formation system consists of four agents and two leaders, and its model equation is as follows:

[0071]

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

[0073]

[0074] The model equation (1) of the surface ship formation system is rewritten as a state space expression:

[0075]

[0076] Among them, x i,1Indicates location information, x i,2 Indicates speed information; f i,1 (x) and f i,2 (x) represents the state-related nonlinear function, which is defined as Represents the inertia matrix after rotation, defined as R i represents the rotation matrix; g i represents the uncertain hydrodynamic coefficient; represents the damping matrix after rotation, defined as represents the rotated Coriolis force matrix, defined as C i represents the original Coriolis force matrix, describing the influence of non-inertial forces; d i,j (t) represents the time-varying external disturbance term, which is defined as d i,j (t) = 2sin(t);

[0077] Two leaders were chosen:

[0078]

[0079] Among them, the fuzzy logic system (FLS) is used to approximate the unknown nonlinear function f in the sea surface ship formation system model. i,j (x);

[0080] The fuzzy logic system is expressed as:

[0081]

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

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

[0084]

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

[0086] y(x)=ξ T φ(x) (6)

[0087] Thus, the unknown nonlinear function f in the robot dynamics model can be approximated. 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, the fuzzy state observer is used to deal with the unmeasurable state, and the fuzzy state observer is designed as:

[0090]

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

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

[0093]

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

[0095] In addition, in order to deal with the discontinuity problem of the virtual control signal, a second-order filter is introduced to ensure the smoothness and stability of the signal, thereby optimizing the performance of surface ship formation control.

[0096] Step 3: Dynamic surface technology is used and a second-order filter is introduced to deal with the discontinuity problem of the virtual control signal, thereby constructing the Lyapunov function.

[0097] For the system state x i,j , system output state y i,r , virtual control signal α i,s and filtered signal To construct a dynamic surface:

[0098]

[0099] Among them, 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 is the connection weight, which represents the strength of the edge in the network topology; z i,1 represents the consistency error between the state variables and the reference trajectory; represents the estimated value of the state variable; represents the filtered signal; z i,2 Represents the error between the state change and the filtered signal; represents the error between the filtered signal and the virtual control function; α i,1 is a virtual control function; the filtered signal Smoothing is performed through a second-order low-pass filter to avoid discontinuity;

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

[0101]

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

[0103] Among them, when constructing the Lyapunov function, the following form of Lyapunov function is selected:

[0104]

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

[0106] Among them, the virtual control signal is designed as:

[0107]

[0108] Among them, z i,1represents the consistency error between the state variables and the reference trajectory; a i,j It represents the connection weight between nodes in the communication topology, reflecting the existence and strength of edges in the network structure, and j represents the index number; 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, which is used to avoid singularity problems; Represents a positive smoothing factor to prevent the tanh function from saturating due to excessive input; and Represents the transposed form of the fuzzy modeling parameter vector; and Represents the basis function vector of the fuzzy system; represents the first-order derivative of the reference trajectory; and represents the observed value of the state variable.

[0109] Step 4: Combined with the backstepping technique, an adaptive law and a preset time quantization controller are designed so that the output state of the surface ship formation system converges to the desired accuracy range within the preset time.

[0110] Among them, the adaptive law is designed as:

[0111]

[0112] in, and is the derivative of the fuzzy parameter estimate, indicating its update speed; Represents a positive adaptive gain parameter; l i,1 、l i,2 and l i represents the adaptive parameter;

[0113] Among them, the preset time quantization controller is designed as:

[0114]

[0115] The simulation results are as follows Figure 2-6 As shown in the figure, the effectiveness of the preset time output feedback control method of the surface ship formation system with multiple quantization mechanisms is verified. Figure 2 The trajectory tracking performance of the surface ship formation system was demonstrated, and the results showed that the proposed method can effectively achieve multiple quantitative control objectives within the preset time and ensure that the system outputs accurate tracking reference signals. Figure 3The state variables of the surface ship formation system and their corresponding quantization process are further demonstrated, reflecting the impact of multiple quantization mechanisms on the 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 The control input response of the system is presented, revealing the dynamic characteristics of the control signal under the preset time control framework. Figure 6 The trajectory tracking error under different design parameters is demonstrated, further verifying the control scheme's ability to ensure system accuracy and its robustness under different parameter configurations.

[0116] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A method for outputting feedback control of a surface vessel formation with preset time and multiple quantization mechanisms, characterized by: The following steps are involved: Step 1: Establish a surface ship formation system model and use a fuzzy logic system to approximate the unknown nonlinear functions in the surface ship formation system model; Step 2: Construct a fuzzy state observer to handle unmeasurable states, and introduce state quantization and input quantization mechanisms; Step 3: Dynamic surface technology is used and a second-order filter is introduced to deal with the discontinuity problem of the virtual control signal, and then the Lyapunov function is constructed; Step 4: Combined with the backstepping technique, an adaptive law and a preset time quantization controller are designed so that the output state of the surface ship formation system converges to the desired accuracy range within the preset time.

