Under cyber attack, dynamic event-triggered adaptive fuzzy preset performance control method for underactuated asv

Abstract

The application discloses a kind of underactuated ASV dynamic event trigger adaptive fuzzy pre-set performance control methods under network attack, including the underactuated ASV model under network attack including model uncertainty term is constructed;According to the underactuated ASV model, an adaptive fuzzy observer is constructed to obtain a state prediction model, and the state prediction error of the underactuated ASV is obtained according to the state prediction model;Performance control function for maintaining follower and leader formation control is constructed;According to the performance control function, a ship fuzzy pre-set performance virtual control law is constructed;According to the state prediction error of the underactuated ASV and the ship fuzzy pre-set performance virtual control law, an adaptive law is constructed;Switching dynamic event trigger mechanism is constructed to obtain the actual input of the controller;Based on switching dynamic event trigger mechanism and adaptive law, and according to the pre-designed N-type function, a switching dynamic event triggered formation controller is constructed.The problems of maliciously changing system signals by information deception attacks, limited system communication resources, the need to achieve specified performance indicators, external marine environment disturbances, autonomous underwater vehicle underactuation, and uncertain nonlinear models in current ASV trajectory tracking tasks, which lead to reduced ASV path tracking robustness and even instability of the entire system, are solved.

Description

Technical Field

[0001] This invention relates to the field of marine technology engineering technology, and in particular to an adaptive fuzzy preset performance control method for underdriven ASV dynamic event triggering under network attacks. Background Technology

[0002] An ASV (Autonomous Surface Vessel) is an intelligent surface platform capable of autonomous navigation and completing a range of tasks. It boasts strong autonomy, a wide operational range, reliable safety performance, and low operating costs, making it widely used in scientific research, seawater monitoring, and maritime reconnaissance and search, with broad application prospects. With increasingly frequent human activities in the marine economy and continuous advancements in marine engineering, ASVs are playing an increasingly important role in areas such as water area exploration, marine scientific research, and maritime military applications.

[0003] To accomplish ASV path tracking, the key lies in implementing guidance and control algorithms for the autonomous navigation component, enabling the ASV to reach its destination along the designated route. Current mainstream guidance technologies include algorithms based on forward line-of-sight, virtual guidance, and artificial potential fields. These technologies all require real-time calculation of reference signals, with the calculation results synchronously transmitted to the control system to drive the ASV towards the reference position. To reduce the excessive communication load caused by continuous transmission of control commands, event-triggered technology is widely used in ASV path tracking control, demonstrating good performance in handling communication load. These event-triggered technologies mainly include static event triggering and dynamic event triggering. Dynamic event triggering technology features dynamically adjustable trigger threshold parameters, saving more communication resources. It is worth noting that high-precision control systems may experience jumps during operation, leading to frequent triggering of actuators and nonlinear switching of dynamic event triggering. However, the trigger threshold still requires manual parameter design, which is difficult for ship operators. Furthermore, event-triggered technology can reduce the control accuracy of the ASV; balancing communication load and control accuracy remains a challenge.

[0004] While the theoretical framework for intelligent control of unmanned surface vessels (ASVs) is developing rapidly, the network interconnection characteristics of control systems like ASVs, which are typical of cyber-physical systems, still present challenges in trajectory tracking research. These challenges include malicious alteration of system signals by information deception attacks, limited system communication resources, the need to meet specified performance indicators, disturbances from the external marine environment, underactuation of autonomous surface vehicles, and uncertain nonlinear models. These issues can reduce the robustness of ASV path tracking or even lead to instability of the entire system.

[0005] In practice, ASVs inevitably encounter various disturbances when operating at sea, requiring real-time acquisition of their state information. However, traditional shipborne equipment can only measure the ASV's position and attitude. A good control method is to utilize a high-gain observer to acquire unmeasurable velocity information and employ an adaptive fixed-time extended state observer to simultaneously approximate the ASV's unknown state and model within a fixed time. However, both methods often suffer from overshoot, potentially leading to poor transient observation performance. Furthermore, since most surface vehicles are underactuated—meaning they drive multi-degree-of-freedom motion with relatively few control inputs—and underactuated ASVs possess complex cascaded structures, the aforementioned methods cannot be directly applied to ASV trajectory tracking tasks. In controller design, the selection of the control structure and the stable operation of the entire system must consider uncontrollable dynamic stability and controllability constraints. Overcoming disturbances while ensuring stable system operation to meet preset performance targets remains a pressing academic and engineering challenge. On the other hand, the ASV's navigation environment and control performance are crucial considerations, especially when navigating in narrow and congested waterways. In such situations, traditional unconstrained control schemes may significantly increase the risk of collisions. Furthermore, in actual marine conditions, the sensing and communication range of airborne sensors is often limited. How to achieve safe long-distance navigation under complex operating conditions is a problem that this application needs to consider. Summary of the Invention

[0006] This invention provides an adaptive fuzzy preset performance control method for underdriven ASV dynamic event triggering under network attacks, in order to overcome the above-mentioned technical problems.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows:

[0008] A method for adaptive fuzzy preset performance control of underdriven ASV dynamic event triggering under network attacks includes the following steps:

[0009] S1: Establish the assumptions about the underactuated ASV model to construct an underactuated ASV model containing model uncertainty terms under network attacks;

[0010] S2: Based on fuzzy logic technology, an adaptive fuzzy observer is constructed according to the underactuated ASV model, and a state prediction model is constructed according to the adaptive fuzzy observer;

[0011] Furthermore, the state prediction error of the underactuated ASV is obtained based on the state prediction model.

[0012] S3: Define the ASV formation configuration of the leader and follower, and construct the performance control function to maintain the formation control of the follower and leader;

[0013] S4: Construct a fuzzy preset performance virtual control law for the ship based on the performance control function;

[0014] S5: Construct an adaptive law based on the ship's fuzzy preset performance virtual control law and the state prediction error of the underactuated ASV;

[0015] S6: Construct a switching dynamic event triggering mechanism to obtain the actual input of the controller, so as to avoid low utilization of the system's communication resources due to frequent updates of the actuator during the controller's operation.

[0016] S7: Based on the switching dynamic event triggering mechanism and adaptive law, and constructing a formation controller for switching dynamic event triggering according to a pre-designed N-type function, and implementing adaptive fuzzy preset performance control of underdriven ASV dynamic event triggering under network attacks according to the formation controller.

