Under-actuated ASV dynamic event triggering adaptive fuzzy preset performance control method under network attack

Abstract

The invention discloses an adaptive fuzzy preset performance control method triggered by an under-actuated ASV dynamic event under a network attack. The method comprises the following steps: constructing an under-actuated ASV model containing model uncertainty items under the network attack; constructing an adaptive fuzzy observer according to the under-actuated ASV model to obtain a state prediction model, and obtaining a state prediction error of the under-actuated ASV according to the state prediction model; constructing a performance control function for keeping formation control of followers and pilots; constructing a ship fuzzy preset performance virtual control law according to the performance control function; according to the ship fuzzy preset performance virtual control law and the state prediction error of the under-actuated ASV, constructing an adaptive law; constructing a switching dynamic event triggering mechanism to obtain the actual input of the controller; and based on the switching dynamic event triggering mechanism and the adaptive law, constructing a formation controller triggered by the switching dynamic event according to a pre-designed N-type function. The problems that in an existing ASV trajectory tracking task, system signals are maliciously changed through information spoofing attacks, system communication resources are limited, specified performance indexes need to be achieved, disturbance of an external marine environment, underactuation of an autonomous water surface vehicle, an uncertain nonlinear model and the like are solved. And the ASV path tracking robustness is reduced, and even the whole system is unstable.

Description

Technical Field

[0001] The present invention relates to the field of marine engineering technology, and in particular to a method for controlling an underactuated ASV dynamic event-triggered adaptive fuzzy preset performance under a network attack. Background Art

[0002] ASV is an intelligent surface platform that can navigate autonomously and complete a series of tasks. It has strong autonomous capabilities, a wide range of activities, reliable safety performance and low operating costs. It is widely used in scientific research, seawater detection and maritime reconnaissance and search, and has broad application prospects. With the increasing frequency of human economic activities in the ocean and the continuous progress of marine engineering, ASV plays an increasingly important role in water detection, marine scientific research, marine military and other fields.

[0003] To complete the ASV path tracking task, the key is to realize the guidance algorithm and control algorithm of the autonomous navigation part, so that the ASV can finally reach the destination along the specified route. Today's mainstream guidance technologies include algorithms based on forward line of sight method, virtual guidance method, artificial potential field method, etc. These technologies require real-time calculation of reference signals, and the calculation results will be transmitted to the control system in real time and synchronously to drive the ASV to navigate towards the reference position. In order to reduce the problem of excessive communication load caused by continuous transmission of control commands, event triggering technology is widely used in the path tracking control field of ASV, which has a good effect in processing communication load. These event triggering technologies mainly include static event triggering and dynamic event triggering. Dynamic event triggering technology has dynamically adjustable trigger threshold parameters, which can save more communication resources. It is worth noting that high-precision control systems may jump during operation, resulting in frequent triggering of actuators and nonlinear switching dynamic event triggering. However, the trigger threshold still requires artificially designed parameters, which is difficult for ship operators. In addition, event triggering technology will reduce the control accuracy of ASV, and how to balance the relationship between communication load and control accuracy is still a difficulty.

[0004] While the ASV intelligent control theory system is developing rapidly, there are still some challenges in the research of trajectory tracking tasks because the control systems of unmanned ships have the network interconnection characteristics of general information-physical systems. For example, information deception attacks maliciously change system signals, limited system communication resources, the need to meet specified performance indicators, disturbances in the external ocean environment, under-actuation of autonomous surface vehicles, and uncertain nonlinear models. These problems may reduce the robustness of ASV path tracking and even cause instability of the entire system.

[0005] In practice, on the one hand, ASVs will inevitably encounter various interferences when working in the ocean, and it is necessary to obtain the state information of ASVs in real time, while traditional shipborne equipment can only measure the position and attitude information of ASVs. A good control method is to use a high-gain observer to obtain unmeasurable speed information, and use an adaptive fixed-time extended state observer to simultaneously approximate the unknown state and model of ASVs in a fixed time. However, both methods usually have overshoot, which may lead to poor transient observation performance. However, since most surface vehicles are underactuated, that is, the motion in multiple degrees of freedom is driven by less control input, and underactuated ASVs have a complex cascade structure, the above methods cannot be directly applied to the trajectory tracking task of ASVs. In controller design, the selection of control structure and the stable operation of the entire system need to consider uncontrollable dynamic stability and controllability constraints. How to overcome interference and make the system run stably while achieving the preset performance indicators is still an academic and engineering problem that needs to be improved. On the other hand, the navigation environment and control performance of ASVs are crucial considerations, especially when navigating in narrow and crowded waterways. In this case, traditional unconstrained control schemes may greatly increase the risk of collision. In addition, under actual ocean conditions, the sensing and communication range of airborne sensors is often limited. How to achieve safe long-distance navigation under complex conditions is an issue that this application needs to consider. Summary of the invention

[0006] The present invention provides an adaptive fuzzy preset performance control method for under-actuated ASV dynamic event triggering under network attack to overcome the above technical problems.