2. The method for outputting feedback control of a surface vessel formation with a multiple quantization mechanism according to claim 1, characterized in that: In step 1, the surface ship formation system consists of four agents and two leaders, and its model equation is as follows: Where i represents the i-th ocean surface unmanned vehicle, i=1,2,3,4, t represents time, C i (ν i ) represents the dependence on the speed ν i Coriolis force matrix, D i (ν i ) represents the dependence on the speed ν i The damping matrix of i represents the longitudinal position coordinate of the ship, Indicates the lateral position coordinates of the vessel; Denotes the longitudinal position coordinate χ of the vessel i and the vessel's lateral position coordinates The position vector of i is the yaw angle vector, represents the longitudinal, lateral and yaw velocity vectors; u i =[u ωi ,u νi ,u ri ] T is the control input vector, where represents the longitudinal propulsion force, represents the lateral thrust, represents the yaw control torque; d i (t) represents the unknown disturbance, g i (η i ,ν i ) indicates that it depends on the position vector η i and speed ν i The uncertain hydrodynamic coefficients, represents the inertia matrix, Denotes dependence on the yaw angle vector ψ i A rotation matrix is expressed as: The model equation (1) of the surface ship formation system is rewritten as a state space expression: Among them, x i,1 Indicates location information, x i,2 Indicates speed information; f i,1 (x) and f i,2 (x) represents the state-related nonlinear function, which is defined as Represents the inertia matrix after rotation, defined as R i represents the rotation matrix; g i represents the uncertain hydrodynamic coefficient; represents the damping matrix after rotation, defined as represents the rotated Coriolis force matrix, defined as C i represents the original Coriolis force matrix, describing the influence of non-inertial forces; d i,j (t) represents the time-varying external disturbance term, which is defined as d i,j (t) = 2sin(t); Two leaders were chosen:

3. The method for controlling a surface vessel formation with preset time output feedback and multiple quantization mechanisms according to claim 1, wherein: 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); The fuzzy logic system is expressed as: in, is the membership function of the output variable, It is a fuzzy basis function used to approximate unknown nonlinear functions; By defining the fuzzy basis function φ l , the fuzzy logic system is expressed as: By introducing the parameter vector ξ=[ξ1,ξ2,…,ξ N ] T , the fuzzy logic system is expressed as: y(x)=ξ T φ(x) (6) Thus, the unknown nonlinear function f in the robot dynamics model can be approximated. i,j (x), where i = 1, 2, j = 1, 2.

4. The method for controlling a surface vessel formation with a preset time output feedback having a multiple quantization mechanism according to claim 1, wherein: In step 2, a fuzzy state observer is used to process the unmeasurable state, and the fuzzy state observer is designed as follows: in, is the true state estimation variable, s=1,2; represents the fuzzy basis function vector; g i,s The observer gain representing the state is used to adjust the strength of the error feedback; Represents the observed value of the system output; y i Indicates the actual output value of the system; for estimated value of; Represents the optimal fuzzy modeling parameter vector corresponding to the state; in definition u i Indicates control input.

5. The method for controlling a surface vessel formation with a preset time output feedback having a multiple quantization mechanism according to claim 1, characterized in that: In step 2, state quantization and input quantization mechanisms are introduced to reduce the communication burden. The quantizer is defined as: Where x is the state variable or its observed value, Represents the quantized value, where q represents the quantization of the variable x, μ>0 is the length of the quantization interval, Q k is the quantized value, and Q1=μ,Q k+1 =Q k +μ; quantization error z x =xx q satisfy 6. The method for controlling a surface vessel formation with a preset time output feedback having a multiple quantization mechanism according to claim 1, characterized in that: In step 3, the system state x i,j , system output state y i,r , virtual control signal α i,s and filtered signal To construct a dynamic surface: Among them, 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 is the connection weight, which represents the strength of the edge in the network topology; z i,1 represents the consistency error between the state variables and the reference trajectory; represents the estimated value of the state variable; represents the filtered signal; z i,2 Represents the error between the state change and the filtered signal; represents the error between the filtered signal and the virtual control function; α i,1 is a virtual control function; the filtered signal Smoothing is performed through a second-order low-pass filter to avoid discontinuity; The dynamic equation of the filter is as follows: Among them, a i,1,1 and a i,1,2 are the damping coefficient and natural frequency of the filter respectively, The final filtering error for And there are 7. The method for controlling a surface vessel formation with preset time output feedback and a multiple quantization mechanism according to claim 1, wherein: In step 3, when constructing the Lyapunov function, the following form of Lyapunov function is selected: Among them, P i is a positive definite matrix, is the estimation error, For the target value Estimates, is the target value The estimation error of For estimated value.

8. The method for outputting feedback control of a surface vessel formation with a multiple quantization mechanism according to claim 1, characterized in that: In step 3, the virtual control signal is designed as follows: Among them, z i,1 represents the consistency error between the state variables and the reference trajectory; a i,j It represents the connection weight between nodes in the communication topology, reflecting the existence and strength of edges in the network structure, and j represents the index number; 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, which is used to avoid singularity problems; Represents a positive smoothing factor to prevent the tanh function from saturating due to excessive input; and Represents the transposed form of the fuzzy modeling parameter vector; and Represents the basis function vector of the fuzzy system; represents the first-order derivative of the reference trajectory; and represents the observed value of the state variable.

9. The method for outputting feedback control of a surface vessel formation with a multiple quantization mechanism according to claim 1, characterized in that: In step 4, the adaptive law is designed as follows: in, and is the derivative of the fuzzy parameter estimate, indicating its update speed; represents a positive adaptive gain parameter; l i,1 、l i,2 and l i represents the adaptive parameter; The preset time quantization controller is designed as:

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