Multi-unmanned surface vessel optimal safe formation collision avoidance control method under DoS attack

Abstract

The invention relates to an optimal safe formation collision avoidance control method for multiple unmanned surface vessels under DoS attack. The method comprises the following steps: constructing an input saturation model; constructing a multi-unmanned surface vessel dynamic model with unknown nonlinear terms; in the obstacle avoidance control design, an integral multiplication tangent obstacle Lyapunov function is designed by using the tangent obstacle Lyapunov function; establishing an attack compensator; carrying out approximation on the unknown nonlinear term by utilizing a fuzzy logic system to obtain an approximation result; combining the approximation result with an attack compensator, constructing a fuzzy state observer with switching gain, and obtaining an observation error; an optimal performance index function is designed according to the consistency formation error, and then a Bellman residual error is constructed; and constructing a weight updating law, and designing an optimal safe formation collision avoidance controller based on a judgment-execution structure according to the weight updating law and an integral multiplication tangent obstacle Lyapunov function. According to the technical scheme, the problem that collaborative optimization of obstacle avoidance and formation control is difficult is solved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of multi-unmanned surface ship control, and particularly relates to a multi-unmanned surface ship optimal safe formation collision avoidance control method under DoS attack. BACKGROUND

[0002] With the rapid development of intelligent control technology and ocean unmanned systems, unmanned surface ships have been widely used in marine patrol, water quality monitoring, search and rescue tasks and cooperative combat scenarios. In actual tasks, through reasonable division of labor and task cooperation, multi-unmanned surface ships can improve the efficiency of the whole system while quickly adapting to task changes and environmental changes, so that multi-unmanned surface ships can quickly respond to emergencies and greatly improve the adaptability and robustness of the system. On the other hand, since the multi-unmanned surface ship formation system usually relies on wireless communication networks for information exchange, it is vulnerable to network attacks, especially DoS attacks. DoS attacks can cause some state information to be unavailable by blocking or interfering with information transmission, seriously affecting the performance of the control system, and even causing the formation to collapse or the system to crash. However, a series of research results have been achieved for the formation control problem of multi-unmanned surface ship systems under DoS attack, but the existing technology still has the following problems:

[0003] First, the existing formation control method often lacks an effective compensation mechanism when facing DoS attacks and system state unavailability, and rarely considers nonlinear dynamics and input saturation problems at the same time, and the existing anti-DoS attack method ignores the influence of attacks on control input.

[0004] Second, in the existing multi-unmanned surface ship formation control method, the influence of obstacles on the formation shape during system operation is ignored. However, in actual operation, not only is it required to maintain the desired formation and track the reference trajectory of each unmanned ship, but also to avoid static or dynamic obstacles in complex environments to ensure the safety and stability of the overall system.

[0005] Third, in the existing formation control technology, a large amount of control energy is consumed while ensuring system convergence, but from the actual environmental protection demand point of view, it is often necessary to achieve optimal control performance with minimal energy consumption. SUMMARY

[0006] The technical problem to be solved by the present application is to make up for the shortcomings of the prior art and provide a multi-unmanned surface ship optimal safe formation collision avoidance control method under DoS attack.

[0007] To solve the above technical problems, the technical scheme of the present application is as follows:

[0008] A multi-unmanned surface ship optimal safe formation collision avoidance control method under DoS attack, comprising the following steps:

[0009] S1: constructing an input saturation model for unmanned surface vehicles;

[0010] S2: constructing a multi-unmanned surface vehicle dynamics model with unknown nonlinear terms according to the input saturation model;

[0011] S3: in the obstacle avoidance control design, using a tangent type obstacle Lyapunov function to design an integral multiplication tangent obstacle Lyapunov function;

[0012] S4: establishing an attack compensator to compensate the output information of the multi-unmanned surface vehicle dynamics model when subjected to a DoS attack, and obtaining the system output when subjected to a DoS attack;

[0013] S5: using a fuzzy logic system to approximate the unknown nonlinear terms in the multi-unmanned surface vehicle dynamics model, and obtaining an approximation result;

[0014] S6: based on the approximation result of step S5, combining the attack compensator established in step S4, constructing a fuzzy state observer with switching gain, and obtaining an observation error by subtracting the state after observation from the state in the multi-unmanned surface vehicle dynamics model;

[0015] S7: according to the multi-unmanned surface vehicle dynamics model, combining the directed communication topology between unmanned surface vehicles, defining a consensus formation error, which includes a consensus formation error when the DoS attack is dormant and a consensus formation error when the DoS attack is activated;

[0016] S8: designing an optimal performance index function when the DoS attack is dormant according to the consensus formation error when the DoS attack is dormant, and designing an optimal performance index function when the DoS attack is activated according to the consensus formation error when the DoS attack is activated; and constructing a Bellman residual according to the optimal performance index function when the DoS attack is dormant and the optimal performance index function when the DoS attack is activated;

[0017] S9: designing a positive function equivalent to making the Bellman residual zero, and solving the positive function using the gradient descent method, constructing a weight update law, which includes a weight update law when the DoS attack is dormant and a weight update law when the DoS attack is activated;

[0018] S10: designing an optimal safety formation collision avoidance controller based on a judge-execute structure according to the weight update law and the integral multiplication tangent obstacle Lyapunov function.

[0019] Further, in step S1, the input saturation model is:

[0020]

[0021] where sat(τ i ) is a saturation function, τ i is the control input of the USV, i = 1, 2, …, N, N represents the number of USVs, is the bound of τ i , and the saturation function sat(τ i ) is approximated by a smooth function u i (τ i ):

[0022]

[0023] The approximation error is defined as d i (τ i ) = sat(τ i )-u i (τ i ).

