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CN109240317B - Finite time configuration inclusion control method of ocean bottom seismic detection flight node considering propeller faults - Google Patents

Finite time configuration inclusion control method of ocean bottom seismic detection flight node considering propeller faults Download PDF

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CN109240317B
CN109240317B CN201811396169.8A CN201811396169A CN109240317B CN 109240317 B CN109240317 B CN 109240317B CN 201811396169 A CN201811396169 A CN 201811396169A CN 109240317 B CN109240317 B CN 109240317B
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flight node
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CN109240317A (en
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秦洪德
孙延超
陈辉
杜雨桐
吴哲远
李骋鹏
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Harbin Engineering University
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Abstract

A finite time configuration containing control method of ocean bottom geophone detection flight nodes considering propeller faults relates to a finite time configuration containing control method of ocean bottom geophone detection flight nodes. The method aims to solve the problems that the existing control method cannot be completely suitable for controlling the ocean bottom seismic demodulation flight node, and the existing control method cannot be used for effectively controlling when a propeller breaks down. Firstly, establishing a dynamics and kinematics equation of a multi-seabed seismic demodulation flight node system, selecting an error function and a finite time sliding mode variable based on the dynamics and kinematics equation of the flight node and the thrust or moment on the flight node corresponding to damage of a propeller, and selecting a nonsingular rapid terminal sliding mode surface; the controller is then designed to achieve ocean bottom geophone flight node finite time configuration containment control. The invention is suitable for finite time configuration including control of the ocean bottom seismic wave detection flight node.

Description

Finite time configuration inclusion control method of ocean bottom seismic detection flight node considering propeller faults
Technical Field
The invention relates to a submarine seismic demodulation flight node configuration containing control method.
Background
Over the past decade, exploration for subsea resources has become increasingly important. Ocean bottom seismic acquisition systems have been developed primarily using marine streamers for deployment and cabling on the ocean floor, but these two methods are too labor and material intensive to collect ocean bottom seismic information for resource exploration.
Currently, a multi-Autonomous Underwater Vehicle (AUV) plays an important role in the detection of the ocean. In order to complete a comprehensive Ocean Bottom seismic wave detection system which is automatically laid and recovered in a large range on the Ocean Bottom, a team of an inventor proposes and uses Ocean Bottom seismic wave flight nodes (OBFN) to complete exploration tasks, wherein the Ocean Bottom seismic wave flight nodes belong to one of autonomous underwater robots.
The cooperative control problem of the AUV of the multi-autonomous underwater robot is also greatly concerned in the technical field of oceans. Compared with a single AUV, the resource exploration by using a plurality of AUVs has remarkable advantages, such as high flexibility, strong adaptability, low operation and maintenance cost and the like. For multi-AUV cooperative control, centralized and distributed control are two main control strategies. Centralized control means that each AUV needs to obtain global information to make adjustments. Compared with centralized control, distributed control has higher flexibility and adaptability, and therefore, in practical engineering, distributed control is more widely applied. The communication topology describes the information transfer relationship among AUVs in the distributed control system, and can be divided into undirected and directed communication topologies. Under the undirected communication topology, information transfer between AUVs is bidirectional. However, in practical application, the requirement of bidirectional information transmission on a communication system is high, and under the directed communication topology, only the requirement that the communication topology of the system has a directed spanning tree is met, so that the research on the directed communication topology has practical application value. Distributed-time-distributed kalman filter design for formats of autonomous vehicles (Viegas, d., Batista, p., oliverira, p., silverle, c., distributed-time-distributed kalman filter design for formats of autonomous vehicles, control end.75, 55-68(2018)) discusses the problem of distributed state estimation of multi-AUV systems, and each AUV estimates its state through limited communication with other AUVs in the vicinity and local measurement results based on a directed communication topology. However, the "dispersed-time distributed kalman filter design for formations of autonomous vehicles" is a study conducted without pilot. For multi-AUV cooperative control, it can be classified into distributed consistency control in a case where there is no pilot, distributed tracking control where there is a single pilot, and distributed containment control where there are multiple pilots.