[0017] Furthermore, the assumptions made in S1 regarding the mathematical model of the underactuated ASV are as follows:

[0018] Assumption 1: External disturbance d of underdriven ASV ι With physical attack signal p ι It is bounded, that is in and d ι With p ι The upper bound;

[0019] Assumption 2: The desired forward velocity u of the underactuated ASV l With the desired lateral velocity v l It is bounded, that is in and Indicate u l With v l The upper bound;

[0020] Hypothesis 3: Network spoofing attacks can increase controller gain. and It becomes an unknown and non-zero constant. Meanwhile, in actual ship navigation, the actuators of an underactuated ASV possess finite positive energy, i.e. and Q u With Q r Indicates a positive design constant;

[0021] The constructed underdriven ASV mathematical model containing model uncertainty terms under the aforementioned network attack is expressed as follows:

[0022]

[0023] Where: μu ,μ v ,μ r This is an intermediate parameter variable, representing the uncertainty term of the underactuated ASV, and

[0024]

[0025] D u D v D r Represented as a damping term, and

[0026] D u =-X u uX |u|u |u|u

[0027] D v =-Y v vY |v|v |v|vY |r|v |r|vY r rY |v|r |v|rY |r|r |r|r

[0028] D r =-N v vN |v|v |v|vN |r|v |r|vN r rN |v|r |v|rN |r|r∣ |r|r;

[0029] X u ,X |u|u ,Y v ,Y |v|v ,Y |r|v ,Y r ,Y |v|r ,Y |r|r N v N |v|v N |r|v N r N |v|r N |r|r∣ The parameters are: x, y, ψ represent the abscissa, ordinate, and yaw angle in the Earth coordinate system; u, v, r represent the forward velocity, lateral velocity, and yaw angular velocity; d u ,d v ,d r This represents an unknown external disturbance to an underactuated ASV; q u ,q r This indicates the control input provided by the thrusters and rudder; p u ,p v ,pr These represent the unknown interference caused by physical attacks on the ship's hull and equipment, respectively. This represents the unknown gain acting on the controller caused by a network spoofing attack; m u ,m v ,m r This represents the additional mass of an underactuated ASV along its forward, lateral, and yaw degrees of freedom.

[0030] Furthermore, S2 specifically includes the following steps:

[0031] S21: The estimate of the original position and velocity of the underactuated ASV is denoted as... And define the uncertainty term of the underactuated ASV as

[0032]

[0033] In the formula: Y ι This represents the output of a fuzzy logic system. The basis functions of the fuzzy logic system; ε ι Indicates the estimation error;

[0034] The position error and velocity error of an underactuated ASV are then defined.

[0035] The position error of the underactuated ASV is expressed as follows:

[0036]

[0037] In the formula: These represent the position horizontal coordinate error, position vertical coordinate error, and bow roll angle error, respectively.

[0038] The speed error of the underdriven ASV is and

[0039] S22: Construct an adaptive fuzzy observer for the underactuated ASV based on its position error, the expression of which is:

[0040]

[0041] In the formula: κ x ,κ y ,κ ψ ,κ u ,κ v and κ r All represent design parameters; o u ,o v and o r Represents intermediate variables and Y represents ιThe estimate and ι=u,v,r;

[0042] Based on the velocity error of the underactuated ASV, and according to equation (3), the adaptive fuzzy observer is rewritten as follows:

[0043]

[0044] In the formula: They represent First derivative; q ι This represents the number of intermediate parameters, and q ι =ε ι +d ι +p ι ,ι=u,v,r;

[0045] S23: Define the prediction error of underactuated ASV as... and And based on the prediction error of underactuated ASV, Construct a state prediction model, the expression of which is:

[0046]

[0047] In the formula: b u ,b v and b r Indicate design parameters; as well as Indicates the output state of the prediction model;

[0048] The state prediction error of the underactuated ASV is obtained according to equations (4) and (6), and its expression is as follows:

[0049]

[0050] Furthermore, S3 specifically includes the following steps:

[0051] S31: Define the virtual reference path for the navigator, and obtain the relative distance d and relative azimuth angle φ with respect to the followers based on the virtual reference path.

[0052]

[0053] In the formula: x l ,y l x and y represent the x and y coordinates of the virtual reference path, respectively; θ represents the intermediate parameter used to obtain the relative azimuth angle; φ represents the relative azimuth angle.

[0054] Based on the relative distance and relative azimuth, constraints are obtained to ensure connectivity and meet collision avoidance requirements; their expressions are as follows:

[0055]

[0056] In the formula: d min d represents the minimum relative distance. max The maximum value of the relative distance d min ,d max >0; This represents the upper bound of the relative azimuth angle, and

[0057] S32: Define the error between relative distance and relative azimuth angle to obtain the ship tracking constraint, the expression of which is as follows:

[0058]

[0059] In the formula: ρ d Represents relative distance error; ρ φ Indicates relative azimuth error; d d φ represents the expected relative distance. d Indicates the desired relative azimuth angle; These represent the lower and upper bounds of the relative distance error, respectively. These represent the lower and upper bounds of the relative azimuth, respectively.

[0060] S33: Constructing a tracking error ρ based on ship tracking constraints to ensure preset performance. k (k=d,φ), and ρ d =dd d ,ρ φ =φ-φ d And based on the tracking error ρ k Define the tracking error boundary function;

[0061] And the expression for the tracking error boundary function is:

[0062] ρ k =( ρ k,0 - ρ k,∞ )exp(- e k t)+ ρ k,∞

[0063]

[0064] In the formula: as well as All represent positive design constants; express The abbreviation of ρ k Represents ρ k (t) is a shorthand form;

[0065] S34: Construct a performance control function z for maintaining the formation control of the follower and navigator based on the tracking error boundary function. k Its expression is

[0066]

[0067] Furthermore, the ship fuzzy preset performance virtual control law constructed in S4 is...

[0068]

[0069] In the formula: ζ u ,ζ v ,ζ r Denotes an intermediate variable and ζ u =γ1tanh(β1),ζ v =γ2tanh(β2),ζ r =γ3tanh(β3); γ u ,γ v and γ r The virtual control laws γ1, γ2, and γ3 represent the forward velocity, lateral velocity, and yaw rate, respectively; β1, β2, and β3 represent the auxiliary system variables, and... ω u ,ω v ,ω r Denotes an intermediate variable and ω u =z d π d cosφ,ω v =-z d π d sinφ,ω r =z φ π φ ;π k , Represents intermediate variables and d d Indicates the expected distance; Represented as design parameters and Represents an unknown parameter, and is derived from the ship's forward pilot velocity u. l The estimated value With lateral leader velocity v l The estimated value get; Representing unknown parameters The estimate.

[0070] Furthermore, S5 specifically includes the following steps:

[0071] S51: Based on the ship's fuzzy preset performance virtual control law, define the intermediate error variable z. ι ,ι=u,v,r, its expression is

[0072]

[0073] S52: Based on the intermediate error variable z ι Based on the state prediction error of the underactuated ASV, an adaptive law is constructed, the expression of which is:

[0074]

[0075] In the formula: express First derivative; Γ ι This indicates the design parameter, which is the threshold for switching between a preset fixed threshold and a dynamic event triggering mechanism; The basis functions of the fuzzy logic system; σ ι This indicates a dynamically adjustable threshold parameter.

