Unperturbed cooperative dynamic positioning method for multiple unmanned surface vessels under deception attack with modeling of switching and multiple compensation

Abstract

The application discloses a kind of untroubled cooperative power positioning methods of multiple unmanned ship switching modeling and multiple compensation under deception attack, by constructing unmanned ship switching interval two type fuzzy system under deception attack, to ensure that due to the problem that part of unmanned ship cannot maintain communication with fleet because of limited communication ability or deception attack tampering neighbor ship data makes each subsystem unstable;By constructing the minimum chattering switching rule of unmanned ship communication topology, to ensure that the smooth transition of control signal in the process of communication topology switching to maintain the cooperative control between unmanned ship and the switching process;Construct distributed event triggering mechanism based on transition time, to obtain the control item of the control system of unmanned ship j to its cooperative controller and the event triggering time of neighbor unmanned ship j transmission data;By constructing multiple compensation, compensating the chattering of unmanned ship control signal within a period of time after communication limited induced topology switching, data updating and deception attack start / end, realize the smooth transition of control signal;By constructing the distributed untroubled switching performance index mechanism of the control input signal u i (t) of unmanned ship i, to obtain multiple unmanned ship cooperative control steady-state and transient performance criterion, to realize the untroubled cooperative power positioning of multiple unmanned ship under deception attack.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of cooperative positioning of unmanned ships, and particularly relates to a method for modeling and multiple compensation of multi-unmanned ship switching under deception attacks. BACKGROUND

[0002] In recent years, the development of unmanned technology is rapid, and unmanned ships have been widely concerned due to their autonomy, flexibility, small size and low cost, and have great potential in avoiding personnel casualties and performing extreme tasks. With the deepening of the understanding and research of unmanned ships, many scholars have found that due to the changes of water flow, wind power, load and other factors, the unmanned ship will show multi-modal characteristics, which makes the control problem of the unmanned ship more complex. Therefore, only a single model cannot accurately describe the dynamic behavior of the unmanned ship. The existing research models the multi-unmanned ship as a switching system with all subsystems stable according to the changes of the communication structure between the unmanned ships. However, on the one hand, due to the scarcity of communication resources in the marine environment, some unmanned ships may not communicate with other ships, making them unable to be effectively controlled; on the other hand, in the network environment, the communication link between the unmanned ships will inevitably encounter deception attacks, causing the unmanned ships to receive tampered neighbor ship state information and the communication topology to change, which will reduce the control effect of the unmanned ships and even seriously affect the performance of the system. The above situations will make the modeling of the unmanned ship as a switching system with each communication topology corresponding to an unstable subsystem. The switching system with all stable subsystems is difficult to describe the multi-unmanned ship model under such adverse communication conditions, and the switching modeling of the multi-unmanned ship under this condition still needs further research.

[0003] When the communication topology changes, the control signal of the USV will have a transient jump phenomenon due to the change of the connection between the ships. This transient jump phenomenon of the control signal is called chattering, which is an undesirable transient behavior. Severe signal chattering can seriously affect system performance, even induce system instability, and also cause mechanical damage or fatigue loading. The emergence and development of bumpless switching control provide new possibilities for improving the reliability and safety of the control system and improving the transient performance of the control system. In order to limit the mutation of the control signal, the control strategy is usually adopted to adjust or compensate the controller signal appropriately to make the control signal as smooth as possible during switching. In addition to the above chattering caused by switching behavior, in the networked structure, when the controller of the USV updates the data or encounters network attacks, the control signal will inevitably have chattering. Existing research proposes a multi-source bumpless switching performance definition to alleviate the chattering phenomenon of the control signal caused by multiple factors such as switching, event triggering, and deception attacks by limiting the amplitude of the control signal, but this will weaken the control effect to some extent, and even affect the system performance. Therefore, it is necessary to design a suitable bumpless switching control scheme for multiple USVs to suppress the control signal chattering caused by multiple factors such as changes in communication topology, controller data updates, and deception attacks.

[0004] Based on the above analysis, the existing USV cooperative dynamic positioning method has the following problems:

[0005] (1) Existing research models the USV as a switching system with stable subsystems according to the change of the communication topology. In fact, some USVs cannot always maintain communication with the fleet due to communication limitations, and the state information transmitted between USVs and the communication topology will be tampered with by attackers, which makes it impossible for the USV to achieve cooperative control, and thus after switching modeling of multiple USVs, each subsystem is unstable.

[0006] (2) Existing research on USV motion control focuses on steady-state performance. However, multiple causes such as changes in communication topology, controller data updates, and deception attacks will cause chattering of the control signal, which will increase the overshoot and affect the transient performance, and even affect the steady-state performance.

[0007] (3) The switching rule design of existing multiple USVs ensures the steady-state performance by constraining the dwell time of the communication topology. However, these switching rule designs do not consider the chattering caused by switching, and the selection of inappropriate switching time and switching mode will make the chattering of the control signal larger, thereby offsetting the effect of the bumpless switching strategy on chattering elimination, and unable to cooperate with the controller to achieve better chattering reduction effect.

[0008] (4) In the existing distributed event-triggered scheme for unmanned ships, there is no fixed lower bound for the interval between two adjacent triggers. The compensation mechanism after the trigger point needs to ensure the transition before the next trigger, which makes it difficult to design the transition time of the compensation mechanism. SUMMARY

[0009] The present application provides a method for modeling and multiple compensation of seamless cooperative dynamic positioning of multiple unmanned ships under spoofing attack to overcome the above technical problems.

[0010] To achieve the above purpose, the technical scheme of the present application is:

[0011] A method for modeling and multiple compensation of seamless cooperative dynamic positioning of multiple unmanned ships under spoofing attack, comprising the following steps:

[0012] S1: obtaining the control item of the distributed cooperative controller of the unmanned ship i under spoofing attack

[0013] and the control item of the distributed cooperative controller of the unmanned ship i under spoofing attack as the control input signal u i (t) of the unmanned ship i, to obtain a seamless cooperative dynamic positioning closed-loop system of multiple unmanned ships;

[0014] obtaining a two-type fuzzy system of the switching interval of the unmanned ship under spoofing attack according to the seamless cooperative dynamic positioning closed-loop system of multiple unmanned ships;

[0015] S2: constructing the minimum chattering switching rule of the communication topology of the unmanned ship according to the control item of the distributed cooperative controller , to select the communication switching time of the communication topology corresponding to the minimum chattering of the control signal, so as to ensure that the unmanned ship group maintains the cooperative control between the unmanned ships and the smooth transition of the control signal in the switching process through the communication topology switching under the condition of limited communication ability;

[0016] S3: according to the communication topology relationship determined by the minimum chattering switching rule, confirming the neighbor unmanned ship j in communication with the unmanned ship i, and constructing a distributed event-triggered mechanism based on transition time, to obtain the control item of the control system of the unmanned ship j to its cooperative controller and the event-triggered time of transmitting data with the neighbor unmanned ship j;

[0017] S4: based on the distributed event-triggered mechanism based on transition time, the minimum chattering switching rule and the control item of the distributed cooperative controller of the unmanned ship i under spoofing attack , a multiple compensation mechanism for compensating the control input signal u i (t) is constructed to reduce chattering;

[0018] S5: According to the multiple compensation mechanism, the switching interval bivalent fuzzy system of the unmanned ship under the deception attack is rewritten, and a disturbance-free cooperative dynamic positioning closed-loop optimization system is obtained;

[0019] S6: According to the disturbance-free cooperative dynamic positioning closed-loop optimization system, the control input signal u i (t) of the distributed disturbance-free switching performance index mechanism is obtained, so that the steady-state and transient performance criteria of the multi-unmanned ship cooperative control are obtained, and the disturbance-free cooperative dynamic positioning of the multi-unmanned ship under the deception attack is realized.

