Unmanned ship formation attack detection method based on distributed fuzzy set membership filtering

Abstract

The invention discloses an unmanned ship formation attack detection method based on distributed fuzzy set membership filtering. The method comprises the following steps: obtaining a state ellipsoid set of unmanned ships at a k moment; predicting the state of the unmanned ship by adopting set membership filtering to obtain a state prediction ellipsoid set of the unmanned ship at the k + 1 moment; performing intersection judgment on the state ellipsoid set of the unmanned ship at the k moment and the state prediction ellipsoid set of the unmanned ship at the k + 1 moment; updating the state prediction ellipsoid set of the unmanned ship at the k + 1 moment by adopting set membership filtering to obtain a state update ellipsoid set of the unmanned ship at the k + 1 moment; and performing intersection judgment on the state prediction ellipsoid set and the state updating ellipsoid set of the unmanned ship at the k + 1 moment. The method solves the problem that although multiple attack detection methods are applied to an unmanned ship system at present, the methods may not timely and comprehensively capture the changes when facing diversified attack means, resulting in missing detection or false alarm.

Description

Technical Field

[0001] The invention relates to the technical field of unmanned boat formation attack detection, and in particular to an unmanned boat formation attack detection method based on distributed fuzzy set membership filtering. Background Art

[0002] With the continuous development of science and technology, unmanned boats can explore and cruise in the water, and have been widely used in many fields such as military reconnaissance, environmental monitoring, marine resource exploration and rescue operations. Therefore, it is necessary to perform state estimation and attack detection on unmanned boats to determine whether the unmanned boats can perform tasks normally. At present, although a variety of attack detection methods have been applied to unmanned boat systems, most of these methods focus on a single component or level of the system, such as anomaly detection of sensor data alone, or security verification of control signals. This local detection strategy is powerless in the face of diverse attack methods, especially when the attacker adopts a strategy to change the attack target, such as changing from directly attacking the sensor to interfering with the communication link or tampering with the control command. The existing detection method may not be able to capture these changes in a timely and comprehensive manner, resulting in missed detection or false alarms, which in turn affects the safe operation of the unmanned boat. Summary of the invention

[0003] In view of the above-mentioned defects, the present invention proposes an unmanned boat formation attack detection method based on distributed fuzzy set membership filtering, aiming to solve the problem that although a variety of attack detection methods have been applied to unmanned boat systems, these methods may not be able to capture these changes in a timely and comprehensive manner when faced with diverse attack methods, resulting in missed detections or false alarms, which in turn affects the safe operation of the unmanned boat.

[0004] To achieve this object, the present invention adopts the following technical solutions:

[0005] A method for detecting an attack of an unmanned boat formation based on distributed fuzzy set membership filtering comprises the following steps:

[0006] Step S1: construct the kinematic and dynamic models of the unmanned boat;

[0007] Step S2: converting the kinematic and dynamic models of the unmanned boat into the state equation of the unmanned boat;

[0008] Step S3: linearize the nonlinear terms in the state equation of the unmanned boat using the TS fuzzy linearization method to obtain a linearized state equation of the unmanned boat;

[0009] Step S4: Obtain the state ellipsoid set of the unmanned boat at time k;

[0010] Step S5: according to the linearized state equation of the unmanned boat and the state ellipsoid set of the unmanned boat at time k, the state of the unmanned boat is predicted by using set membership filtering to obtain the state prediction ellipsoid set of the unmanned boat at time k+1;

[0011] Step S6: performing an intersection operation on the state ellipsoid set of the unmanned boat at time k and the state prediction ellipsoid set of the unmanned boat at time k+1 to obtain a first intersection, and determining whether the first intersection is an empty set. If so, it means that the unmanned boat is attacked, and the state prediction ellipsoid set of the unmanned boat at time k+1 is replaced; if not, it means that the unmanned boat is not attacked;

[0012] Step S7: using set membership filtering to update the state prediction ellipsoid set of the unmanned boat at time k+1, and obtaining the state update ellipsoid set of the unmanned boat at time k+1;

[0013] Step S8: Perform an intersection operation on the state prediction ellipsoid set of the unmanned boat at time k+1 and the state update ellipsoid set of the unmanned boat at time k+1 to obtain a second intersection, and determine whether the second intersection is an empty set. If not, it means that the unmanned boat is not attacked; if so, it means that the unmanned boat is attacked, and the state prediction ellipsoid set of the unmanned boat at time k+1 and the state update ellipsoid set are replaced.

