Event-triggered control method for synchronization of multiple USV clusters considering thruster failure

Abstract

Multi-USV cluster synchronization event-triggered control method considering thruster faults, belonging to the technical field of unmanned surface vehicle control. To solve the problems that current multi-cluster control does not consider thruster faults in multi-USV multi-cluster control and there is a problem of resource waste. The present invention aims at a multi-USV system divided into s cluster groups. First, the position information and speed information of the virtual leader USV and the dynamic model of the USV in the σ i -th cluster are determined. Then, appropriate USVs are selected as pinning nodes according to the communication topology structure. The thruster fault information is compensated by means of an adaptive input method. The neural network technology is used to estimate the nonlinear uncertainty of the system model and external disturbances. An event-triggered mechanism and a multi-cluster USV distributed fault-tolerant tracking control method based on event-triggering are designed, and then the multi-USV cluster synchronization event-triggered control is realized.

Description

Technical Field

[0001] The invention belongs to the technical field of unmanned boat control, and in particular relates to a multi-cluster USV distributed event triggering control method. Background Art

[0002] Unmanned surface vessels (USVs) can autonomously perform long-term operations without human intervention, which not only reduces work intensity and risk, but also reduces mission costs. In recent years, with the increase in the complexity and difficulty of missions, a single USV has many deficiencies in situational awareness, mission completion capability, and system robustness, which has become a key factor restricting its further application. Therefore, a multi-USV system consisting of multiple USVs has become an important research direction. Through information exchange between USVs, a multi-USV system can quickly obtain more accurate and comprehensive status information and perform corresponding task allocation.

[0003] When facing complex tasks, multi-USV systems need to be divided into multiple clusters to complete them together. For example, in a specific area, multiple USV systems need to perform a series of complex tasks at the same time, including environmental monitoring and mine removal. In order to complete the task more efficiently, the multi-USV system can be divided into multiple clusters, and different equipment can be carried out to perform tasks separately to improve the work efficiency. In addition, the performance and normal operation of the propeller are directly related to the work efficiency and safety of the USV. It is also one of the most prone to failure in actual operation. In order to ensure that the USV can still sail to the target sea area to complete the task in the event of a propeller failure, fault-tolerant technology needs to be considered. Since the USV needs to transmit information frequently to ensure the stability of the system, it is also necessary to design event trigger conditions during the communication process to reduce the burden on the communication equipment. However, the current research on multi-cluster control mainly focuses on multi-agents, and has not been deeply studied on multi-USV systems. It cannot meet the actual application scenarios of USV well, does not consider the problem of propeller failure, and needs to transmit information frequently to ensure the stability of the system, and there is a problem of waste of communication resources. Summary of the invention

[0004] The present invention aims to solve the problem that the current multi-cluster control does not take into account the propeller failure in the USV multi-cluster control and the problem of resource waste.

[0005] A synchronous event-triggered control method for a multi-USV cluster considering thruster failure is provided. For each USV in a multi-USV system, the kinematic and dynamic equations of the USV are established. The multi-USV system comprises N USVs numbered 1, 2...N respectively. The N USVs are divided into s clusters, {v1, v2, .... v s} represents the node set of cluster s; if the i-th USV and the j-th USV belong to the same cluster, then σ i =σ j ;The communication topology between USVs is a directed graph;

[0006] No. i The position and speed information of the virtual leader USV of the cluster is

[0007]

[0008] Among them, v ησi is the σth i The velocity information of the virtual leader USV of the cluster in the inertial coordinate system; v σi is the σth i The velocity information of the cluster's virtual leader USV in the motion coordinate system; J σi is the transformation matrix between the inertial coordinate system and the motion coordinate system;

[0009] Based on the kinematic and dynamic equations of USV, the σ i The dynamic model of the i-th follower USV in the cluster is expressed as:

[0010]

[0011] Where η i represents η corresponding to the i-th follower USV, η=[x,y,ψ] T Represents the position x, y and attitude ψ of the USV in the inertial coordinate system; is the velocity information of the i-th follower USV in the inertial coordinate system; is the mass inertia matrix in the inertial coordinate system, is the Coriolis force and centripetal force matrix in the inertial coordinate system, is the hydrodynamic damping matrix in the inertial coordinate system, g i (η i ) are the restoring force and torque vectors generated by gravity and buoyancy, w i It is unknown external interference; are the control forces and torques acting on the USV under thruster failure;

[0012] based on The fault model of (3) is transformed into:

[0013]

[0014] Among them, F i represents the generalized interference composed of model uncertainty and external interference, and uses neural network approximation to approximate F i Approximation; ρ i(t) is the thruster multiplication fault, which satisfies 0<ρ i (t)≤1;r i (t) = [r i1 (t),r i2 (t),r i3 (t)] T is the thruster additive fault, where r i1 (t),r i2 (t) is the control force addition fault, r i3 (t) is the control torque addition fault;

[0015] Then, the clustering consistency pinning node selection under the directed communication topology is performed: based on the fact that the communication topology between USVs is a directed graph, the directed spanning tree of the communication topology is determined, and the Laplacian matrix L corresponding to the directed graph is converted to [l ij ] is defined as and l ij =-a ij ,i≠j;a ij Indicates whether node j in the directed graph can receive information from node i. ij =1, otherwise a ij =0; degree matrix Defined as For the communication relationship between the virtual leader and the follower, the diagonal matrix B = diag(b1,···,b N ) to describe that if node i receives the information from the leader, then b i =1, otherwise b i =0; determine the pinning node based on the pinning control method, and determine the pinning control part:

[0016]

[0017] in, is the i-th USV cluster Ξ σi sub-clusters; Indicates that the i-th USV can receive information sent by USVs in other groups. represents the i-th USV cluster Ξ σi The set of USVs that can be received in other groups; represents the i-th USV cluster Ξ σi Remove After the collection of USV, Indicates that the i-th USV cannot receive information transmitted by other USVs; the condition will be met and The USV is used as a containment node;