[0007] In order to achieve the above object, the technical solution of the present invention is:

[0008] A method for controlling the performance of an underactuated ASV under a network attack under dynamic event triggering adaptive fuzzy preset performance includes the following steps:

[0009] S1: Establish 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] and obtaining a state prediction error of the under-actuated ASV according to the state prediction model;

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

[0013] S4: constructing a fuzzy preset performance virtual control law for the ship according to the performance control function;

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

[0015] S6: Construct a switching dynamic event trigger mechanism to avoid low utilization of control system communication resources due to frequent updates of actuators during controller operation, so as to obtain the actual input of the controller;

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

[0017] Furthermore, the assumptions for establishing the mathematical model of underactuated ASV in S1 are:

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

[0019] Assumption 2: Expected forward velocity u of the underactuated ASV l and the expected lateral velocity v l is bounded, that is in and Indicates u l With v l The upper bound of

[0020] Assumption 3: Network spoofing attacks can make the controller gain and becomes an unknown and non-zero constant. At the same time, in the actual ship navigation process, the actuator of the underactuated ASV has limited positive energy, that is, and Where Q u With Q r represents a positive design constant;

[0021] The underactuated ASV mathematical model containing model uncertainty terms under the network attack is constructed, and its expression is:

[0022]

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

[0024]

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

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

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

[0028] D r =-N v v |v|v |v|vN |r|v |r|vN r R |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∣ represents the hydrodynamic parameters; x, y, ψ represent the horizontal coordinate, vertical coordinate and yaw angle of the position in the earth coordinate system; u, v, r represent the forward speed, lateral speed and yaw angle speed; d u ,d v ,d r represents the external unknown disturbance of the under-actuated ASV; q u ,q r represents the control input provided by the thrusters and rudder; p u ,p v ,pr They represent the unknown interference caused by physical attacks on the hull and equipment respectively; represents the unknown gain acting on the controller caused by the network deception attack; m u ,m v ,m r represents the additional mass of the underactuated ASV along the forward, lateral and yaw degrees of freedom.

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

[0031] S21: The original values ​​of the position and velocity of the underactuated ASV are estimated as And define the uncertainty of underactuated ASV as

[0032]

[0033] Where: Y ι Represents the output of the fuzzy logic system; Represents the basis function of the fuzzy logic system; ε ι represents the estimation error;

[0034] Then define the position error and velocity error of the underactuated ASV;

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

[0036]

[0037] Where: They represent the position abscissa error, position ordinate error and heading angle error respectively;

[0038] The velocity error of the underactuated ASV is and

[0039] S22: Construct an adaptive fuzzy observer of the underactuated ASV according to the position error of the underactuated ASV, and its expression is:

[0040]

[0041] Where: κ x ,κ y ,κ ψ ,κ u ,κ v and κ r All represent design parameters; o u ,o v and r represents an intermediate variable and Represents Y ιThe estimated amount and ι=u,v,r;

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

[0043]

[0044] Where: Respectively The first derivative of q ι represents the intermediate parameter quantity, 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 the prediction error based on underactuated ASV is Construct a state prediction model, whose expression is

[0046]

[0047] Where: b u ,b v and b r represents the design parameters; as well as Represents the output status of the prediction model;

[0048] According to equations (4) and (6), the state prediction error of the under-actuated ASV is obtained, which is expressed as:

[0049]

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

[0051] S31: Define the virtual reference path of the leader, and obtain the relative distance d and relative azimuth φ with the follower according to the virtual reference path:

[0052]

[0053] Where: x l ,y l They represent the horizontal coordinate and vertical coordinate of the virtual reference path respectively; x, y represent the horizontal coordinate and vertical coordinate of the follower respectively; θ represents the intermediate parameter used to obtain the relative azimuth; φ represents the relative azimuth;

[0054] Based on the relative distance and relative azimuth, the constraint conditions for ensuring connectivity and meeting collision avoidance requirements are obtained, and the expression is:

[0055]

[0056] Where: d min Indicates the minimum value of relative distance, d max Indicates the maximum value of the relative distance d min ,d max >0; represents the upper limit of the relative azimuth, and

[0057] S32: Define the error of relative distance and relative azimuth to obtain the ship tracking constraint. The expression of the ship tracking constraint is:

[0058]

[0059] Where: d Represents the relative distance error; ρ φ Represents the relative azimuth error; d d represents the expected relative distance; φ d represents the expected relative azimuth; Respectively represent the lower and upper bounds of the relative distance error; Respectively represent the lower and upper bounds of the relative azimuth;

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

[0061] And the expression of the tracking error boundary function is

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

[0063]

[0064] Where: as well as All represent positive design constants; express The abbreviation of ρ k Represents ρ k (t) is an abbreviation of

[0065] S34: Constructing a performance control function z for maintaining formation control of the follower and the leader according to the tracking error boundary function k , whose expression is

[0066]

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

[0068]

[0069] Where: u ,ζ v ,ζ r represents an intermediate variable and ζ u =γ1tanh(β1),ζ v =γ2tanh(β2),ζ r =γ3tanh(β3);γ u ,γ v and γ r is the virtual control law representing the forward speed, lateral speed and yaw angular velocity; γ1, γ2 and γ3 represent the design parameters; β1, β2 and β3 represent the auxiliary system variables and ω u ,ω v ,ω r represents the 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 an intermediate variable and d d represents the expected distance; is represented as a design parameter and represents the unknown parameters, and is determined by the forward pilot speed u l Estimated value of With lateral leading speed v l Estimated value of get; Indicates unknown parameters Estimates.

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

[0071] S51: Define the intermediate error variable z according to the virtual control law of the ship's fuzzy preset performance ι ,ι=u,v,r, its expression is

[0072]

[0073] S52: According to the intermediate error variable z ι The adaptive law is constructed by combining the state prediction error of the under-actuated ASV with the expression:

[0074]

[0075] Where: express The first derivative of Γ ι represents the design parameter, i.e., the threshold for switching between a preset fixed threshold and a dynamic event trigger mechanism; represents the basis function of the fuzzy logic system; σ ι Represents a dynamically adjustable threshold parameter.