[0014] Preferably, in step S1, the kinematic and dynamic models of the unmanned boat are expressed as:

[0015]

[0016] in, represents the position vector of the unmanned boat, x represents the lateral coordinate of the unmanned boat, t represents the longitudinal coordinate of the unmanned boat, Indicates the yaw angle of the unmanned boat; represents the first-order derivative of θ; μ = [w, v, r] T represents the state vector of the unmanned boat, w represents the longitudinal velocity of the unmanned boat, v represents the lateral velocity of the unmanned boat, and r represents the angular velocity of the unmanned boat; represents the first-order derivative of μ; ω represents the noise of the external environment; u represents the input of the controller; M represents the inertia matrix composed of the mass of the unmanned boat and the additional mass of the hull; represents the rotation matrix between the unmanned vehicle carrier coordinates and the earth coordinates; C(μ) represents the Coriolis centripetal force matrix; D(μ) represents the water surface damping matrix; M, C(μ) and D(μ) are expressed as:

[0017]

[0018] Among them, m x and m yRespectively represent the inertial parameters of the unmanned boat in the horizontal and vertical directions, which are obtained by subtracting the additional mass from its own weight; m r It represents the inertia parameter obtained by subtracting the additional mass in the direction of rotation from the moment of inertia; d x ,d y and d r They represent the hydrodynamic damping coefficients of the unmanned boat in the lateral, longitudinal and rotational directions respectively.

[0019] Preferably, in step S2, the kinematic and dynamic models of the unmanned boat are converted into the state equation of the unmanned boat, and the state equation of the unmanned boat includes the state equation of the leader unmanned boat and the state equation of the follower unmanned boat. The state equation of the leader unmanned boat is as follows:

[0020]

[0021] in, represents the system state of the leader unmanned boat at the kth moment; represents the nonlinear state matrix of the leader unmanned vehicle;

[0022] The state equation of the follower unmanned boat is as follows:

[0023]

[0024] Among them, i∈{1,...,N}, N represents the number of follower unmanned boats; x i,k represents the system state of the i-th follower unmanned boat at the k-th moment; y i,k represents the measurement value of the i-th follower unmanned boat at the k-th moment; a i,k represents the controller input of the i-th follower unmanned boat at the k-th time; b i,k represents the system noise of the i-th follower unmanned boat at time k; c i,k represents the measurement noise of the i-th follower unmanned boat at time k; B i 、E i and H i Both represent the system matrix of the i-th follower unmanned boat.

[0025] Preferably, in step S3, the TS fuzzy linearization method is specifically as follows:

[0026] RULE l i :IF yes yes yes THEN

[0027]

[0028] Among them, l i={1,...,d} represents the number of fuzzy rules, d represents the maximum number of fuzzy rules; It represents the antecedent variable in the fuzzy rule, that is, the nonlinear variable in the state equation of the unmanned boat; represents a fuzzy set, q represents the number of fuzzy sets; and All represent the system matrix after fuzzy linearization;

[0029] The linearized state equation of the unmanned boat is as follows:

[0030]

[0031] in, represents the normalized weight of each fuzzy rule; Δf i (x i,k ) represents the error after fuzzy linearization and satisfies the following formula:

[0032] Δf i (c i,k )=J i,k Δ i,k K i,k x i,k ;

[0033] Among them, J i,k and K i,k represents a known matrix; Δ i,k is unknown but bounded, and ||Δ i,k ||≤1.

[0034] Preferably, in step S4, the state ellipsoid set of the unmanned boat at time k is in, represents the state prediction value of the i-th follower unmanned boat at the kth moment, P i,k|k Represents the shape matrix of the ellipsoid set where the state at the kth moment is located.

[0035] Preferably, in step S5, the following sub-steps are specifically included:

[0036] Step S51: According to the TS fuzzy linearization method, the predicted value of the state of the i-th follower unmanned boat at the k+1 time is obtained, wherein the predicted value of the state of the i-th follower unmanned boat at the k+1 time is specifically as follows:

[0037]

[0038] in, represents the predicted value of the state of the i-th follower unmanned boat at time k+1; represents the predicted state value of the i-th follower unmanned boat at time k;

[0039] Step S52: Calculate the next prediction error of the set membership filter based on the predicted value of the state of the i-th follower unmanned boat at time k+1 and the linearized state equation of the unmanned boat and the error of the leader's unmanned boat

[0040] Step S53: Based on the state ellipsoid set of the unmanned boat at time k And the predicted value of the state of the i-th follower unmanned boat at time k+1 The first state prediction ellipsoid set is calculated using matrix inequality in, represents the shape matrix of the first state prediction ellipsoid set, which contains the predicted state information of the i-th follower unmanned boat at time k+1;