[0018] Then, based on the event trigger mechanism, a multi-cluster USV distributed event-triggered fault-tolerant control law is adopted for control;

[0019] The event triggering mechanism is as follows:

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] Where: is the triggering time of the i-th USV, is the triggering moment of the jth USV; is the position error of the i-th USV at the time of triggering, is the speed error of the i-th USV at this time; parameter κ i ,θ i , λ1, λ2 are all normal values; inf represents the infimum;

[0026] The multi-cluster USV distributed event-triggered fault-tolerant control law is as follows:

[0027] τ i (t) = τ 1i (t)+τ 2i (t)+τ 3i (t)+τ 4i (t) (14)

[0028]

[0029]

[0030]

[0031]

[0032] In the formula, is the adaptive update law; sign(·) is the sign function; the neural network estimation law is is the weight matrix ω i The estimated value of the weight matrix estimation error φ i represents the activation function; is the upper bound of the uncertainty Adaptive law for approximation, upper bound of uncertainty approximation error is the approximate value of the upper bound of the uncertainty term The estimated value of i is a normal value;

[0033]

[0034]

[0035]

[0036] In the formula, m i and n i is the adaptive pinning parameter. If the i-th USV is selected as the pinning node, then m i >0,n i >0, otherwise m i =0,n i =0; control parameters is a constant; the adaptive traction parameter m i and n i The update method is as follows:

[0037]

[0038]

[0039] In the formula, h 1i ,h 2i is a positive constant; μ 1i (t),μ 2i (t) is a continuous bounded function that is always positive; and is the estimate of the adaptive pinning parameter.

[0040] Furthermore, the fault model is

[0041] Furthermore, the fault model satisfies the following relationship:

[0042]

[0043]

[0044] where ρ i , denote the upper and lower bounds of the thruster multiplication fault, respectively, Represents an upper bound on thruster additive failure.

[0045] Furthermore, the generalized disturbance consisting of model uncertainty and external disturbance Where ΔM ηi ,ΔCηi ,ΔD ηi It represents the error between the actual model hydrodynamic coefficient and the theoretical model hydrodynamic coefficient.

[0046] Furthermore, the kinematic and dynamic equations of the USV are as follows:

[0047]

[0048]

[0049] Where η = [x, y, ψ] T Represents the position x, y and attitude ψ of the USV in the inertial coordinate system, v = [u, v′, r] T represents the velocity u, v′ and angular velocity r in the motion coordinate system; J(η) is the transformation matrix between the inertial coordinate system and the motion coordinate system; M is the mass inertia matrix, C(v) is the Coriolis force and centripetal force matrix, D(v) is the hydrodynamic damping matrix, g(η) is the restoring force and torque vector generated by gravity and buoyancy, τ=[τ1,τ2,τ3] T are the control forces τ1, τ2 and torque τ3 generated by the propulsion system, and w is the unknown external disturbance.

[0050] Furthermore, the continuously bounded function μ is always positive. 1i (t),μ 2i (t) Satisfaction They are μ 1i (t),μ 2i The upper bound of (t).

[0051] Furthermore, the adaptive update law as follows:

[0052]

[0053] Where: Adaptively update parameter γ i is a positive constant, satisfy in Is a normal number.

[0054] Beneficial effects:

[0055] Aiming at the problems of model uncertainty, external interference and thruster failure in the coordinated control of multi-cluster USV system, the present invention selects appropriate USV as the restraining node according to the communication topology, compensates the thruster failure information with the help of adaptive input method, estimates the nonlinear uncertainty and external interference of the system model by using neural network technology, and designs a new type of multi-cluster USV distributed fault-tolerant tracking control method based on event triggering. The event triggering condition is designed by state measurement error, which proves that the proposed control algorithm realizes the intermittent update of the controller while ensuring the stability of the multi-cluster USV system, thereby reducing the consumption of the controller. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 Schematic diagram of the communication topology between the virtual leader USV and the follower USV.

[0057] Figure 2 Tracking curve diagram of the follower USV trajectory (angle).

[0058] Figure 3 It is the speed tracking curve diagram of the follower USV.

[0059] Figure 4 This is the follower USV trajectory (angle) error diagram.

[0060] Figure 5 is the speed error diagram of the follower USV.

[0061] Figure 6 Figure 2 is the control force and torque diagram of USV3.

[0062] Figure 7 This is the event triggering time diagram of the follower USV.

[0063] Figure 8 The event triggering interval for follower USV1.

[0064] Fig. 9 The event triggering interval for follower USV2.

[0065] Fig.10 The event triggering interval for follower USV3.

[0066] Fig.11 The event triggering interval for the follower USV4.

[0067] Fig.12 The event triggering interval of follower USV5.

[0068] Fig.13 The event triggering interval of follower USV6. DETAILED DESCRIPTION

[0069] The present invention aims at the multi-cluster distributed control problem of multi-USV system, considers the influence of propeller failure, and combines event-triggered control to propose a multi-cluster USV distributed fault-tolerant tracking control method based on directed communication topology. In order to realize the trajectory tracking control of multi-cluster USV system with propeller failure through multi-cluster USV distributed fault-tolerant collaborative tracking control algorithm under event triggering, the goal of the present invention is to design a controller u so that the position and attitude quantity η of the multi-cluster USV system can still track the expected value η in the presence of nonlinear uncertainty of the model, external interference and propeller failure. d And let the tracking error e = η-η d There are pre-given dynamic performance and steady-state response conditions. The following is an explanation in conjunction with a specific implementation. Before the specific description, the coordinate system and parameter definition of the present invention are first explained with the event trigger mechanism and multi-cluster collaborative control:

[0070] Inertial coordinate system (E-ξηζ): The origin E can be selected at a point on the horizontal plane. The Eξ axis and the Eη axis are placed in the horizontal plane and are perpendicular to each other. The positive direction of the Eξ axis points to the due north, and the positive direction of the Eη axis points to the due east. Eζ is perpendicular to the Eξη plane, and its positive direction points to the center of the earth.