[0076] Furthermore, the switching dynamic event triggering mechanism constructed in S6 is as follows:

[0077]

[0078] In the formula: This represents the output of the controller to be designed, and for The abbreviation of ; t j ,t j+1 Indicates the time threshold parameter; e p (t) represents the error of switching the dynamic event triggering mechanism, and e p (t)= σ p (t) and η p (t) represents the dynamically adjustable threshold parameter for event triggering; Γ p This represents the threshold parameter that switches between a preset fixed threshold and a dynamic event triggering mechanism, and Γ p >C p C p Indicates the trigger interval and C p >σ p (t)·|q p (t)|+η p (t); q p (t) represents the actual input to the controller;

[0079] The update law for the event-triggered dynamically adjustable threshold parameter is as follows:

[0080]

[0081] In the formula: c p ,j p and θ p All are design parameters;

[0082] Based on the update law of the dynamically adjustable threshold parameter triggered by the event and the switching dynamic event triggering mechanism, the actual input of the controller is obtained, specifically:

[0083] According to formula (18), we can obtain

[0084]

[0085] According to formula (19), we can obtain

[0086]

[0087] In the formula: η p (0) represents a positive integer;

[0088] The error of switching dynamic event triggering mechanism can be rewritten according to formula (20) as follows:

[0089]

[0090] In the formula: α p1 ,α p2 Indicate the design parameters, and satisfy the following:

[0091] Then, according to formula (21), the actual input of the controller is obtained as follows:

[0092]

[0093] Furthermore, the formation controller triggered by the switching dynamic event constructed in S7 is expressed as follows:

[0094]

[0095] In the formula: Indicates the output of the controller to be designed; τ u ,T u ,τ r ,T r Indicates intermediate variables; An N-type function representing an underdriven ASV; Represents the design parameters of the N-type function, and k p ,μ pIndicates design parameters; σ p (t) represents a dynamically adjustable threshold parameter and p = u,r.

[0096] Beneficial effects: This invention provides a method for adaptive fuzzy preset performance control of underactuated ASV dynamic event triggering under network attacks.

[0097] First, while ensuring the preset performance, this invention designs an N-type function to effectively mitigate the impact of unknown actuator gain caused by deceptive attacks. Furthermore, unlike traditional control strategies, this invention studies the preset performance control of underactuated ASVs under network attacks, constructing a performance control function for maintaining follower and leader formation control, significantly improving the system's ability to resist deceptive attacks, thereby ensuring the safety of ASVs when performing trajectory tracking tasks.

[0098] Second, based on fuzzy logic technology, an adaptive fuzzy observer is constructed according to the underactuated ASV model, and a state prediction model is constructed based on the adaptive fuzzy observer. The proposed fuzzy logic system achieves a balance between ensuring the stability of the closed-loop system and the uncertainty of the approximation model, and uses the prediction error between the original system and the adaptive fuzzy observer as the input of the state prediction model, thus eliminating the peak phenomenon in the high-gain fuzzy observer.

[0099] Third, a switching dynamic event triggering mechanism is constructed that can effectively reduce communication burden and save system communication resources. Compared with time sampling mechanism, event triggering mechanism and dynamic event triggering mechanism, the switching dynamic event triggering mechanism constructed in this invention can dynamically switch between fixed threshold mechanism and dynamic event triggering mechanism. By applying the switching dynamic event triggering mechanism, communication resources can be further saved even when the actuator jumps. Attached Figure Description

[0100] 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.

[0101] Figure 1 The flowchart is a process for the adaptive fuzzy preset performance control method for underdriven ASV dynamic event triggering under network attacks according to the present invention.

[0102] Figure 2 This is a comparison curve of the trajectory tracking control plane of this embodiment and the comparison algorithm;

[0103] Figure 3 This is a position error diagram for this embodiment;

[0104] Figure 4 This is an angle error diagram for this embodiment;

[0105] Figure 5 This refers to the observation error of the adaptive fuzzy observer in this embodiment.

[0106] Figure 6 This refers to the prediction error of the adaptive fuzzy observer in this embodiment.

[0107] Figure 7 These are the adaptive parameters for this embodiment;

[0108] Figure 8 This is a gain curve diagram based on the N-type function and its independent variable in this embodiment;

[0109] Figure 9 This is a schematic diagram illustrating the size and duration of the network attack in this embodiment;

[0110] Figure 10 This is the actual control input for this embodiment;

[0111] Figure 11 This refers to the time interval under the dynamic event triggering mechanism in this embodiment. Detailed Implementation

[0112] 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.

[0113] This embodiment provides a method for adaptive fuzzy preset performance control of underactuated ASV dynamic event triggering under network attacks, such as... Figure 1 As shown, it includes the following steps:

[0114] S1: Establish the assumptions about the underactuated ASV model to construct an underactuated ASV model containing model uncertainty terms under network attacks;

[0115] Specifically, the assumptions for establishing the mathematical model of underactuated ASV are as follows:

[0116] Assumption 1: External disturbance d of underdriven ASV ι With physical attack signal p ι It is bounded, that is in and d ιWith p ι The upper bound;

[0117] Assumption 2: The desired forward velocity u of the underactuated ASV l With the desired lateral velocity v l It is bounded, that is in and Indicate u l With v l The upper bound;

[0118] Hypothesis 3: Network spoofing attacks can increase controller gain. and It becomes an unknown and non-zero constant. Meanwhile, in actual ship navigation, the actuators of an underactuated ASV possess finite positive energy, i.e. and Q u With Q r Indicates a positive design constant;

[0119] The constructed underactuated ASV mathematical model containing model uncertainty terms under network attacks is expressed as follows:

[0120]

[0121] Where: μ u ,μ v ,μ r This is an intermediate parameter variable, representing the uncertainty term of the underactuated ASV, and

[0122]

[0123] D u D v D r Represented as a damping term, and

[0124] D u =-X u uX |u|u |u|u

[0125] D v =-Y v vY |v|v |v|vY |r|v |r|vY r rY |v|r |v|rY |r|r |r|r

[0126] D r =-N v vN |v|v |v|vN |r|v |r|vNr rN |v|r |v|rN |r|r∣ |r|r;

[0127] X u ,X |u|u ,Y v ,Y |v|v ,Y |r|v ,Y r ,Y |v|r ,Y |r|r N v N |v|v N |r|v N r N |v|r N |r|r∣ The parameters are: x, y, ψ represent the abscissa, ordinate, and yaw angle in the Earth coordinate system; u, v, r represent the forward velocity, lateral velocity, and yaw angular velocity; d u ,d v ,d r This represents an unknown external disturbance to an underactuated ASV; q u ,q r This indicates the control input provided by the thrusters and rudder; p u ,p v ,p r These refer to the unknown interference caused by physical attacks to the hull and equipment. Physical attacks refer to behaviors that directly cause damage or interference to the physical components of the ASV, mainly involving external collisions and similar interference. This represents the unknown gain acting on the controller caused by a network spoofing attack; m u ,m v ,m r This represents the additional mass of an underactuated ASV along its forward, lateral, and yaw degrees of freedom.