[0041] Step S54: Based on the error of the leader unmanned boat Define a state ellipsoid set as Among them, U i,k The shape matrix representing the ellipsoid set of this state;

[0042] Step S55: According to the state ellipsoid set And use the matrix inequality to calculate the second state prediction ellipsoid set Among them, the second state prediction ellipsoid set contains the predicted state information of the i-th follower unmanned boat at time k+1;

[0043] Step S56: Set the first state prediction ellipsoid set and the second state predicted ellipsoid set Perform intersection operation and calculate the minimum ellipsoid set containing the intersection of the two ellipsoid sets through the interior point algorithm of semidefinite programming That is, the state prediction ellipsoid set of the unmanned boat at time k+1.

[0044] Preferably, in step S7, the following sub-steps are specifically included:

[0045] Step S71: Update the state of the unmanned boat using the measurement value of the i-th follower unmanned boat at the k-th time in the state equation of the follower unmanned boat. The update equation is as follows:

[0046]

[0047] in, represents the state prediction value of the i-th follower unmanned boat at time k+1 obtained through data update; represents the predicted state value of the i-th follower unmanned boat at time k+1; represents the parameter matrix; y i,k+1 represents the measurement value of the i-th follower unmanned boat at the k+1th moment; represents the predicted value obtained by predicting the measured value of the i-th follower unmanned boat at the k+1th time;

[0048] Step S72: Calculate the update error according to the update equation and the linearized state equation of the unmanned boat

[0049] Step S73: Update the error e i,k+1|k+1 , define another state ellipsoid set as

[0050] Step S74: According to the state ellipsoid set The matrix inequality is used to calculate the state update ellipsoid set of the unmanned boat at time k+1

[0051] The technical solution provided by the embodiments of the present application may have the following beneficial effects:

[0052] In this scheme, the state of the unmanned boat is predicted and updated by using set membership filtering, and attack detection is performed after prediction and update. Specifically, whether the unmanned boat is attacked is determined by whether the intersection of the two ellipsoid sets is an empty set. This two-step attack detection method, which determines whether the unmanned boat is attacked based on whether the intersection of the two ellipsoids is an empty set, can timely and comprehensively capture these attacks in the face of diverse attacks, whether the unmanned boat's sensors, control inputs or other parts are attacked, and when the attacker adopts a strategy to change the attack target, thereby ensuring the normal operation of the unmanned boat. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 The present invention is a flowchart of the steps of an unmanned boat formation attack detection method based on distributed fuzzy set membership filtering. DETAILED DESCRIPTION

[0054] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals represent the same or similar elements or elements having the same or similar functions from beginning to end. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.

[0055] A method for detecting an attack of an unmanned boat formation based on distributed fuzzy set membership filtering comprises the following steps:

[0056] Step S1: construct the kinematic and dynamic models of the unmanned boat;

[0057] Step S2: converting the kinematic and dynamic models of the unmanned boat into the state equation of the unmanned boat;

[0058] Step S3: linearize the nonlinear terms in the state equation of the unmanned boat using the TS fuzzy linearization method to obtain a linearized state equation of the unmanned boat;

[0059] Step S4: Obtain the state ellipsoid set of the unmanned boat at time k;

[0060] Step S5: according to the linearized state equation of the unmanned boat and the state ellipsoid set of the unmanned boat at time k, the state of the unmanned boat is predicted by using set membership filtering to obtain the state prediction ellipsoid set of the unmanned boat at time k+1;

[0061] Step S6: performing an intersection operation on the state ellipsoid set of the unmanned boat at time k and the state prediction ellipsoid set of the unmanned boat at time k+1 to obtain a first intersection, and determining whether the first intersection is an empty set. If so, it means that the unmanned boat is attacked, and the state prediction ellipsoid set of the unmanned boat at time k+1 is replaced; if not, it means that the unmanned boat is not attacked;

[0062] Step S7: using set membership filtering to update the state prediction ellipsoid set of the unmanned boat at time k+1, and obtaining the state update ellipsoid set of the unmanned boat at time k+1;

[0063] Step S8: Perform an intersection operation on the state prediction ellipsoid set of the unmanned boat at time k+1 and the state update ellipsoid set of the unmanned boat at time k+1 to obtain a second intersection, and determine whether the second intersection is an empty set. If not, it means that the unmanned boat is not attacked; if so, it means that the unmanned boat is attacked, and the state prediction ellipsoid set of the unmanned boat at time k+1 and the state update ellipsoid set are replaced.

