An error-constrained cluster synchronization control method for submarine flying nodes

Abstract

A method for error-constrained cluster synchronization control of submarine flight nodes belongs to the field of autonomous underwater vehicle control technology. To address the limited control accuracy and poor stability of cluster synchronization control of oblique-fiber network (OBFN), the present invention utilizes a six-degree-of-freedom nonlinear model based on the Fossen outline. A controller τ is designed in the presence of external disturbances and model uncertainty, ensuring that position and attitude quantities still track expected values ​​and that the tracking error has predetermined dynamic performance and steady-state response. An adaptive neural network controller based on pinning control and preset performance methods implements cluster synchronization control of the OBFN. The present invention is used for error-constrained cluster synchronization control of submarine flight nodes.

Description

Technical Field

[0001] The present invention belongs to the technical field of autonomous underwater vehicle control, and in particular relates to a cluster synchronization control method for seabed flight nodes. Background Art

[0002] Autonomous underwater vehicles (AUVs) have become a research hotspot due to their excellent performance. With the deepening of research on AUVs, the scope of their application has also become wider. AUVs not only play an important role in the sampling and collection of seabed resources, but can also complete tasks such as the maintenance of underwater facilities and underwater topography mapping. Among them, the Ocean bottom flying node (OBFN) belongs to a type of extended model AUV, and its model is as follows: Figure 1 shown.

[0003] Maritime missions are complex and diverse. To execute multiple tasks simultaneously and efficiently, a multi-AUV system needs to be divided into multiple subgroups, with each group performing different tracking tasks. For example, when searching and surveying a large ocean area, dividing the AUVs into multiple subgroups allows for simultaneous coverage of different areas, improving search efficiency. However, due to high nonlinearity, cross-coupling, and external ocean current disturbances, these can cause random deviations in the AUV's trajectory. Therefore, it is crucial to control the AUV's position within the expected range, which places further demands on the AUV's control accuracy.

[0004] There are external disturbances and nonlinear model uncertainties in the AUV system. The common approach is to assume that the factors that affect the stability of the system have a constant upper bound and estimate this constant. This method has low accuracy and poor stability. Alternatively, the above factors are considered separately and algorithms are designed to control them, but this increases the complexity of the calculation. In recent years, a method has emerged that integrates factors such as external disturbances and nonlinear model uncertainties, regards them as general uncertainties of the system, and uses neural networks for estimation and approximation. However, this method has limited control accuracy for AUVs. As the requirements for AUV operations gradually increase, simple multi-AUV formation control can no longer meet people's control needs. More and more research has begun to involve how to improve the control accuracy of multi-AUV systems. Summary of the Invention

[0005] The present invention aims to solve the problems of limited control accuracy and poor stability in OBFN cluster synchronization control.

[0006] A method for error-constrained cluster synchronization control of submarine flight nodes, comprising:

[0007] S1. Based on the dynamic model of the seabed flight node OBFN, the model of the OBFN with interference is obtained:

[0008]

[0009]

[0010] Wherein, the subscript i represents the parameter corresponding to the i-th OBFN in the multi-OBFN system, M ηi 、C RBηi 、C Aηi 、D ηi 、g ηi Indicates the M corresponding to the i-th OBFN η =MJ -1 、 C Aη =C A (v r )J -1 、D η =D(v r )J -1 、g η =g(η),v r =vv c , v r is the velocity of OBFN relative to the ocean current, v c is the velocity of the ocean current in the motion coordinate system; M is the mass inertia matrix, J is the transformation matrix between the earth coordinate system and the motion coordinate system, C RB is the Coriolis force and centripetal force matrix of the rigid body, C A is the Coriolis force and centripetal force matrix of the added mass, D is the hydrodynamic damping matrix, g η are the force and torque vectors generated by gravity and buoyancy, and the parameter subscript η represents the parameter in the geodetic coordinate system; v ηi =J i (η i )v i represents the velocity in the geodetic coordinate system, v i represents the velocity of the i-th OBFN in the body coordinate system, v = [u,v,w,p,q,r] T is the velocity and angular velocity in the motion coordinate system; is η i First-order derivative, the parameters above represent the first-order derivative of the corresponding parameters, η i is the η of the i-th OBFN, η=[x,y,z,φ,θ,ψ] T F represents the vector consisting of the position coordinates and yaw angle of the USV in the geodetic coordinate system; i is the generalized disturbance composed of model uncertainty and external disturbance; τ iis the control force and torque generated by the propulsion system of the i-th OBFN; the generalized disturbance F i Using neural network φ i Approximation method is used for processing;