[0071] Motion coordinate system (G-xyz): The origin G is taken at the center of gravity of the USV, and the x-axis, y-axis and z-axis are the intersection lines of the waterline, transverse section and mid-longitudinal section passing through the origin respectively. Gx points from the center of gravity to the bow along the mid-longitudinal axis, Gy points from the center of gravity to the starboard side of the USV, and Gz is perpendicular to the XOY plane and points from the center of gravity to the bottom of the ship.

[0072] Parameter definition:

[0073] M is the mass inertia matrix; η=[x,y,z,φ,θ,ψ] T is the six-degree-of-freedom position and attitude value of USV in the fixed coordinate system; η d =[x d ,y d ,z d ,φ d ,θ d ,ψ d ] T is the expected value of the six-degree-of-freedom position and attitude of the USV in the fixed coordinate system; e = η-η d is the tracking error; v = [u, v, w, p, q, r] T is the velocity and angular velocity in the moving coordinate system; J(η) is the transformation matrix between the fixed coordinate system and the moving coordinate system; C(v) is the Coriolis force and centripetal force matrix; D(v) is the hydrodynamic damping matrix; g(η) is the force and torque vector generated by gravity and buoyancy; τ is the control force and torque generated by the propulsion system; are the control force and torque under thruster failure; w is the unknown external interference; χ is an unknown positive constant.

[0074] Since the mathematical model of the six degrees of freedom of USV is too complicated, the following assumptions are proposed based on the actual movement of USV and its own characteristics:

[0075] (1) USV is a rigid body with uniform mass distribution;

[0076] (2) USV is symmetric about the XOZ plane;

[0077] (3) Ignore other movements of the USV outside the horizontal plane.

[0078] Based on the above assumptions, the six degrees of freedom of the USV are converted into three degrees of freedom in the horizontal plane, namely, sway, swing and bow pitch. The motion states and symbol definitions of the USV are shown in Table 1.

[0079] Table 1 USV motion status and symbol definitions

[0080]

[0081] Note: In order to distinguish the representation, [u,v,w,p,q,r] T The v in is represented by v′.

[0082] Event trigger mechanism: In actual engineering applications, the behavior of USVs is mainly controlled by embedded microprocessors. In the past, sampling data, transmitting information, or updating controllers were all completed at fixed time intervals, which belonged to the time trigger mechanism. The disadvantage of this trigger strategy is that it lacks intelligence and causes a certain waste of resources. The event trigger mechanism can design appropriate trigger conditions, and data and controllers can only be updated when the conditions are met.

[0083] Multi-cluster collaborative control: refers to dividing the multi-agent system into multiple different groups, and the states of the agents in each group are consistent. When facing complex tasks, the multi-USV system needs to be divided into multiple clusters to complete them together, and each group of USVs performs its own tasks separately, which can improve the efficiency of task operations. Specific implementation method one:

[0085] This embodiment is a multi-USV cluster synchronization event triggering control method considering thruster failure, including the following steps:

[0086] S1. Establish the kinematic and dynamic equations of USV:

[0087]

[0088] Where η=[x,y,ψ] TRepresents the position x, y and attitude ψ of the USV in the inertial coordinate system, v = [u, v′, r] T represents the velocity u, v′ and angular velocity r in the moving coordinate system; J(η) is the transformation matrix between the inertial coordinate system and the moving coordinate system. is the mass inertia matrix, are the Coriolis and centripetal force matrices, is the hydrodynamic damping matrix, g(η) is the restoring force and torque vector generated by gravity and buoyancy, τ=[τ1,τ2,τ3] T are the control forces τ1, τ2 and torque τ3 generated by the propulsion system, and w is the unknown external disturbance.

[0089] S2. USV model transformation under thruster failure:

[0090] Assume that there is a multi-USV system, which includes N USVs, numbered 1, 2...N. These USVs are divided into s clusters, and the USVs in each cluster perform different tracking tasks. s} represents the node set of cluster s, σ i = n means that the i-th USV belongs to the n-th cluster. If the i-th USV and the j-th USV belong to the same cluster, then σ i =σ j The communication topology between USVs is a directed graph.

[0091] By setting up a virtual navigator USV and defining the motion path of the virtual navigator, the path of the USV cluster is defined, increasing the robustness of the USV formation system. Because the virtual navigator is virtual, it has more accurate position and attitude information. By accurately positioning the virtual navigator, the precise expected position of the USV cluster can be obtained.

[0092] No. i The position and speed information of the virtual leader USV of the cluster is

[0093]

[0094] Among them, v ησi is the σth i The velocity information of the virtual leader USV of the cluster in the inertial coordinate system; v σi is the σth i The velocity information of the cluster’s virtual leader USV in the motion coordinate system.

[0095] In view of the model's nonlinear uncertainty, external disturbances and thruster failures, a feasible mathematical expression is considered. Based on formula (1), the σ i The dynamic model of the i-th follower USV in the cluster can be expressed as:

[0096]

[0097] Where η i represents η corresponding to the i-th follower USV, η=[x,y,ψ] T Represents the position x, y and attitude ψ of the USV in the inertial coordinate system; is the velocity information of the i-th follower USV in the inertial coordinate system; is the mass inertia matrix in the inertial coordinate system, is the Coriolis force and centripetal force matrix in the inertial coordinate system, is the hydrodynamic damping matrix in the inertial coordinate system, g i (η i ) are the restoring force and torque vectors generated by gravity and buoyancy, w i It is unknown external interference; are the control forces and torques acting on the USV under thruster failure.

[0098] The fault model is as follows:

[0099]

[0100] Where ρ i (t) is the thruster multiplication fault, which satisfies 0<ρ i (t)≤1;r i (t) = [r i1 (t),r i2 (t),r i3 (t)] T is the thruster additive fault, where r i1 (t),r i2 (t) is the control force addition fault, r i3 (t) is the control torque addition fault.