If the multi-OBFN system is controlled by the inclusion, when only the pilot OBFN receives the information of the mother ship, the whole system goes to the target area together, so that only the pilot is provided with equipment capable of communicating with the mother ship in a long distance, and only the follower needs to carry equipment capable of communicating with a close follower or pilot, and the cost of the equipment is reduced.
In the field of marine craft, there have been some research efforts to include control. The Containment control of a multi-surface vessel is achieved by using a recurrent neural network and designing a controller module based on distributed path manipulation and linear tracking differentiators (Peng, Z., Wang, J., Wang, D.: Containment management of marine subsurface vessels with multi-parameter partial-temporal characteristics. IEEE-ASTRAME. Mechartron.22 (2),1026-1036 (2017)). However, only asymptotic convergence of the system can be achieved, and limited time convergence cannot be achieved. For the containment control of multiple OBFN systems, convergence time is an important performance indicator. For example, when avoiding a danger, a follower needs to enter a convex hull surrounded by a pilot as quickly as possible. Based on integral sliding mode control and artificial potential fields, a distributed intelligent finite time controller is provided by the aid of a bus fine-time connection prediction coordination of second-order multi-agent system (Sun, C., Hu, G., Xie, L., Egerstedt, M., bus fine-time connection prediction coordination of second-order multi-agent system, Automatica.89,21-27(2018)), and finite time consistency control of multiple intelligent bodies is achieved. However, fault tolerant control strategies or the occurrence of propeller faults are not considered. Due to the complexity of the marine environment, the propeller of the OBFN may fail during the voyage to reduce the efficiency, and it is necessary to ensure that the multiple OBFN system can still sail to the target sea area under the condition.
Disclosure of Invention
The invention aims to solve the problems that the existing control method cannot be completely suitable for controlling the ocean bottom seismic wave detection flight node, and the existing control method cannot be used for effectively controlling when a propeller fails. Further, a finite time configuration containing control method of the ocean bottom seismic detection flight node considering the propeller faults is provided.
A finite time configuration inclusion control method for a ocean bottom geophone detection flight node considering propeller faults comprises the following steps:
step 1, establishing a dynamics and kinematics equation of a multi-ocean bottom seismic wave detection flight node system;
the ocean bottom seismic wave detection flight node comprises a pilot flight node and a follower flight node;
the influence caused by propeller damage is represented as the change of a thrust distribution matrix, defined as delta B, and the thrust or moment actually acting on the flight node is changed from tau to tau + delta tau;
step 2, selecting an error function and a finite time sliding mode variable based on a dynamics and kinematics equation of a flight node and thrust or moment on the flight node corresponding to damage of a propeller; selecting a nonsingular rapid terminal sliding mode surface;
and 3, designing a controller according to the selected error function, the finite time sliding mode variable and the nonsingular rapid terminal sliding mode surface, thereby realizing the finite time configuration inclusion control of the submarine seismic demodulation flight node.