[0128] S2: Based on fuzzy logic technology, an adaptive fuzzy observer is constructed according to the underactuated ASV model, and a state prediction model is constructed according to the adaptive fuzzy observer;

[0129] Furthermore, the state prediction error of the underactuated ASV is obtained based on the state prediction model.

[0130] In this embodiment, the uncertainty of the underactuated ASV mathematical model is approximated using a fuzzy logic system, and the uncertainty of the quality switching mathematical model is approximated using adaptive fuzzy control technology to obtain an estimate of the underactuated ASV state information.

[0131] The establishment of the fuzzy logic system is as follows:

[0132] The fuzzy logic system approximates the uncertainties in (2) through four main components: a fuzzy rule base, a fuzzifier, a defuzzifier, and a fuzzy inference engine. For a fuzzy logic system with N rules, the l-th rule R l The following is the definition of (l=1,...,N):

[0133] Rule R l If x1 corresponds to Corresponding to Up to x n Corresponding to Then the output y of the fuzzy logic system corresponds to G. l ;

[0134] Where x = [x1, x2, ..., x n ] T y represents the input of the fuzzy logic system; y represents the output of the fuzzy logic system; F i l G represents a fuzzy set, i = 1, ..., n; l Each has its own membership function membership function

[0135] Fuzzy logic systems can be described as:

[0136]

[0137] In the formula:

[0138] The fuzzy basis function can be described as:

[0139]

[0140] By defining fuzzy basis function vectors and Fuzzy logic systems can be described as: The above derivation process must satisfy the description of Lemma 1, the specific content of which is as follows: The membership function represents the fuzzy logic function; W represents the weight matrix of the fuzzy logic system.

[0141] Lemma 1: For any continuous function G(x), the existence of a fuzzy logic system that satisfies the following conditions is always guaranteed. The upper bound of the error ε is

[0142] Specifically, the following steps are included:

[0143] S21: The estimate of the original position and velocity of the underactuated ASV is denoted as... And define the uncertainty term of the underactuated ASV as

[0144]

[0145] In the formula: Y ι This represents the output of a fuzzy logic system. The basis functions of the fuzzy logic system; ε ι Indicates the estimation error;

[0146] The position error and velocity error of an underactuated ASV are then defined.

[0147] The position error of the underactuated ASV is expressed as follows:

[0148]

[0149] In the formula: These represent the position abscissa error, position ordinate error, and bow roll angle error, respectively; the velocity error of the underactuated ASV is... and

[0150] S22: Construct an adaptive fuzzy observer for the underactuated ASV based on its position error, the expression of which is:

[0151]

[0152]

[0153] In the formula: κ x ,κ y ,κ ψ ,κ u ,κ v and κ r All represent design parameters; o u ,o v and o r Represents intermediate variables and

[0154] Y represents ι The estimate and

[0155] Based on the velocity error of the underactuated ASV, and according to equation (3), the adaptive fuzzy observer is rewritten as follows:

[0156]

[0157] In the formula: They represent First derivative; q ι This represents the number of intermediate parameters, and qι =ε ι +d ι +p ι ,ι=u,v,r;

[0158] S23: Define the prediction error of underactuated ASV as... and And based on the prediction error of underactuated ASV, Construct a state prediction model, the expression of which is:

[0159]

[0160] In the formula: b u ,b v and b r Indicate design parameters; as well as Indicates the output state of the prediction model;

[0161] The state prediction error of the underactuated ASV is obtained according to equations (4) and (6), and its expression is as follows:

[0162]

[0163] This embodiment designs an adaptive fuzzy observer based on the underactuated ASV mathematical model, and extracts the model uncertainty and low-frequency content in the ocean disturbance through a given adaptive controller. The obtained prediction error of the underactuated ASV is used in the subsequent controller design process through a composite adaptive control method to achieve a balance between stability and approximation accuracy.

[0164] S3: Define the ASV formation configuration of the leader and follower, and construct the performance control function to maintain the formation control of the follower and leader;

[0165] Specifically, in this implementation, a certain vehicle in the formation will be designated as the navigator, and the other vehicles will act as its followers. The navigator will follow a pre-set reference trajectory, and the followers will follow the navigator at certain intervals and angles, thereby realizing navigator and follower formation control. The movement of the navigator will guide the behavior of the entire formation, which is easy to understand and execute. Moreover, when the navigator is disturbed and causes perturbation, it can still maintain the formation. This process requires first defining the trajectory of the virtual vehicle and building a performance control function to make the trajectory converge to the reference trajectory of the follower. Then, a position tracking controller is designed to make the follower track the virtual ship, thereby realizing formation control.

[0166] Specifically, the following steps are included:

[0167] S31: Define the virtual reference path for the navigator, and obtain the relative distance d and relative azimuth angle φ with respect to the followers based on the virtual reference path.

[0168]

[0169] θ=atan2(y l -y,x l -x) (8)

[0170] φ=θ-ψ

[0171] In the formula: x l ,y l x and y represent the x and y coordinates of the virtual reference path, respectively; θ represents the intermediate parameter used to obtain the relative azimuth angle; φ represents the relative azimuth angle.

[0172] Because the sensing range of road sensors is limited, in order to ensure connectivity and meet collision avoidance requirements, constraints are obtained based on relative distance and relative azimuth angle to ensure connectivity and meet collision avoidance requirements. The expression for these constraints is as follows:

[0173]

[0174] In the formula: d min d represents the minimum relative distance. max The maximum value of the relative distance d min ,d max >0; This represents the upper bound of the relative azimuth angle, and Where d min ,d max , This is determined by the nature of the sensor. Only when the constraint condition (9) is met can the follower detect the leader in order to ensure connectivity and avoid collisions.

[0175] S32: Define the error between relative distance and relative azimuth angle to obtain the ship tracking constraint, the expression of which is as follows:

[0176]

[0177] In the formula: ρ d Represents relative distance error; ρ φ Indicates relative azimuth error; d d φ represents the expected relative distance. d Indicates the desired relative azimuth angle; These represent the lower and upper bounds of the relative distance error, respectively. These represent the lower and upper bounds of the relative azimuth, respectively.