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

[0077]

[0078] Where: represents the output of the controller to be designed, and for The abbreviation of t j ,t j+1 represents the time threshold parameter; e p (t) represents the error of switching dynamic event trigger mechanism, and e p (t)= σ p (t) and η p (t) represents the event-triggered dynamically adjustable threshold parameter; Γ p represents the threshold parameter for switching between the preset fixed threshold and the dynamic event trigger 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 of the controller;

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

[0080]

[0081] Where: c p ,j p and θ p All are design parameters;

[0082] According to the update law of the event-triggered dynamically adjustable threshold parameters and the switching dynamic event triggering mechanism, the actual input of the controller is obtained. Specifically,

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

[0084]

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

[0086]

[0087] Where: η p (0) indicates a positive constant;

[0088] According to formula (20), the error of switching dynamic event trigger mechanism is rewritten as

[0089]

[0090] Where: α p1 ,α p2 represents the design parameters and satisfies

[0091] According to formula (21), the actual input of the controller is

[0092]

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

[0094]

[0095] Where: represents the output of the controller to be designed; τ u ,T u ,τ r ,T r represents an intermediate variable; N-type function representing underactuated ASV; represents the design parameters of the N-type function, and k p ,μ prepresents the design parameter; σ p (t) is represented as a dynamically adjustable threshold parameter and p=u,r.

[0096] Beneficial effect: The present invention provides a method for controlling the performance of an under-actuated ASV under a network attack under dynamic event triggering adaptive fuzzy preset.

[0097] First, while ensuring the preset performance, the present invention designs an N-type function to effectively reduce the impact of unknown actuator gain caused by deceptive attacks. Different from traditional control strategies, the present invention studies the preset performance control of underactuated ASV under network attacks, constructs a performance control function for maintaining the formation control of followers and leaders, and significantly improves the system's ability to resist deceptive attacks, thereby ensuring the safety of ASV when performing trajectory tracking tasks.

[0098] Second, based on fuzzy logic technology, an adaptive fuzzy observer is constructed according to the under-driven 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 approximating the uncertainty of the model, and the prediction error between the original system and the adaptive fuzzy observer is used as the input of the state prediction model, eliminating the peak phenomenon in the high-gain fuzzy observer.

[0099] Third, a switching dynamic event trigger mechanism is constructed that can effectively reduce the communication burden and save system communication resources. Compared with the time sampling mechanism, event trigger mechanism and dynamic event trigger mechanism, the switching dynamic event trigger mechanism constructed by the present invention can dynamically switch between the fixed threshold mechanism and the dynamic event trigger mechanism. By applying the switching dynamic event trigger mechanism, communication resources can be further saved even in the case of actuator jump. BRIEF DESCRIPTION OF THE DRAWINGS

[0100] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0101] Figure 1 It is a flow chart of the adaptive fuzzy preset performance control method of underactuated ASV dynamic event triggering under network attack of the present invention;

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

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

[0104] Figure 4 is the angle error diagram of this embodiment;

[0105] Figure 5 is the observation error of the adaptive fuzzy observer of this embodiment;

[0106] Figure 6 is the prediction error of the adaptive fuzzy observer of this embodiment;

[0107] Figure 7 is the adaptive parameter of this embodiment;

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

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

[0110] Fig.10 is the actual control input of this embodiment;

[0111] Fig.11 It is the time interval under the dynamic event triggering mechanism of this embodiment. DETAILED DESCRIPTION

[0112] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0113] This embodiment provides a method for controlling the performance of an under-actuated ASV under a network attack by triggering an adaptive fuzzy preset performance. Figure 1 As shown, the following steps are included:

[0114] S1: Establish 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 underactuated ASV ι With physical attack signal p ι is bounded, that is in and Indicates d ιWith p ι The upper bound of

[0117] Assumption 2: Expected forward velocity u of the underactuated ASV l and the expected lateral velocity v l is bounded, that is in and Indicates u l With v l The upper bound of

[0118] Assumption 3: Network spoofing attacks can make the controller gain and becomes an unknown and non-zero constant. At the same time, in the actual ship navigation process, the actuator of the underactuated ASV has limited positive energy, that is, and Where Q u With Q r represents a positive design constant;

[0119] The mathematical model of underactuated ASV under network attack with model uncertainty is constructed as follows:

[0120]

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

[0122]

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

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

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

[0126] D r =-N v v |v|v |v|vN |r|v |r|vNr R |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∣ represents the hydrodynamic parameters; x, y, ψ represent the horizontal coordinate, vertical coordinate and yaw angle of the position in the earth coordinate system; u, v, r represent the forward speed, lateral speed and yaw angle speed; d u ,d v ,d r represents the external unknown disturbance of the under-actuated ASV; q u ,q r represents the control input provided by the thrusters and rudder; p u ,p v ,p r They represent the unknown interference to the hull and equipment caused by physical attacks. Physical attacks refer to behaviors that directly cause damage or interference to the physical components of the ASV, mainly involving external collisions and similar interferences; represents the unknown gain acting on the controller caused by the network deception attack; m u ,m v ,m r represents the additional mass of the underactuated ASV along the 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] and obtaining a state prediction error of the under-actuated ASV according to the state prediction model;

[0130] That is, in this embodiment, the uncertainty part of the mathematical model of the underactuated ASV is approximated by the fuzzy logic system, and the uncertainty part of the mathematical model of the quality switching is approximated by the adaptive fuzzy control technology to obtain the estimated amount of the state information of the underactuated ASV.