Further, the specific process of step 1 is as follows:
establishing a dynamics and kinematics equation of a multi-ocean bottom seismic wave detection flight node system:
Figure BDA0001874563770000031
in the formula: the corner mark i represents that the parameter is a parameter for a flight node i; mηi＝MiJi -1，JiFor transformation matrix from body coordinate system to inertial coordinate system, MiAn inertial matrix including an additional mass; cRBηiAs flight nodes i and CRBiThe matrix of the correlation is then determined,
Figure BDA0001874563770000032
Figure BDA0001874563770000033
is JiFirst derivative of, CRBiA rigid body Coriolis centripetal force matrix which is a flight node i; cAηi＝CAi(νri)Ji -1，CAiIs an additional mass coriolis centripetal force matrix; dηi＝Di(νri)Ji -1，DiA damping coefficient matrix; gηi＝gi(ηi)，gi(ηi) Is the restoring force (moment) vector created by gravity and buoyancy;
Figure BDA0001874563770000034
for flight nodes i and vriThe vector of the correlation is then calculated,
Figure BDA0001874563770000035
νriis the velocity of the flight node relative to the ocean current; v isi＝[ui vi wi pi qi ri]TThe velocity-related vector, ν, is defined for the flight node i in the body coordinate systemri＝νi-νci，νciThe speed of the ocean current under a fixed coordinate system;
Figure BDA0001874563770000036
for vectors, x, defined in an inertial coordinate system with respect to position and orientationi、yi、ziRespectively longitudinal displacement, transverse displacement and vertical displacement;
Figure BDA0001874563770000037
θi、ψirespectively a rolling angle, a pitching angle and a yawing angle; tau isiControl forces and moments acting on the center of mass of the flight node;
the ocean bottom seismic wave detection flight node comprises a pilot flight node and a follower flight node;
for the pilot flight node, no interference exists; for i ∈ vLIs provided with
Figure BDA0001874563770000038
vLRepresenting a set of pilot flight nodes; tau isLiA controller representing a pilot flight node;
the influence caused by propeller damage is represented as the change of a thrust distribution matrix, defined as delta B, and the thrust or moment actually acting on the flight node is changed from tau to tau + delta tau;
τ+Δτ＝(Bz-KB)u＝(Bz+ΔB)u (3)
wherein, BzIs an estimate of the thrust distribution matrix; u is the control input of the propeller; k is a diagonal matrix, element Kii∈[0,1]Indicating the magnitude of the corresponding propeller fault; Δ τ is the variation of thrust or torque;
according to (3), converting (1) into
Figure BDA0001874563770000041
In the formula, subscript z is defined as an estimated value corresponding to each parameter; fiFor general uncertainty, i.e. general disturbance, expressed as
Figure BDA0001874563770000042
Wherein,
Figure BDA0001874563770000043
representing the influence of the ocean current disturbance; Δ Mηi、ΔBi、ΔCRBηi、ΔCAηi、ΔDηi、ΔgηiRespectively represent Mηi、Bi、CRBηi、CAηi、Dηi、gηiEach corresponding uncertainty value.
Further, the process of selecting the error function and the finite time sliding mode variable and selecting the nonsingular fast terminal sliding mode surface in the step 2 is as follows:
selecting an error function and a finite time sliding mode variable:
Figure BDA0001874563770000044
Figure BDA0001874563770000045
wherein v isFRepresenting a set of follower flight nodes; a isijElements related to the flight node i and the flight node j in the weighted adjacency matrix of the directed graph are shown;
from (4) and (7), it is possible to obtain
Figure BDA0001874563770000046
The error function is defined as (6), (7) and (8), and according to finite time theory, the following nonsingular fast terminal sliding mode surfaces are selected:
Figure BDA0001874563770000047
in the formula: alpha is alpha1、α2、β1、β2Are all constants, 1 < alpha1＜2，
Figure BDA0001874563770000048
q1、q2Is a positive odd integer, α2＞α1，β1＞1，β2＞0；
According to
Figure BDA0001874563770000051
And
Figure BDA0001874563770000052
to obtain
Figure BDA0001874563770000053
And
Figure BDA0001874563770000054
according to (9) obtaining
Figure BDA0001874563770000055
And arranged into the following forms:
Figure BDA00018745637700000522
wherein: enIs an n × n unit array.
Further, the controller is designed in step 3, so that the process of controlling according to the finite-time configuration of the control law ocean bottom geophone flight node comprises the following steps:
the control law is designed as follows:
ui＝ui1+ui2 (11)
Figure BDA0001874563770000056
Figure BDA0001874563770000057
wherein k is a normal number, sign (·) is a sign function;
Figure BDA0001874563770000058
is the intermediate variable(s) of the variable,
Figure BDA0001874563770000059
Figure BDA00018745637700000510
is wiEstimated value of, wiIs a weight matrix; phi is aiIs an activation function;
Figure BDA00018745637700000511
is composed of
Figure BDA00018745637700000512
Is determined by the estimated value of (c),
Figure BDA00018745637700000513
represents an intermediate quantity;
therefore, the finite time configuration containing control of the ocean bottom seismic wave detection flight node is realized.