[0178] S33: Constructing a tracking error ρ based on ship tracking constraints to ensure preset performance.k (k=d,φ), and ρ d =dd d ,ρ φ =φ-φ d And based on the tracking error ρ k Define the tracking error boundary function;

[0179] Assumption 4: In this embodiment, the tracking error ρ k The initial state satisfies constraint (10), that is and To ensure the tracking error ρ of the preset performance k (k = d, φ), a tracking error boundary function needs to be defined:

[0180] And the expression for the tracking error boundary function is:

[0181] ρ k =( ρ k,0 - ρ k,∞ )exp(- l k t)+ ρ k,∞

[0182]

[0183] In the formula: as well as All represent positive design constants; express The abbreviation of ρ k Represents ρ k (t) is a shorthand form;

[0184] Furthermore, differentiating formula (11) yields:

[0185]

[0186] According to hypothesis two, road sensors cannot directly measure the leading u. l and v l The speed; therefore, it is necessary to estimate. and This embodiment defines The estimation error is Representing unknown parameters The estimate, k represents the upper bound of the speed of the unknown leader ship. ξ Represent the design parameters and satisfy the following adaptation rules

[0187]

[0188] S34: To ensure the tracking error ρ k (k=d,φ) converges to the specified boundary (11). The following performance control function is introduced to define the tracking error, that is, a performance control function z for maintaining the formation control of the follower and the navigator is constructed based on the tracking error boundary function. k Its expression is

[0189]

[0190] Furthermore, it can be deduced from equation (15) that z k →±∞ respectively correspond to ρ k →- ρ k and And z k =0 corresponds to In this embodiment, the derivative of (15) is obtained as follows:

[0191]

[0192] in:

[0193]

[0194] In this embodiment, the Lyapunov function is selected as follows:

[0195]

[0196] The derivative of (17) is obtained from equations (12), (13), and (15) and can be expressed as:

[0197]

[0198] S4: Construct a fuzzy preset performance virtual control law for the ship based on the performance control function; the constructed fuzzy preset performance virtual control law for the ship is as follows:

[0199]

[0200] In the formula: ζ u ,ζ v ,ζ r Denotes an intermediate variable and ζ u =γ1tanh(β1),ζ v =γ2tanh(β2),ζ r =γ3tanh(β3); γ u ,γ v and γ rThe virtual control laws γ1, γ2, and γ3 represent the forward velocity, lateral velocity, and yaw rate, respectively; β1, β2, and β3 represent the auxiliary system variables, and... ω u ,ω v ,ω r Denotes an intermediate variable and ω u =z d π d cosφ,ω v =-z d π d sinφ,ω r =z φ π φ ;π k , Represents intermediate variables and

[0201] d d Indicates the expected distance; Represented as design parameters and Represents an unknown parameter, and is derived from the ship's forward pilot velocity u. l The estimated value With lateral leader velocity v l The estimated value get; Representing unknown parameters The estimate;

[0202] S5: Based on the ship's fuzzy preset performance virtual control law and the state prediction error of the underactuated ASV, an adaptive law is constructed, which includes the following steps:

[0203] S51: Based on the ship's fuzzy preset performance virtual control law, define the intermediate error variable z. ι ,ι=u,v,r, its expression is

[0204]

[0205] Substituting equations (20), (19), and (14) into (18), we get:

[0206]

[0207] In the formula, ω u =z d π d cosφ,ω v =-z d π d sinφ and ω r =z φ π φ ;

[0208] Using Lemma 2 and Assumption 2, (21) can be expressed as:

[0209]

[0210] in, For positive design parameters,

[0211] Furthermore, by differentiating (20), we can obtain:

[0212]

[0213] S52: Based on the intermediate error variable z ι Based on the state prediction error of the underactuated ASV, an adaptive law is constructed, the expression of which is:

[0214]

[0215] In the formula: express First derivative; Γ ι This indicates the design parameter, which is the threshold for switching between a preset fixed threshold and a dynamic event triggering mechanism; The basis functions of the fuzzy logic system; σ ι This indicates a dynamically adjustable threshold parameter;

[0216] S6: Construct a switching dynamic event triggering mechanism to obtain the actual input of the controller, so as to avoid low utilization of the system's communication resources due to frequent updates of the actuator during the controller's operation.

[0217] In this embodiment, the switching dynamic event triggering mechanism is proposed for high-precision control systems. The controller usually exhibits obvious oscillations during initial operation. When only the dynamic event triggering mechanism is used, it usually leads to frequent updates of the actuator, resulting in low utilization of system communication resources. To solve this problem, a switching dynamic event triggering mechanism is proposed.

[0218] The switching dynamic event triggering mechanism is as follows:

[0219]

[0220] In the formula: This represents the output of the controller to be designed, and for The abbreviation of ; t j ,t j+1 Indicates the time threshold parameter; e p (t) represents the error in switching the dynamic event triggering mechanism, and σ p (t) and ηp (t) represents the dynamically adjustable threshold parameter for event triggering; Γ p This represents the threshold parameter that switches between a preset fixed threshold and a dynamic event triggering mechanism. To ensure effectiveness, Γ p It should be large enough, i.e., Γ p >C p C p Indicates the trigger interval and, to avoid unnecessary resource waste caused by skipping, C p It should be greater than the trigger interval of the dynamic event triggering mechanism, i.e., C. p >σ p (t)·|q p (t)|+η p (t); q p (t) represents the actual input to the controller; furthermore, to prevent Zeno's phenomenon, the following conditions must be met:

[0221] Γ p >C p >σ p (t)·|q p (t)|+η p (t)>η p (t)

[0222] The update law for the event-triggered dynamically adjustable threshold parameter is as follows:

[0223]

[0224] In the formula: and θ p All are design parameters;

[0225] Based on the update law of the dynamically adjustable threshold parameter triggered by the event and the switching dynamic event triggering mechanism, the actual input of the controller is obtained, specifically:

[0226] According to formula (27), we can obtain

[0227]

[0228] According to formula (28), we can obtain

[0229]

[0230] In the formula: η p (0) represents a positive integer;

[0231] The error of switching dynamic event triggering mechanism can be rewritten according to formula (29) as follows:

[0232]

[0233] In the formula: αp1 ,α p2 Indicate the design parameters, and satisfy the following:

[0234] The actual input to the controller is obtained according to formula (30).

[0235]

[0236] S7: Based on the switching dynamic event triggering mechanism and adaptive law, and according to the pre-designed N-type function, a formation controller for switching dynamic event triggering is constructed, and the adaptive fuzzy preset performance of underactuated ASV dynamic event triggering under network attack is controlled according to the formation controller.

[0237] The N-type function and constraints of the ASV described in this embodiment are as follows:

[0238] Definition 1: A continuous function A function can be called an N-type function if it satisfies the following properties, as shown below:

[0239]

[0240] According to definition 1, N-type functions have the characteristics of infinite gain and infinite switching frequency. Several functions satisfy these conditions, such as... and In this embodiment, select As an N-type function, where ζ is a variable;

[0241] Lemma 2: For any And s∈R can lead to:

[0242] in It is a positive constant;

[0243] Lemma 3: For any x∈R and any constant ε>0, in this embodiment we have:

[0244]

[0245] Lemma 4: For the N-type function chosen according to Definition 1, let V(t), and It is defined in [0, t f A smooth function on ), and Then the following inequalities hold:

[0246]

[0247] Where C1 > 0, It is a non-zero constant, C2 represents a constant; and V(t), ζ(t) and All are based on [0,t f () as the boundary;

[0248] Furthermore, based on the switching dynamic event triggering mechanism and adaptive law, and according to the pre-designed N-type function, a formation controller for switching dynamic event triggering is constructed, the expression of which is:

[0249]

[0250] In the formula: Indicates the output of the controller to be designed; τ u ,T u ,τ r ,T r Indicates intermediate variables; An N-type function representing an underdriven ASV; Represents the design parameters of the N-type function, and k p ,μ p Indicates design parameters; σ p (t) represents a dynamically adjustable threshold parameter and p = u,r.