[0011] Based on the OBFN model, a cluster synchronization controller is used to synchronize the OBFN clusters. The cluster synchronization controller is as follows:

[0012] Cluster synchronization control law:

[0013] τ i =τ i1 +τ i2 +τ i3

[0014]

[0015]

[0016]

[0017] in, is the σth i Cluster V σi A subset of The OBFN system in the cluster receives information from the OBFNs of other clusters, and the containment control needs to reduce the influence of the OBFNs from other clusters; i = 0 means that the i-th OBFN cannot receive information from other OBFNs; these OBFNs are selected as pinning nodes; ω i The estimated value of The adaptive law is for The estimated value of Δ i is a positive constant; definition is the position error and velocity error, η σi represents the expected position and attitude of the i-th OBFN; v ησi Indicates the expected velocity and angular velocity of the i-th OBFN; the subscript σ i Used to represent the σth i The expected value of the cluster; Υ=diag[ρ i (t)], R=diag[r i ], i=1,...,N, N represents the number of OBFNs; ρ i (t) is the performance function, δi is the adjustment parameter, δ i 、 Represents δ i The upper and lower bounds of S(·) is a smooth function.

[0018] Furthermore, the performance function Among them, ρ i0 , ρ i∞ and is a positive constant and t is time.

[0019] Furthermore, the performance function ρ i (t) satisfies the following time-varying constraints:

[0020]

[0021] Where t≥0 and δ i is the adjustment parameter, δ i 、 Represents δ i The upper and lower bounds of , i=1,...,N.

[0022] Furthermore, the smooth function

[0023] Furthermore, the dynamic model of the seabed flying node OBFN is as follows:

[0024]

[0025] Where τ is the control force and torque generated by the propulsion system.

[0026] Furthermore, the generalized interference F i Using neural network φ i The approach is as follows:

[0027]

[0028] in, F i Estimated value, that is, F approximated by neural network i , is the estimated value of the weight matrix, is the neural network input, e i =η i -η σi Represents the tracking error.

[0029] Furthermore, the φ i (z i ) uses Gaussian basis function.

[0030] Furthermore, generalized interference Among them F i is the generalized disturbance composed of model uncertainty and external disturbance, d i Indicates ocean current disturbances, Indicates the disturbance caused by uncertainty of the OBFN model, ΔM ηi , ΔC RBηi , ΔD ηi , Δg ηi They represent the M generated by system uncertainty. ηi 、C RBηi 、D ηi 、g ηi The corresponding uncertainty values.

[0031] Beneficial effects:

[0032] This paper addresses the problem of OBFN cluster synchronization control, comprehensively considers the influence of external disturbances and model uncertainty, and proposes an adaptive neural network controller based on pinning control and preset performance to achieve error-constrained cluster synchronization control of OBFN. This can effectively solve the problem of poor stability of OBFN cluster synchronization control and improve control accuracy. The results obtained through simulation are as follows Figure 3 and Figure 4 The control law designed in this invention shows the cluster consistency control effect of the multi-OBFN system. The curves in the figure represent the posture states of the virtual leader OBFN and the follower OBFN in six degrees of freedom. Figure 5 and Figure 6 The figure shows the constraint effect of the control law designed in the present invention on the position error and attitude error. The curves in the figure respectively represent the difference between the posture state of each follower OBFN in the six degrees of freedom and the desired state. The two curves that always constrain the error are the set constraint boundary curves. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is a model diagram of the submarine flight node.

[0034] Figure 2 Schematic diagram of the communication topology between the virtual leader and the follower OBFN;

[0035] Figure 3 Linear displacement tracking curves of the follower and virtual navigator OBFN;

[0036] Figure 4 Angular displacement tracking curves of the follower and virtual navigator OBFN;

[0037] Figure 5 The position error curve and error boundary diagram following OBFN;

[0038] Figure 6 The posture error curve and error boundary diagram following OBFN. DETAILED DESCRIPTION Specific implementation method one:

[0040] This embodiment is an error-constrained cluster synchronization control method for submarine flight nodes. Before describing it in detail, the coordinate system and parameter definitions involved in the present invention are first described:

[0041] The geodetic coordinate system is represented by E-ξηζ, where E is the origin, which can be selected as any point in the OBFN working sea area. The selected datum plane is tangent to the surface of the OBFN operating area. Eζ is the axis with the positive direction pointing to the center of the earth. The Eξ axis points to the geographic north, and the Eη axis points to the geographic east.