Further, u isi2For compensating general disturbances FiBy using neural network techniques to correct general disturbances FiAnd estimating the upper bound of the data, wherein the specific process is as follows:
design of
Figure BDA00018745637700000514
For general disturbance FiEstimating and then providing
Figure BDA00018745637700000515
Estimating error for neural network
Figure BDA00018745637700000516
Estimating the upper bound of (c);
wherein, for
Figure BDA00018745637700000517
Design a neural network estimation law as
Figure BDA00018745637700000518
Wherein, ΛiIs a normal number;
estimating errors for neural networks
Figure BDA00018745637700000519
To the upper bound of
Figure BDA00018745637700000523
Design the adaptive law as
Figure BDA00018745637700000520
Wherein, DeltaiIs a normal number and is defined
Figure BDA00018745637700000521
Further, the neural network is an autoregressive neural network, and the activation function of the autoregressive neural network is a gaussian equation.
The invention has the following beneficial effects:
the method is completely suitable for controlling the submarine seismic demodulation flight node, and ensures effective control when the propeller fails, namely the pilot flight node can realize the finite time fault-tolerant inclusion control of a follower flight node system.
The invention is used for controlling, the follower flight node needs larger force and moment output in the initial time period, after t is 10s, the control force amplitude is reduced to be in the range of 60N, and the control moment amplitude is reduced to be in the range of 100 Nm. Since the propeller T1 affects the longitudinal and yaw motion of the flight node, it can be seen from fig. 3 and 8 that before 20s, the follower flight node follows the pilot and the yaw angle has converged to 0; after 20s, the flying node of the follower still moves forward along with the pilot, the yawing angle floats, but the amplitude of the yawing angle is small, and the influence on the overall performance is small.
Drawings
FIG. 1 is a phase trajectory analysis diagram for a multi-flight node system;
FIG. 2 is a communication topology diagram between a pilot flight node and a follower flight node;
FIG. 3 is a position trajectory of a flight node surge direction;
FIG. 4 is a position trajectory of a flight node in a yaw direction;
FIG. 5 is a position trajectory of a flight node heave direction;
FIG. 6 is a change in the roll angle of a flight node;
FIG. 7 is a change in pitch angle of a flight node;
FIG. 8 is a change in the yaw angle of a flight node;
fig. 9 t is 0s, the relative position change of the pilot flight node and the follower flight node;
fig. 10 t is 20s for the relative position change of the pilot flight node and the follower flight node;
fig. 11 t is the relative position change of the pilot flight node and the follower flight node at 50 s;
fig. 12 t is 80s for the relative position change of the pilot flight node and the follower flight node;
FIG. 13 follower flight node 5 surge direction control force;
FIG. 14 follower flight node 5 yaw direction control force;
FIG. 15 follower flight node 5 heave direction control force;
FIG. 16 follower flight node 5 roll angle control moment;
FIG. 17 follower flight node 5 pitch angle control moment;
fig. 18 follows the control moment of the yaw angle of the flight node 5.
Detailed Description
The first embodiment is as follows:
a finite time configuration inclusion control method for a ocean bottom geophone detection flight node considering propeller faults comprises the following steps:
step 1, establishing a dynamics and kinematics equation of a multi-ocean bottom seismic wave detection flight node system;
the ocean bottom seismic wave detection flight node comprises a pilot flight node and a follower flight node;
the influence caused by propeller damage is represented as the change of a thrust distribution matrix, defined as delta B, and the thrust or moment actually acting on the flight node is changed from tau to tau + delta tau;
step 2, selecting an error function and a finite time sliding mode variable based on a dynamics and kinematics equation of a flight node and thrust or moment on the flight node corresponding to damage of a propeller; selecting a nonsingular rapid terminal sliding mode surface;
and 3, designing a controller according to the selected error function, the finite time sliding mode variable and the nonsingular rapid terminal sliding mode surface, thereby realizing the finite time configuration inclusion control of the submarine seismic demodulation flight node.