[0251] This embodiment also includes performing stability analysis by selecting a Lyapunov function, proving that the controller in this embodiment will not exhibit the Zeno phenomenon and obtaining relevant constraints.

[0252] Specifically, for underactuated ASVs subjected to deception and physical attacks, if all conditions of the previous assumptions 1, 2, and 3 are met, it is possible to prove, by appropriately setting control parameters, that all signals in the closed-loop control systems (1) and (2) converge to any small neighborhood of the origin, based on the formulas of fuzzy logic system, state prediction model (6), event triggering rule (25), event triggering parameter threshold update law (26), (27), controller (34), and adaptive update law (24). The proof is as follows:

[0253] Consider the following Lyapunov candidate function:

[0254]

[0255] Differentiating V2 according to equations (5) and (7), we can obtain:

[0256]

[0257] Choose the Lyapunov function as:

[0258]

[0259] By differentiating V3 using the condition in (24), we can obtain:

[0260]

[0261] Consider the following Lyapunov function V4:

[0262]

[0263] We can obtain it through (38):

[0264] ˉˉ

[0265]

[0266] Substituting equations (31) and (23) into equation (39), we get:

[0267]

[0268] From equation (31), we can obtain:

[0269]

[0270] According to the lemma triple (32), we can deduce that:

[0271]

[0272] According to Young's inequality, this embodiment yields:

[0273]

[0274] Substituting (42) into (40) and combining it with (43), we can obtain:

[0275]

[0276] Will Substituting into equation (44) and combining it with equation (34), we can obtain:

[0277]

[0278] Choosing V = V2 + V3 + V4, by combining equations (35), (37), and (45), we can obtain its differential.

[0279] According to Lemma 4, this embodiment shows that:

[0280]

[0281] Where C1 and C2 are both positive constants, satisfying the following formula:

[0282]

[0283] Integrating (45), we can obtain:

[0284]

[0285] Using Lemma 4, this embodiment can obtain It is based on [0,t f The boundary is defined as ). Therefore, the definition is... Equation (47) can be rewritten as:

[0286]

[0287] in, Integrating equation (49), this embodiment can deduce that:

[0288]

[0289] This embodiment can infer that as time approaches infinity, V(t) tends to... The appropriate design parameters can be chosen to make it arbitrarily small. Therefore, all signals in the closed-loop system will eventually be uniformly bounded. This embodiment will demonstrate that the controller does not exhibit the Zeno phenomenon, which means that t ★ >0, making the sampling interval {t j+1 -t j}≥t ＊ For all j∈Z + .

[0290] From equations (26) and (27), this embodiment can derive that the sampling interval satisfies the following inequality:

[0291]

[0292] Based on equations (41) and (42), this embodiment can be derived It is differentiable. Previous stability analysis confirmed that all signals in the system are bounded. Therefore, there exists a positive constant. Make This means It is bounded. It's important to note that e p (t j ) equals zero, and when t is close to t j+1 ,e p (t) tends towards η p The positive limit of (t). Therefore, the sampling interval must satisfy t. ＊ ≥η p (t) / p >0, to prevent Zeno behavior.

[0293] Through equation (25), this embodiment can obtain

[0294] and

[0295] Therefore, applying the above results to (51), regarding |e p (t j The relative increment of |e| = 0 p (t)|in [t j ,t j+1 During this period, the following must be met:

[0296]

[0297] This indicates that:

[0298]

[0299] Therefore, the minimum interval between events is positive and lower bounded to exclude the Zeno phenomenon. Ultimately, it is proven that the Zeno phenomenon caused by switching dynamic event triggering mechanisms can be avoided.

[0300] To verify the superiority and effectiveness of the present invention, this embodiment verifies the effectiveness of the present invention through a numerical simulation example, the specific implementation of which is as follows:

[0301] In this embodiment, the specific parameters are set as follows:

[0302] d max =15,d min =5d d =10,θ vf =π / 6,θ d =π / 3,κ x =1,κ y =2,κ ψ =1.5,

[0303] κ u =2,κ v =3,κ r =0.5,σ u (0)=σ r (0)=0.3,η u (0)=η r (0) = 0.5, c p =0.2,

[0304]

[0305] k u =1.5,k v =0.7,k r =2.6,μ u =10,μ r =5,Γu =Γ v =Γ r =0.1I 5*5 ,

[0306] σ u =1.2,σ v =1.1,σ r =3.3, γ1=20, γ2=30, γ3=50

[0307] Modeling attacker behavior using random numbers is considered an effective way to address the inherent uncertainty in deception attacks, especially in situations where information is scarce. By incorporating random elements, it more accurately reflects the unpredictable and variable patterns of attacks.

[0308] The deception attack signal is selected as:

[0309]

[0310] External disturbances can be represented as:

[0311] w=[1+sin(0.01t),0.7+cos(0.6t),0.3+sin(1.1t)] T

[0312] The parameters specified for performance control are:

[0313] ρ θ (t)=-π / 6exp(-0.02t)-0.03

[0314]

[0315] ρ d (t) = -5exp(-0.05t) + 0.2

[0316]

[0317] The navigator's initial velocity is u l =3m / s,v l =0m / s, and r L The following conditions must be met:

[0318]

[0319] Define the initial condition for the navigator as η l (0) = [0,0,0] T The initial conditions for the followers are defined as η = [-7, -8, π / 6]. T and ν = [0,0,0]T .

[0320] This embodiment compares and analyzes with existing algorithms in adaptive output feedback trajectory tracking formation control based on finite-time velocity observation, and mainly focuses on, for example... Figures 2-11 As shown. Figure 2 As shown, Figure 2 The control plane is used for trajectory tracking in two algorithms. From Figure 3 and Figure 4 It can be seen that, compared with the adaptive output feedback trajectory tracking formation control algorithm based on finite-time velocity observation, the position and angle errors of the method in this embodiment are more stable. Figure 5 and Figure 6 The observation and prediction errors of the adaptive fuzzy observer are described, demonstrating that the observer proposed in this invention achieves higher accuracy. From... Figure 7 It can be seen that after a certain learning period, the norm of the adaptive parameter tends to stabilize. Figure 8 It shows the changes in the N-type function and its independent variable. Figure 9 This indicates the size and duration of the deception attack. Figure 10 The actual control inputs are displayed. Figure 11 The time interval under SDETM is displayed.