[0042] O-xyz represents the body-following coordinate system. Because it moves with the OBFN, it is also called the motion coordinate system. It should be noted that as long as the body-following coordinate system can be guaranteed to move with the OBFN, in this embodiment, for ease of explanation, the origin O of the motion coordinate system is chosen to be the OBFN's center of gravity. The x-axis points along the OBFN's mid-longitudinal axis toward the OBFN's bow. The y-axis points from the OBFN's center of gravity to the OBFN's starboard side. The z-axis is perpendicular to the xOy plane and points from the OBFN's center of gravity toward the OBFN's bottom, with a positive value downward.

[0043] Parameter definition: M - mass inertia matrix; η = [x, y, z, φ, θ, ψ] T ——OBFN six-degree-of-freedom position and attitude value in the geodetic coordinate system; η σ =[x σ ,y σ ,z σ ,φ σ ,θ σ ,ψ σ ] T ——Expected values ​​of the six-degree-of-freedom position and attitude of the OBFN cluster in the geodetic coordinate system; e = η - η σ ——Tracking error; v = [u, v, w, p, q, r] T ——Velocity and angular velocity in the motion coordinate system; J——Transformation matrix between the earth coordinate system and the motion coordinate system; C RB ——Coriolis force and centripetal force matrix of rigid body; C A ——Coriolis force and centripetal force matrix of added mass; D——hydrodynamic damping matrix; g η — force and torque vectors due to gravity and buoyancy; τ — control forces and torques due to the propulsion system; v r ——the speed of OBFN relative to the ocean current; vc ——the velocity of the ocean current in the moving coordinate system; F——the generalized uncertainty of the system;

[0044] The present invention utilizes OBFN for control, achieving the effect of grouping. This containment control method effectively reduces communication costs and computational complexity compared to full-equipment control methods. Simultaneously, a preset performance control method ensures that the designed error is contained within a set from the outset and gradually converges to a predefined small set, while also meeting the required convergence speed and overshoot. The preset performance function is used to provide a smooth tracking response with a sufficient range of control signals, while ensuring transient and tracking performance with specified characteristics.

[0045] In order to achieve cluster synchronization control of OBFN using an adaptive neural network controller based on pinning control and preset performance method, the goal of this invention is to design a controller τ so that the position and attitude η of the OBFN system can still track the expected value η in the presence of external disturbances and model uncertainty. σ And the tracking error e = η - η σ There are predetermined dynamic performance and steady-state response conditions.

[0046] This embodiment is an error-constrained cluster synchronization control method for submarine flight nodes, including the following steps:

[0047] S1. Transformation of submarine flight node dynamics model:

[0048] Establish the dynamic model of the submarine flight node OBFN. The dynamic equation of OBFN is expressed by the six-degree-of-freedom nonlinear model based on the Fossen outline.

[0049]

[0050] Where M η =MJ -1 , C Aη =C A (v r )J -1 , D η =D(v r )J -1 , g η =g(η), v r =vv c ; M is the mass inertia matrix, η=[x,y,z,φ,θ,ψ] T The vector represents the position and attitude of the OBFN in the geodetic coordinate system, v = [u,v,w,p,q,r] Trepresents the velocity and angular velocity in the motion coordinate system, J is the transformation matrix between the earth coordinate system and the motion coordinate system; C RB is the Coriolis force and centripetal force matrix of the rigid body, C A is the Coriolis force and centripetal force matrix of the added mass; D 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, v r is the velocity of OBFN relative to the ocean current, v c is the velocity of the ocean current in the moving coordinate system.

[0051] Considering the model uncertainty and external interference of OBFN, it can be rewritten as follows

[0052]

[0053] Among them, the parameter subscript i represents the parameter corresponding to the i-th OBFN in the multi-OBFN system, v ηi =J i (η i )v i Indicates the velocity in the geodetic coordinate system (the OBFN system directly obtains v i body coordinate system), is the generalized disturbance composed of model uncertainty and external disturbance, where d i Indicates ocean current disturbances, Denotes the disturbance caused by uncertainty of the OBFN model, ΔM ηi , ΔC RBηi , ΔD ηi , Δg ηi They represent the M generated by system uncertainty. ηi 、C RBηi 、D ηi 、g ηi The corresponding uncertainty value. i The neural network approach is used for processing.