[0024] In step S2, the multi-USV dynamics model is:

[0025]

[0026] where t represents time, x i , respectively represent the surge displacement, sway displacement and yaw angle of the USV in the earth-fixed coordinate system; υ i (t) = [u i , v i , r i ] T represent the velocity state vector of the USV, u i , v i , r i respectively represent the surge velocity, sway velocity and yaw angular velocity of the USV in the inertial coordinate system; y i represents the output of the USV; is the state transition matrix and satisfies M i represents the mass of the USV and is a positive definite symmetric matrix; C(υ i (t)) represents the Coriolis and centrifugal force matrix, and satisfies D i (υ i (t)) represents the nonlinear damping matrix;

[0027] The formula (3) is coordinate-transformed as:

[0028]

[0029] wherein,

[0030] is the unknown nonlinear term.

[0031] Further, in step S3, the tangent type barrier Lyapunov function is:

[0032]

[0033] wherein, D j is the repulsion force range generated by the barrier, j > 0; K rep is a design constant; μ = r c -r a , r a is a safety radius, r c is a repulsion radius, r g is a perception radius; is the distance between the unmanned surface vehicle and the barrier, is the position of the barrier;

[0034] The integral multiplication tangent barrier Lyapunov function is:

[0035]

[0036] wherein, s is a certain time between [0, t], η i，1 (s) is the pose state vector of the unmanned surface vehicle at time s, l = 1, 2, …, m0, m0 represents the number of barriers entering the i-th unmanned surface vehicle, D i，l represents the repulsion force range of the l-th barrier entering the i-th unmanned surface vehicle.

[0037] Further, in step S4, the attack compensator is:

[0038]

[0039] wherein, represents the system output of the system under DoS attack; η i (T l - ) represents the final output signal available before the l-th attack. t l is the duration of the l-th DoS attack, [T l , T l +t l ) is the time interval of the l-th DoS attack, T l is the start time of the l-th DoS attack;

[0040] Defining system control input under DoS attack For

[0041]

[0042] wherein Ξ i (0,∞) is the activation time of DoS attack in the whole time interval, A i (0,∞) is the dormant time of DoS attack in the whole time interval.

[0043] Further, in step S5, the approximation result is:

[0044]

[0045] wherein, is the optimal weight vector; φ i is the activation function, δ i is the approximation error.

[0046] Further, in step S6, the fuzzy state observer with switching gain is:

[0047]

[0048] wherein, is the estimation of (·); if the DoS attack is in dormant state; if the DoS attack is in active state; is the output of the observer;

[0049]

[0050] The observation error includes a first-order observation error and a second-order observation error;

[0051] The first-order observation error is:

[0052] The second-order observation error is:

[0053] The derivation of the first-order observation error and the second-order observation error is:

[0054]

[0055] wherein e i =[e i，1 , e i，2 ] T represents the vector form of the observation error, and represents the first-order observation error when the attack is in active, is the Hurwitz matrix, C i = [1, 0], B i = [0, 1] T , respectively the first and second order observer gains when the attack is active, is the gain vector when the attack is active, respectively the first and second order observer gains when the attack is active, is the gain vector when the attack is dormant, is the estimation error of the weight vector when the attack is active, is the estimation error of the weight vector when the attack is dormant, denotes the approximation error vector when the attack is active, denotes the approximation error vector when the attack is dormant.

[0056] Further, the step S7 specifically comprises the following steps:

[0057] S71: defining the formation error when the DoS attack is dormant:

[0058]

[0059] wherein η r (t) is the ideal reference trajectory, η i，d (t) is the desired formation distance.

[0060] According to equation (13), the consistency formation error when the DoS attack is dormant is defined as follows

[0061]

[0062] wherein j e N denotes the jth neighbor USV of the ith USV, η j (t) denotes the pose state vector of the jth neighbor USV, η j，d (t) denotes the desired formation distance of the jth neighbor USV, a ij denotes the element variable of the adjacency matrix in the directed communication topology, b i denotes the element variable of the weighted link matrix of the directed communication topology;

[0063] defining the formation error when the DoS attack is active:

[0064]

[0065] According to equation (15), the consistency formation error when the DoS attack is active is defined as follows

[0066]

[0067] S72: Derivation of the formation error when the DoS attack is dormant, yields:

[0068]

[0069] According to formula (17), derivation of the consensus formation error when the DoS attack is dormant, yields:

[0070]

[0071] wherein,

[0072] Derivation of the formation error when the DoS attack is active, yields:

[0073]

[0074] According to formula (19), derivation of the consensus formation error when the DoS attack is active, yields:

[0075]

[0076] Further, the step S8 specifically comprises the following steps:

[0077] S81: The optimal performance index function when the DoS attack is dormant includes a first-order optimal performance index function when the attack is dormant and a second-order optimal performance index function when the attack is dormant;

[0078] Let be the optimal virtual controller when the attack is dormant, and the first-order optimal performance index function when the attack is dormant is designed as:

[0079]

[0080] wherein, is the first-order cost function when the attack is dormant, represents the virtual controller at the moment when the attack is dormant, and Ω i，1 represents the admissible set of the virtual controller.

[0081] Let be the actual optimal controller when the attack is dormant, and the second-order optimal performance index function when the attack is dormant is designed as:

[0082]

[0083] wherein, is the second-order cost function when the attack is dormant, denote the actual controller when the attack is dormant, Ω i,2 denote the admissible set of the actual controller;

[0084] the optimal performance index function when the attack is active includes a first-order optimal performance index function when the attack is active and a second-order optimal performance index function when the attack is active;

[0085] Let be the optimal virtual controller when the attack is active, the first-order optimal performance index function when the attack is active is designed as:

[0086]

[0087] wherein, is the first-order cost function when the attack is active; is the virtual controller when the attack is active;

[0088] Let be the actual optimal controller when the attack is active, the second-order optimal performance index function when the attack is active is designed as:

[0089]

[0090] wherein, is the second-order cost function when the attack is active, denote the actual controller when the attack is active;

[0091] S82: the Bellman residual is constructed as:

[0092]

[0093] wherein, is a positive design parameter, is an auxiliary term.