[0131] Wherein, the fuzzy logic system is established as follows:

[0132] The fuzzy logic system approximates the uncertain terms in (2) through four main components: fuzzifier, defuzzifier and fuzzy inference engine. For a fuzzy logic system with N rules, the lth rule R l , (l=1,...,N) is defined as follows:

[0133] Rule R l : If x1 corresponds to Corresponds to Until x n Corresponds to Then the output y of the fuzzy logic system corresponds to G l ;

[0134] where x=[x1,x2,...,x n ] T represents the input of the fuzzy logic system; y represents the output of the fuzzy logic system; F i l represents a fuzzy set, i=1,...,n; G l Have their own membership functions With membership function

[0135] A fuzzy logic system can be described as:

[0136]

[0137] Where:

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

[0139]

[0140] By defining the fuzzy basis function vector and A fuzzy logic system can be described as: The above derivation process must satisfy the description of Lemma 1, and its specific contents are as follows: represents the membership function of 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] The specific steps include:

[0143] S21: The original values ​​of the position and velocity of the underactuated ASV are estimated as And define the uncertainty of underactuated ASV as

[0144]

[0145] Where: Y ι Represents the output of the fuzzy logic system; Represents the basis function of the fuzzy logic system; ε ι represents the estimation error;

[0146] Then define the position error and velocity error of the underactuated ASV;

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

[0148]

[0149] Where: They represent the position abscissa error, position ordinate error and heading angle error respectively; the speed error of the underactuated ASV is and

[0150] S22: Construct an adaptive fuzzy observer of the underactuated ASV according to the position error of the underactuated ASV, and its expression is:

[0151]

[0152]

[0153] Where: κ x ,κ y ,κ ψ ,κ u ,κ v and κ r All represent design parameters; o u ,o v and r represents an intermediate variable and

[0154] Represents Y ι The estimated amount and

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

[0156]

[0157] Where: Respectively The first derivative of q ι represents the intermediate parameter quantity, and qι =ε ι +d ι +p ι ,ι=u,v,r;

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

[0159]

[0160] Where: b u ,b v and b r represents the design parameters; as well as Represents the output status of the prediction model;

[0161] According to equations (4) and (6), the state prediction error of the under-actuated ASV is obtained, which is expressed as:

[0162]

[0163] This embodiment designs an adaptive fuzzy observer based on the mathematical model of the underactuated ASV, and extracts the low-frequency content in the model uncertainty and ocean disturbance through a given adaptive controller, and uses the obtained prediction error of the underactuated ASV for 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 for maintaining the formation control of the follower and leader;

[0165] Specifically, in this implementation, a certain aircraft in the formation is designated as the leader, and the other aircraft are its followers. The leader tracks a preset reference trajectory, and the followers track the leader at a certain interval distance and angle, thereby realizing the piloting and following formation control, so that the movement of the leader guides the entire formation behavior, which is easy to understand and execute, and when the leader is disturbed and perturbed, the formation can still be maintained. This process requires first defining the trajectory of the virtual aircraft and constructing a performance control function so that the trajectory converges to the reference trajectory of the follower, and then designing a position tracking controller so that the follower tracks the virtual ship, thereby realizing formation control;

[0166] The specific steps include:

[0167] S31: Define the virtual reference path of the leader, and obtain the relative distance d and relative azimuth φ with the follower according to the virtual reference path:

[0168]

[0169] θ=atan2(y l -y,x l -x) (8)

[0170] φ=θ-ψ

[0171] Where: x l ,y l They represent the horizontal coordinate and vertical coordinate of the virtual reference path respectively; x, y represent the horizontal coordinate and vertical coordinate of the follower respectively; θ represents the intermediate parameter used to obtain the relative azimuth; φ represents the relative azimuth;

[0172] Since the sensing range of the road sensor is limited, in order to ensure connectivity and meet the collision avoidance requirements, the constraint conditions for ensuring connectivity and meeting the collision avoidance requirements are obtained based on the relative distance and relative azimuth. The expression is:

[0173]

[0174] Where: d min Indicates the minimum value of relative distance, d max Indicates the maximum value of the relative distance d min ,d max >0; represents the upper limit of the relative azimuth, and where d min ,d max , It is determined by the nature of the sensor. Only when constraint (9) is satisfied can the follower detect the leader to ensure connectivity and avoid collision.

[0175] S32: Define the error of relative distance and relative azimuth to obtain the ship tracking constraint. The expression of the ship tracking constraint is:

[0176]

[0177] Where: d Represents the relative distance error; ρ φ Represents the relative azimuth error; d d represents the expected relative distance; φ d represents the expected relative azimuth; Respectively represent the lower and upper bounds of the relative distance error; Respectively represent the lower and upper bounds of the relative azimuth;

[0178] S33: Constructing the tracking error ρ based on the ship tracking constraint to ensure the preset performancek (k=d,φ), and ρ d =dd d ,ρ φ =φ-φ d , and according to the tracking error ρ k Define the tracking error boundary function;

[0179] Assumption 4: Tracking error ρ in this embodiment k The initial state satisfies constraint (10), namely and In order to ensure the preset performance tracking error ρ k (k=d,φ), it is necessary to define the tracking error boundary function:

[0180] And the expression of the tracking error boundary function is

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

[0182]

[0183] Where: as well as All represent positive design constants; express The abbreviation of ρ k Represents ρ k (t) is an abbreviation of

[0184] And by derivation of formula (11), we can get:

[0185]

[0186] According to the second assumption, the road sensor cannot directly measure the leading u l and v l speed; therefore, it is necessary to estimate and This embodiment defines The estimated error is Indicates unknown parameters The estimate, represents the upper bound of the unknown leader ship’s speed, k ξ represents the design parameters and satisfies the following adaptability law

[0187]

[0188] S34: To ensure the tracking error ρ k (k=d,φ) converges to the specified boundary (11), and the following specified performance control function is introduced to define the tracking error, that is, the performance control function z for maintaining the follower and leader formation control is constructed according to the tracking error boundary function: k , whose expression is

[0189]

[0190] And from formula (15) we can infer that z k →±∞ respectively correspond to ρ k →- ρ k and And z k = 0 corresponds to In this embodiment, (15) is differentiated to obtain:

[0191]

[0192] in:

[0193]

[0194] The selection of Lyapunov function in this embodiment is 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 ship fuzzy preset performance virtual control law according to the performance control function; the constructed ship fuzzy preset performance virtual control law is

[0199]

[0200] Where: u ,ζ v ,ζ r represents an intermediate variable and ζ u =γ1tanh(β1),ζ v =γ2tanh(β2),ζ r =γ3tanh(β3);γ u ,γ v and γ ris the virtual control law representing the forward speed, lateral speed and yaw angular velocity; γ1, γ2 and γ3 represent the design parameters; β1, β2 and β3 represent the auxiliary system variables and ω u ,ω v ,ω r represents the 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 an intermediate variable and

[0201] d d represents the expected distance; is represented as a design parameter and represents the unknown parameters, and is determined by the forward pilot speed u l Estimated value of With lateral leading speed v l Estimated value of get; Indicates unknown parameters estimates;

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

[0203] S51: Define the intermediate error variable z according to the virtual control law of the ship's fuzzy preset performance ι ,ι=u,v,r, its expression is

[0204]

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

[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, is a positive design parameter,

[0211] And by taking the derivative of (20), we can get:

[0212]

[0213] S52: According to the intermediate error variable z ι The adaptive law is constructed by combining the state prediction error of the under-actuated ASV with the expression:

[0214]

[0215] Where: express The first derivative of Γ ι represents the design parameter, i.e., the threshold for switching between a preset fixed threshold and a dynamic event trigger mechanism; represents the basis function of the fuzzy logic system; σ ι represents a dynamically adjustable threshold parameter;

[0216] S6: Construct a switching dynamic event trigger mechanism to avoid low utilization of control system communication resources due to frequent updates of actuators during controller operation, so as to obtain the actual input of the controller;

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

[0218] The switching dynamic event triggering mechanism is:

[0219]

[0220] Where: represents the output of the controller to be designed, and for The abbreviation of t j ,t j+1 represents the time threshold parameter; e p (t) represents the error of switching dynamic event trigger mechanism, and σ p (t) and ηp (t) represents the event-triggered dynamically adjustable threshold parameter; Γ p Indicates the threshold parameter for switching between the preset fixed threshold and the dynamic event trigger mechanism. To ensure effectiveness, Γ p Should be large enough, i.e., Γ p >C p ; C p Indicates the trigger interval and to avoid unnecessary resource waste caused by jumping, C p Should be greater than the trigger interval of the dynamic event trigger mechanism, that is, C p >σ p (t)·|q p (t)|+η p (t);q p (t) represents the actual input of the controller; in addition, in order to prevent the occurrence of Zeno 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 of the event-triggered dynamically adjustable threshold parameter is:

[0223]

[0224] Where: and θ p All are design parameters;

[0225] According to the update law of the event-triggered dynamically adjustable threshold parameters and the switching dynamic event triggering mechanism, the actual input of the controller is obtained. Specifically,

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

[0227]

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

[0229]

[0230] Where: η p (0) indicates a positive constant;

[0231] According to formula (29), the error of switching dynamic event trigger mechanism is rewritten as

[0232]

[0233] Where: αp1 ,α p2 represents the design parameters and satisfies

[0234] According to formula (30), the actual input of the controller is

[0235]

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

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

[0238] Definition 1: A continuous function If the following properties are met, it can be called an N-type function, and the properties are as follows:

[0239]

[0240] According to Definition 1, the N-type function has the characteristics of infinite gain and infinite switching frequency. There are several functions that meet these conditions, such as and In this embodiment, select as an N-type function with ζ as a variable;

[0241] Lemma 2: For any and s∈R can be derived:

[0242] in is a positive constant;

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

[0244]

[0245] Lemma 4: For the N-type function selected according to Definition 1, let V(t), and is defined in [0,t f ), and Then the following inequality holds:

[0246]

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

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

[0249]

[0250] Where: represents the output of the controller to be designed; τ u ,T u ,τ r ,T r represents an intermediate variable; N-type function representing underactuated ASV; represents the design parameters of the N-type function, and k p ,μ p represents the design parameter; σ p (t) is represented as a dynamically adjustable threshold parameter and p=u,r.