[0101] For fault model (3), it satisfies the following relationship

[0102]

[0103] in ρ i , denote the upper and lower bounds of the thruster multiplication fault, respectively, Represents an upper bound on thruster additive failure.

[0104] Combined with fault model (4), (3) can be transformed into:

[0105]

[0106] Generalized disturbance consisting of model uncertainty and external disturbance Where ΔM ηi ,ΔC ηi ,ΔD ηi It represents the error between the actual model hydrodynamic coefficient and the theoretical model hydrodynamic coefficient. i It can be processed by neural network approximation.

[0107] S3, cluster consistency control node selection under directed communication topology:

[0108] Assume that there is a multi-USV system, which includes N USVs, numbered 1, 2...N. These USVs are divided into s clusters, and the USVs in each cluster perform different tracking tasks. s} represents the node set of cluster s, σ i =n means that the i-th USV belongs to the n-th cluster.

[0109] In practical applications, due to the influence of the ocean environment and distance, two-way communication may not be possible between USVs. Under directed communication topology, control can be achieved as long as the system's communication topology has a directed spanning tree.

[0110] G = (υ, ε, A) represents a directed graph, υ is a node set, is an edge set, A=[a ij ] represents the weighted adjacency matrix of the directed graph. For nodes i and j, (υ i ,υ j )∈ε means that node j can receive information from node i, where υ i is called the root node, j is called a child node. i Neighbors use N i =(υ j :( j ,υ i )∈ε}. If (υ i ,υ j )∈ε, then A=[a ij ] elements satisfy a ij =1, otherwise a ij = 0. General provisions a ii = 0, indicating that each node has no connectivity. In a directed graph G, if, except for the root node, each node has only one parent node, and there is a directed path from the root node to the remaining nodes, then G is called a directed tree. If the directed tree contains all the nodes of G, then the directed tree is a directed spanning tree of the directed graph. If a directed graph contains a subgraph of a directed spanning tree, then the directed graph has a directed spanning tree. Laplacian matrix L = [l ij ] is defined as and l ij =-a ij ,i≠j. Degree matrix Defined as For the communication relationship between the virtual leader and the follower, the diagonal matrix B = diag(b1,···,b N ). If node i can receive the information from the leader, then b i =1, otherwise b i =0.

[0111] The pinning control method is to divide a group of nodes into several subclusters. The nodes in the same subcluster are synchronized to a consistent state, but the nodes in different subclusters may not be synchronized to a consistent state. The pinning control method only needs to control a small number of nodes, and these controlled nodes are called pinning nodes.

[0112] Pinning control part τ 2i As shown below

[0113]

[0114] in, is the i-th USV cluster Ξ σi sub-clusters of; Indicates that the i-th USV can receive information sent by USVs in other groups. represents the i-th USV cluster Ξ σi The set of USVs in other groups can be received in the control method. The containment control method can compensate for the influence of other USVs. represents the i-th USV cluster Ξ σi Remove The subsequent collection of USVs, D i =0 means that the i-th USV cannot receive information transmitted by other USVs. and The USV is used as the pinning node. The pinning node is a node that is directly controlled by the pinning control method.

[0115] S4. Event trigger mechanism design

[0116] Considering that frequent controller updates will cause resource waste, for the i-th USV, the event trigger mechanism is proposed as follows:

[0117]

[0118]

[0119]

[0120]

[0121]

[0122] Where: is the triggering time of the i-th USV, is the triggering moment of the jth USV; is the position error of the i-th USV at the time of triggering, is the speed error of the i-th USV at this time; parameter κ i ,θ i , λ1, λ2 are all normal values. inf represents the infimum.

[0123] S5. Design of multi-cluster USV distributed event-triggered fault-tolerant control law:

[0124] Considering the influence of model nonlinear uncertainty, external disturbance and thruster failure, the following distributed fault-tolerant cooperative control law for multi-cluster USV is proposed:

[0125] τ i (t) = τ 1i (t)+τ 2i (t)+τ 3i (t)+τ 4i (t) (14)

[0126]

[0127]

[0128]

[0129]

[0130] In the formula, is the adaptive update law; sign(·) is the sign function; the neural network estimation law is is the weight matrix ω i The estimated value of the weight matrix estimation error φ i represents the activation function; is the upper bound of the uncertainty Adaptive law for approximation, upper bound of uncertainty approximation error is the approximate value of the upper bound of the uncertainty term The estimated value of i is a normal value.

[0131]

[0132]

[0133]

[0134] In the formula, m i and n i is the adaptive pinning parameter. If the i-th USV is selected as the pinning node, then m i >0,n i >0, otherwise m i =0,n i =0; control parameters is a constant; the adaptive traction parameter m i and n i The updated design is as follows

[0135]

[0136] Where: h 1i ,h 2i is a positive constant; μ 1i (t),μ 2i (t) is a continuously positive bounded function that satisfies They are μ 1i (t),μ 2i The upper bound of (t); and is the estimate of the adaptive pinning parameter.

[0137] The distributed fault-tolerant cooperative control law of multi-cluster USVs consists of four parts, among which the feedback compensation part τ1 and the containment control part τ2 are used to realize the distributed cooperative tracking of multi-cluster USVs. The adaptive input compensation part τ3 is used to solve the problem of thruster failure. The neural network part τ4 can estimate nonlinear uncertainties and external interference.

[0138] Adaptive Update Law The design is as follows

[0139]

[0140] Where: Adaptively update parameter γ i is a positive constant, satisfy in Is a normal number.

[0141] Theoretical derivation of the designed control law:

[0142] A1. Dynamic model of USV

[0143] The three-degree-of-freedom nonlinear model based on Newton's basic theorem of kinematics and the relationship between coordinate systems is expressed as follows:

[0144]

[0145] Where η=[x,y,ψ] T Represents the position and attitude of USV in the inertial coordinate system, v = [u, v, r] T represents the velocity and angular velocity in the moving coordinate system, and J(η) is the transformation matrix between the inertial coordinate system and the moving coordinate system. is the mass inertia matrix, are the Coriolis and centripetal force matrices, is the hydrodynamic damping matrix, g(η) is the restoring force and torque vector generated by gravity and buoyancy, τ=[τ1,τ2,τ3] T is the control force and torque generated by the propulsion system, and w is the unknown external disturbance.