[0094] Further, in step S9, the weight update law when the attack is dormant includes a first-order critic network weight update law when the attack is dormant, a first-order execution network weight update law when the attack is dormant, a second-order weight update law when the attack is dormant, a second-order critic network weight update law when the attack is dormant, and a second-order execution network weight update law when the attack is dormant;

[0095] the weight update law when the attack is active includes a first-order critic network weight update law when the attack is active, a first-order execution network weight update law when the attack is active, a second-order weight update law when the attack is active, a second-order critic network weight update law when the attack is active, and a second-order execution network weight update law when the attack is active;

[0096] Step S9 specifically comprises the following steps:

[0097] S91: The positive function is:

[0098]

[0099] By solving the positive function by using the gradient descent method, the derivative is:

[0100]

[0101] Then, the weight update law is designed to ensure that ;

[0102] S92: Construct the first-order critic network weight update law when the attack is in sleep:

[0103]

[0104] Wherein, is the learning gain of the first-order critic network when the attack is in sleep, is the first-order activation function when the attack is in sleep;

[0105] Construct the first-order executive network weight update law when the attack is in sleep:

[0106]

[0107] Wherein, is the learning gain of the first-order executive network when the attack is in sleep;

[0108] Construct the second-order weight update law when the attack is in sleep:

[0109]

[0110] Wherein, r i s is a positive definite matrix when the attack is in sleep;

[0111] Construct the second-order critic network weight update law when the attack is in sleep:

[0112]

[0113] Wherein, is the learning gain of the second-order critic network when the attack is in sleep, is the second-order activation function when the attack is in sleep;

[0114] Construct the second-order executive network weight update law when the attack is in sleep:

[0115]

[0116] wherein, is the learning gain of the attack on the first-order critic network in the active state;

[0117] constructing the weight update law of the attack on the first-order critic network in the active state:

[0118]

[0119] wherein, is the learning gain of the attack on the first-order critic network in the active state, is the first-order activation function of the attack in the active state;

[0120] constructing the weight update law of the attack on the first-order critic network in the active state:

[0121]

[0122] wherein, is the learning gain of the attack on the first-order critic network in the active state;

[0123] constructing the weight update law of the attack on the first-order critic network in the active state:

[0124]

[0125] wherein, r i a is a positive definite matrix of the attack in the active state;

[0126] constructing the weight update law of the attack on the first-order critic network in the active state:

[0127]

[0128] wherein, is the learning gain of the attack on the first-order critic network in the active state, is the first-order activation function of the attack in the active state;

[0129] constructing the weight update law of the attack on the first-order critic network in the active state:

[0130]

[0131] wherein, is the learning gain of the attack on the first-order critic network in the active state.

[0132] Further, the optimal safety formation collision avoidance controller comprises: an optimal virtual controller of the attack in the dormant state, an actual optimal controller of the attack in the dormant state, an optimal virtual controller of the attack in the active state, and an actual optimal controller of the attack in the active state;

[0133] the optimal virtual controller of the attack in the dormant state:

[0134]

[0135] wherein, is a first order positive design parameter when attacking in sleep, is an auxiliary term when attacking in sleep;

[0136] the actual optimal controller when attacking in sleep:

[0137]

[0138] wherein, is a second order positive design parameter when attacking in activation;

[0139] the optimal virtual controller when attacking in activation:

[0140]

[0141] wherein, is a first order positive design parameter when attacking in activation, is an auxiliary term when attacking in activation;

[0142] the actual optimal controller when attacking in activation:

[0143]

[0144] wherein, is a second order positive design parameter when attacking in activation.

[0145] The present application can achieve the beneficial effects that:

[0146] 1. The present application provides a kind of optimal safety formation collision avoidance control method of multi-unmanned surface ship under DoS attack, by constructing attack compensator, the output signal that cannot be obtained when DoS attack occurs is effectively estimated, the fault tolerance and operating reliability of system in the case where communication is limited or interrupted are significantly improved;Based on attack compensator, fuzzy state observer with switching gain is constructed, in combination with the approximation ability of fuzzy logic system to nonlinear dynamics, the problem of unmeasurable system state is solved;Auxiliary dynamic system is introduced, effectively compensates the input saturation influence of actuator;

[0147] 2. The present application can ensure that unmanned surface ship always keeps a safe distance from the obstacle during movement, avoids collision by designing integral multiplication tangent obstacle Lyapunov function, and makes unmanned surface ship converge to preset formation position by optimal safety formation collision avoidance control strategy, solves the problem that obstacle avoidance and formation control are difficult to optimize in traditional method;

[0148] 3、The application utilizes backstepping technique and reinforcement learning technique, wherein the critic network evaluates the control behavior and provides feedback to the execution network, the execution network executes the control behavior, and an optimal control scheme based on the critic-execution structure is designed, and a corresponding optimal safe formation collision avoidance controller is derived, so that the formation error converges to the neighborhood of the origin while the cost function is minimized. BRIEF DESCRIPTION OF DRAWINGS

[0149] Figure 1 is a directed communication topology graph between unmanned surface ships in the embodiment of the application.

[0150] Figure 2 is an ideal formation mode of four unmanned surface ships in the embodiment of the application.

[0151] Figure 3 is an observation error trajectory in the embodiment of the application.

[0152] Figure 4 is a control input trajectory in the embodiment of the application.

[0153] Figure 5 is a norm of the update law of the critic network and in the embodiment of the application.

[0154] Figure 6 is a norm of the update law of the execution network and in the embodiment of the application.