[0251] This embodiment also includes performing stability analysis by using a selected Lyapunov function, completing the proof that the controller in this embodiment will not have the Zeno phenomenon and obtaining relevant constraint conditions;

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

[0253] Consider the following Lyapunov candidate function:

[0254]

[0255] By taking the derivative of V2 according to equations (5) and (7), we can obtain:

[0256]

[0257] Choose the Lyapunov function as:

[0258]

[0259] Using the conditions of (24) to derive V3, we can obtain:

[0260]

[0261] Consider the following Lyapunov function V4:

[0262]

[0263] It can be obtained through (38):

[0264] ˉˉ

[0265]

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

[0267]

[0268] From formula (31), we can get:

[0269]

[0270] According to Lemma 3 and formula (32), we can infer:

[0271]

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

[0273]

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

[0275]

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

[0277]

[0278] Select V = V2 + V3 + V4, and combine equation (35), equation (37) and equation (45) to get its differential:

[0279] According to Lemma 4, this embodiment can be known:

[0280]

[0281] Among them, C1 and C2 are both positive numbers, satisfying the following formula:

[0282]

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

[0284]

[0285] Using Lemma 4, this embodiment can obtain is [0,t f ) is bounded. Therefore, the definition Formula (47) can be rewritten as:

[0286]

[0287] in, By integrating equation (49), this embodiment can infer:

[0288]

[0289] This embodiment can infer that when time tends to infinity, V(t) tends to It can be made arbitrarily small by choosing appropriate design parameters. Therefore, all signals in the closed-loop system are ultimately uniformly bounded. This example will prove that the controller does not exhibit the Zeno phenomenon, which means that t ★ > 0, so that the sampling interval {t j+1 -t j}≥t ＊ , for all j∈Z + .

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

[0291]

[0292] According to equations (41) and (42), this embodiment can derive is differentiable. The stability analysis performed earlier confirms that all signals in the system are bounded. Therefore, there exists a positive constant Make This means is bounded. It is important to note that e p (t j ) is equal to zero, and when t is close to t j+1 ,e p (t) tends to η p (t). Therefore, the sampling interval must satisfy t ＊ ≥η p (t) / p >0 to prevent Zeno behavior.

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

[0294] and

[0295] Therefore, applying the above results to (51), about |e p (t j )|=0 relative increment|e p (t)|In [t j ,t j+1 ) period, must meet the following requirements:

[0296]

[0297] This shows that:

[0298]

[0299] Therefore, the minimum inter-event interval is positive and is lower bounded to exclude the Zeno phenomenon. Finally, it is proved that the Zeno phenomenon of the switching dynamic event triggering mechanism is avoided.

[0300] In order to verify the superiority and effectiveness of the present invention, the effectiveness of the present invention is verified by numerical simulation examples in this embodiment. The specific implementation methods are as follows:

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

[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,Γ u =Γv =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 to be an effective way to address the inherent uncertainty in deception attacks, especially when information is scarce. By integrating random elements, it more accurately reflects the unpredictable and variable pattern characteristics of attacks.

[0308] The deception attack signal selection is:

[0309]

[0310] The external disturbance can be expressed as:

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

[0312] The parameter choices 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 initial speed of the leader is u l =3m / s,v l = 0m / s, and r L The following conditions are met:

[0318]

[0319] Define the initial condition of the leader as η l (0) = [0,0,0] T The initial condition of the follower is defined as η=[-7,-8,π / 6] T and ν=[0,0,0] T .

[0320] This embodiment is compared and analyzed with the algorithm in the prior art for adaptive output feedback trajectory tracking formation control based on finite time velocity observation, and mainly compares Figure 2-Figure 11 As shown. Figure 2 As shown, Figure 2 Trajectory tracking control planes for both algorithms. Figure 3 and Figure 4 It can be seen that compared with the algorithm of adaptive output feedback trajectory tracking formation control based on finite time velocity observation, the position and angle errors of the method of this embodiment are more stable. Figure 5 and Figure 6 The observation error and prediction error of the adaptive fuzzy observer are described, and it can be seen that the observer proposed in the present invention achieves higher accuracy. Figure 7 It can be seen that after a certain learning cycle, the norm of the adaptive parameter tends to be stable. Figure 8 The variation of the N-type function and its independent variables is shown. Fig. 9 Indicates the size and duration of the spoofing attack. Fig.10 The actual control input is shown. Fig.11 The time intervals under SDETM are shown.

[0321] In order to intuitively display the comparison effect and demonstrate the effectiveness of the method of this embodiment, this embodiment is compared and analyzed with the algorithm introduced in the adaptive output feedback trajectory tracking formation control based on finite time velocity observation. Although both methods follow the performance boundary, the method proposed in this embodiment has higher accuracy and minimal oscillation compared with the algorithm in the adaptive output feedback trajectory tracking formation control based on finite time velocity observation. In order to further verify the comparison results, this embodiment introduces commonly used performance indicators for quantitative analysis, including the mean absolute error and average absolute input control The mean absolute error reflects the stability performance of the control system, and the mean absolute input control is used to evaluate the energy consumption of the control system. The results of the performance indicators are shown in Table 1:

[0322] Table 1. Results of performance indicators

[0323]

[0324] Table 2 shows the comparison of the triggering frequencies between the switching dynamic event triggering mechanism of this embodiment, the adaptive neural output feedback control method based on composite learning, and the other two event triggering mechanisms of robust neural event triggering for unmanned surface vehicle network attack control based on nussbaus-type function. It can be seen that compared with the common event triggering mechanism 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] Combining the existing technology, guidance law construction, controller design and numerical simulation comparison, the overall beneficial effects of this embodiment compared with the existing technology are as follows:

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

[0329] Second, this embodiment takes advantage of the composite learning technology, and the proposed fuzzy logic system strikes a balance between ensuring the stability of the closed-loop system and approximating the uncertainty of the model. The prediction error between the original system and the estimation model is incorporated into the series-parallel estimation model, while eliminating the peak phenomenon in the high-gain observer.