[0064] This scheme is a method for detecting unmanned boat formation attack based on distributed fuzzy set membership filtering. Figure 1As shown, the first step is to construct the kinematic and dynamic models of the unmanned boat. Specifically, by constructing the kinematic and dynamic models of the unmanned boat, it is beneficial to discretize the continuous system of the unmanned boat. The second step is to convert the kinematic and dynamic models of the unmanned boat into the state equation of the unmanned boat. Specifically, by converting the kinematic and dynamic models of the unmanned boat into the state equation of the unmanned boat, it is beneficial to subsequently linearize the nonlinear terms in the state equation of the unmanned boat. In this embodiment, for an unmanned boat formation of a leader-follower system, there is an unmanned boat in a leading position and coordinated to control the remaining unmanned boats to carry out target activities. Therefore, the state equation of the unmanned boat includes the state equation of the leader unmanned boat and the state equation of the follower unmanned boat. The third step is to linearize the nonlinear terms in the state equation of the unmanned boat using the TS fuzzy linearization method to obtain the linearized state equation of the unmanned boat. Specifically, the TS fuzzy linearization method is an existing linearization method. Since there are nonlinear terms in the state equation of the unmanned boat, this scheme uses the TS fuzzy linearization method to effectively process the nonlinear terms. The TS fuzzy linearization method has stronger robustness to noise and is easy to implement, with small calculation amount and easier to use. The fourth step is to obtain the state ellipsoid set of the unmanned boat at time k. In this embodiment, for the unmanned boat, its state such as position, speed and heading will be affected by various factors during the actual operation, such as water flow, wind and waves, and sensor noise, etc., which will introduce uncertainty. By obtaining the state ellipsoid set of the unmanned boat at time k, the state of the unmanned boat at time k and its uncertainty can be contained in an ellipsoid, so as to more comprehensively understand the current state of the unmanned boat. The fifth step is to use the set membership filter to predict the state of the unmanned boat based on the linearized state equation of the unmanned boat and the state ellipsoid set of the unmanned boat at time k, and obtain the state prediction ellipsoid set of the unmanned boat at time k+1. In this embodiment, since the unmanned boat formation will be disturbed by external noise when performing tasks on the water surface, and most of these external noises cannot obtain their statistical characteristics, this scheme uses set membership filtering to estimate the state of the unmanned boat. The estimation includes two steps. The first step of the estimation is to use the state ellipsoid set of the unmanned boat at time k to predict the state of the unmanned boat at time k+1. Set membership filtering is an algorithm for state estimation in an uncertain environment. The sixth step is to perform an intersection operation on the state ellipsoid set of the unmanned boat at time k and the state prediction ellipsoid set of the unmanned boat at time k+1 to obtain the first intersection, and determine whether the first intersection is an empty set. If so, it means that the unmanned boat is under attack, and the state prediction ellipsoid set of the unmanned boat at time k+1 is replaced; if not, it means that the unmanned boat is not under attack. In this embodiment, after predicting the state of the unmanned boat, an attack detection is required, specifically, by determining whether the intersection of the state ellipsoid set of the unmanned boat at time k and the state prediction ellipsoid set of the unmanned boat at time k+1 is an empty set to determine whether the unmanned boat is under attack.The seventh step is to use set membership filtering to update the state prediction ellipsoid set of the unmanned boat at time k+1, and obtain the state update ellipsoid set of the unmanned boat at time k+1. In this embodiment, the second step of estimation is to update the state prediction value of the unmanned boat at time k+1, so that the state prediction value can be more accurate. The eighth step is to perform an intersection operation on the state prediction ellipsoid set of the unmanned boat at time k+1 and the state update ellipsoid set of the unmanned boat at time k+1 to obtain a second intersection, and determine whether the second intersection is an empty set. If not, it means that the unmanned boat is not attacked; if so, it means that the unmanned boat is attacked, and the state prediction ellipsoid set of the unmanned boat at time k+1 is replaced with the state update ellipsoid set. In this embodiment, after the state prediction value of the unmanned boat is updated, an attack detection is also required. Specifically, it is determined whether the unmanned boat is attacked by determining whether the intersection of the state prediction ellipsoid set of the unmanned boat at time k+1 and the state update ellipsoid set of the unmanned boat at time k+1 is an empty set. It is further explained that when the unmanned boat is attacked, the state prediction ellipsoid set and the state update ellipsoid set obtained through the state estimation of the unmanned boat may deviate seriously. Therefore, it is necessary to replace the data of the state prediction ellipsoid set and the state update ellipsoid set that have deviated seriously at this time, so as to reduce the impact of the network attack on the subsequent state estimation of the unmanned boat, thereby ensuring the normal operation of the unmanned boat.