[0054] Determine position error and velocity error

[0055]

[0056]

[0057] Among them, η σi Indicates the i-th OBFN (located at the σ i The expected position and attitude of the cluster; v ησi Indicates the expected velocity and angular velocity of the i-th OBFN; the subscript σ i Used to represent the σth i The expected value of the cluster.

[0058] S2. Designing performance functions based on a preset performance control method:

[0059] Performance function ρ(t) and error component Related, and ρ(t) should be a smooth function such that ρ(t)∈R + is a positive decreasing function, The preset performance function can be written as

[0060]

[0061] Among them, R + represents a positive real number, ρ i0 , ρ i∞ and is a positive constant; t is time.

[0062] In order to achieve the desired preset performance, the following time-varying constraints are proposed:

[0063]

[0064] Where t≥0 and δ i is the adjustment parameter, δ i 、 Represents δ i The upper and lower bounds of , i=1,...,N.

[0065] In order to transform the error of the nonlinear system from constrained to unconstrained in (4), the following transformation is performed:

[0066]

[0067] Where ψ(·) is an intermediate variable function, representing a nonlinear time-varying dynamic constraint;

[0068] (5) can be converted into the following form

[0069]

[0070] where S(·) is a smooth function and the inverse of ψ(·).

[0071] The general form of S(·) is as follows

[0072]

[0073] The conversion error

[0074]

[0075] Because ρ i(t)>0, then (8) can be rewritten as

[0076]

[0077] The conversion error in (5) is as follows:

[0078]

[0079] To reduce the impact of chattering, the following form of transformation error is used:

[0080]

[0081] in, ξ>0 is a design parameter.

[0082] Derivative (11) is expressed as follows

[0083]

[0084] set up

[0085]

[0086] Combining (12) and (13), we have

[0087]

[0088] where Ξ=[Ξ1,Ξ2,...,Ξ N ] T , Υ=diag[ρ i (t)], R=diag[r i ], i=1,...,N represents the number of OBFNs;

[0089] S3. Select radial basis function neural network parameters:

[0090] For the generalized interference term in the system, an adaptive neural network is used to approximate it, and the neural network input is taken as Then the estimate of the generalized interference term can be written as

[0091]

[0092] in, is the estimated value of the weight matrix; φ i (z i ) can be in the form of Gaussian basis function, φ i (z i )=[φ i1 (z i ),φ i2 (zi ),...,φ ij (z i ),...,φ im (z i )] T ∈R m , m is the number of hidden layer nodes in the network; e i =η i -η σi Represents the tracking error.

[0093] S4. Design cluster synchronization controller:

[0094] The following cluster synchronization control law is proposed:

[0095] τ i =τ i1 +τ i2 +τ i3 (16)

[0096]

[0097]

[0098] in, is the σth i Cluster V σi A subset of . The OBFN system in the cluster can receive information from the OBFN of other clusters, and the containment control needs to reduce the influence of the OBFN from other clusters. i = 0 means that the i-th OBFN cannot receive information from other OBFNs. These OBFNs can be selected as pinning nodes.

[0099]

[0100]

[0101]

[0102] in, ω i The estimated value of

[0103] Design the adaptive law as

[0104]

[0105] in for The estimated value of Δ i is a positive constant. And define

[0106] The controller design and verification process is as follows:

[0107] 1. Dynamic model of OBFN:

[0108] The dynamic equation of OBFN is expressed as a six-degree-of-freedom nonlinear model based on the Fossen outline.

[0109]

[0110] Where M η =MJ -1 , C Aη =C A (v r )J -1 , D η =D(v r )J -1 , g η =g(η), v r =vv c ; M is the mass inertia matrix, η=[x,y,z,φ,θ,ψ] T The vector represents the motion and posture of the OBFN in the body coordinate system, v = [u,v,w,p,q,r] T represents the velocity and angular velocity in the motion coordinate system, J is the transformation matrix between the earth coordinate system and the motion coordinate system; C RB is the Coriolis force and centripetal force matrix of the rigid body, C A is the Coriolis force and centripetal force matrix of the added mass; D 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, v r is the velocity of OBFN relative to the ocean current, v c is the velocity of the ocean current in the moving coordinate system.