[0321] To visually demonstrate the comparison and effectiveness of the method in this embodiment, a comparative analysis was conducted with the algorithm described in the adaptive output feedback trajectory tracking formation control based on finite-time velocity observation. Although both methods adhere to performance boundaries, the method proposed in this embodiment exhibits higher accuracy and minimal oscillations compared to the algorithm in the adaptive output feedback trajectory tracking formation control based on finite-time velocity observation. To further validate the comparison results, this embodiment introduced commonly used performance metrics for quantitative analysis, including mean absolute error. and average absolute input control Mean absolute error reflects the stability performance of the control system, and mean absolute input control is used to evaluate the energy consumption of the control system. The performance results are shown in Table 1:

[0322] Table 1. Results of performance indicators

[0323]

[0324] Table 2 shows a comparison of the triggering frequencies between the switching dynamic event triggering mechanism, the adaptive neural output feedback control method based on composite learning, and the robust neural event triggering unmanned surface vehicle network attack control method based on the nussbaus-type function in this embodiment. It can be seen that compared with common event triggering mechanisms under the same algorithm, the switching dynamic event triggering mechanism proposed in this embodiment has fewer triggers [10,36], which can further save communication resources;

[0325] Table 2. Comparison results of trigger frequencies

[0326]

[0327] Based on comparisons of existing technologies, guidance law construction, controller design, and numerical simulations, the overall beneficial effects of this embodiment compared to existing technologies are as follows:

[0328] First, this embodiment, while ensuring the preset performance, designs an N-type function to effectively mitigate the impact of unknown actuator gain caused by deceptive attacks. Unlike traditional control strategies, this invention first studies the preset performance control of underactuated ASVs under network attacks. This algorithm significantly improves the system's ability to resist deceptive attacks, thereby ensuring the safety of ASVs when performing trajectory tracking tasks.

[0329] Second, this embodiment leverages the advantages of composite learning technology, achieving a balance between ensuring the stability of the closed-loop system and the uncertainty of the approximation model. The prediction error between the original system and the estimated model is incorporated into the series-parallel estimation model, while simultaneously eliminating the peaking phenomenon in the high-gain observer.

[0330] Third, a switching dynamic event triggering mechanism is proposed that can effectively reduce communication burden and save system communication resources. Compared with time sampling mechanism, event triggering mechanism and dynamic event triggering mechanism, the switching dynamic event triggering mechanism proposed in this embodiment can dynamically switch between fixed threshold mechanism and dynamic event triggering mechanism. By applying the switching dynamic event triggering mechanism, communication resources can be further saved even in the case of actuator jump.

[0331] This invention proposes an adaptive fuzzy performance control method for underactuated ASVs triggered by dynamic events under network attacks. This control method has two main characteristics:

[0332] To address the trajectory tracking problem of underactuated SVs, a switching dynamic event-triggered adaptive fuzzy preset performance control algorithm is proposed to address network and physical attacks on underactuated SVs. This algorithm improves the transient and steady-state performance of the system, ensuring the connectivity, collision avoidance, and communication resource protection of the underactuated SV in a network environment. A fuzzy logic system is used to approximate the uncertainty, an adaptive fuzzy observer is established, and a serial-parallel estimation model is constructed based on this observer. The composite adaptive algorithm, while considering the observation accuracy issue, guarantees the preset performance of the system.

[0333] Within the backstepping framework, an N-type function is designed to mitigate the impact of unknown perturbation gains caused by deception attacks. Furthermore, a switching dynamic event triggering mechanism is developed, which effectively conserves communication resources even under oscillating conditions. Numerical simulations verify the effectiveness of the algorithm.

[0334] 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 therein. Such 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 adaptive fuzzy preset performance control of underactuated ASV dynamic event triggering under network attacks, characterized in that, Includes the following steps: S1: Establish the assumptions about the underactuated ASV model to construct an underactuated ASV model containing model uncertainty terms under network attacks; S2: Based on fuzzy logic technology, an adaptive fuzzy observer is constructed according to the underactuated ASV model, and a state prediction model is constructed according to the adaptive fuzzy observer; Furthermore, the state prediction error of the underactuated ASV is obtained based on the state prediction model. S3: Define the ASV formation configuration of the leader and follower, and construct the performance control function to maintain the formation control of the follower and leader; S4: Construct a fuzzy preset performance virtual control law for the ship based on the performance control function; S5: Construct an adaptive law based on the ship's fuzzy preset performance virtual control law and the state prediction error of the underactuated ASV; S6: Construct a switching dynamic event triggering mechanism to obtain the actual input of the controller, so as to avoid low utilization of the system's communication resources due to frequent updates of the actuator during the controller's operation. S7: Based on the switching dynamic event triggering mechanism and adaptive law, and constructing a formation controller for switching dynamic event triggering according to a pre-designed N-type function, and implementing adaptive fuzzy preset performance control of underdriven ASV dynamic event triggering under network attacks according to the formation controller.

2. The method for adaptive fuzzy preset performance control of underactuated ASV dynamic event triggering under network attack as described in claim 1, characterized in that, The assumptions made in S1 for establishing the mathematical model of the underdriven ASV are as follows: Assumption 1: External disturbance d of underdriven ASV ι With physical attack signal p ι It is bounded, that is in and d ι With p ι The upper bound; Assumption 2: The desired forward velocity u of the underactuated ASV l With the desired lateral velocity v l It is bounded, that is in and Indicate u l With v l The upper bound; Hypothesis 3: Network spoofing attacks can increase controller gain. and It becomes an unknown and non-zero constant. Meanwhile, in actual ship navigation, the actuators of an underactuated ASV possess finite positive energy, i.e. and Q u With Q r Indicates a positive design constant; The constructed underdriven ASV mathematical model containing model uncertainty terms under the aforementioned network attack is expressed as follows: Where: μ u ,μ v ,μ r This is an intermediate parameter variable, representing the uncertainty term of the underactuated ASV, and D u D v D r Represented as a damping term, and D u =-X u u-X |u|u |u|u D v =-Y v v-Y |v|v |v|v-Y |r|v |r|v-Y r r-Y |v|r |v|r-Y |r|r |r|r D r =-N v v-N |v|v |v|v-N |r|v |r|v-N r r-N |v|r |v|r-N |r|r∣ |r|r; X u ,X |u|u ,Y v ,Y |v|v ,Y |r|v ,Y r ,Y |v|r ,Y |r|r N v N |v|v N |r|v N r N |v|r N |r|r∣ The parameters are: x, y, ψ represent the abscissa, ordinate, and yaw angle in the Earth coordinate system; u, v, r represent the forward velocity, lateral velocity, and yaw angular velocity; d u ,d v ,d r This represents an unknown external disturbance to an underactuated ASV; q u ,q r This indicates the control input provided by the thrusters and rudder; p u ,p v ,p r These represent the unknown interference caused by physical attacks on the ship's hull and equipment, respectively. This represents the unknown gain acting on the controller caused by a network spoofing attack; m u ,m v ,m r This represents the additional mass of an underactuated ASV along its forward, lateral, and yaw degrees of freedom.