[0155] Figure 7 is a norm of the update law of the execution network and in the embodiment of the application.

[0156] Figure 8 is a trajectory of the cost functions c i，1 and c i，2 in the embodiment of the application.

[0157] Figure 9 is a distance between an unmanned surface ship and an obstacle in the embodiment of the application.

[0158] Figure 10 is a trajectory of the consistency formation error in the embodiment of the application. DETAILED DESCRIPTION

[0159] The application will be further described in detail below in combination with the drawings and specific embodiments.

[0160] A DoS attack under a multi-unmanned surface ship optimal safe formation collision avoidance control method, comprising the following steps:

[0161] S1: Construct an input saturation model for USVs.

[0162] The input saturation model is:

[0163]

[0164] where sat(τ i ) is a saturation function, τ i is the control input of USVs, i = 1, 2, … N, N represents the number of USVs, is the bound of τ i , and the saturation function sat(τ i ) is approximated by a smooth function u i (τ i ):

[0165]

[0166] Define the approximation error as d i (τ i ) = sat(τ i )-u i (τ i ).

[0167] S2: Construct a multi-USVs dynamics model with unknown nonlinear terms according to the input saturation model.

[0168] The multi-USVs dynamics model is:

[0169]

[0170] where t represents time, represents the pose state vector of USVs, x i , are the surge displacement, sway displacement and yaw angle of USVs in the earth-fixed coordinate system, respectively; υ i (t) = [u i , v i , r i ] T represents the velocity state vector of USVs, u i , v i , r i are the surge velocity, sway velocity and yaw angular velocity of USVs in the inertial coordinate system, respectively; represents the saturation control input of USVs before transformation, y i represents the output of USVs; is the state transition matrix and satisfies the matrix M idenotes the mass of the USV and is a positive definite symmetric matrix; C(v i (t)) denotes the Coriolis and centrifugal force matrix and satisfies D i (υ i (t)) denotes the nonlinear damping matrix;

[0171] The coordinate transformation of formula (3) is:

[0172]

[0173] wherein,

[0174] is the unknown nonlinear term.

[0175] S3: In the obstacle avoidance control design, the tangent type obstacle Lyapunov function is used to design the integral multiplication tangent obstacle Lyapunov function.

[0176] The tangent type obstacle Lyapunov function is:

[0177]

[0178] wherein, D j is the repulsion force range generated by the obstacle, j>0; K rep is a design constant; μ=r c -r a , r a is the safety radius, r c is the repulsion radius, and r g is the perception radius. is the distance between the USV and the obstacle, is the position of the obstacle.

[0179] The integral multiplication tangent obstacle Lyapunov function is:

[0180]

[0181] wherein, s is a certain time between [0, t], η i，1 (s) is the pose state vector of the USV at time s, l=1, 2, …, m0, m0 represents the number of obstacles entering the i-th USV, D i，l represents the repulsion force range of the l-th obstacle entering the i-th USV.

[0182] S4: An attack compensator is established to compensate for the output information of the multi-USV dynamics model when subjected to DoS attacks, and the system output when subjected to DoS attacks is obtained.

[0183] The attack compensator is:

[0184]

[0185] wherein, denotes the system output of the system under DoS attack; η i (T l - denotes the final output signal available before the lth attack. t l is the duration of the lth DoS attack, [T l , T l +t l is the time interval of the lth DoS attack, T l is the start time of the lth DoS attack.

[0186] The system control input of the system under DoS attack is defined as

[0187]

[0188] wherein, Ξ i (0, ∞) is the activation time of the DoS attack in the entire time interval, A i (0, ∞) is the dormant time of the DoS attack in the entire time interval.

[0189] S5: The unknown nonlinear terms existing in the multi-unmanned surface ship dynamics model are approximated by using the fuzzy logic system, and an approximation result is obtained.

[0190] The approximation result is:

[0191]

[0192] wherein, is the optimal weight vector; φ i is an activation function, δ i is an approximation error.

[0193] S6: Based on the approximation result of step S5, the fuzzy state observer with switching gain is constructed by combining the attack compensator established in step S4, the state in the multi-unmanned surface ship dynamics model is subtracted from the observed state, and an observation error is obtained.

[0194] The fuzzy state observer with switching gain is:

[0195]

[0196] wherein, is the estimation of (·); if the DoS attack is in the dormant state; if​ the DoS attack is in the active state; is the output of the observer;

[0197]

[0198] The observation error includes a first-order observation error and a second-order observation error;

[0199] The first-order observation error is:

[0200] The second-order observation error is:

[0201] The derivation of the first-order observation error and the second-order observation error can be obtained as follows:

[0202]

[0203] wherein e i = [e i，1 , e i，2 ] T represents a vector form of the observation error, and represents the first-order observation error when the attack is in the active state, is a Hermitian matrix, C i = [1, 0], B i = [0, 1] T , are the first-order observer gain and the second-order observer gain when the attack is in the active state, respectively, is a gain vector when the attack is in the active state, are the first-order observer gain and the second-order observer gain when the attack is in the active state, respectively, is a gain vector when the attack is in the dormant state, is an estimation error of the weight vector when the attack is in the active state, is an estimation error of the weight vector when the attack is in the dormant state, represents an approximation error vector when the attack is in the active state, represents an approximation error vector when the attack is in the dormant state.

[0204] S7: According to the multi-unmanned surface ship dynamics model, combined with the directed communication topology between unmanned surface ships, a consensus formation error is defined, which includes a consensus formation error when the DoS attack is in the dormant state and a consensus formation error when the DoS attack is in the active state.

[0205] Specifically, the following steps are included:

[0206] S71: Define the formation error when the DoS attack is in the dormant state:

[0207]

[0208] where η r (t) is the ideal reference trajectory, η i，d (t) is the desired platoon distance.