[0111] Considering the model uncertainty and external interference of OBFN, it can be rewritten as follows

[0112]

[0113] in The generalized interference composed of model uncertainty and external interference is processed by neural network approximation.

[0114] Defining position error and velocity error

[0115]

[0116] If in any initial state, OBFN satisfies the following conditions

[0117]

[0118]

[0119] Then the position and velocity information of OBFNs in different clusters are bounded, and the state error converges to an arbitrary small neighborhood of zero in a finite time, and the multi-OBFN system can achieve cluster synchronization.

[0120] Assumption 1: i The location and speed information of the cluster's virtual navigator OBFN are:

[0121]

[0122] Assumption 2 For a multi-cluster OBFN system, there exists at least one directed spanning tree.

[0123] Assumption 3 By choosing appropriate parameters, we can get the following inequality

[0124]

[0125]

[0126] in L is the Laplacian matrix of the directed graph, Is the submatrix of L minus l rows and columns. i is the pinning coefficient, for M∈R N×N and D=diag(d1,d2,...d l ...0,...0) N×N , where d l > 0.

[0127]

[0128] Where M is a symmetric matrix; M l is the submatrix of matrix M with the first l rows and l columns removed; Both B and C are matrices of corresponding dimensions.

[0129] For the matrix (29), if all d l Satisfy d l >λ max (B-CM l -1 C T ), then M l <0 is equivalent to MD<0.

[0130] 2. Preset performance control method:

[0131] Performance function ρ(t) and error component Related, and ρ(t) should be a smooth function such that ρ(t)∈R + is a positive decreasing function The default performance function can be written as

[0132]

[0133] where ρ i0 ,ρ i∞ and is a positive constant. In order to achieve the desired preset performance, the following time-varying constraints are proposed:

[0134]

[0135] where t ≥ 0 and 0 ≤ δ i ≤1, i=1,...,N.

[0136] In order to transform the error of the nonlinear system from constrained to unconstrained in (4), the following transformation is performed:

[0137]

[0138] (5) can be converted into the following form

[0139]

[0140] where S(·) is a smooth function and the inverse of ψ(·).

[0141] The general form of S(·) is as follows

[0142]

[0143] The conversion error

[0144]

[0145] Due to ρ i (t)>0, then (8) can be rewritten as

[0146]

[0147] The conversion error in (5) is as follows:

[0148]

[0149] In order to reduce the impact of chattering, the following form of transformation error is used:

[0150]

[0151] in ξ>0 is a design parameter.

[0152] Derivative (11) is expressed as follows

[0153]

[0154] set up

[0155]

[0156] Combining (12) and (13), we have

[0157]

[0158] where Ξ=[Ξ1,Ξ2,...,Ξ N ] T , Υ=diag[ρ i (t)], R=diag[r i ], i=1,...,N. If the controller τ is designed to make Ξ bounded, then according to formula (41) we can get and Bounded.

[0159] 3. Cluster synchronization controller design:

[0160] For the generalized interference term in the system, an adaptive neural network is used to approximate it, namely

[0161]

[0162] where ω i is the weight matrix, φ i (z i )=[φ1(z i ),φ2(z i ),...,φ j (z i ),…,φ m (z i )] T ∈R m , m is the number of hidden layer nodes in the network, φ i (z i ) can be in the form of Gaussian basis function,

[0163]

[0164] where c ij and b ij are the center and width of the Gaussian function respectively.

[0165] Take the neural network input as Then the estimate of the generalized interference term can be written as

[0166]

[0167] in is the estimated value of the weight matrix.

[0168] The following cluster synchronization control law is proposed:

[0169] τ i =τ i1 +τ i2 +τ i3 (45)

[0170]

[0171]

[0172] in is the σth i Cluster V σi A subset of . The OBFN system in the cluster can receive information from the OBFN of other clusters, and the containment control needs to reduce the influence of the OBFN from other clusters. i = 0 means that the i-th OBFN cannot receive information from other OBFNs. These OBFNs can be selected as pinning nodes.