[0146] The thruster is an important component of USV and also the main source of failure problems. i The dynamic model of the i-th follower USV in the cluster can be expressed as:

[0147]

[0148] In the formula are the control forces and torques acting on the USV under thruster failure.

[0149] Consider the following error model:

[0150]

[0151] Where ρ i (t) is the thruster multiplication fault, which satisfies 0<ρ i (t)≤1;r i (t) = [r i1 (t),r i2 (t),r i3 (t)] T Addition fault for thrusters.

[0152] For the error model (23), it satisfies the following relationship

[0153]

[0154]

[0155] in ρ i , denote the upper and lower bounds of the thruster multiplication fault, respectively, Represents an upper bound on thruster additive failure.

[0156] The control objective of the present invention can be expressed as: designing the controller u so that the position and attitude quantity η of the multi-cluster USV system can still track the expected value η in the presence of model nonlinear uncertainty, external disturbance and thruster failure d , and make the tracking error e = η-η d It has predetermined dynamic performance and steady-state response.

[0157] Combining the actual engineering background, we put forward three assumptions:

[0158] Assumption 1: Position and attitude angle η and its first-order derivative Measurable.

[0159] Assumption 2: The expected position and attitude angle η d Its first- and second-order derivatives are known and bounded.

[0160] Assumption 3 The total uncertainty F of the system is bounded, that is, ||F||≤χ, where χ is an unknown positive constant.

[0161] A2. Design of distributed event-triggered multi-cluster fault-tolerant control law

[0162] Based on the event trigger mechanism, combined with the adaptive input compensation strategy and adaptive pinning control method, a multi-cluster USV distributed fault-tolerant cooperative control law is designed.

[0163] τ i (t) = τ 1i (t)+τ 2i (t)+τ 3i (t)+τ 4i (t) (26)

[0164]

[0165]

[0166]

[0167] in Yes σi A subset of .

[0168]

[0169] If the i-th USV is selected as the pinning node, then m i >0,n i >0, otherwise m i =0,n i = 0. Adaptive control parameter mi and n i Estimated value of and The updated design is as follows

[0170]

[0171] Where: h mi is a positive constant; μ mi (t) is a positive continuous bounded function that satisfies is μ mi The upper bound of (t)(m=1,2).

[0172] The diagonal matrix is ​​defined as follows

[0173]

[0174] Adaptive Update Law The design is as follows

[0175]

[0176] Where: γ i >0, satisfy is a normal number.

[0177] From (26), we can see that the distributed fault-tolerant cooperative control law of multi-cluster USVs consists of four parts. The feedback compensation part τ1 and the containment control part τ2 are used to realize the distributed cooperative tracking of multi-cluster USVs. The adaptive input compensation part τ3 is used to solve the problem of thruster failure. In addition, the neural network part τ4 can estimate nonlinear uncertainty and external interference, which will be given in the subsequent design.

[0178] In the containment control part τ2, is the i-th USV cluster Ξ σi sub-clusters; Indicates that the i-th USV can receive information sent by USVs in other groups. represents the i-th USV cluster Ξ σi The set of USVs in other groups can be received in the control method. The containment control method can compensate for the influence of other USVs. represents the i-th USV cluster Ξ σi Remove After the collection of USV, It means that the i-th USV cannot receive the information transmitted by other USVs, and these USVs are selected as pinning nodes.

[0179] For the i-th USV, when time t satisfies At this time, the trigger condition is not met. From (9), we can know that: Φ i (t)<0.

[0180] According to Φ i (t)<0, combined with (10)-(13), we can get:

[0181]

[0182] Define the following vector:

[0183]

[0184]

[0185]

[0186] According to Young's inequality, (34) can be rewritten as

[0187]

[0188] Furthermore, (35) can be simplified to

[0189]

[0190] Where ζ and ξ are:

[0191]

[0192]

[0193] Select the following Lyapunov function

[0194]

[0195] in When the parameter satisfy , Ω is a positive definite matrix.

[0196] Taking the derivative of (39) and substituting (6) and (7) into (39), we can obtain

[0197]

[0198] Unknown Term F i The neural network control technology is used for approximation, and the neural network part of the control law is designed as follows:

[0199]

[0200] Design the neural network estimation law as

[0201]

[0202] Where: and Yes i The estimated value of .

[0203] To approach the upper bound The design adaptive law is as follows

[0204]

[0205] Where: and yes The estimated value of i is a normal value; Select appropriate parameters to make the following inequality hold. The inequality is defined as:

[0206]

[0207]

[0208]

[0209] in L is the Laplacian matrix of the directed graph; is the submatrix of matrix L with the first l rows and columns removed; m i and n i are the restraining parameters; B, C and M l The definition of is as follows.

[0210] for and D = diag(d1, d2, ... d l ...0,...0) N×N , where d l > 0.

[0211]

[0212] Where M is a symmetric matrix; M l is the submatrix of the matrix M with the first l rows and columns removed; Both B and C are matrices of corresponding dimensions.

[0213] For the matrix (47), if all d l satisfy Then M l<0 is equivalent to MD<0. Therefore, the selection range of the parameters in (44)-(46) can be obtained. These parameters are related to the Laplacian matrix L of the directed graph and the efficiency parameters of the propeller. Appropriate parameters can be selected to satisfy the inequalities in (44)-(46).

[0214] A3. Stability Analysis of Distributed Event-Triggered Multi-Cluster Fault-Tolerant Control

[0215] For multi-cluster USV systems (6) and (7) with model uncertainty, external interference and thruster failure, on the basis of assumptions 1 to 3, based on the event trigger mechanism (9)-(13), then under the action of control law (14), parameter adaptive update law (19), (20) and neural network update law (42), (43), the follower USV can follow the trajectory formed by the virtual leader USV in the same group, realizing distributed fault-tolerant tracking control of multi-cluster USVs.