[0209] According to equation (13), the consistency platoon error when the DoS attack is dormant is defined as follows

[0210]

[0211] where j e N represents the jth neighbor USV of the ith USV, η j (t) represents the pose state vector of the jth neighbor USV, η j，d (t) represents the desired platoon distance of the jth neighbor USV, a ij represents the element variable of the adjacency matrix in the directed communication topology, b i represents the element variable of the weighted link matrix of the directed communication topology.

[0212] The platoon error when the DoS attack is active is defined as follows

[0213]

[0214] According to equation (15), the consistency platoon error when the DoS attack is active is defined as follows

[0215]

[0216] S72: Derive the platoon error when the DoS attack is dormant, as follows

[0217]

[0218] According to equation (17), derive the consistency platoon error when the DoS attack is dormant, as follows

[0219]

[0220] where

[0221] Derive the platoon error when the DoS attack is active, as follows

[0222]

[0223] According to equation (19), derive the consistency platoon error when the DoS attack is active, as follows

[0224]

[0225] S8: design the optimal performance index function of the DoS attack in the dormant state according to the consistency formation error of the DoS attack in the dormant state, and design the optimal performance index function of the DoS attack in the active state according to the consistency formation error of the DoS attack in the active state; design the Bellman residual according to the optimal performance index function of the DoS attack in the dormant state and the optimal performance index function of the DoS attack in the active state.

[0226] Specifically, the following steps are included:

[0227] S81: the optimal performance index function of the DoS attack in the dormant state includes a first-order optimal performance index function of the attack in the dormant state and a second-order optimal performance index function of the attack in the dormant state;

[0228] Let be the optimal virtual controller of the attack in the dormant state, and the first-order optimal performance index function of the attack in the dormant state is designed as:

[0229]

[0230] wherein, is the first-order cost function of the attack in the dormant state, represents the virtual controller at the moment when the attack is in the dormant state, Ω i，1 represents the admissible set of the virtual controller.

[0231] Let be the actual optimal controller of the attack in the dormant state, and the second-order optimal performance index function of the attack in the dormant state is designed as:

[0232]

[0233] wherein, is the second-order cost function of the attack in the dormant state, represents the actual controller at the moment when the attack is in the dormant state, Ω i，2 represents the admissible set of the actual controller.

[0234] The optimal performance index function of the DoS attack in the active state includes a first-order optimal performance index function of the attack in the active state and a second-order optimal performance index function of the attack in the active state;

[0235] Let be the optimal virtual controller of the attack in the active state, and the first-order optimal performance index function of the attack in the active state is designed as:

[0236]

[0237] wherein, a first-order cost function in the active state is attacked; a virtual controller in the active state is attacked;

[0238] Let a real optimal controller in the active state is attacked, a second-order optimal performance index function in the active state is designed as

[0239]

[0240] wherein, a second-order cost function in the active state is attacked, a real controller in the active state is attacked;

[0241] S82: the Bellman residual error is constructed as

[0242]

[0243] wherein, a positive design parameter, an auxiliary term.

[0244] S9: a positive function equivalent to the Bellman residual error being zero is designed, and the positive function is solved by using a gradient descent method, and a weight update law is constructed, the weight update law including a weight update law of the DoS attack in the dormant state and a weight update law of the DoS attack in the active state.

[0245] The weight update law of the DoS attack in the dormant state includes a first-order judgment network weight update law of the attack in the dormant state, a first-order execution network weight update law of the attack in the dormant state, a second-order weight update law of the attack in the dormant state, a second-order judgment network weight update law of the attack in the dormant state, and a second-order execution network weight update law of the attack in the dormant state.

[0246] The weight update law of the DoS attack in the active state includes a first-order judgment network weight update law of the attack in the active state, a first-order execution network weight update law of the attack in the active state, a second-order weight update law of the attack in the active state, a second-order judgment network weight update law of the attack in the active state, and a second-order execution network weight update law of the attack in the active state.

[0247] Specifically, the following steps are included:

[0248] S91: the positive function is

[0249]

[0250] By using the gradient descent method to solve the positive function, the derivative thereof is obtained as

[0251]

[0252] Then, the weight update law of the first-order critic network is constructed when the attack is in the active state:

[0253] S92: Construct the weight update law of the first-order critic network when the attack is in the dormant state:

[0254]

[0255] wherein, is the learning gain of the first-order critic network when the attack is in the dormant state, is the first-order activation function when the attack is in the dormant state;

[0256] Construct the weight update law of the first-order executive network when the attack is in the dormant state:

[0257]

[0258] wherein, is the learning gain of the first-order executive network when the attack is in the dormant state;

[0259] Construct the weight update law of the second-order when the attack is in the dormant state:

[0260]

[0261] wherein, r i s is a positive definite matrix when the attack is in the dormant state;

[0262] Construct the weight update law of the second-order critic network when the attack is in the dormant state:

[0263]

[0264] wherein, is the learning gain of the second-order critic network when the attack is in the dormant state, is the second-order activation function when the attack is in the dormant state;

[0265] Construct the weight update law of the second-order executive network when the attack is in the dormant state:

[0266]

[0267] wherein, is the learning gain of the second-order executive network when the attack is in the dormant state;

[0268] Construct the weight update law of the first-order critic network when the attack is in the active state:

[0269]

[0270] wherein, is the learning gain of the first-order critic network when the attack is in the active state, ​is the first-order activation function when the attack is in activation;

[0271] The first-order weight update law of the execution network when the attack is in activation is constructed as

[0272]

[0273] wherein, is the learning gain of the execution network when the attack is in activation;

[0274] The second-order weight update law of the execution network when the attack is in activation is constructed as

[0275]

[0276] wherein, r i a is a positive definite matrix when the attack is in activation;

[0277] The second-order weight update law of the judgment network when the attack is in activation is constructed as

[0278]

[0279] wherein, is the learning gain of the judgment network when the attack is in activation, is the second-order activation function when the attack is in activation;

[0280] The second-order weight update law of the execution network when the attack is in activation is constructed as

[0281]

[0282] wherein, is the learning gain of the execution network when the attack is in activation.