[0173]

[0174]

[0175]

[0176] in ω i The estimated value of

[0177] Design the adaptive law as

[0178]

[0179] in for The estimated value of Δ i is a positive constant. And define

[0180] By using the control algorithm (45) and the adaptive laws (50) and (51), the signal of the multi-OBFN system will be semi-globally uniformly bounded. The follower OBFNs can follow the trajectory of the virtual leader OBFN in the same subgroup, and cluster synchronization of multiple OBFNs can be achieved.

[0181] Proof: Design the following Lyapunov function

[0182]

[0183] in By properly designing φ i accomplish.

[0184] make Then, taking the derivative of (52), substituting (2), (26) and (25) into (52), we can obtain

[0185]

[0186] Select a suitable Lyapunov function

[0187]

[0188] Taking the derivative we get

[0189]

[0190] in χ i =I6-κ i .

[0191] Position error is bounded, then

[0192] According to the properties of the matrix, we can get

[0193]

[0194] Similarly, we can get

[0195]

[0196] We can further obtain

[0197]

[0198] Where N, α1 and β1 satisfy the following conditions

[0199]

[0200]

[0201]

[0202] in Σ=diag[ε1,ε2,...,ε N], Λ=diag[||Λ1|| / 2,||Λ2|| / 2,...,||Λ N || / 2].

[0203] Simplifying (58) we can get

[0204]

[0205] The expressions of α2 and β2 are as follows

[0206]

[0207]

[0208] Then we can conclude that the system is uniformly ultimately bounded.

[0209]

[0210] Design the following parameters

[0211]

[0212] Through (60) and (61) we can get

[0213]

[0214] in

[0215] because Then we can get

[0216]

[0217] From (62) and (63), it can be seen that all error variables of the system can converge to a finite range, and it can be judged that the multi-OBFN system can eventually achieve cluster synchronization.

[0218] Example

[0219] In order to verify the effectiveness of the control method designed in the present invention, it is combined with the OBFN model for simulation, taking into account the influence of external disturbances and model uncertainty.

[0220] Since the communication between multiple AUVs (i.e. OBFN) will be greatly affected underwater, the communication between multiple AUVs is carried out using a directed communication topology. The communication topology between multiple AUVs is directed communication. The information transmission relationship between the leader and follower AUV is as follows: Figure 2 As shown. Figure 2 In the above equation, we know that AUV3 in group G2 cannot obtain information from other AUVs in groups G1 and G2, so in the containment control law (47), AUV2 and AUV4 in the G1 group can obtain information from AUV3 in the G2 group, that is, they can obtain information from AUVs in other groups, so and Therefore, AUV2, AUV3 and AUV4 were selected as the containment nodes.

[0221] The hydrodynamic parameters, inertia coefficients, initial values ​​of position and attitude, initial values ​​of velocity and expected trajectory of the corresponding models are shown in Table 1.

[0222] Table 1 Inertial parameters of AUVs in group G1

[0223]

[0224] Table 2 Inertial parameters of AUVs in group G2

[0225]

[0226] Table 3 Hydrodynamic coefficients of AUVs in group G1

[0227]

[0228] Table 4 Hydrodynamic coefficients of AUVs in group G2

[0229]

[0230] Table 5 Initial position of following AUV

[0231]

[0232]

[0233] Table 6 Initial speed of following AUV

[0234]

[0235] Table 7 Motion trajectories of the virtual pilot AUVs of subgroups G1 and G2

[0236]

[0237] Model uncertainty: In view of the uncertainty of the AUV model itself, a 30% model error was selected in the simulation experiment, i.e. Δ in =0.3.

[0238] Ocean current disturbance: Assume that the external disturbance is described as

[0239] d i (t)=[d i1 (t),d i2 (t),d i3 (t),di4 (t),d i5 (t),d i6 (t)] T (64)

[0240]

[0241] Controller parameters: The control parameter is selected as ρ i0 =10,ρ i∞ =0.6, l i =1, i=1,...,6, the default performance form is ρ i (t) = 9.4exp(-t) + 0.6. In the error conversion function δ 1= δ 2= δ 4=0.5, δ 3=0.1, δ 5=0.3, δ 6=0.6. The control gain parameters in the control method are d2=d4=15, d3=20. The parameters Δ in the adaptive law are i =0.03, i=1,...,6.