[0065] In this scheme, the state of the unmanned boat is predicted and updated by using set membership filtering, and attack detection is performed after prediction and update. Specifically, whether the unmanned boat is attacked is determined by whether the intersection of the two ellipsoid sets is an empty set. This two-step attack detection method, which determines whether the unmanned boat is attacked based on whether the intersection of the two ellipsoids is an empty set, can timely and comprehensively capture these attacks in the face of diverse attacks, whether the unmanned boat's sensors, control inputs or other parts are attacked, and when the attacker adopts a strategy to change the attack target, thereby ensuring the normal operation of the unmanned boat.

[0066] Preferably, in step S1, the kinematic and dynamic models of the unmanned boat are expressed as:

[0067]

[0068] in, represents the position vector of the unmanned boat, x represents the lateral coordinate of the unmanned boat, y represents the longitudinal coordinate of the unmanned boat, Indicates the yaw angle of the unmanned boat; represents the first-order derivative of θ; μ = [w, v, r] T represents the state vector of the unmanned boat, w represents the longitudinal velocity of the unmanned boat, v represents the lateral velocity of the unmanned boat, and r represents the angular velocity of the unmanned boat; represents the first-order derivative of μ; ω represents the noise of the external environment; u represents the input of the controller; M represents the inertia matrix composed of the mass of the unmanned boat and the additional mass of the hull; represents the rotation matrix between the unmanned vehicle carrier coordinates and the earth coordinates; C(μ) represents the Coriolis centripetal force matrix; D(μ) represents the water surface damping matrix; M, C(μ) and D(μ) are expressed as:

[0069]

[0070]

[0071] Among them, m x and m y Respectively represent the inertial parameters of the unmanned boat in the horizontal and vertical directions, which are obtained by subtracting the additional mass from its own weight; m r It represents the inertia parameter obtained by subtracting the additional mass in the direction of rotation from the moment of inertia; d x d y and d r They represent the hydrodynamic damping coefficients of the unmanned boat in the lateral, longitudinal and rotational directions respectively.

[0072] In this embodiment, by establishing the kinematic and dynamic models of the unmanned boat, it is beneficial to discretize the continuous system of the unmanned boat. The discrete system has the advantages of good stability, controllability and observability.

[0073] Preferably, in step S2, the kinematic and dynamic models of the unmanned boat are converted into the state equation of the unmanned boat, and the state equation of the unmanned boat includes the state equation of the leader unmanned boat and the state equation of the follower unmanned boat. The state equation of the leader unmanned boat is as follows:

[0074]

[0075] in, represents the system state of the leader unmanned boat at the kth moment; represents the nonlinear state matrix of the leader unmanned vehicle;

[0076] The state equation of the follower unmanned boat is as follows:

[0077]

[0078] Among them, i∈{1,...,N}, N represents the number of follower unmanned boats; x i,k represents the system state of the i-th follower unmanned boat at the k-th moment; y i,k represents the measurement value of the i-th follower unmanned boat at the k-th moment; a i,k represents the controller input of the i-th follower unmanned boat at the k-th time; bi,k represents the system noise of the i-th follower unmanned boat at time k; c i,k represents the measurement noise of the i-th follower unmanned boat at time k; B i 、E i and H i Both represent the system matrix of the i-th follower unmanned boat.

[0079] In this embodiment, by converting the kinematic and dynamic models of the unmanned boat into the state equations of the leader unmanned boat and the follower unmanned boat, it is beneficial to subsequently linearize the nonlinear terms in the state equations of the leader unmanned boat and the follower unmanned boat.

[0080] Preferably, in step S3, the TS fuzzy linearization method is specifically as follows:

[0081] RULEl i :IF yes yes yes THEN

[0082]

[0083] Among them, l i ={1,...,d} represents the number of fuzzy rules, d represents the maximum number of fuzzy rules; It represents the antecedent variable in the fuzzy rule, that is, the nonlinear variable in the state equation of the unmanned boat; represents a fuzzy set, q represents the number of fuzzy sets; and All represent the system matrix after fuzzy linearization;

[0084] The linearized state equation of the unmanned boat is as follows:

[0085]

[0086] in, represents the normalized weight of each fuzzy rule; Δf i (x i,k ) represents the error after fuzzy linearization and satisfies the following formula:

[0087] Δf i (x i,k )=J i,k Δ i,k K i,k x i,k ;

[0088] Among them, J i,kand K i,k represents a known matrix; Δ i,k is unknown but bounded, and ||Δ i,k ||≤1.