[0216] Proof: Choose a suitable Lyapunov function:

[0217]

[0218] Where:

[0219] Substituting (40) into the derivative of V2, we can obtain

[0220]

[0221] make Based on (14) and (19), (49) can be rewritten as:

[0222]

[0223] Substituting (15) and (16) into (50), we can obtain:

[0224]

[0225] according to have (51) can be rewritten as

[0226]

[0227] Note that in (52), combined with (36), we have:

[0228]

[0229] in

[0230] definition

[0231]

[0232] Substituting the adaptive input compensation law (29) and (54) into (50), we have

[0233]

[0234] Note that in (50), there is

[0235]

[0236] Combining (55) and (56), we can obtain

[0237]

[0238] Consider μ 1i (t)>0 and μ 2i (t)>0, note that in (50), we can get

[0239]

[0240] Similarly, we can get

[0241]

[0242] Substituting (52), (53) and (57)-(59) into (50), we obtain:

[0243]

[0244] Define the following matrix:

[0245]

[0246] According to (61), (60) can be rewritten as

[0247]

[0248] For multi-cluster USV systems (2) and (7), assuming that there is at least one directed spanning tree, then the Laplacian matrix L has one and only one eigenvalue that is zero, and the real parts of the other eigenvalues ​​are all positive. and is a negative definite matrix. Simplifying (62) to

[0249]

[0250] Here N, α1, β1 satisfy the following conditions

[0251]

[0252]

[0253]

[0254] Define the following Lyapunov function

[0255]

[0256] Taking the derivative of (64), we have

[0257]

[0258] Substituting (41)-(43) into (65), we can obtain

[0259]

[0260] because (66) can be simplified to

[0261]

[0262] Consider the trace of a matrix with the following properties

[0263] tr(A+B)=tr(A)+tr(B)

[0264] tr(AB)=tr(BA) (68)

[0265] 2tr(AB)≤tr(A T A)+tr(B T B)

[0266] Note that in (67), based on (68), there exists

[0267]

[0268] According to Young's inequality, we can get

[0269]

[0270] Combining (69) and (70), (67) can be rewritten as

[0271]

[0272] (71) can be further simplified as

[0273]

[0274] where α2 and β2 are

[0275]

[0276]

[0277] Integrating both sides of (72) in the range [t0, t], we obtain

[0278]

[0279] Assume that there is a time T m , satisfying V3(T m )=V m , where V m is a normal number. Based on (73), we have

[0280]

[0281] If t ≥ T m , then V3(t)≤V m According to the definition of V3,

[0282]

[0283] Select the following parameters

[0284]

[0285] According to (74) and (75), we can get

[0286]

[0287] Because v i =J i -1 v ηi and v σi =J σi -1 v ησi ,exist

[0288]

[0289] Based on (76) and (77), we have

[0290]

[0291] in

[0292] From (73) and (78), we can see that the signal of the multi-cluster USV system can converge to a small neighborhood around 0, and the trajectory error and speed error in the system are bounded. Therefore, the USV can satisfy the following conditions in any initial state:

[0293]

[0294]

[0295] Therefore, the USV can follow the virtual leader USV in the same group to form a trajectory, and the multi-USV system achieves cluster synchronization. The proof is complete.

[0296] A4. Distributed event-triggered multi-cluster fault-tolerant control Zeno behavior proof

[0297] For the multi-cluster USV systems (6) and (7), under the action of the event triggering mechanism (9)-(13), the system does not have Zeno behavior.

[0298] Proof: When time t satisfies At this time, the event triggering condition is not met. Based on the event triggering mechanism (9)-(13), we can get:

[0299]

[0300] Define the following equation:

[0301]

[0302] e * (t)=||e ηi (t)||+||e vηi (t)||+||e ησi (t)||+||e vησi (t)|| (81)

[0303] Based on (80), (79) can be further transformed into

[0304]

[0305] By taking the derivative of (81), we can obtain

[0306]

[0307] Where: Denotes the generalized interference F i The upper bound of π and They are defined as

[0308]

[0309]

[0310] All signals in the system are bounded, so and are all convergent. When the event triggering condition is met, there is

[0311]

[0312] According to (83) and (86), we can get

[0313]

[0314] When the event triggering condition is met again at a certain moment, there is

[0315]

[0316] Combining (87) and (88), we can get

[0317]

[0318] assumed Then there exists a value k i , so that According to formula (89), we know

[0319]

[0320] From (90), we can see that at this time κ i ≤0. However, according to the event trigger mechanism, we can judge κ i >0, the assumption does not match the actual situation, so the above assumption is not valid. From the above analysis, we can get and Therefore, under the proposed event triggering conditions, there is no Zeno behavior in the system. The proof is complete.

[0321] Example

[0322] In order to verify the effectiveness of the control method designed by the present invention, a simulation test is carried out. The multi-cluster USV system consists of 6 followers (numbered 1, ..., 6) and two virtual navigators (numbered 01, 02), and the effects caused by model uncertainty, external disturbances, and thruster failure are considered.

[0323] The USV used in the present invention is a Cybership II model ship, and the corresponding hydrodynamic parameters of the USV model are:

[0324] m=23.8,I z =1.76,x g =0.046;

[0325] X u =-0.7225, X uu =-1.3274,X uuu=-5.8664;

[0326] Y v =-0.8612, Y vv =-36.2823, Y r =0.1079;

[0327] N v =0.1052, N vv =5.0437, N r =-1.9;

[0328] X du = -2.0;

[0329] Y dv =-10.0, Y dr =0;

[0330] N dv =0,N dr = -1.0;

[0331] Y rv =-8.05, Y vr =-0.845, Y rr =-3.45;

[0332] N rv =0.13, N vr =0.08, N rr =-0.75.

[0333] The position (angle) of the virtual navigator USV is shown in Table 2.