[0020] Beneficial effects: The present application provides a switching modeling and multiple compensation disturbance-free cooperative dynamic positioning method for multi-unmanned ship under deception attack, which builds a switching interval bivalent fuzzy system of unmanned ship under deception attack to ensure that the problem of instability of each subsystem caused by the communication ability limitation or the deception attack tampering with the neighbor ship data so that part of the unmanned ship cannot maintain communication with the fleet; By building the minimum chatter switching rule of the communication topology of the unmanned ship, it is ensured that the unmanned ship group can maintain the cooperative control between the unmanned ships and the smooth transition of the control signal in the switching process under the condition of limited communication ability; Based on the minimum chatter switching rule, the neighbor unmanned ship j in communication with the unmanned ship i is determined, and a distributed event triggered mechanism based on the transition time is constructed to obtain the control item of the control system of the unmanned ship j to its cooperative controller; the event triggered moment of transmitting data with the neighbor unmanned ship j; through the construction of multiple compensation, the chatter of the control signal of the unmanned ship is compensated within a period of time after the communication limited induced topology switching, data updating and deception attack start / end, and the smooth transition of the control signal is realized; through the disturbance-free cooperative dynamic positioning closed-loop optimization system constructed by the method, the control input signal u i of the unmanned ship i is created, and the distributed disturbance-free switching performance index mechanism of (t) is obtained, so that the steady-state and transient performance criteria of the multi-unmanned ship cooperative control are obtained, and the disturbance-free cooperative dynamic positioning of the multi-unmanned ship under the deception attack is realized. BRIEF DESCRIPTION OF DRAWINGS

[0021] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiment or prior art description will be briefly introduced below. Obviously, the drawings in the following description are some embodiments of the present application, and those skilled in the art can also obtain other drawings according to these drawings without creative labor.

[0022] Figure 1 The flowchart of the switching modeling and multiple compensation disturbance-free cooperative dynamic positioning method for multi-unmanned ship under deception attack of the present application;

[0023] Figure 2 The communication connection block diagram of the unmanned ship i in the present embodiment;

[0024] Figure 3 Fig. 2 is a switching topology diagram of multiple unmanned ships in the embodiment;

[0025] Figure 4 Fig. 3 is a position and heading angle error curve diagram of three unmanned ships under communication topology 1 in the embodiment;

[0026] Figure 5 Fig. 4 is a position and heading angle error curve diagram of three unmanned ships under communication topology 2 in the embodiment;

[0027] Figure 6 Fig. 5 is a position and heading angle error curve diagram of three unmanned ships under communication topology 3 in the embodiment;

[0028] Figure 7 Fig. 6 is a schematic diagram of the original switching signal σ(t) and the tampered switching signal σ'(t) in the embodiment; Fig. 7 is a schematic diagram of the original switching signal σ(t) and the tampered switching signal σ'(t) in the embodiment;

[0029] Figure 8 Fig. 8 is a trajectory curve diagram of the unmanned ship on the X-axis and Y-axis in the embodiment;

[0030] Figure 9 Fig. 9 is a position and heading angle error curve diagram of three unmanned ships in the embodiment;

[0031] Figure 10 Fig. 10 is a control signal comparison diagram of unmanned ship 1 in the embodiment;

[0032] Figure 11 Fig. 11 is a control signal comparison diagram of unmanned ship 2 in the embodiment;

[0033] Figure 12 Fig. 12 is a control signal comparison diagram of unmanned ship 3 in the embodiment. DETAILED DESCRIPTION

[0034] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some embodiments of the present application, but not all embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0035] The embodiment provides a disturbance-free cooperative dynamic positioning method for switching modeling and multiple compensation of multiple unmanned ships under a deception attack, as shown in Figures 1-2 Fig. 1, which includes the following steps:

[0036] S1: According to the kinematic and dynamic nonlinear model of unmanned ship and interval type-2 fuzzy rules, in the case of communication restriction and communication edge being attacked and tampered by deception attack, a switching fuzzy model of multi-unmanned ship cooperative dynamic positioning is established, and the control term of the distributed cooperative controller of unmanned ship i under deception attack is obtained

[0037] and the control term of the distributed cooperative controller is taken as the control input signal u of unmanned ship i i (t) to obtain a disturbance-free cooperative dynamic positioning closed-loop system of multi-unmanned ship;

[0038] According to the disturbance-free cooperative dynamic positioning closed-loop system of multi-unmanned ship, a switching interval type-2 fuzzy system of unmanned ship under deception attack is obtained

[0039] Specifically, as shown in Figure 3 , due to the limited communication ability of unmanned ship, some unmanned ships cannot always maintain communication with the unmanned ship formation, and cannot always maintain a fixed communication topology, and thus need to change the communication topology to realize the cooperative dynamic positioning of the ship group. Therefore, the communication topology switching signal is introduced to describe the situation that the communication topology needs to be changed to realize the cooperative dynamic positioning of the ship group due to the limited communication ability of the unmanned ship. For the cooperative dynamic positioning problem of N unmanned ships, the positioning point ship is taken as the 0th unmanned ship, and the mutual relationship between each unmanned ship is represented by a directed graph ; wherein represents the set of unmanned ships, the edge set of the directed graph is represented as and each edge (i,j) E σ(t) represents that the unmanned ship i can receive the information of the unmanned ship j; represents a non-negative weighted adjacency matrix, wherein if the unmanned ship i can receive the information of the unmanned ship j, otherwise it is assumed that the 0th unmanned ship does not accept any information from other unmanned ships, the neighbor set of the unmanned ship i is represented as and the extended Laplacian matrix associated with the directed graph is represented as

[0040]

[0041] wherein represents the adjacency relationship vector between the 0th unmanned ship and other unmanned ships, and represents the degree matrix, and represents the degree of the unmanned ship i, i.e. the number of edges triggered by the unmanned ship i; ​

[0042] Assuming a communication topology of multiple unmanned ships In a finite set is changed, i.e. denotes the Laplacian matrix, and denotes the number of candidate communication topologies;

[0043] S11: the dynamics model of the i-th unmanned ship, expressed as

[0044]

[0045] In the formula: and both represent the state of unmanned ship i; φ i (t), υ i (t) and r i (t) represent the surge speed, sway speed and yaw rate of unmanned ship i, respectively; and ψ i (t) represent the position horizontal coordinate, position vertical coordinate and yaw angle in the preset ship coordinate system, respectively; represents the external environmental disturbance caused by wind, wave and current; represents the control input of unmanned ship i; Ω i (ψ i (t)) represents the conversion matrix; M i represents the inertia matrix; D i both represent the damping coefficient matrix;

[0046]

[0047] where m i , x i,g and I i,z represent the mass, the center of gravity on the X-axis and the moment of inertia on the yaw of the i-th ship, is the added mass in the surge direction, and represent the added mass in the sway direction, is the added moment of inertia on the yaw, X i,φ , Y i,υ , Y i,r , N i,υ and N i,r are linear damping coefficients;

[0048] S12: according to the dynamics model of unmanned ship i, define the state vector ζ i (t) = col{η i (t), ν i ​(t)}, then formula (1) is rewritten as

[0049]

[0050] wherein: denotes an intermediate parameter variable; A i (t), B i denote system matrix and control matrix, respectively;

[0051] and

[0052] S13: The cooperative dynamic positioning of the unmanned ship group is achieved by designing appropriate control signals u i (t) so that the positions of the X-axis and Y-axis of the unmanned ship i (1) and the bow angle ψ i (t) can be kept within a small neighborhood of their desired values , i.e. wherein is the th positioning point, represents the reference state corresponding to the th positioning point, and denotes the formation vector of the unmanned ship i, denotes a predefined scalar;