3. The method for adaptive fuzzy preset performance control of underactuated ASV dynamic event triggering under network attack as described in claim 2, characterized in that, S2 specifically includes the following steps: S21: The estimate of the original position and velocity of the underactuated ASV is denoted as... And define the uncertainty term of the underactuated ASV as In the formula: Y ι This represents the output of a fuzzy logic system. The basis functions of the fuzzy logic system; ε ι Indicates the estimation error; The position error and velocity error of an underactuated ASV are then defined. The position error of the underactuated ASV is expressed as follows: In the formula: These represent the position horizontal coordinate error, position vertical coordinate error, and bow roll angle error, respectively. The speed error of the underdriven ASV is and S22: Construct an adaptive fuzzy observer for the underactuated ASV based on its position error, the expression of which is: In the formula: κ x ,κ y ,κ ψ ,κ u ,κ v and κ r All represent design parameters; o u ,o v and o r Represents intermediate variables and Y represents ι The estimate and Based on the velocity error of the underactuated ASV, and according to equation (3), the adaptive fuzzy observer is rewritten as follows: In the formula: They represent First derivative; q ι This represents the number of intermediate parameters, and q ι =ε ι +d ι +p ι ,ι=u,v,r; S23: Define the prediction error of underactuated ASV as... and And based on the prediction error of underactuated ASV, Construct a state prediction model, the expression of which is: In the formula: b u ,b v and b r Indicate design parameters; as well as Indicates the output state of the prediction model; The state prediction error of the underactuated ASV is obtained according to equations (4) and (6), and its expression is as follows:

4. The method for adaptive fuzzy preset performance control of underactuated ASV dynamic event triggering under network attack as described in claim 3, characterized in that, S3 specifically includes the following steps: S31: Define the virtual reference path for the navigator, and obtain the relative distance d and relative azimuth angle φ with respect to the followers based on the virtual reference path. In the formula: x l ,y l x and y represent the x and y coordinates of the virtual reference path, respectively; θ represents the intermediate parameter used to obtain the relative azimuth angle; φ represents the relative azimuth angle. Based on the relative distance and relative azimuth, constraints are obtained to ensure connectivity and meet collision avoidance requirements; their expressions are as follows: In the formula: d min d represents the minimum relative distance. max The maximum value of the relative distance d min ,d max >0; This represents the upper bound of the relative azimuth angle, and S32: Define the error between relative distance and relative azimuth angle to obtain the ship tracking constraint, the expression of which is as follows: In the formula: ρ d Represents relative distance error; ρ φ Indicates relative azimuth error; d d φ represents the expected relative distance. d Indicates the desired relative azimuth angle; These represent the lower and upper bounds of the relative distance error, respectively. These represent the lower and upper bounds of the relative azimuth, respectively. S33: Constructing a tracking error ρ based on ship tracking constraints to ensure preset performance. k (k=d,φ), and ρ d =dd d ,ρ φ =φ-φ d And based on the tracking error ρ k Define the tracking error boundary function; And the expression for the tracking error boundary function is: r k =(ρ k,0 -r k,∞ )exp(-l k t)+r k,∞ In the formula: as well as All represent positive design constants; express The abbreviation of ρ k Represents ρ k (t) is a shorthand form; S34: Construct a performance control function z for maintaining the formation control of the follower and navigator based on the tracking error boundary function. k Its expression is 5. The method for adaptive fuzzy preset performance control of underactuated ASV dynamic event triggering under network attack as described in claim 4, characterized in that, The virtual control law for ship fuzzy preset performance constructed in S4 is as follows: In the formula: ζ u ,ζ v ,ζ r Denotes an intermediate variable and ζ u =γ1tanh(β1),ζ v =γ2tanh(β2),ζ r =γ3tanh(β3); γ u ,γ v and γ r The virtual control laws γ1, γ2, and γ3 represent the forward velocity, lateral velocity, and yaw rate, respectively; β1, β2, and β3 represent the auxiliary system variables, and... ω u ,ω v ,ω r Denotes an intermediate variable and ω u =z d π d cosφ,ω v =-z d π d sinφ,ω r =z φ π φ ; Represents intermediate variables and k = d, φ; d d Indicates the expected distance; Represented as design parameters and Represents an unknown parameter, and is derived from the ship's forward pilot velocity u. l The estimated value With lateral leader velocity v l The estimated value get; Representing unknown parameters The estimate.

6. The method for adaptive fuzzy preset performance control of underactuated ASV dynamic event triggering under network attack as described in claim 5, characterized in that, S5 specifically includes the following steps: S51: Based on the ship's fuzzy preset performance virtual control law, define the intermediate error variable z. ι ,ι=u,v,r, its expression is S52: Based on the intermediate error variable z ι Based on the state prediction error of the underactuated ASV, an adaptive law is constructed, the expression of which is: In the formula: express First derivative; Γ ι This indicates the design parameter, which is the threshold for switching between a preset fixed threshold and a dynamic event triggering mechanism; The basis functions of the fuzzy logic system; σ ι This indicates a dynamically adjustable threshold parameter.

7. The method for adaptive fuzzy preset performance control of underactuated ASV dynamic event triggering under network attack as described in claim 6, characterized in that, The switching dynamic event triggering mechanism built in S6 is as follows: In the formula: This represents the output of the controller to be designed, and for The abbreviation of ; t j ,t j+1 Indicates the time threshold parameter; e p (t) represents the error in switching the dynamic event triggering mechanism, and σ p (t) and η p (t) represents the dynamically adjustable threshold parameter for event triggering; Γ p This represents the threshold parameter that switches between a preset fixed threshold and a dynamic event triggering mechanism, and Γ p >C p C p Indicates the trigger interval and C p >σ p (t)·|q p (t)|+η p (t); q p (t) represents the actual input to the controller; The update law for the event-triggered dynamically adjustable threshold parameter is as follows: In the formula: and θ p All are design parameters; Based on the update law of the dynamically adjustable threshold parameter triggered by the event and the switching dynamic event triggering mechanism, the actual input of the controller is obtained, specifically: According to formula (18), we can obtain According to formula (19), we can obtain In the formula: η p (0) represents a positive integer; The error of switching dynamic event triggering mechanism can be rewritten according to formula (20) as follows: In the formula: α p1 ,α p2 Indicate the design parameters, and satisfy the following: Then, according to formula (21), the actual input of the controller is obtained as follows:

8. The method for adaptive fuzzy preset performance control of underactuated ASV dynamic event triggering under network attack as described in claim 7, characterized in that, The formation controller triggered by the switching dynamic event constructed in S7 has the following expression: In the formula: Indicates the output of the controller to be designed; τ u ,T u ,τ r ,T r Indicates intermediate variables; An N-type function representing an underdriven ASV; Represents the design parameters of the N-type function, and k p ,μ p Indicates design parameters; σ p (t) represents a dynamically adjustable threshold parameter and p = u,r.

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