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

[0331] That is, the present invention proposes a dynamic event-triggered adaptive fuzzy performance control method for underactuated ASV under network attack. The control method has two main characteristics:

[0332] Aiming at the trajectory tracking problem of underactuated ASV, a switching dynamic event-triggered adaptive fuzzy preset performance control algorithm is proposed. The algorithm improves the transient and steady-state performance of the system, and ensures the connectivity, collision avoidance and communication resource protection of the underactuated ASV in the network environment. The fuzzy logic system is used to approximate uncertainty, and an adaptive fuzzy observer is established. Based on the observer, a serial-parallel estimation model is constructed. The composite adaptive algorithm ensures the preset performance of the system while considering the observation accuracy problem.

[0333] In the backstepping framework, an N-type function is designed to mitigate the impact of unknown perturbation gain caused by spoofing attacks. In addition, a switching dynamic event triggering mechanism is developed to effectively save communication resources even under oscillating conditions. The effectiveness of the algorithm is verified by numerical simulation.

[0334] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements 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 controlling the performance of an underactuated ASV under a network attack under dynamic event triggering adaptive fuzzy preset performance, characterized in that: The following steps are involved: S1: Establish 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; and obtaining a state prediction error of the under-actuated ASV according to the state prediction model; S3: Define the ASV formation configuration of the leader and follower, and construct the performance control function for maintaining the formation control of the follower and leader; S4: constructing a fuzzy preset performance virtual control law for the ship according to the performance control function; S5: construct an adaptive law based on the virtual control law of the ship's fuzzy preset performance and the state prediction error of the underactuated ASV; S6: Construct a switching dynamic event trigger mechanism to avoid low utilization of control system communication resources due to frequent updates of actuators during controller operation, so as to obtain the actual input of the controller; S7: Based on the switching dynamic event triggering mechanism and the adaptive law, a formation controller for switching dynamic event triggering is constructed according to a pre-designed N-type function, and the control of the adaptive fuzzy preset performance of the under-actuated ASV dynamic event triggering under a network attack is realized according to the formation controller.

2. According to claim 1, a method for controlling the performance of an underactuated ASV under a network attack under dynamic event triggering adaptive fuzzy preset performance, characterized in that: The assumptions for establishing the mathematical model of underactuated ASV in S1 are: Assumption 1: External disturbance d of underactuated ASV ι With physical attack signal p ι is bounded, that is in and Indicates d ι With p ι The upper bound of Assumption 2: Expected forward velocity u of the underactuated ASV l and the expected lateral velocity v l is bounded, that is in and Indicates u l With v l The upper bound of Assumption 3: Network spoofing attacks can make the controller gain and becomes an unknown and non-zero constant. At the same time, in the actual ship navigation process, the actuator of the underactuated ASV has limited positive energy, that is, and Where Q u With Q r represents a positive design constant; The underactuated ASV mathematical model containing model uncertainty terms under the network attack is constructed, and its expression is: Where: μ u ,μ v ,μ r is an intermediate parameter variable, representing the uncertainty of the underactuated ASV, and D u ,D v ,D r is 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∣ represents the hydrodynamic parameters; x, y, ψ represent the horizontal coordinate, vertical coordinate and yaw angle of the position in the earth coordinate system; u, v, r represent the forward speed, lateral speed and yaw angle speed; d u ,d v ,d r represents the external unknown disturbance of the under-actuated ASV; q u ,q r represents the control input provided by the thrusters and rudder; p u ,p v ,p r They represent the unknown interference caused by physical attacks on the hull and equipment respectively; represents the unknown gain acting on the controller caused by the network deception attack; m u ,m v ,m r represents the additional mass of the underactuated ASV along the forward, lateral and yaw degrees of freedom.

3. The method for controlling the performance of an under-actuated ASV under a network attack under dynamic event triggering adaptive fuzzy preset performance according to claim 2, characterized in that: The S2 specifically includes the following steps: S21: The original values ​​of the position and velocity of the underactuated ASV are estimated as And define the uncertainty of underactuated ASV as Where: Y ι Represents the output of the fuzzy logic system; Represents the basis function of the fuzzy logic system; ε ι represents the estimation error; Then define the position error and velocity error of the underactuated ASV; The position error of the underactuated ASV is expressed as Where: They represent the position abscissa error, position ordinate error and heading angle error respectively; The velocity error of the underactuated ASV is and S22: Construct an adaptive fuzzy observer of the underactuated ASV according to the position error of the underactuated ASV, and its expression is: Where: κ x ,κ y ,κ ψ ,κ u ,κ v and κ r All represent design parameters; u ,o v and r represents an intermediate variable and Represents Y ι The estimated amount and Based on the speed error of the underactuated ASV, the adaptive fuzzy observer is rewritten according to equation (3) as Where: Respectively The first derivative of q ι represents the intermediate parameter quantity, and q ι =ε ι +d ι +p ι ,ι=u,v,r; S23: Define the prediction error of underactuated ASV as and And the prediction error based on underactuated ASV is Construct a state prediction model, whose expression is Where: b u ,b v and b r represents the design parameters; as well as Represents the output status of the prediction model; According to equations (4) and (6), the state prediction error of the under-actuated ASV is obtained, which is expressed as:

4. The method for controlling the performance of an underactuated ASV under a network attack under dynamic event triggering adaptive fuzzy preset performance according to claim 3, characterized in that: The S3 specifically includes the following steps: S31: Define the virtual reference path of the leader, and obtain the relative distance d and relative azimuth φ with the follower according to the virtual reference path: Where: x l ,y l They represent the horizontal coordinate and vertical coordinate of the virtual reference path respectively; x, y represent the horizontal coordinate and vertical coordinate of the follower respectively; θ represents the intermediate parameter used to obtain the relative azimuth; φ represents the relative azimuth; Based on the relative distance and relative azimuth, the constraint conditions for ensuring connectivity and meeting collision avoidance requirements are obtained, and the expression is: Where: d min Indicates the minimum value of the relative distance, d max Indicates the maximum value of the relative distance d min ,d max >0; represents the upper limit of the relative azimuth, and S32: Define the error of relative distance and relative azimuth to obtain the ship tracking constraint. The expression of the ship tracking constraint is: Where: d Represents the relative distance error; ρ φ Represents the relative azimuth error; d d represents the expected relative distance; φ d represents the expected relative azimuth; Respectively represent the lower and upper bounds of the relative distance error; Respectively represent the lower and upper bounds of the relative azimuth; S33: Constructing the tracking error ρ based on the ship tracking constraint to ensure the preset performance k (k=d,φ), and ρ d =dd d ,ρ φ =φ-φ d , and according to the tracking error ρ k Define the tracking error boundary function; And the expression of the tracking error boundary function is r k =(ρ k,0 -r k,∞ )exp(-l k t)+r k,∞ Where: as well as All represent positive design constants; express The abbreviation of ρ k Represents ρ k (t) is an abbreviation of S34: Constructing a performance control function z for maintaining formation control of the follower and the leader according to the tracking error boundary function k , whose expression is 5. The method for controlling the performance of an underactuated ASV under a network attack under dynamic event triggering adaptive fuzzy preset performance according to claim 4, characterized in that: The virtual control law of the ship fuzzy preset performance constructed in S4 is: Where: u ,ζ v ,ζ r represents an intermediate variable and ζ u =γ1tanh(β1),ζ v =γ2tanh(β2),ζ r =γ3tanh(β3);γ u ,γ v and γ r is the virtual control law representing the forward speed, lateral speed and yaw angular velocity; γ1, γ2 and γ3 represent the design parameters; β1, β2 and β3 represent the auxiliary system variables and ω u ,ω v ,ω r represents the intermediate variable and ω u =z d π d cosφ,ω v =-z d π d sinφ,ω r =z φ π φ ; represents an intermediate variable and k=d,φ;d d represents the expected distance; is represented as a design parameter and represents the unknown parameters, and is determined by the forward pilot speed u l Estimated value of With lateral leading speed v l Estimated value of get; Indicates unknown parameters Estimates.

6. The method for controlling the performance of an underactuated ASV under a network attack under dynamic event triggering adaptive fuzzy preset performance according to claim 5, characterized in that: The S5 specifically includes the following steps: S51: Define the intermediate error variable z according to the virtual control law of the ship's fuzzy preset performance ι ,ι=u,v,r, its expression is S52: According to the intermediate error variable z ι The adaptive law is constructed by combining the state prediction error of the under-actuated ASV with the expression: Where: express The first derivative of Γ ι represents the design parameter, i.e., the threshold for switching between a preset fixed threshold and a dynamic event trigger mechanism; represents the basis function of the fuzzy logic system; σ ι Represents a dynamically adjustable threshold parameter.

7. The method for controlling the performance of an underactuated ASV under a network attack under dynamic event triggering adaptive fuzzy preset performance according to claim 6, characterized in that: The switching dynamic event triggering mechanism constructed in S6 is: Where: represents the output of the controller to be designed, and for The abbreviation of t j ,t j+1 represents the time threshold parameter; e p (t) represents the error of switching dynamic event trigger mechanism, and σ p (t) and η p (t) represents the event-triggered dynamically adjustable threshold parameter; Γ p represents the threshold parameter for switching between the preset fixed threshold and the dynamic event trigger 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 of the controller; The update law of the event-triggered dynamically adjustable threshold parameter is: Where: and θ p All are design parameters; According to the update law of the event-triggered dynamically adjustable threshold parameters and the switching dynamic event triggering mechanism, the actual input of the controller is obtained. Specifically, According to formula (18), we can get According to formula (19), we can get Where: η p (0) indicates a positive constant; According to formula (20), the error of switching dynamic event trigger mechanism is rewritten as Where: α p1 ,α p2 represents the design parameters and satisfies According to formula (21), the actual input of the controller is 8. The method for controlling the performance of an underactuated ASV under a network attack under dynamic event triggering adaptive fuzzy preset performance according to claim 7, characterized in that: The formation controller triggered by the switching dynamic event constructed in S7 is expressed as follows: Where: represents the output of the controller to be designed; τ u ,T u ,τ r ,T r represents an intermediate variable; N-type function representing underactuated ASV; represents the design parameters of the N-type function, and k p ,μ p represents the design parameter; σ p (t) is represented as a dynamically adjustable threshold parameter and p=u,r.

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