[0089] In this embodiment, the nonlinear terms in the state equation of the leader unmanned boat and the state equation of the follower unmanned boat are linearized by the TS fuzzy linearization method to make them close to the original linear equations.

[0090] Preferably, in step S4, the state ellipsoid set of the unmanned boat at time k is in, represents the state prediction value of the i-th follower unmanned boat at the kth moment, P i,k|k Represents the shape matrix of the ellipsoid set where the state at the kth moment is located.

[0091] In this embodiment, by obtaining the state ellipsoid set of the unmanned boat at time k, it is beneficial to perform attack detection in the subsequent state prediction stage.

[0092] Preferably, in step S5, the following sub-steps are specifically included:

[0093] Step S51: According to the TS fuzzy linearization method, the predicted value of the state of the i-th follower unmanned boat at the k+1 time is obtained, wherein the predicted value of the state of the i-th follower unmanned boat at the k+1 time is specifically as follows:

[0094]

[0095] in, represents the predicted value of the state of the i-th follower unmanned boat at time k+1; represents the predicted state value of the i-th follower unmanned boat at time k;

[0096] Step S52: Calculate the next prediction error of the set membership filter based on the predicted value of the state of the i-th follower unmanned boat at time k+1 and the linearized state equation of the unmanned boat and the error of the leader's unmanned boat

[0097] Step S53: Based on the state ellipsoid set of the unmanned boat at time k And the predicted value of the state of the i-th follower unmanned boat at time k+1 The first state prediction ellipsoid set is calculated using matrix inequality in, represents the shape matrix of the first state prediction ellipsoid set, which contains the predicted state information of the i-th follower unmanned boat at time k+1;

[0098] Step S54: Based on the error of the leader unmanned boat Define a state ellipsoid set as Among them, U i,k The shape matrix representing the ellipsoid set of this state;

[0099] Step S55: According to the state ellipsoid set And use the matrix inequality to calculate the second state prediction ellipsoid set Among them, the second state prediction ellipsoid set contains the predicted state information of the i-th follower unmanned boat at time k+1;

[0100] Step S56: Set the first state prediction ellipsoid set and the second state predicted ellipsoid set Perform intersection operation and calculate the minimum ellipsoid set containing the intersection of the two ellipsoid sets through the interior point algorithm of semidefinite programming That is, the state prediction ellipsoid set of the unmanned boat at time k+1.

[0101] In this embodiment, the matrix inequality and the interior point algorithm of semidefinite programming are both existing algorithms. For a leader-follower system unmanned boat formation, according to the control protocol of the leader-follower system, the controller input a' i,k as follows:

[0102]

[0103] in, is a regular matrix; represents the follower unmanned boat adjacent to the i-th unmanned boat; represents the state prediction value of the jth follower unmanned boat obtained through data update at the kth time; when the i-th unmanned boat receives the information of the j-th unmanned boat, h ij =1, otherwise h ij = 0. Since the entire follower unmanned boat system is controlled by the leader unmanned boat, when the i-th follower unmanned boat receives the information of the leader unmanned boat at time k, λ i ≥0, otherwise λ i = 0. From the predicted value of the state of the i-th follower unmanned boat at time k+1 and the controller input a' of the leader-follower system i,k It can be seen that the state of the i-th follower unmanned boat at the k+1th time is not only related to itself, but also to the leader unmanned boat. Therefore, the error of the leader unmanned boat is Define a state ellipsoid set as And use the matrix inequality to calculate the second state prediction ellipsoid set Since the first state predicts the ellipsoid set and the second state predicted ellipsoid set Both contain the predicted state information of the i-th follower unmanned boat at time k+1. Therefore, the intersection of the two can be taken to further obtain the state prediction ellipsoid set of the unmanned boat at time k+1.