[0283] S10: An optimal safety formation collision avoidance controller based on the judgment-execution structure is designed according to the weight update law and the integral multiplication tangent obstacle Lyapunov function.

[0284] The optimal safety formation collision avoidance controller comprises an optimal virtual controller when the attack is in dormancy, an actual optimal controller when the attack is in dormancy, an optimal virtual controller when the attack is in activation, and an actual optimal controller when the attack is in activation.

[0285] The optimal virtual controller when the attack is in dormancy is:

[0286]

[0287] wherein, is a first-order positive design parameter when the attack is in dormancy, is an auxiliary term when the attack is in dormancy.

[0288] Attacking the actual optimal controller when in sleep:

[0289]

[0290] wherein, is a second order positive design parameter for attacking when in sleep.

[0291] Attacking the optimal virtual controller when in activation:

[0292]

[0293] wherein, is a first order positive design parameter for attacking when in activation, is a secondary term for attacking when in activation.

[0294] Attacking the actual optimal controller when in activation:

[0295]

[0296] wherein, is a second order positive design parameter for attacking when in activation.

[0297] The present application combines backstepping recursive technique and reinforcement learning technique, and proposes an optimal safe formation collision avoidance control strategy for multiple unmanned surface ships based on an observer, so that under the control strategy, the unmanned ships converge to the neighborhood of the origin under the premise of keeping a safe distance from the obstacles, and the cost function is minimized.

[0298] In this embodiment, a multi-agent system consisting of 4 follower unmanned surface ships and 1 leader unmanned surface ship is specifically considered as the controlled object, a dynamic model of the multiple unmanned surface ships is established, a consistent formation error can be obtained by analyzing the dynamic model, a fuzzy logic system is used to process unknown nonlinear functions, and a corresponding Lyapunov function is established. A tangent type obstacle Lyapunov function is introduced to ensure that a safe distance exists between the unmanned surface ships and the obstacles, and an optimal safe formation collision avoidance controller based on the judge-execution structure is designed.

[0299] In order to verify the effectiveness of the proposed optimal safe formation method, in this embodiment, a multi-unmanned surface ship system consisting of 4 follower unmanned surface ships and 1 leader unmanned surface ship is considered, and the topological graph is shown in Figure 1 .

[0300] The matrix information in the dynamic model of the unmanned surface ship is as follows

[0301]

[0302] wherein, c 13i (v i, r i ) = -33.8v i -1.0115r i , c 23i (v i , r i ) = 25.8u i , d 11i (u i ) = 0.72+1.33u i , d 22i (v i , r i ) = 0.86+36.82v i , d 23i (v i , r i ) = -0.11, d 32i = -0.11-5.04v i , d 33i = 0.5.

[0303] The ideal reference trajectory is selected as η r = [3cos(0.5t), 2cos(0.7), 002t] T

[0304] The initial values of the pose state vector and the velocity state vector are selected as η1= [6, 3, 1] T , η2= [-3, 2, 1] T , η3= [3, -2, 1] T , η4= [-2, -3, 1] T ; v1= [-3, 0.6, 0] T , v2= [2, 0.6, 0] T , v3= [2, 0.6, 0] T , v4= [2, 0.6, 0] T ; the initial conditions of the fuzzy state observer with switching gain are selected as R a1 = R a2 = R a3 = R a4 = 0; the entire time interval is 25s, and the step length is selected as 0.01.

[0305] The other design parameters of the application are selected as, r i a = r i s = 0.4, Solving the observer gain vector using MATLAB LMI toolbox

[0306]

[0307] The time interval for the first DoS attack is chosen as [1.1, 1.3], the time interval for the second DoS attack is chosen as [7.5, 7.7], the time interval for the third DoS attack is chosen as [11.6, 11.9], and the time interval for the fifth DoS attack is chosen as [20, 10.3].

[0308] Figure 2 The ideal formation pattern of four USVs is shown. It is shown that the designed control strategy can make the USVs converge to the preset formation position.

[0309] Figure 3 The trajectory of the observation error is shown. It is shown that the observation error converges to the neighborhood of the origin, i.e., the designed fuzzy state observer with switching gain is effective.

[0310] Figure 4 The trajectory of the control input is shown. It is shown that the control input of the USVs is bounded even when suffering from DoS attacks.

[0311] Figure 5 The norm of the update law and is shown. It is shown that the weight update law is bounded.

[0312] Figure 6 The norm of the update law of the critic network and is shown. It is shown that the critic network weight update law is bounded when the attack is in sleep / active.

[0313] Figure 7 The norm of the update law of the executive network and is shown. It is shown that the executive network weight update law is bounded when the attack is in sleep / active.

[0314] Figure 8 The trajectory of the cost function c i，1 and c i，2 is shown.

[0315] Figure 9 The distance between the USVs and the obstacle is shown, which clearly shows that the proposed collision avoidance control scheme will not cause collision in the formation task.

[0316] Figure 10 The trajectory of the formation error is shown. It is shown that the designed method guarantees that the consensus formation error can converge to a small neighborhood of zero.