[0053] An interval type-2 fuzzy method is adopted to obtain the interval type-2 fuzzy model of the unmanned ship i according to formula (2), i.e. the interval type-2 fuzzy method is used to process the nonlinear term Ω i (ψ i (t)) in the model (2) of the i th unmanned ship. In order to be general, it is assumed that the bow angle ψ i (t) changes within the interval [- (π / 6), (π / 6)], so that Π i1 (ψ i (t)) = sin (ψ i (t)) ∈ [-1 / 2, 1 / 2] and then the interval type-2 fuzzy form of the unmanned ship i in (2) is as follows:

[0054] The m th fuzzy rule of the unmanned ship i (2): if Π i1 (ψ i (t)) is an antecedent variable, and Π i2 (ψ i (t)) is an antecedent variable, then

[0055]

[0056] wherein m = 1, 2, 3, 4, with is the existing interval type-2 fuzzy set,

[0057]

[0058] denotes the system parameter matrix in the mth fuzzy rule);

[0059] The activation strength of the mth fuzzy rule is denoted as

[0060]

[0061] denotes the activation strength of the mth fuzzy rule;

[0062] The obtained interval type-2 fuzzy model of the unmanned ship i is expressed as

[0063]

[0064] In the formula: denotes the membership function of the unmanned ship i under the mth fuzzy rule, and

[0065] respectively denote the lower membership function and the upper membership function of the unmanned ship; all denote predefined nonlinear weight functions, and m denotes a counter parameter;

[0066] S14: In this embodiment, the influence of the communication network between multiple unmanned ships suffering from periodic deception attacks is considered, and is defined as and respectively denote the activation and sleep intervals of the deception attack;

[0067] wherein and respectively represent the start time and the end time of the κth attack;

[0068] denotes the attack period;

[0069] and respectively denote the activation and sleep time of the attack in a period, that is

[0070] Then, under the deception attack, the state information ζ j (t) received by the unmanned ship i from the edge (i, j) of the unmanned ship j is tampered as And the attacker tampers the connection of multiple unmanned ship communication links to change the switching signal of the unmanned ship and the Laplacian matrix for obtaining the communication topology;

[0071] The expression of the switching signal change of the unmanned ship is

[0072]

[0073] The connection of the corresponding edge (i, j) is changed to That is, the communication topology is changed to and the extended Laplacian matrix is

[0074]

[0075] In the formula: represents the non-negative weighted adjacency matrix under the deception attack; represents the degree matrix under the deception attack, and represents the adjacent relationship vector between the set 0 unmanned ship and other unmanned ships after being tampered by the attacker, and represents the change of the Laplacian matrix; represents the connection of the edge (i, j) under the deception attack; represents the degree of the unmanned ship i after being tampered by the deception attack, that is, the number of edges starting from the unmanned ship i after being tampered by the deception attack, and represents the Laplacian matrix of , and is the number of candidate communication topologies;

[0076] S15: The energy, frequency, and duration of the deception attack satisfy the following general assumptions:

[0077] Assumption 1 (attack energy): Under the deception attack, the attack function in the communication link (i, j) from the unmanned ship j to the unmanned ship i satisfies where G ij represents a given constant matrix; x i (t) represents the state vector of the unmanned ship i after formation transformation;

[0078] Assumption 2 (attack frequency): There is a lower bound parameter of the number of unmanned ship communication switching times and the residence time τ a satisfies where represents the number of times of deception attack occurring within the attack period interval ; and τ​a ≥0;

[0079] Under the general assumption of a deception attack, the control terms of the interval type-2 fuzzy distributed cooperative controller are obtained based on the interval type-2 fuzzy model of the unmanned vessel i. Designed for

[0080] The nth fuzzy rule for controller i: If Υ i1 (ψ i (t) is The premise variable, and Υ i2 (ψ i (t) is Given the premise variables, then

[0081]

[0082] in n = 1, 2, 3, 4, It is the first unmanned ship i i Next trigger time This is the most recent trigger time for the unmanned vessel j. Υ i1 (ψ i (t))=sin(ψ i (t)) and Υ i2 (ψ i (t))=cos(ψ i (t) is the premise variable. and It is an interval-type fuzzy set;

[0083] The activation strength of the nth fuzzy rule is expressed as:

[0084]

[0085] in These are the membership functions with upper and lower bounds, respectively. Upper and lower bound member functions for management;

[0086] The control terms of the obtained interval type II fuzzy distributed cooperative controller are... Its expression is

[0087]

[0088] In the formula: The lth term of unmanned vessel i i The next trigger moment; Indicates the most recent trigger time of unmanned vessel j, and This represents the control gain matrix of unmanned vessel i under the nth fuzzy rule; This represents the connection status of edge (i,j) under a deception attack; This represents the connectivity of the edge (i,0) under a spoofing attack; α(t) is the attack indicator function, taking the value 1 or 0, indicating whether the communication network is under a spoofing attack or not.

[0089] S16: Using the interval type-two fuzzy method, the control terms of the interval type-two fuzzy distributed collaborative controller obtained by formula (6) are... Rewritten as

[0090]

[0091] In the formula: Let represent the membership function of unmanned vessel i under the nth fuzzy rule, and

[0092] These represent control items. The lower bound membership function and the upper bound membership function; Both represent predefined nonlinear weighting functions, and Let i represent the formation vector of the unmanned vessel i; Let represent the formation vector of unmanned vessel j; Indicates the unmanned ship corresponds to the first Reference status of each positioning point;

[0093] S17: Define the measurement error of unmanned vessel i as...

[0094] The control term of formula (7) As the control input signal u of the unmanned vessel i i (t) is used to obtain the non-disruptive cooperative dynamic positioning system of multiple unmanned vessels, and its expression is:

[0095]

[0096] The state vector after introducing the unmanned vessel i formation transformation is: The uninterrupted cooperative dynamic positioning system for multiple unmanned vessels is then transformed into an uninterrupted cooperative dynamic positioning closed-loop system for multiple unmanned vessels, the expression of which is:

[0097]

[0098] in To suppress external environmental disturbances The impact on the cooperative dynamic positioning of unmanned vessels is addressed by introducing the controlled output of unmanned vessel i.

[0099] yi (t) = C i x i (t)

[0100] where y i (t) denotes the controlled output of the USV i; x i (t) denotes the state vector of the USV i after formation transformation; C i denotes a constant matrix with a set dimension; and

[0101] S18: Obtain the USV switching interval bimodal fuzzy system under deception attack according to the disturbance-free cooperative dynamic positioning closed-loop system of the multiple USVs, which is expressed as

[0102]

[0103] wherein x(t) denotes the set form of x i (t) and x(t) = col{x1(t), …, x N (t)}. denotes the membership function of the controller of the USV j under the nth fuzzy rule; denotes the time delay term A m denotes the intermediate matrix parameter, and ω(t) = col{ω1(t), …, ω N (t)}.

[0104] In this embodiment, the cooperative dynamic positioning problem of the original USV is further converted into the safety control problem of the switching interval bimodal fuzzy system (10) under deception attack. Due to the communication restriction, the switching rule σ(t) needs to be designed so that the communication topology changes, and the start / stop of the deception attack will also cause the communication topology to change. In order to distinguish the different causes of topology switching, the switching sequence caused by communication restriction and the switching sequence caused by attack start / stop are respectively denoted as and , and thus the total switching sequence of the communication topology of the multiple USVs is In addition, is divided into stable switching sequence and unstable switching sequence to depict the order of stable and unstable switching time;

[0105] S2: Obtain the control term of the distributed cooperative controller The magnitude of the jitter is used to construct the minimum jitter switching rule for the communication topology of the unmanned vessel, which is used to select the communication switching time corresponding to the communication topology with the minimum jitter of the control signal, so as to ensure that the unmanned vessel group can maintain the coordinated control between unmanned vessels and the smooth transition of control signals during the switching process through appropriate communication topology switching when the communication capability is limited.