[0104] Preferably, in step S7, the following sub-steps are specifically included:

[0105] Step S71: Update the state of the unmanned boat using the measurement value of the i-th follower unmanned boat at the k-th time in the state equation of the follower unmanned boat. The update equation is as follows:

[0106]

[0107] in, represents the state prediction value of the i-th follower unmanned boat at time k+1 obtained through data update; represents the predicted state value of the i-th follower unmanned boat at time k+1; represents the parameter matrix; y i,k+1 represents the measurement value of the i-th follower unmanned boat at the k+1th moment; represents the predicted value obtained by predicting the measured value of the i-th follower unmanned boat at the k+1th time;

[0108] Step S72: Calculate the update error according to the update equation and the linearized state equation of the unmanned boat

[0109] Step S73: Update the error e i,k+1|k+1 , define another state ellipsoid set as

[0110] Step S74: According to the state ellipsoid set The matrix inequality is used to calculate the state update ellipsoid set of the unmanned boat at time k+1

[0111] In this embodiment, the state prediction ellipsoid set of the unmanned boat at time k+1 is updated, so that the state prediction ellipsoid set can be more accurate.

[0112] In addition, each functional unit in each embodiment of the present invention may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into one module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0113] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A method for detecting unmanned boat formation attack based on distributed fuzzy set membership filtering. Features: The following steps are involved: Step S1: construct the kinematic and dynamic models of the unmanned boat; Step S2: converting the kinematic and dynamic models of the unmanned boat into the state equation of the unmanned boat; Step S3: linearize the nonlinear terms in the state equation of the unmanned boat using the TS fuzzy linearization method to obtain a linearized state equation of the unmanned boat; Step S4: Obtain the state ellipsoid set of the unmanned boat at time k; Step S5: according to the linearized state equation of the unmanned boat and the state ellipsoid set of the unmanned boat at time k, the state of the unmanned boat is predicted by using set membership filtering to obtain the state prediction ellipsoid set of the unmanned boat at time k+1; Step S6: performing an intersection operation on the state ellipsoid set of the unmanned boat at time k and the state prediction ellipsoid set of the unmanned boat at time k+1 to obtain a first intersection, and determining whether the first intersection is an empty set. If so, it means that the unmanned boat is attacked, and the state prediction ellipsoid set of the unmanned boat at time k+1 is replaced; if not, it means that the unmanned boat is not attacked; Step S7: using set membership filtering to update the state prediction ellipsoid set of the unmanned boat at time k+1, and obtaining the state update ellipsoid set of the unmanned boat at time k+1; Step S8: Perform an intersection operation on the state prediction ellipsoid set of the unmanned boat at time k+1 and the state update ellipsoid set of the unmanned boat at time k+1 to obtain a second intersection, and determine whether the second intersection is an empty set. If not, it means that the unmanned boat is not attacked; if so, it means that the unmanned boat is attacked, and the state prediction ellipsoid set of the unmanned boat at time k+1 and the state update ellipsoid set are replaced.

2. According to claim 1, a method for detecting an attack of an unmanned boat formation based on distributed fuzzy set membership filtering, Features: In step S1, the kinematic and dynamic models of the unmanned boat are expressed as: in, represents the position vector of the unmanned boat, x represents the lateral coordinate of the unmanned boat, y represents the longitudinal coordinate of the unmanned boat, Indicates the yaw angle of the unmanned boat; represents the first-order derivative of θ; μ = [w, v, r] T represents the state vector of the unmanned boat, w represents the longitudinal velocity of the unmanned boat, v represents the lateral velocity of the unmanned boat, and r represents the angular velocity of the unmanned boat; represents the first-order derivative of μ; ω represents the noise of the external environment; u represents the input of the controller; M represents the inertia matrix composed of the mass of the unmanned boat and the additional mass of the hull; represents the rotation matrix between the unmanned vehicle carrier coordinates and the earth coordinates; C(μ) represents the Coriolis centripetal force matrix; D(μ) represents the water surface damping matrix; M, C(μ) and D(μ) are expressed as: Among them, m x and m y Respectively represent the inertial parameters of the unmanned boat in the horizontal and vertical directions, which are obtained by subtracting the additional mass from its own weight; m r It represents the inertia parameter obtained by subtracting the additional mass in the direction of rotation from the moment of inertia; d x ,d y and d r They represent the hydrodynamic damping coefficients of the unmanned boat in the lateral, longitudinal and rotational directions respectively.

3. According to claim 1, a method for detecting an attack of an unmanned boat formation based on distributed fuzzy set membership filtering, Features: In step S2, the kinematic and dynamic models of the unmanned boat are converted into the state equation of the unmanned boat. The state equation of the unmanned boat includes the state equation of the leader unmanned boat and the state equation of the follower unmanned boat. The state equation of the leader unmanned boat is as follows: in, represents the system state of the leader unmanned boat at the kth moment; represents the nonlinear state matrix of the leader unmanned vehicle; The state equation of the follower unmanned boat is as follows: Among them, i∈{1,...,N}, N represents the number of follower unmanned boats; x i,k represents the system state of the i-th follower unmanned boat at the k-th moment; y i,k represents the measurement value of the i-th follower unmanned boat at the k-th moment; a i,k represents the controller input of the i-th follower unmanned boat at the k-th time; b i,k represents the system noise of the i-th follower unmanned boat at time k; c i,k represents the measurement noise of the i-th follower unmanned boat at time k; B i 、E i and H i Both represent the system matrix of the i-th follower unmanned boat.