[0242] The results obtained through simulation are as follows Figure 3 and Figure 4 The figure shows the cluster consistency control effect of the control law designed in the present invention on the multi-AUV system. The curves in the figure represent the posture states of the virtual leader AUV and the follower AUV in six degrees of freedom.

[0243] Figure 5 and Figure 6 The figure shows the constraint effect of the control law designed in the present invention on the position error and attitude error. The curves in the figure respectively represent the difference between the posture state of each follower AUV in six degrees of freedom and the desired state. The two curves that always constrain the error are the set constraint boundary curves.

[0244] from Figure 3-Figure 6 It can be seen that the method proposed in the present invention can enable the system to be grouped, and the system error can converge to a specific range, realizing error-constrained cluster consistent control.

[0245] Comparison with existing technical solutions: If external disturbances and model uncertainties are taken into account to achieve the requirements for synchronous control of submarine flight node clusters, in addition to the algorithm of the present invention, there are also solutions based on full-equipment control methods, adaptive neural networks, etc. The following briefly introduces these two solutions and compares them with the algorithm of the present invention.

[0246] A. Solution based on full equipment control

[0247] "Scaled group consensus in multiagent systems with first / second-order continuous dynamics" studies the scaled cluster synchronization problem of multi-agents with first-order / second-order linear continuous dynamics based on the full-device control method. "Adaptive Output Consensus Design in Clustered Networks of Heterogeneous Linear Multi-Agent Systems" mainly studies the cluster synchronization problem in a network divided into heterogeneous agent clusters, and achieves consistency control by controlling each node. Both are based on the full-device control method to achieve cluster consistency control. However, compared with the full-device control method that controls the entire agent system, the containment control method in the present invention only needs to control a part of the agent system, which will effectively reduce communication costs and computational complexity.

[0248] Therefore, the present invention adopts a pinning control method to realize the synchronous control of multiple AUV system clusters, regards external disturbances and model uncertainties as system generalized interference, and uses an adaptive neural network to estimate and approximate them, which reduces the complexity of calculation, saves computing resources, and is closer to actual engineering needs.

[0249] B. Neural Network-Based Solutions

[0250] Radial basis function neural networks and adaptive methods are often used to deal with unknown external disturbances. "Sliding mode based neural adaptive formation control of underactuated AUVs with leader-followers strategy" combines backstepping, adaptive neural networks, and dynamic surface control technology to propose a robust sliding mode formation control strategy to solve the master-slave formation control problem of underactuated underwater vehicles under uncertain ocean disturbances. "Three-dimensional neural network tracking control of a moving target by underactuated autonomous underwater vehicles" uses a multi-layer neural network to approximate an unknown nonlinear dynamic system and uses adaptive robust control technology to compensate for the disturbances caused by waves, wind, and ocean currents to ensure that the tracking error of the AUV is semi-globally consistent and ultimately bounded. "Robust adaptive sliding mode control of underactuated autonomous underwater vehicles with uncertain dynamics" studies the trajectory tracking control problem of a class of underactuated five-degree-of-freedom underwater vehicles under uncertain dynamics and unknown environmental disturbances. Considering the actual situation of system parameter uncertainty and external disturbances, a direct adaptive neural network controller combined with a conditional integrator is proposed to improve the robustness and adaptability of the system.

[0251] All three methods use adaptive neural networks to estimate and approximate factors affecting system stability. However, compared to the algorithm presented in this paper, these solutions do not consider the issue of system control accuracy. Therefore, the algorithm presented in this paper improves on this basis by introducing a preset performance method to control the system error within a specific range, thereby improving system stability.

[0252] The above examples are merely illustrative of the calculation model and process of the present invention and are not intended to limit the embodiments of the present invention. Persons skilled in the art will readily appreciate that other variations or modifications based on the above description are possible. This list of embodiments is not exhaustive; however, any obvious variations or modifications derived from the technical solution of the present invention remain within the scope of protection of the present invention.