[0334] Table 2 Position (angle) trajectory of virtual navigator USV

[0335]

[0336] The initial position (angle) and speed information of the follower USV are shown in Tables 3 and 4.

[0337] Table 3 Initial position (angle) of USV

[0338]

[0339] Table 4 Initial (angular) velocity of USV

[0340]

[0341] Model uncertainty

[0342] In order to facilitate simulation analysis, the present invention quantifies the model uncertainty. In view of the model uncertainty of the USV itself, a 30% model error is selected in the simulation test, that is, the dynamic model value in the controller is 70% of the actual value.

[0343] External disturbance

[0344] The random external interference that USV may encounter during navigation is defined as:

[0345] w i (t) = [w i1 (t),w i2 (t),w i3 (t)] T (91)

[0346] Where: w i1 (t) and w i2 (t) is Gaussian white noise with mean 3 and variance 1; w i3 (t) is Gaussian white noise with mean 0.2 and variance 1.

[0347] Communication topology

[0348] The multi-cluster USV system consists of six followers (numbered 1, ..., 6) and two virtual leaders (numbered 01, 02). The communication topology of the multi-cluster USV system is as follows: Figure 1 shown.

[0349] from Figure 1 It can be seen that USV3 of cluster G2 cannot receive information from USV of cluster G1, and it cannot receive information from other USVs in cluster G2, satisfying For USV2 and USV4 of cluster G1, they can receive information about USV in cluster G2, satisfying and Therefore, USV2, USV3, and USV4 are selected as pinning nodes.

[0350] Thruster failure

[0351] In the experiment simulating potential thruster failure, considering that the thruster failure gradually becomes serious, the thruster failure mode is shown in equations (92)-(93):

[0352]

[0353]

[0354] according to The definition of

[0355]

[0356]

[0357]

[0358] Controller Parameters

[0359] The controller parameters are selected as

[0360] h 12 =h 22 =0.01, h 14 =h 24 = 0.01 and h 13 =h 23 =0.7. The adaptive update parameter is chosen as γ i =0.001,ζ i (t) = 10e -2t and The initial values ​​of m i and n i The initial values ​​are m i (0) = 0.2 and n i (0) = 0.1. The parameter selected in the event trigger condition is θ i =0.3,κ i =0.03, λ1=0.0001 and λ2=0.0001.

[0361] The other parameters are selected as μ 22 (t) = μ 23 (t) = μ 24 (t) = 2e -2t , Δ i = 0.03 and μ 12 (t) = μ 13 (t) = μ 14 (t) = 2e -t For neural network technology, the activation function is selected as Gaussian function, and the number of neurons is 11. The activation function center c ij Evenly distributed in the area [-0.1, 0.1] 6 , width b ij Select b ij =30. and The initial value of is 0.

[0362] Simulation Analysis

[0363] The multi-cluster USV system consists of six followers (numbered 1, ..., 6) and two virtual leaders (numbered 01, 02). The control effect of the multi-cluster USV distributed fault-tolerant cooperative controller is shown in Figures 2 to 5 shown.

[0364] Without loss of generality, this simulation test shows the control force and control torque of the follower USV 3, such as Figure 6 shown.

[0365] The event triggering time within each follower USV5s is as follows Figure 7 shown.

[0366] For each follower USV, the event triggering time interval within 5s is as follows Figures 8 to 13 shown.

[0367] The event triggering times and triggering ratios of the follower USV are shown in Table 5.

[0368] Table 5 Event triggering times and triggering ratios of follower USVs

[0369]

[0370] According to the thruster failure expressions (92) and (93), the thruster of the system gradually deteriorates over time. Figures 2 to 5 It can be seen that the follower USVs achieve trajectory and speed tracking of the virtual leader USVs in their respective clusters. Figure 2 The trajectory (angle) curve shows that at any initial position, after 5s, each follower USV in each cluster can track the trajectory of the virtual leader USV in its own cluster, realizing the coordinated tracking control of the multi-cluster USV system, so the impact of the thruster failure on the USV is small. Figure 6 It can be seen that the control input of the follower USV is large in the initial stage, but after the system is relatively stable, the control force and torque are limited to 50N and 30Nm respectively. When the bowing angle of the USV changes greatly, the control torque of the follower USV also changes suddenly. However, after a period of time, the curve of the control input will become relatively smooth.

[0371] Figure 7 It is the time when the USV updates the controller within 5s. It can be seen from the figure that only when the trigger condition is met, the USVs communicate to update the information. Combined with Table 3, it can be seen that the number of triggers for each USV is different, and the rate of event triggering is between 31.63% and 51.78%.

[0372] From the above analysis, it can be seen that under the action of event trigger mechanism (9)-(13) and control law (14), in order to solve the problems of model uncertainty, external interference and thruster failure in the coordinated control of multi-cluster USV system, appropriate USV is selected as the restraining node according to the communication topology structure, and the thruster failure information is compensated by adaptive input method. The nonlinear uncertainty and external interference of the system model are estimated by neural network technology, and a new type of multi-cluster USV distributed fault-tolerant tracking control method based on event trigger is designed. The event trigger condition is designed by state measurement error, which proves that the proposed control algorithm can realize the intermittent update of the controller while ensuring the stability of the multi-cluster USV system, thereby reducing the consumption of the controller.