4. According to claim 3, a method for detecting an attack of an unmanned boat formation based on distributed fuzzy set membership filtering, Features: In step S3, the TS fuzzy linearization method is as follows: RULE l i :IF yes yes yes THEN Among them, l i ={1,...,d} represents the number of fuzzy rules, d represents the maximum number of fuzzy rules; It represents the antecedent variable in the fuzzy rule, that is, the nonlinear variable in the state equation of the unmanned boat; represents a fuzzy set, q represents the number of fuzzy sets; and All represent the system matrix after fuzzy linearization; The linearized state equation of the unmanned boat is as follows: in, represents the normalized weight of each fuzzy rule; Δf i (x i,k ) represents the error after fuzzy linearization and satisfies the following formula: Δf i (x i,k )=J i,k Δ i,k K i,k x i,k ; Among them, J i,k and K i,k represents a known matrix; Δ i,k is unknown but bounded, and ||Δ i,k ||≤1.

5. According to claim 4, a method for detecting an attack of an unmanned boat formation based on distributed fuzzy set membership filtering, Features: In step S4, the state ellipsoid set of the unmanned boat at time k is in, represents the state prediction value of the i-th follower unmanned boat at the kth moment, P i,k|k Represents the shape matrix of the ellipsoid set where the state at the kth moment is located.

6. According to claim 5, a method for detecting an attack of an unmanned boat formation based on distributed fuzzy set membership filtering, Features: In step S5, the following sub-steps are specifically included: Step S51: According to the TS fuzzy linearization method, the predicted value of the state of the i-th follower unmanned boat at the k+1 time is obtained, wherein the predicted value of the state of the i-th follower unmanned boat at the k+1 time is specifically as follows: in, represents the predicted value of the state of the i-th follower unmanned boat at time k+1; represents the predicted state value of the i-th follower unmanned boat at time k; Step S52: Calculate the next prediction error of the set membership filter based on the predicted value of the state of the i-th follower unmanned boat at time k+1 and the linearized state equation of the unmanned boat and the error of the leader's unmanned boat Step S53: Based on the state ellipsoid set of the unmanned boat at time k And the predicted value of the state of the i-th follower unmanned boat at time k+1 The first state prediction ellipsoid set is calculated using matrix inequality in, represents the shape matrix of the first state prediction ellipsoid set, which contains the predicted state information of the i-th follower unmanned boat at time k+1; Step S54: Based on the error of the leader unmanned boat Define a state ellipsoid set as Among them, U i,k The shape matrix representing the ellipsoid set of this state; Step S55: According to the state ellipsoid set And use the matrix inequality to calculate the second state prediction ellipsoid set Among them, the second state prediction ellipsoid set contains the predicted state information of the i-th follower unmanned boat at time k+1; Step S56: Set the first state prediction ellipsoid set and the second state predicted ellipsoid set Perform intersection operation and calculate the minimum ellipsoid set containing the intersection of the two ellipsoid sets through the interior point algorithm of semidefinite programming That is, the state prediction ellipsoid set of the unmanned boat at time k+1.

7. The unmanned boat formation attack detection method based on distributed fuzzy set membership filtering according to claim 6, Features: In step S7, the following sub-steps are specifically included: Step S71: Update the state of the unmanned boat using the measurement value of the i-th follower unmanned boat at the k-th time in the state equation of the follower unmanned boat. The update equation is as follows: in, represents the state prediction value of the i-th follower unmanned boat at time k+1 obtained through data update; represents the predicted state value of the i-th follower unmanned boat at time k+1; represents the parameter matrix; y i,k+1 represents the measurement value of the i-th follower unmanned boat at the k+1th moment; represents the predicted value obtained by predicting the measured value of the i-th follower unmanned boat at the k+1th time; Step S72: Calculate the update error according to the update equation and the linearized state equation of the unmanned boat Step S73: Update the error e i,k+1|k+1 , define another state ellipsoid set as Step S74: According to the state ellipsoid set The matrix inequality is used to calculate the state update ellipsoid set of the unmanned boat at time k+1

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