Claims

1. A method for optimal safe formation collision avoidance control of multiple unmanned surface vessels under DoS attack, characterized by: Includes the following steps: S1: Construct an input saturation model for unmanned surface vessels; S2: Based on the input saturation model, construct a dynamic model of multiple unmanned surface vessels with unknown nonlinear terms; S3: In obstacle avoidance control design, the integral multiplication tangent obstacle Lyapunov function is designed using the tangent obstacle Lyapunov function; S4: Establish an attack compensator to compensate for the output information of the dynamics model of multiple unmanned surface vessels when subjected to a DoS attack, and obtain the system output when subjected to a DoS attack. S5: Use a fuzzy logic system to approximate the unknown nonlinear terms in the dynamics model of multiple unmanned surface vessels and obtain the approximation results; S6: Based on the approximation results of step S5, and combined with the attack compensator established in step S4, construct a fuzzy state observer with switching gain, and subtract the state in the dynamic model of the multi-unmanned surface vessel from the state after observation to obtain the observation error. S7: Based on the dynamics model of multiple unmanned surface vessels and combined with the directed communication topology between unmanned surface vessels, define the consensus formation error. The consensus formation error includes the consensus formation error when the DoS attack is dormant and the consensus formation error when the DoS attack is active. S8: Design the optimal performance index function for a DoS attack when it is dormant based on the consistency array error when the DoS attack is dormant; design the optimal performance index function for a DoS attack when it is active based on the consistency array error when the DoS attack is active; construct the Bellman residual based on the optimal performance index function for a DoS attack when it is dormant and the optimal performance index function for a DoS attack when it is active. S9: Design a positive function that is equivalent to making the Bellman residual zero, and solve the positive function using the gradient descent method to construct the weight update law. The weight update law includes the weight update law when the DoS attack is dormant and the weight update law when the DoS attack is active. S10: Design an optimal safe formation collision avoidance controller based on the evaluation-execution structure, according to the weight update law and the integral multiplication tangent obstacle Lyapunov function.

2. The optimal safe formation collision avoidance control method for multiple unmanned surface vessels under DoS attack as described in claim 1, characterized in that: In step S1, the input saturation model is: Among them, sat(τ) i ) is a saturation function, τ i These are the control inputs for the unmanned surface vessels, i = 1, 2, ..., N, where N represents the number of unmanned surface vessels. It is τ i The bound of the saturation function sat(τ) i ) by the smooth function u i (τ i Approaching: The approximation error is defined as: d i (τ i ) = sat(τ i )-u i (τ i ). In step S2, the dynamic model of the multi-unmanned surface vessel is as follows: Where t represents time. Let x represent the pose state vector of the unmanned surface vessel. i , These represent the pitch displacement, sway displacement, and yaw angle of the unmanned surface vessel in a fixed Earth coordinate system; υ i (t)=[u i v i r i ] T u represents the velocity state vector of the unmanned surface vessel. i v i r i These are the pitch velocity, sway velocity, and yaw rate of the unmanned surface vessel in the inertial coordinate system, respectively. This represents the saturation control input of the unmanned surface vessel before the transformation, y i Indicates the output of the unmanned surface vessel; It is a state transition matrix and satisfies Matrix M i C(υ) represents the mass of the unmanned surface vessel and is a positive definite symmetric matrix; i (t) represents the Coriolis force and centrifugal force matrix, and satisfies D i (υ i (t) represents the nonlinear damping matrix; Equation (3) is transformed by coordinates to: in, Let be the unknown nonlinear term.

3. The optimal safe formation collision avoidance control method for multiple unmanned surface vessels under DoS attack as described in claim 2, characterized in that: In step S3, the tangent barrier Lyapunov function is: Among them, D j It is the range of repulsive force generated by the obstacle, j>0; K rep It is a design constant; μ = r c -r a r a For the safety radius, r c r is the repulsion radius. g For sensing radius; The distance between the unmanned surface vessel and the obstacle. It is the location of the obstacle; The Lyapunov function that forms the tangent barrier of integral multiplication is: Where s is a certain time between [0, t], and η i，1 (s) is the pose state vector of the unmanned surface vessel at time s, l = 1, 2, ..., m0, where m0 represents the number of obstacles entering the i-th unmanned surface vessel, and D i,l This represents the range of repulsive forces entering the l-th obstacle of the i-th unmanned surface vessel.

4. The optimal safe formation collision avoidance control method for multiple unmanned surface vessels under DoS attack as described in claim 3, characterized in that: In step S4, the attack compensator is: in, This indicates the system output under a DoS attack. This represents the final output signal obtainable before the l-th attack. l The duration of the l-th DoS attack, [T] l T l +t l T represents the time interval between the l-th DoS attack. l The start time of the lth DoS attack; Define system control inputs under DoS attack. for Among them, Ξ i (0, ∞) represents the activation time of the DoS attack over the entire time interval, A i (0, ∞) represents the dormancy time during the entire DoS attack interval.

5. The optimal safe formation collision avoidance control method for multiple unmanned surface vessels under DoS attack as described in claim 4, characterized in that: In step S5, the approximation result is: in, φ is the optimal weight vector. i δ is the activation function. i This represents the approximate error.

6. The optimal safe formation collision avoidance control method for multiple unmanned surface vessels under DoS attack as described in claim 5, characterized in that: In step S6, the fuzzy state observer with switching gain is: in, It is an estimate of (·); if The DoS attack is then dormant; if Then D O The S attack is active; The output of the observer; The observation error includes first-order observation error and second-order observation error; The first-order observation error is: The second-order observation error is: Differentiating the first-order and second-order observation errors yields: Among them, e i =[e i，1 e i，2 ] T Represent the observation error in vector form, and This represents the first-order observation error when the attack is active. The Herwitz matrix is... C i =[1,0],B i =[0,1] T , These represent the first-order observer gain and the second-order observer gain when the attack is active, respectively. This is the gain vector when the attack is active. These represent the first-order observer gain and the second-order observer gain when the attack is in a dormant state, respectively. This represents the gain vector when the attack is in a dormant state. The estimation error of the weight vector when the attack is active. To attack the estimation error of the weight vector when it is dormant, This represents the approximation error vector when the attack is active. This represents the approximation error vector when the attack is in a dormant state.