[0106] Specifically, the constructed minimum jitter switching rule is as follows:

[0107] In the switching control of unmanned surface vessels, selecting inappropriate switching times and modes to be switched can cause more severe chattering. This is particularly relevant for communication topology switching sequences caused by communication limitations. Design the following minimum jitter switching rules:

[0108] That is, when the duration of the communication topology switch of unmanned vessel i during the k-th switch exceeds the minimum dwell time. Then the next switching time t of unmanned ship i k+1 The selected rule expression is

[0109]

[0110] And at the next switching time t k+1 The switching signal for the communication topology of multiple unmanned vessels is switched to σ(t). k+1 ), and σ(t) k+1 This is the candidate topology with the least jitter after the handover, so as to... Convert to The switching signal switches σ(t) k+1 The expression for ), is

[0111]

[0112] In the formula: Indicates the first The Kronecker product of the Laplace matrix and the 6th-order identity matrix corresponding to each candidate communication topology; θ n Let the diagonal matrix of membership functions of unmanned surface vessels 1 to N under the nth fuzzy rule be represented.

[0113] Defined as the total number of unstable switching points in the communication topology within the unmanned surface vessel's operating range [0, t). With stable switching point The total number satisfies:

[0114]

[0115] Where: N * Indicate design parameters;

[0116] Minimum residence time satisfies:

[0117]

[0118] wherein: denotes the minimum trigger interval of the unmanned ship i.

[0119] The minimum chattering switching rules (11) - (14) in this embodiment select a trigger point or attack end as the communication topology switching time caused by communication restriction, and switch to the communication topology that produces the minimum chattering. When the communication topology is switched at time t k , (11) selects the first trigger or attack end time that satisfies the minimum residence time condition as the next switching time t k+1 caused by communication restriction. By binding the switching time and the trigger or attack end time, the number of chattering occurrences can be reduced. At the switching time t k+1 caused by communication restriction, (12) selects the communication topology that produces the minimum chattering after switching;

[0120] S3: According to the communication topology relationship determined by the minimum chattering switching rule, the neighbor unmanned ship j communicating with the unmanned ship i is confirmed, and a distributed event trigger mechanism based on transition time is constructed to obtain the event trigger time of the control system of the unmanned ship j transmitting data to the neighbor unmanned ship j.

[0121] Specifically, the unmanned ship i (1) needs to transmit data to its remote controller u i (t) and the neighbor ship j, and leaves a smooth transition time for the compensation mechanism at the previous trigger point. Therefore, a distributed event trigger mechanism based on transition time needs to be designed in this embodiment to obtain the event trigger time of the control system of the unmanned ship j transmitting data to the neighbor unmanned ship j. The expression of the distributed event trigger mechanism based on transition time constructed is

[0122]

[0123] wherein: z i (t) denotes an intermediate variable, and

[0124]

[0125] δ i > 0 denotes a trigger threshold parameter; and denote the control item of the control system of the unmanned ship j to its collaborative controller, respectively. ​The minimum event-trigger interval and the maximum event-trigger interval of the event-trigger moment of transmitting data with the neighbor unmanned ship j, and The minimum residence time of the designed communication topology.

[0126] The distributed event-trigger mechanism (15) based on the transition time in this embodiment leaves a time length for the compensation mechanism at the previous trigger point to make a smooth transition. After each trigger, the inequality needs to be waited for before being continuously detected; in addition, since the lower bound of the adjacent two trigger intervals is Zeno phenomenon is excluded;

[0127] S4: According to the minimum chattering switching rule, the distributed event-trigger mechanism of the transition time, and the control item of the distributed collaborative controller of the unmanned ship i under the deception attack A multiple compensation mechanism is constructed to compensate the control input signal u i (t) to reduce chattering;

[0128] Specifically, in order to reduce the chattering of the distributed collaborative control item caused by the change of the communication topology, the data update of the trigger mechanism, and the deception attack, a multiple compensation mechanism needs to be designed: a multiple compensation mechanism is constructed to compensate the control input signal u i (t) to reduce chattering, which includes a switching compensation item an attack compensation item and a trigger compensation item

[0129] The switching compensation item At the switching time t k induced by the limited communication, if the chattering of the control input signal u i (t) of the unmanned ship i is caused by the change of the communication topology, then in section, the switching compensation item added to the control item of the distributed collaborative controller reduces the chattering of the control signal, and its expression is

[0130]

[0131] In the formula: represents the chattering value of the collaborative control item of the unmanned ship i at the switching time t k , and represents the value of the collaborative control item of the unmanned ship i at the moment after the switching time t k ; represents the chattering value of the collaborative control item of the unmanned ship i at the switching time t kthe value of the cooperative control term of the USV i at the instant after the attack start time;

[0132] denotes the attack compensation transition time and δ s (t) denotes the transition function of the attack compensation,

[0133] attack compensation term at the attack start / stop time of the USV i control input signal u i (t) is caused by the attack start / stop, then an attack compensation term is added to the control term of the distributed cooperative controller to reduce the control signal chattering, which is expressed as

[0134]

[0135] wherein: denotes the chattering value of the cooperative control term of the USV i at the instant after the attack start time denotes the value of the cooperative control term of the USV i at the instant before the attack start time denotes the chattering value of the cooperative control term of the USV i at the instant before the attack start time

[0136] denotes the attack compensation transition time and δ a (t) denotes the transition function of the attack compensation,

[0137]

[0138] trigger compensation term at the trigger time of the USV j and v denotes the number of USVs; the chattering of the USV i control input signal u i (t) is caused by the data update, then a trigger compensation term is added to the control term of the distributed cooperative controller to reduce the control signal chattering, which is expressed as

[0139]

[0140] wherein: denotes the chattering value of the USV j at the trigger time ​​​​​The data update affects the chattering value generated by the unmanned vessel's collaborative control term, and This indicates that the unmanned vessel's collaborative control item is in touch.

[0141] Release time The value at that instant; This indicates the trigger time of the unmanned vessel i-cooperative control term. The value at the previous instant; Indicates the trigger time The deceitfully attacked and tampered unmanned ship i and its neighboring unmanned ships The sum of the adjacency parameters, and Indicates the trigger time The deceitfully attacked and tampered unmanned ship i and its neighboring unmanned ships The adjacency relationship parameters; Indicates the trigger time The adjacency parameters between unmanned vessel i and unmanned vessel j after being deceived and altered by the attack; This represents the transition function that triggers compensation, and Indicates the time required to trigger the compensation transition;

[0142] Then based on the switching compensation item Attack Compensation Items and trigger compensation items Obtain total compensation

[0143] And the total compensation item Rewritten as:

[0144]

[0145] In the formula: This indicates the time t between unmanned vessel i and unmanned vessel 0. k The adjacency parameter value at the next instant; This indicates the time t between unmanned vessel i and unmanned vessel 0. k The adjacency parameter values ​​at the previous instant; Indicates that the unmanned vessel i is in t k The most recent time that was triggered before the current time. The state vector after the formation change at the location; This indicates the time t between unmanned surface vessel i and unmanned surface vessel j. k The adjacency parameter value at the next instant; This indicates the time t between unmanned surface vessel i and unmanned surface vessel j. k The adjacency parameter values ​​at the previous instant; Indicates that the unmanned ship j is in t kthe state vector of the formation transformation at the time instant the state vector of the formation transformation at the time instant denotes the switching time instant t k the attack function of the spoofing attack in the communication link (i, j) from the UAV j to the UAV i the product with the current attack indicator function a(t); denotes the adjacency parameter value of the UAV i and the UAV j at the attack start / stop time instant the adjacency parameter value of the UAV i and the UAV j at the attack start / stop time instant denotes the adjacency parameter value of the UAV i and the UAV j at the attack start / stop time instant the adjacency parameter value of the UAV i and the UAV j at the attack start / stop time instant denotes the state vector of the formation transformation at the time instant the state vector of the formation transformation at the time instant the state vector of the formation transformation at the time instant the state vector of the formation transformation at the time instant the state vector of the formation transformation at the time instant the state vector of the formation transformation at the time instant denotes the attack start / stop time instant denotes the normalized form of the adjacency parameter value of the UAV i and the UAV j without attack at the attack start / stop time instant denotes the attack start / stop time instant the attack function of the spoofing attack in the communication link (i, j) from the UAV j to the UAV i denotes the adjacency parameter value of the UAV i and the UAV j at the attack start / stop time instant the adjacency parameter value of the UAV i and the UAV j at the attack start / stop time instant the adjacency parameter value of the UAV i and the UAV j at the attack start / stop time instant the adjacency parameter value of the UAV i and the UAV j at the attack start / stop time instant denotes the attack start / stop time instant the sum of the adjacency parameter of the UAV i and the neighbor UAVs after the spoofing attack tampering at the attack start / stop time instant the sum of the adjacency parameter of the UAV i and the neighbor UAVs after the spoofing attack tampering at the attack start / stop time instant denotes the attack start / stop time instant the state vector of the formation transformation at the time instant denotes the attack start / stop time instant denotes the attack start / stop time instant k the attack start / stop time instant the attack start / stop time instant the attack start / stop time instant