The second embodiment is as follows:
the specific process of step 1 in this embodiment is as follows:
establishing a dynamics and kinematics equation of a multi-ocean bottom seismic wave detection flight node system:
Figure BDA0001874563770000071
in the formula: the corner mark i represents that the parameter is a parameter for a flight node i; mηi＝MiJi -1，JiFor transformation matrix from body coordinate system to inertial coordinate system, MiAn inertial matrix including an additional mass; cRBηiAs flight nodes i and CRBiThe matrix of the correlation is then determined,
Figure BDA0001874563770000076
Figure BDA0001874563770000072
is JiFirst derivative of, CRBiA rigid body Coriolis centripetal force matrix which is a flight node i; cAηi＝CAi(νri)Ji -1，CAiIs an additional mass coriolis centripetal force matrix; dηi＝Di(νri)Ji -1，DiA damping coefficient matrix; gηi＝gi(ηi)，gi(ηi) Is the restoring force (moment) vector created by gravity and buoyancy;
Figure BDA0001874563770000073
for flight nodes i and vriThe vector of the correlation is then calculated,
Figure BDA0001874563770000077
νriis the velocity of the flight node relative to the ocean current; v isi＝[ui vi wi pi qi ri]TThe velocity-related vector, ν, is defined for the flight node i in the body coordinate systemri＝νi-νci，νciThe speed of the ocean current under a fixed coordinate system;
Figure BDA0001874563770000074
for vectors, x, defined in an inertial coordinate system with respect to position and orientationi、yi、ziRespectively longitudinal displacement, transverse displacement and vertical displacement;
Figure BDA0001874563770000075
θi、ψirespectively a rolling angle, a pitching angle and a yawing angle; tau isiControl forces and moments acting on the center of mass of the flight node;
the ocean bottom seismic wave detection flight node comprises a pilot flight node and a follower flight node;
for the pilot flight node, no interference exists; for i ∈ vLIs provided with
Figure BDA0001874563770000081
vLRepresenting a set of pilot flight nodes; tau isLiThe controller representing the flight node of the pilot is in fact the τ corresponding to the flight node of the piloti；
The propeller is the most common and important fault source, and the influence caused by propeller damage can be expressed as the change of a thrust distribution matrix, defined as delta B, so that the thrust or moment actually acting on the flight node is changed from tau to tau + delta tau;
τ+Δτ＝(Bz-KB)u＝(Bz+ΔB)u (3)
wherein, BzIs an estimate of the thrust distribution matrix; u is the control input of the propeller; k is a diagonal matrix, element Kii∈[0,1]Indicating the magnitude of the corresponding propeller fault; Δ τ is the variation of thrust or torque;
according to (3), converting (1) into
Figure BDA0001874563770000082
In the formula, subscript z is defined as an estimated value corresponding to each parameter; fiFor general uncertainty, i.e. general disturbance, expressed as
Figure BDA0001874563770000083
Wherein,
Figure BDA0001874563770000086
representing the influence of the ocean current disturbance; Δ Mηi、ΔBi、ΔCRBηi、ΔCAηi、ΔDηi、ΔgηiRespectively represent Mηi、Bi、CRBηi、CAηi、Dηi、gηiEach corresponding uncertainty value.
The other processes are the same as those in the first embodiment.
The third concrete implementation mode:
in step 2 of this embodiment, a process of selecting an error function and a finite time sliding mode variable and selecting a nonsingular fast terminal sliding mode surface is as follows:
selecting an error function and a finite time sliding mode variable:
the following error function is defined:
Figure BDA0001874563770000084
Figure BDA0001874563770000085
wherein v isFRepresenting a set of follower flight nodes; a isijElements related to the flight node i and the flight node j in the weighted adjacency matrix of the directed graph are shown;
from (4) and (7), it is possible to obtain
Figure BDA0001874563770000091
The error function is defined as (6), (7) and (8), and according to finite time theory, the following nonsingular fast terminal sliding mode surfaces are selected:
Figure BDA0001874563770000092
in the formula: alpha is alpha1、α2、β1、β2Are all constants, 1 < alpha1＜2，
Figure BDA0001874563770000093
q1、q2Is a positive odd integer, α2＞α1，β1＞1，β2＞0；
According to
Figure BDA0001874563770000094
And
Figure BDA0001874563770000095
to obtain
Figure BDA0001874563770000096
And
Figure BDA0001874563770000097
according to (9) obtaining
Figure BDA0001874563770000098
And arranged into the following forms:
Figure BDA0001874563770000099
wherein: enIs an n × n unit array.