7. The optimal safe formation collision avoidance control method for multiple unmanned surface vessels under DoS attack as described in claim 6, characterized in that: Step S7 specifically includes the following steps: S71: Defines the formation error when a DoS attack is in a dormant state: Where, η r (t) is the ideal reference trajectory, η i，d (t) represents the desired formation distance. According to equation (13), the consistency grouping error when a DoS attack is in a dormant state is defined as follows: Where j∈N represents the j-th neighbor unmanned surface vessel of the i-th unmanned surface vessel, η j (t) represents the pose state vector of the j-th neighboring unmanned surface vessel, η j，d (t) represents the expected formation distance of the j-th neighboring unmanned surface vessel, a ij represents the element variable of the adjacency matrix in the directed communication topology, and bi represents the element variable of the weighted link matrix in the directed communication topology; Define the grouping error when a DoS attack is active: According to equation (15), the consistency grouping error when a DoS attack is active is defined as follows: S72: Differentiating the formation error when the array is dormant during a DoS attack, we get: According to equation (17), the derivative of the consistency formation error when the DoS attack is in a dormant state is obtained: in, Differentiating the array error when the DoS attack is active, we get: According to equation (19), taking the derivative of the consistency formation error when the DoS attack is active, we get:

8. The optimal safe formation collision avoidance control method for multiple unmanned surface vessels under DoS attack as described in claim 7, characterized in that: Step S8 specifically includes the following steps: S81: The optimal performance index function when the DoS attack is in a dormant state includes a first-order optimal performance index function and a second-order optimal performance index function when the attack is in a dormant state. make To attack the optimal virtual controller when it is in a dormant state, the first-order optimal performance index function for attacking the dormant state is designed as follows: in, To attack the first-order cost function when it is dormant, This indicates an attack on a virtual controller that is in a dormant state. (Ω) i，1 This represents the allowable set of the virtual controller. make To attack the actual optimal controller when it is in a dormant state, the second-order optimal performance index function for attacking the controller when it is in a dormant state is designed as follows: in, To attack the second-order cost function when it is dormant, This indicates that the attack targets the actual controller during its dormant state, Ω. i,2 Represents the allowable set of the actual controller; The optimal performance index function when the DoS attack is active includes a first-order optimal performance index function and a second-order optimal performance index function when the attack is active. make To determine the optimal virtual controller when the attack is active, the first-order optimal performance index function when the attack is active is designed as follows: in, The first-order cost function is the attack in active condition. To attack a virtual controller that is active; make To determine the actual optimal controller when the attack is active, the second-order optimal performance index function when the attack is active is designed as follows: in, The second-order cost function is the attack's active state. This indicates the actual controller when the attack is active; S82: Construct the Bellman residual as follows: in, Positive design parameters This is an auxiliary item.

9. The optimal safe formation collision avoidance control method for multiple unmanned surface vessels under DoS attack as described in claim 8, characterized in that: In step S9, the weight update law when the DoS attack is in a dormant state includes the first-order evaluation network weight update law, the first-order execution network weight update law, the second-order weight update law, the second-order evaluation network weight update law, and the second-order execution network weight update law. The weight update laws when a DoS attack is active include the first-order judgment network weight update law, the first-order execution network weight update law, the second-order weight update law, the second-order judgment network weight update law, and the second-order execution network weight update law. Step S9 specifically includes the following steps: S91: The positive function is: By using the gradient descent method to solve for the positive function, and taking its derivative, we obtain: Then, design a weight update law to ensure... Established; S92: Constructing the first-order evaluation network weight update law when the attack is dormant: in, It is the learning gain of the first-order evaluation network when it is dormant. For attacking the first-order activation function when it is dormant; Construct the first-order execution network weight update law when the attack is dormant: in, To learn the gain of the first-order execution network when it is dormant; Constructing a second-order weight update law when the attack is dormant: in, To attack a positive definite matrix that is in a dormant state; Constructing the weight update law of the second-order evaluation network when the attack is dormant: in, To learn gain for a second-order evaluation network that is in a dormant state. To attack the second-order activation function when it is dormant; Constructing the weight update law for the second-order execution network when the attack is dormant: in, To attack the learning gain of a second-order execution network when it is dormant; Construct the first-order evaluation network weight update law when the attack is active: in, It is the learning gain of the first-order evaluation network when the attack is active. The first-order activation function is used when the attack is active; Construct the first-order execution network weight update law when the attack is active: in, The attack is a first-order execution network learning gain when it is active; Construct a second-order weight update law when the attack is active: Where, r i a The positive definite matrix when the attack is active; Construct the weight update law of the second-order evaluation network when the attack is active: in, To learn gain for the second-order evaluation network when it is active during an attack. The second-order activation function is the one used when the attack is active; Construct the weight update law of the second-order execution network when the attack is active: in, The learning gain of the second-order execution network when the attack is active.

10. The optimal safe formation collision avoidance control method for multiple unmanned surface vessels under DoS attack as described in claim 9, characterized in that: The optimal safe formation collision avoidance controller includes: the optimal virtual controller when the attack is dormant, the actual optimal controller when the attack is dormant, the optimal virtual controller when the attack is active, and the actual optimal controller when the attack is active. Attacking the optimal virtual controller while it is dormant: in, The first-order positive design parameters are for the attack when the target is dormant. This is an auxiliary item for attacking items that are in a dormant state; Attacking the actual optimal controller when it is dormant: in, The second-order positive design parameters are used when the attack is in a dormant state; Optimal virtual controller when the attack is active: in, The first-order positive design parameters are given when the attack is active. This is an auxiliary item used when the attack is active; The actual optimal controller when the attack is active: in, The second-order positive design parameters are given when the attack is active.

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