Claims

1. A method for error-constrained cluster synchronization control of submarine flight nodes, characterized in that: include: Based on the dynamic model of the seabed flight node OBFN, the model of the OBFN with interference is obtained: Wherein, the subscript i represents the parameter corresponding to the i-th OBFN in the multi-OBFN system, M ηi 、C RBηi 、C Aηi 、D ηi 、g ηi Indicates the M corresponding to the i-th OBFN η =MJ -1 、 C Aη =C A (v r )J -1 、D η =D(v r )J -1 、g η =g(η),v r =vv c , v r is the velocity of OBFN relative to the ocean current, v c is the velocity of the ocean current in the motion coordinate system; M is the mass inertia matrix, J is the transformation matrix between the earth coordinate system and the motion coordinate system, C RB is the Coriolis force and centripetal force matrix of the rigid body, C A is the Coriolis force and centripetal force matrix of the added mass, D is the hydrodynamic damping matrix, g η are the force and torque vectors generated by gravity and buoyancy, and the parameter subscript η represents the parameter in the geodetic coordinate system; v ηi =J i (η i )v i represents the velocity in the geodetic coordinate system, v i represents the velocity of the i-th OBFN in the body coordinate system, v = [u,v,w,p,q,r] T is the velocity and angular velocity in the motion coordinate system; is η i First-order derivative, the parameters above represent the first-order derivative of the corresponding parameters, η i is the η of the i-th OBFN, η=[x,y,z,φ,θ,ψ] T F represents the vector consisting of the position coordinates and yaw angle of the USV in the geodetic coordinate system; i is the generalized disturbance composed of model uncertainty and external disturbance; τ i is the control force and torque generated by the propulsion system of the i-th OBFN; the generalized disturbance F i Using neural network φ i Approximation method is used for processing; Based on the OBFN model, a cluster synchronization controller is used to synchronize the OBFN clusters. The cluster synchronization controller is as follows: Cluster synchronization control law: t i =t i1 +t i2 +t i3 in, is the σth i Cluster V σi A subset of The OBFN system in the cluster receives information from the OBFNs of other clusters, and the containment control needs to reduce the influence of the OBFNs from other clusters; i = 0 means that the i-th OBFN cannot receive information from other OBFNs; these OBFNs are selected as pinning nodes; j represents the jth OBFN; ω i The estimated value of ω i is the weight matrix; The adaptive law is for The estimated value of Δ i is a positive constant; definition is the position error and velocity error, η σi represents the expected position and attitude of the i-th OBFN; v ησi Indicates the expected velocity and angular velocity of the i-th OBFN; the subscript σ i Used to represent the σth i The expected value of the cluster; Υ = diag[ρ i (t)], R = diag[r i , i = 1, ..., N, N represents OBFN the number of ρ i (t) is the performance function, δ i To adjust the parameters, δ i 、 Represents δ i The upper and lower bounds of S(·) is a smooth function; ε i is the containment coefficient.

2. The error-constrained cluster synchronization control method for submarine flight nodes according to claim 1 is characterized in that: Performance function ρ i (t)=(ρ i0 -ρ i∞ )exp(-l i t)+ρ i∞ , where ρ i0 , ρ i∞ and l i is a positive constant and t is time.

3. The error-constrained cluster synchronization control method for submarine flight nodes according to claim 2, characterized in that: Performance function ρ i (t) satisfies the following time-varying constraints: Where t≥0 and δ i To adjust the parameters, δ i 、 Represents δ i The upper and lower bounds of , i=1,...,N.

4. The error-constrained cluster synchronization control method for submarine flight nodes according to claim 3, characterized in that: Smooth function 5. The error-constrained cluster synchronization control method for submarine flight nodes according to any one of claims 1 to 4, characterized in that: The dynamic model of the seabed flying node OBFN is as follows: Where τ is the control force and torque generated by the propulsion system.

6. The error-constrained cluster synchronization control method for submarine flight nodes according to any one of claims 1 to 4, wherein the generalized interference F i Using neural network φ i The approach is as follows: in, F i Estimated value, that is, F approximated by neural network i , is the estimated value of the weight matrix, is the neural network input, e i =η i -η σi Represents the tracking error.

7. The error-constrained cluster synchronization control method for submarine flight nodes according to claim 6, characterized in that: The φ i (z i ) uses Gaussian basis function.

8. The error-constrained cluster synchronization control method for submarine flight nodes according to claim 6, characterized in that: Generalized interference Among them F i is the generalized disturbance composed of model uncertainty and external disturbance, d i Indicates ocean current disturbances, Denotes the disturbance caused by uncertainty of the OBFN model, ΔM ηi , ΔC RBηi , ΔD ηi , Δg ηi They represent the M generated by system uncertainty. ηi 、C RBηi 、D ηi 、g ηi The corresponding uncertainty values.

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