[0146] The multiple compensation mechanisms in this embodiment respectively implement compensation on the control signal at the switching time induced by communication restriction, the attack start / stop time and the trigger site, to reduce chattering. At the switching time t k , the switching compensation term (16) offsets the distributed cooperative control term (7) The difference between t k and t T is then attenuated to 0 within τ i , and the control signal u i (t) smoothly transitions to At the attack start / stop time , the attack compensation term offsets The difference between t and t can also be completed before t At the trigger time , the trigger compensation term (18) offsets the difference between t and t , and the transition can also be completed before the next trigger; in order to enable the various compensation terms to cooperatively apply compensation and complete the transition before the next chattering occurs, the total compensation term is set as

[0147] S5: rewriting the two-type fuzzy system in the switching interval of the unmanned ship under the deception attack according to the multiple compensation mechanisms, to obtain a disturbance-free cooperative dynamic positioning closed-loop optimization system;

[0148] Specifically, the following steps are included:

[0149] S51: updating the control input signal u i (t) of the unmanned ship i according to the total compensation term

[0150]

[0151] S52: based on the input time delay method, expressing as a form with a time-varying time delay term wherein represents the time-varying time delay term, and

[0152] is updated to and represents the maximum residence time of the communication topology;

[0153] is updated to and wherein

[0154] then the updated control input signal u i (t) of the unmanned ship i (20) is N (t) = col{u1(t),…u

[0155]

[0156] wherein:

[0157]

[0158] S53: According to formula (21) and formula (10), the unmanned ship switching interval two-type fuzzy system under the deception attack is rewritten into a disturbance-free cooperative dynamic positioning closed-loop optimization system, and the expression is

[0159]

[0160] wherein: represents the simultaneous form of the formation transformed state vectors of the N unmanned ships at the respective triggering time , and represents the initial value function, that is, represents the simultaneous form of the formation transformed state vectors of the N unmanned ships at the respective triggering time k , and represents the initial value function, that is, represents the product of the attack function and the attack indication function a(t) in all communication links between the N unmanned ships . represents the simultaneous form of the formation transformed state vectors of the N unmanned ships at the respective triggering time , and represents the initial value function, that is, represents the simultaneous form of the formation transformed state vectors of the N unmanned ships at the respective triggering time , and represents the initial value function, that is, represents the total gain matrix of the 1~N unmanned ships in the communication topology after being tampered by the deception attack under the nth fuzzy rule, and represents the total gain matrix of the 0~N unmanned ships in the communication topology after being tampered by the deception attack under the nth fuzzy rule, and represents the switching time t​k the total gain matrix of 0-N unmanned ships under the n-th fuzzy rule before and after the communication topology is tampered by the deception attack, and denotes the switching time t k the total gain matrix of 0-N unmanned ships under the n-th fuzzy rule after the communication topology is tampered by the deception attack; denotes the switching time t k the total gain matrix of 0-N unmanned ships under the n-th fuzzy rule before the communication topology is tampered by the deception attack; denotes the switching time t k the total gain matrix of 1-N unmanned ships under the n-th fuzzy rule before and after the communication topology is tampered by the deception attack, and denotes the switching time t k the total gain matrix of 1-N unmanned ships under the n-th fuzzy rule after the communication topology is tampered by the deception attack; denotes the switching time t k the total gain matrix of 1-N unmanned ships under the n-th fuzzy rule before the communication topology is tampered by the deception attack; denotes a binary parameter; denotes an attack function in all communication links among N unmanned ships at the attack start / stop time ; C denotes a diagonal matrix composed of output matrices of N unmanned ships.

[0161] The embodiment further converts the original multi-unmanned ship disturbance-free cooperative dynamic positioning problem into three control tasks of the closed-loop switching system (22): 1) when ω(t)≠0, under the zero initial condition, that is, for a normal number γ, ω(t)∈L2[0,∞) and y(t) satisfies 2) when ω(t)≡0, the closed-loop switching system (23) is exponentially stable; and 3) the control signal u i (t) satisfies the distributed disturbance-free switching performance (23).

[0162] S6: According to the disturbance-free cooperative dynamic positioning closed-loop optimization system, a distributed disturbance-free switching performance index mechanism of the control input signal u i of the unmanned ship i is constructed to obtain a multi-unmanned ship cooperative control steady-state and transient performance criterion, and then the disturbance-free cooperative dynamic positioning of the multi-unmanned ship under the deception attack is realized.

[0163] Specifically, the communication topology change induced by the limited communication, the attack start / stop and the data update cause the distributed cooperative control item (7) chattering occurs. To design a smooth distributed cooperative controller, the definition of distributed chattering-free switching performance is given as follows. The control input signal u i of the USV i

[0164] For a given chattering-free performance index parameter and if the switching time t k induced by the communication restriction, the attack start / stop time the triggering time of the current USV i and the triggering time of the neighbor USV j all satisfy formula (23), it is confirmed that the control signal u i of the USV i k satisfies the distributed chattering-free switching performance.

[0165]

[0166] wherein: denotes the control signal of the USV i after any communication restriction-induced time; denotes the control signal of the USV i before any communication restriction-induced time;

[0167]

[0168]

[0169] The embodiment also includes step S7: giving a solvability criterion for ensuring the cooperative dynamic positioning performance and the distributed chattering-free switching performance:

[0170] (1) The solvability criterion for ensuring the cooperative dynamic positioning performance is given by Theorem 1 and Theorem 2:

[0171] To be general, it is assumed that the switching signal σ(t) is changed from mode q to mode p at time t k , the attacker tampers the switching signal to in the interval [t k , t k+1 ), the attacker tampers the switching signal to

[0172] Theorem 1: Given constant and matrix if there exists a scalar satisfying and there exists a positive definite matrix the matrix and the symmetric matrix such that

[0173]

[0174] is satisfied, then the closed-loop system (23) is exponentially stable and has H performance under the switching rule σ(t) of (13)-(16), and

[0175] ∞ where is composed of the matrix blocks

[0176]

[0177]

[0178] Proof: First, the control task 1) will be proved. Without loss of generality, assume and corresponding to the attack-sleep and activate modes α(t) = 0 and α(t) = 1, respectively, select the candidate Lyapunov function as follows:

[0179]

[0180] where

[0181]

[0182] Subsequently, the evolution of the Lyapunov function in the interval [t k k+1 ) will be analyzed. Differentiating along the trajectories of (23), we obtain

[0183]

[0184]

[0185] where According to (28) and Jensen's inequality, it can be concluded that

[0186]

[0187] where According to (30) and (31), it can be concluded that

[0188]

[0189] where

[0190] ​​

[0191] Since The following can be obtained

[0192]

[0193] Substituting (33) into (32), from (24) and (25), we have

[0194]

[0195] According to (26), we have The increasing relationship of Lyapunov function before and after t is as follows:

[0196]

[0197] From (34) and (35), we have the evolution of Lyapunov function in the switching interval [t k , t k+1 ] as follows:

[0198]

[0199] where and represent the length of attack dormancy and activation in the interval [t k , t k+1 ], respectively.