[0373] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A synchronous event triggering control method for a multi-USV cluster considering thruster failure, characterized in that: For each USV in a multi-USV system, the kinematic and dynamic equations of the USV are established; the multi-USV system comprises N USVs, numbered 1, 2...N; the N USVs are divided into s clusters, {v1, v2, .... v s } represents the node set of cluster s; if the i-th USV and the j-th USV belong to the same cluster, then σ i =σ j ;The communication topology between USVs is a directed graph; No. i Speed ​​information of the virtual leader USV of the cluster and acceleration information for Among them, v ησi is the σth i The velocity information of the virtual leader USV of the cluster in the inertial coordinate system; v σi is the σth i The velocity information of the cluster's virtual leader USV in the motion coordinate system; J σi is the transformation matrix between the inertial coordinate system and the motion coordinate system; Based on the kinematic and dynamic equations of USV, the σ i The dynamic model of the i-th follower USV in the cluster is expressed as: Where η i represents η corresponding to the i-th follower USV, η=[x,y,ψ] T represents the position x, y and attitude ψ of USV in the inertial coordinate system; v ηi is the velocity information of the i-th follower USV in the inertial coordinate system; M ηi is the mass inertia matrix in the inertial coordinate system, C ηi is the Coriolis force and centripetal force matrix in the inertial coordinate system, D ηi is the hydrodynamic damping matrix in the inertial coordinate system, g i (η i ) are the restoring force and torque vectors generated by gravity and buoyancy, w i It is unknown external interference; are the control forces and torques acting on the USV under thruster failure; based on The fault model of (3) is transformed into: Among them, F i represents the generalized interference composed of model uncertainty and external interference, and uses neural network approximation to approximate F i Approximation; ρ i (t) is the thruster multiplication fault, which satisfies 0<ρ i (t)≤1;r i (t) = [r i1 (t),r i2 (t),r i3 (t)] T is the thruster additive fault, where r i1 (t),r i2 (t) is the control force addition fault, r i3 (t) is the control torque addition fault; Then, the clustering consistency pinning node selection under the directed communication topology is performed: based on the fact that the communication topology between USVs is a directed graph, the directed spanning tree of the communication topology is determined, and the Laplacian matrix L corresponding to the directed graph is converted to [l ij ] is defined as and l ij =-a ij ,i≠j;a ij Indicates whether node j in the directed graph can receive information from node i. ij =1, otherwise a ij =0; degree matrix Defined as For the communication relationship between the virtual leader and the follower, the diagonal matrix B = diag(b1,…,b N ) to describe that if node i receives the information from the leader, then b i =1, otherwise b i =0; determine the pinning node based on the pinning control method, and determine the pinning control part: in, is the i-th USV cluster Ξ σi sub-clusters; Indicates that the i-th USV can receive information sent by USVs in other groups. represents the i-th USV cluster Ξ σi The set of USVs that can be received in other groups; represents the i-th USV cluster Ξ σi Remove After the USV collection, Indicates that the i-th USV cannot receive information transmitted by other USVs; the condition will be met and The USV is used as a containment node; Then, based on the event trigger mechanism, a multi-cluster USV distributed event-triggered fault-tolerant control law is adopted for control; The event triggering mechanism is as follows: Where: is the triggering time of the i-th USV, is the triggering moment of the jth USV; is the position error of the i-th USV at the time of triggering, is the speed error of the i-th USV at this time; parameter κ i , λ1, λ2 are both normal values; inf represents the infimum; The multi-cluster USV distributed event-triggered fault-tolerant control law is as follows: t i (t)=τ 1i (t)+τ 2i (t)+τ 3i (t)+τ 4i (t) (14) In the formula, is the adaptive update law; sign(·) is the sign function; the neural network estimation law is is the weight matrix ω i The estimated value of the weight matrix estimation error Φ i represents the activation function; is the upper bound of the uncertainty Adaptive law for approximation, upper bound of uncertainty approximation error is the approximate value of the upper bound of the uncertainty term The estimated value of i is a normal value; In the formula, m i and n i is the adaptive pinning parameter. If the i-th USV is selected as the pinning node, then m i >0,n i >0, otherwise m i =0,n i =0; control parameters is a constant; the adaptive traction parameter m i and n i The update method is as follows: In the formula, h 1i ,h 2i is a positive constant; μ 1i (t),μ 2i (t) is a continuous bounded function that is always positive; and is the estimate of the adaptive pinning parameter.

2. A method for synchronous event triggering control of a multi-USV cluster considering thruster failure according to claim 1, characterized in that: The fault model is 3. A method for synchronous event triggering control of a multi-USV cluster considering thruster failure according to claim 2, characterized in that: The fault model satisfies the following relationship in denote the upper and lower bounds of the thruster multiplication fault, respectively, represents the upper bound of thruster additive failure, r i (t) = [r i1 (t),r i2 (t),r i3 (t)] T is the thruster additive fault, where r i1 (t),r i2 (t) is the control force addition fault, r i3 (t) is the control torque addition fault.

4. A method for controlling a multi-USV cluster synchronous event triggering considering thruster failure according to claim 3, characterized in that: Generalized disturbance consisting of model uncertainty and external disturbance Where △M ηi ,△C ηi ,△D ηi It represents the error between the actual model hydrodynamic coefficient and the theoretical model hydrodynamic coefficient.

5. A method for controlling a multi-USV cluster synchronous event triggering considering thruster failure according to claim 4, characterized in that: The kinematic and dynamic equations of the USV are as follows: Where η = [x, y, ψ] T Represents the position x, y and attitude ψ of the USV in the inertial coordinate system, v = [u, v′, r] T represents the velocity u, v′ and angular velocity r in the motion coordinate system; J(η) is the transformation matrix between the inertial coordinate system and the motion coordinate system; M is the mass inertia matrix, C(v) is the Coriolis force and centripetal force matrix, D(v) is the hydrodynamic damping matrix, g(η) is the restoring force and torque vector generated by gravity and buoyancy, τ=[τ1,τ2,τ3] T are the control forces τ1, τ2 and torque τ3 generated by the propulsion system, and w is the unknown external disturbance.

6. A method for controlling a multi-USV cluster synchronization event triggering considering thruster failure according to any one of claims 1 to 5, characterized in that: A continuous bounded function μ that is always positive 1i (t),μ 2i (t) Satisfaction They are μ 1i (t),μ 2i The upper bound of (t).

7. A method for controlling a multi-USV cluster synchronous event triggering considering thruster failure according to claim 6, characterized in that: The adaptive update law as follows: Where: Adaptively update parameter γ i is a normal number, satisfy in is a positive constant;

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