[0200] Next, we analyze the increasing relationship of Lyapunov function before and after the switching time t k induced by the communication restriction.

[0201] According to (27), we have

[0202]

[0203] From (36) and (37), we have the evolution relationship from t to t . By recursion, we have

[0204]

[0205] where From we have According to this inequality, we have where From (14), we have where Therefore, from (29), we have Thus According to (38), we have

[0206]

[0207] Multiplying both sides of (39) by we obtain

[0208]

[0209] Therefore, under zero initial conditions, V σ(0) (0) = 0,

[0210]

[0211] Integrating both sides of (41) from t = 0 to ∞ and changing the order of integration, we obtain

[0212]

[0213] Control task 1) is achieved.

[0214] Next, we prove control task 2). When ω(t)≡0, according to (39), we have

[0215]

[0216] From the positive definite matrix property in (30) and we can deduce that

[0217]

[0218] where Control task 2) is achieved. The proof is completed.

[0219] The matrix inequalities (24)-(25) are in a nonlinear form, so it is difficult to solve Theorem 1. In the following, we give a sufficient condition with solvability.

[0220] Theorem 2: Given constants and matrix if there exists a scalar satisfying and there exists a positive definite matrix matrix and symmetric matrix such that (11)-(14), (26)-(29) and the following linear matrix inequalities:

[0221]

[0222] hold, the closed-loop system (22) is exponentially stable and has H ∞ performance, where It consists of the following matrix blocks

[0223]

[0224] Proof: First, multiply the left and right sides of (43) and (44) by matrices respectively. and its transpose, in which

[0225]

[0226] We can obtain three matrix inequalities consisting of 15×15 matrix blocks. Then, we apply Schur's complement lemma and... It can be deduced that these three matrix inequalities are equivalent to (24) and (25), respectively. Therefore, (43) and (44) can ensure that (24) and (25) hold. According to Theorem 1, the control tasks 1) and 2) of the closed-loop system (23) are achieved.

[0227] (2) The solvability criterion for ensuring the performance of distributed, disturbance-free handover is given by Theorem 3:

[0228] Theorem 3: For unmanned ships If in distributed collaborative control items Add a switching compensation item Attack Compensation Items and trigger compensation items Then the control signal u of the unmanned surface vessel i i (t) satisfies the distributed, disturbance-free handover performance (23).

[0229] Proof: Based on the different causes of control signal chattering, we will discuss different cases below.

[0230] Scenario 1: When distributed collaborative control items exist When the jitter at a certain point is caused by the topology handover induced by the k-th communication constraint, i.e. Switch compensation item Activated, control signal u i (t) at t k Boom value at the location

[0231]

[0232] Satisfy the performance requirements of distributed, non-disruptive handover (23).

[0233] Scenario 2: When distributed collaborative control items exist The chattering at the first The start / end of the attack caused by, i.e. Attack Compensation Items Activated, control signal ui (t) at the chattering value

[0234]

[0235] The distributed seamless switching performance (23) is satisfied.

[0236] Case 3: When the distributed cooperative control term The chattering at is caused by the l i trigger of the own ship, that is The triggered compensation term is activated, and the control signal u i (t) at the chattering value

[0237]

[0238] The distributed seamless switching performance (23) is satisfied.

[0239] Case 4: When the distributed cooperative control term The chattering at is caused by the l j trigger of the neighbor ship j, that is The triggered compensation term is activated, and the control signal u i (t) at the chattering value

[0240]

[0241] The distributed seamless switching performance (23) is satisfied.

[0242] Therefore, at any communication-restricted induced switching time t k , the attack start / stop time The trigger time of the own ship and the trigger time of the neighbor ship j The distributed seamless switching performance (23) is satisfied, and the control objective 3) is completed.

[0243] Simulation verification of the embodiment

[0244] Table 1 Parameters of three unmanned ships

[0245]

[0246]

[0247] The simulation part considers an unmanned ship group containing three unmanned ships, that is The positioning point is taken as the 0th ship, and the communication topology set of the multi-unmanned ship group​​​ Figure 3 Three communication topologies of multi-unmanned surface vehicle (USV) groups are demonstrated. Parameters are set in simulation,

[0248] λ = 3.4, λ0= 0.2, λ1= 0.4, δ1= δ2= δ3= 0.1,

[0249] The minimum dwell time is chosen according to (14) The maximum dwell time is chosen according to (29) The period of deception attack τ a = 0.4 s, G ij = I. Compensate transition time The parameters of three USV models (1) are chosen as shown in Table 1. The upper and lower membership functions of the ith USV are as follows:

[0250]

[0251] The weighting coefficients are The desired two reference states are ζ 0,1 = col{3, 3, π / 6, 0, 0, 0}, ζ 0,2 = col{6, 6, 0, 0, 0, 0}, ζ 0,3 = col{9, 3, -π / 6, 0, 0, 0}.

[0252] The initial states of three USVs are

[0253]

[0254] The formation vector is

[0255]

[0256] Suppose the external environmental disturbance is

[0257]

[0258] Solving Theorem 2, the gain matrix of the distributed cooperative control term (7) is

[0259]

[0260]

[0261]

[0262] As Figures 4-12 The undisturbed cooperative dynamic positioning performance of three USVs under the method of the embodiment is demonstrated.

[0263] In this embodiment, a two-type fuzzy system for switching interval of unmanned ship under spoofing attack is constructed to ensure that the problem of instability of each subsystem caused by the communication ability limitation or spoofing attack tampering with the neighbor ship data to make part of the unmanned ship unable to maintain communication with the fleet; the minimum chattering switching rule of the communication topology of the unmanned ship is constructed to ensure that the unmanned ship group maintains the cooperative control between the unmanned ships and the smooth transition of the control signal in the switching process through the communication topology switching under the condition of limited communication ability; the neighbor unmanned ship j communicating with the unmanned ship i is determined based on the minimum chattering switching rule, and a distributed event-triggered mechanism based on the transition time is constructed to obtain the control item of the control system of the unmanned ship j to its cooperative controller The event-triggered moment of transmitting data with the neighbor unmanned ship j; through the construction of multiple compensation, the chattering of the control signal of the unmanned ship is compensated within a period of time after the communication limited induced topology switching, data updating and spoofing attack starts / ends, and the smooth transition of the control signal is realized; through the construction of the disturbance-free cooperative dynamic positioning closed-loop optimization system, the control input signal u i of the unmanned ship i is created, and the distributed disturbance-free switching performance index mechanism of (t) is constructed to obtain the steady-state and transient performance criterion of the multi-unmanned ship cooperative control, and then the disturbance-free cooperative dynamic positioning of the multi-unmanned ship under spoofing attack is realized.

[0264] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement to part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A jerk-free cooperative positioning method for modeling and multiple compensation of multi-unmanned ship switching under deception attack, characterized in that, The method comprises the following steps: S1: Constructing the control item of the distributed cooperative controller of the unmanned ship i under the deception attack and the control items of the distributed cooperative controller as control input signals u of the unmanned ships i i (t) to obtain a disturbance-free cooperative dynamic positioning closed-loop system of the unmanned ships According to the undisturbed cooperative dynamic positioning closed-loop system of multiple unmanned ships, an interval type-2 fuzzy system of the unmanned ship switching interval under a deception attack is obtained; S2: control item according to the distributed cooperative controller The minimum chattering switching rule of the unmanned ship communication topology is constructed, which is used to select the communication switching time of switching to the communication topology corresponding to the minimum chattering of the control signal, so as to ensure that the unmanned ship group maintains the cooperative control among the unmanned ships and the smooth transition of the control signal in the switching process through the communication topology switching under the condition of limited communication capability. S3: Confirm the neighbor unmanned ship j in communication with the unmanned ship i according to the communication topology relationship determined according to the minimum chattering switching rule, and construct a distributed event triggering mechanism based on the transition time to obtain the control item of the control system of the unmanned ship j to its collaborative controller Event triggering moment of data transmission with the neighbor unmanned ship j; S4: Control item of the distributed cooperative controller of the unmanned ship i based on the distributed event-triggered mechanism of transition time, the minimum chattering switching rule and the deception attack constructing a control input signal u i (t) a multiple compensation mechanism to reduce chattering S5: According to the multiple compensation mechanism, the interval type-2 fuzzy system of the unmanned ship switching interval under a deception attack is rewritten to obtain an undisturbed cooperative dynamic positioning closed-loop optimization system; S6: According to the undisturbed cooperative positioning closed-loop optimization system, the control input signal u of the unmanned ship i is constructed i (t) Distributed undisturbed switching performance index mechanism to obtain multi-unmanned ship cooperative control steady-state and transient performance criteria, and then realize the undisturbed cooperative positioning of multi-unmanned ship under deception attack.

2. The method of claim 1, wherein, The S1 specifically comprises the following steps: S11: The dynamic model of the unmanned ship i is obtained, and the expression is wherein: and both represent the state of the unmanned ship i; φ i (t), v i (t) and r i (t) represent the surge velocity, sway velocity and yaw rate of the unmanned ship i, respectively; and i (t) represent the position lateral coordinate, position longitudinal coordinate and yaw angle in the preset ship coordinate system, respectively; represents the external environmental disturbance caused by wind, wave and current; represents the control input of the unmanned ship i; Ω i (Ψ i (t)) represents a conversion matrix; M i represents an inertia matrix; D i both represent a damping coefficient matrix; S12: Define a state vector ζ according to the dynamic model of the unmanned ship i i (t) = col{η i (t), v i (t)}, then formula (1) is rewritten as wherein: denotes an intermediate parameter variable; A i (t), B i denote a system matrix and a control matrix, respectively; and S13: An interval type-2 fuzzy method is used to obtain the interval type-2 fuzzy model of the unmanned ship i according to formula (2), and the expression is wherein: denotes the membership function of the unmanned ship i under the mth fuzzy rule, and respectively denote the lower and upper membership functions of the unmanned ship; both denote predefined nonlinear weight functions, and denotes an intermediate parameter matrix, and denotes Ω i (Ψ i (t)) in short form, m denotes a counter parameter; S14: In the case that the communication network between multiple unmanned ships may suffer from periodic deception attack, define and respectively represent the deception attack activation and sleep interval for the κth time. wherein with respectively represent the start and end times of the kth attack. represents an attack period; with respectively represent the length of the attack's activation and dormancy within a cycle, i.e. Then under the deception attack, the unmanned ship i receives the state information ζ of the unmanned ship j from the edge (i, j) j (t) is tampered with And the attacker changes the switching signals of the unmanned ship by tampering with the connection of multiple unmanned ship communication links, and the Laplacian matrix for obtaining the communication topology The expression of the switching signal change of the unmanned ship is The corresponding edge (i,j) is connected if is changed to The communication topology is given by is changed to The Laplacian matrix is further extended to In the formula: denotes the non-negative weighted adjacency matrix under the deception attack; denotes the degree matrix under the deception attack, and denotes the set 0th unmanned ship and other unmanned ships between the adjacent relationship vectors after being tampered with by the attacker, and denotes the change of the Laplacian matrix; denotes the connection of the edge (i, j) under the deception attack; denotes the degree of the unmanned ship i after being tampered with by the deception attack, i.e., the number of edges from which the unmanned ship i departs after being tampered with by the deception attack; denotes the Laplacian matrix of S15: Hypothesis 1: attack function in the communication link (i,j) from unmanned ship j to unmanned ship i under deception attack satisfies where G ij represents a given constant matrix; x i (t) represents the state vector of unmanned ship i after formation transformation Assumption 2: There exists a lower bound parameter θ for the number of communication handovers of the unmanned ship a with the residence time τ a satisfying where denotes the number of deceptive attacks occurring within the attack period interval θ a ≥ 0, τ a ≥ 0; Then, the control term of the interval type-2 fuzzy distributed cooperative controller is obtained according to the interval type-2 fuzzy model of the unmanned ship i The expression is In the formula: represents the lth trigger time of the unmanned ship i i ; represents the latest trigger time of the unmanned ship j, and represents the control gain matrix of the unmanned ship i under the nth fuzzy rule; represents the connection condition of the edge (i, j) under the deception attack; represents the connection condition of the edge (i, 0) under the deception attack; α(t) is an attack indicator function, that is, it represents whether the communication network is subjected to a deception attack or not, and S16: Using interval type-2 fuzzy method, the control term of the interval type-2 fuzzy distributed cooperative controller obtained by formula (6) is rewritten as is rewritten as wherein: denotes the membership function of the unmanned ship i under the nth fuzzy rule, and respectively denote the lower and upper membership functions of the control term both denote a predefined nonlinear weight function, and l i denotes the formation vector of the unmanned ship i; l j denotes the formation vector of the unmanned ship j; denotes the reference state of the unmanned ship corresponding to the th positioning point;​ S17: define the measurement error of the unmanned ship i as and the control term of formula (7) as the control input signal u i (t), to obtain a disturbance-free cooperative dynamic positioning system for multiple unmanned ships, which is expressed as The state vector of the formation transformation of the unmanned ship team is introduced as The undisturbed cooperative dynamic positioning system of the multi-unmanned ship is converted into an undisturbed cooperative dynamic positioning closed-loop system of the multi-unmanned ship, and the expression is y i (t) = C i x i (t) where: y i (t) denotes the controlled output of the unmanned ship i; C i denotes a constant matrix of the set dimension; S18: According to the undisturbed cooperative dynamic positioning closed-loop system of multiple unmanned ships, an interval type-2 fuzzy system of the unmanned ship switching interval under a deception attack is obtained; wherein: x(t) represents the set of x i (t) and x(t) = col{x1(t),..., x N (t)}. μnj(t) represents the membership function of the controller of the unmanned ship j under the nth fuzzy rule; A m represents the intermediate matrix parameter, and ω(t) = col{ω1(t),..., ω N (t)}. y(t) = col{y1(t),...,y N N}(t), B = diag{B1,...,BN} N}, C = diag{C1,...,CN} N}, 3. The method of claim 2, wherein, The minimum chatter switching rule constructed in S2 is specifically When the duration of the communication topology of the kth switching of the unmanned ship i exceeds the minimum residence time Then the next switching time t of the unmanned ship i k+1 The selected rule expression is and the next switching time t k+1 , the switching signal of the communication topology of the multi-unmanned ship is switched to σ(t k+1 ), and the is converted to The expression of the switching signal σ(t k+1 ) is In the formula: represents the Kronecker product of the Laplacian matrix corresponding to the candidate communication topology and the 6-order unit matrix; θ n represents a diagonal matrix composed of the membership functions of the unmanned ships 1 to N under the nth fuzzy rule, and Definition: the total number of unstable switching points of the communication topology in the running interval [0, t) of the unmanned ship with the stable switching points satisfies: wherein: N * denotes a design parameter; Minimum residence time Satisfies: In the formula: denotes the minimum triggering interval of the unmanned ship i.

4. The method of claim 3, wherein, The expression of the distributed event-triggered mechanism based on the transition time constructed in S3 is In the formula: z i (t) denotes an intermediate variable, and delta i > 0 represents a triggering threshold parameter; with respectively represent the control item of the control system of the unmanned ship j to its collaborative controller and the minimum and maximum event triggering intervals of the event triggering moment of the neighbor unmanned ship j transmitting data, and represent the minimum residence time of the designed communication topology.

5. The method of claim 4, wherein, the control input signal u constructed in S4 i (t) a multiple compensation mechanism for reducing chattering, the multiple compensation mechanism comprising a switching compensation term an attack compensation term and a trigger compensation term switching compensation term At the switching time t induced by the communication restriction k The chattering of the input signal u i (t) is caused by the change of the communication topology, then in The switching compensation term added to the control term of the distributed cooperative controller is In the formulae: denotes the chattering value of the cooperative control item of the unmanned ship i at the switching time t k , and denotes the value of the cooperative control item of the unmanned ship i at the instant after the switching time t k ; denotes the value of the cooperative control item of the unmanned ship i at the instant before the switching time t k ; denotes the switching compensation transition time and δ s (t) denotes a transition function of the switching compensation, and Attack compensation term At attack start / stop instants The chattering of the input signal u i (t) is caused by the attack start / stop, then at The attack compensation term added to the distributed cooperative controller's control term is wherein: represents the buffeting value of the cooperative control item of the unmanned ship i at the attack start / stop time point , and represents the value of the cooperative control item of the unmanned ship i at the moment after the attack start / stop time point ; represents the value of the cooperative control item of the unmanned ship i at the moment before the attack start / stop time point ; denotes the attack compensation transition time and δ a (t) denotes the attack compensation transition function, Triggered compensation term At the triggering time of the unmanned ship j And V represents the number of unmanned ships; the unmanned ship i controls the input signal u i If the chattering of (t) is caused by data updating, then during the time period The control term added to the distributed collaborative controller The triggered compensation term of is In the formula: represents the value of the cooperative control item of the unmanned ship i at the moment after the triggering time ; and represents the value of the cooperative control item of the unmanned ship i at the moment before the triggering time . represents the value of the cooperative control item of the unmanned ship i at the moment before the triggering time . represents the sum of the neighboring relationship parameters of the unmanned ship i and the neighboring unmanned ship after being tampered by the deception attack at the triggering time ; and represents the neighboring relationship parameters of the unmanned ship i and the neighboring unmanned ship after being tampered by the deception attack at the triggering time . represents the neighboring relationship parameters of the unmanned ship i and the unmanned ship j after being tampered by the deception attack at the triggering time . represents a transition function triggering compensation, and represents a transition time triggering compensation. then the switching compensation term attack compensation term and the trigger compensation term the total compensation term and the total compensation term is rewritten as: wherein: denotes the adjacency parameter value between unmanned ship i and unmanned ship 0 at the switching time t k before the instant; denotes the adjacency parameter value between unmanned ship i and unmanned ship 0 at the switching time t k after the instant; denotes the state vector of the formation after the transformation at the last triggering time before the time t k ; ; denotes the adjacency parameter value between unmanned ship i and unmanned ship j at the switching time t k after the instant; denotes the adjacency parameter value between unmanned ship i and unmanned ship j at the switching time t k before the instant; denotes the state vector of the formation after the transformation at the last triggering time before the time t k ; ; denotes the attack function of the deception attack in the communication link (i, j) from unmanned ship j to unmanned ship i at the switching time t k ; ; denotes the adjacency parameter value between unmanned ship i and unmanned ship j at the attack start / end time after the instant; denotes the adjacency parameter value between unmanned ship i and unmanned ship j at the attack start / end time before the instant; denotes the state vector of the formation after the transformation at the last triggering time before the time ; ; denotes the state vector of the formation after the transformation at the last triggering time before the time ; ; denotes the attack start / end time ; denotes the normalized form variable of the adjacency parameter value between unmanned ship i and unmanned ship j without attack at the attack start / end time ; denotes the attack function of the deception attack in the communication link (i, j) from unmanned ship j to unmanned ship i at the attack start / end time ; denotes the adjacency parameter value between unmanned ship i and unmanned ship 0 at the attack start / end time after the instant; denotes the adjacency parameter value between unmanned ship i and unmanned ship 0 at the attack start / end time before the instant; denotes the triggering time the neighbor unmanned ship i after being attacked by the deception attack tampering and the adjacency relationship parameter of the neighbor unmanned ship i; represent the state vector of the formation transformation of the unmanned ship j at the triggering time represent the start / end time of the latest attack; represent the latest triggering time of the unmanned ship i before the time t k represent the latest triggering time of the unmanned ship i before the time t ​​​ 6. The method of claim 5, wherein, The S5 specifically comprises the following steps: S51: determining the total compensation term based on the total compensation term updating the control input signal u of the unmanned ship i i (t) is S52: Based on the input time-delay method, the is expressed in the form of a time-varying time delay term wherein denotes the time-varying time delay term, and then is updated to and denotes the communication topology maximum residence time; is updated to and wherein The control input signal u of the updated unmanned ship i is then i (t) is rewritten as the control signal u(t) = col{u1(t), = u N (t)} of the multi-unmanned ship group, which is expressed as In the formula: S53: According to formula (21) and formula (10), the interval type-2 fuzzy system of the unmanned ship switching interval under a deception attack is rewritten to an undisturbed cooperative dynamic positioning closed-loop optimization system, and the expression is wherein: denotes the simultaneous form of the state vectors of the formation transformation of the N USVs at their respective triggering instants and denotes the initial value function, i.e. denotes the simultaneous form of the state vectors of the formation transformation of the N USVs at their respective triggering instants k and and denotes the initial value function, i.e. denotes the attack function in all the communication links between the N USVs and the product of the attack indication function a(t); denotes the simultaneous form of the state vectors of the formation transformation of the N USVs at their respective triggering instants and denotes the initial value function, i.e. denotes the simultaneous form of the state vectors of the formation transformation of the N USVs at their respective triggering instants and denotes the initial value function, i.e. denotes the total gain matrix of the 1~N USVs under the n-th fuzzy rule in the communication topology after being tampered by the deception attack, and denotes the total gain matrix of the 0~N USVs under the n-th fuzzy rule in the communication topology after being tampered by the deception attack, and denotes the chattering of the total gain matrix of the 0~N USVs under the n-th fuzzy rule in the communication topology after being tampered by the deception attack before and after the switching instant t k , and denotes the total gain matrix of the 0~N USVs under the n-th fuzzy rule in the communication topology after being tampered by the deception attack after the switching instant t k , and denotes the total gain matrix of the 0~N USVs under the n-th fuzzy rule in the communication topology after being tampered by the deception attack before the switching instant t k , and denotes the chattering of the total gain matrix of the 1~N USVs under the n-th fuzzy rule in the communication topology after being tampered by the deception attack before and after the switching instant t k , and denotes the total gain matrix of the 1~N USVs under the n-th fuzzy rule in the communication topology after being tampered by the deception attack after the switching instant t k total gain matrix of 1~N USVs under the n-th fuzzy rule in the communication topology after being tampered by the deception attack at the moment; denotes the switching time t k total gain matrix of 1~N USVs under the n-th fuzzy rule in the communication topology before being tampered by the deception attack at the moment; denotes the binary parameter; denotes the attack function in all communication links among N USVs at the attack start / stop time ; C denotes a diagonal matrix composed of the output matrix of N USVs.

7. The method of claim 6, wherein, The control input signal u of the unmanned ship i described in S6 i The distributed disturbance-free switching performance index mechanism for (t) is for a given disturbance performance index parameter and If formula (23) is satisfied, the control signal u i (t) satisfies the distributed disturbance-free switching performance; wherein: represents the control signal of the unmanned ship i at the time after the arbitrary communication-restricted inducing time; represents the control signal of the unmanned ship i at the time before the arbitrary communication-restricted inducing time; represents the control signal of the unmanned ship i at the time after the arbitrary communication-restricted inducing time; represents the control signal of the unmanned ship i at the time before the arbitrary communication-restricted inducing time; represents the triple time parameter of the arbitrary communication-restricted inducing time; and

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