The other processes are the same as those in the first or second embodiment.
The fourth concrete implementation mode:
in this embodiment, the controller is designed in step 3, so that the process including control according to the finite time configuration of the control law ocean bottom geophone flight node is as follows:
the distributed finite time fault-tolerant configuration of the multi-ocean bottom seismic wave detection flight node comprises the following control law designs:
ui＝ui1+ui2 (11)
Figure BDA00018745637700000910
Figure BDA00018745637700000911
wherein k is a normal number, sign (·) is a sign function;
Figure BDA00018745637700000912
is the intermediate variable(s) of the variable,
Figure BDA00018745637700000913
Figure BDA00018745637700000914
is wiEstimated value of, wiIs a weight matrix; phi is aiIs an activation function;
Figure BDA00018745637700000915
is composed of
Figure BDA00018745637700000916
Is determined by the estimated value of (c),
Figure BDA00018745637700000917
represents an intermediate quantity;
therefore, the finite time configuration containing control of the ocean bottom seismic wave detection flight node is realized.
The other processes are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode:
description of the present embodimenti2For compensating general disturbances FiBy using neural network techniques to correct general disturbances FiAnd estimating the upper bound of the data, wherein the specific process is as follows:
design of
Figure BDA0001874563770000101
For general disturbance FiEstimating and then providing
Figure BDA0001874563770000102
Estimating error for neural network
Figure BDA0001874563770000103
Estimating the upper bound of (c);
wherein, for
Figure BDA0001874563770000104
Design a neural network estimation law as
Figure BDA0001874563770000105
Wherein, ΛiIs a normal number;
estimating errors for neural networks
Figure BDA0001874563770000106
To the upper bound of
Figure BDA0001874563770000107
Design the adaptive law as
Figure BDA0001874563770000108
Wherein, DeltaiIs a normal number and is defined
Figure BDA0001874563770000109
The other processes are the same as those in the fourth embodiment.
The sixth specific implementation mode:
the neural network described in this embodiment is an autoregressive neural network, and the activation function of the autoregressive neural network is a gaussian equation.
The other processes are the same as those in the fifth embodiment.
The theoretical basis of the invention is as follows: firstly, parameters are defined: j. the design is a squareiA transformation matrix from a body coordinate system to an inertial coordinate system; mηi＝MiJi -1；MiAn inertial matrix including an additional mass;
Figure BDA00018745637700001010
CRBiis a rigid Coriolis centripetal force matrix; cAηi＝CAi(νri)Ji -1；CAiIs an additional mass coriolis centripetal force matrix; dηi＝Di(νri)Ji -1；DiA damping coefficient matrix; gηi＝gi(ηi)；gi(ηi) Is the restoring force (moment) vector created by gravity and buoyancy;
Figure BDA00018745637700001011
νri＝νi-νci；νrispeed of flight node relative to sea flow, vciThe velocity of the ocean current under an inertial coordinate system; v isiIs a vector defined under a body coordinate system and related to the speed; tau isiControl forces and moments acting on the center of mass of the flight node; etaiVectors relating to position and orientation defined for the inertial frame; b iszAn estimated value of a thrust distribution matrix; fiIs a general uncertainty; 1nIs an n-dimensional all-1 column vector; 0nIs an n-dimensional all-0 column vector; 0n×nIs an n multiplied by n all 0 matrix; enIs an n multiplied by n unit array;
Figure BDA0001874563770000111
a real number set;
Figure BDA0001874563770000112
is a set of n-dimensional real column vectors;
Figure BDA0001874563770000113
a set of m multiplied by n real number matrixes; diag (x)1,…,xn) Is a diagonal line element composed of x1,…,xnForming a diagonal matrix; | x | non-conducting phosphor1Is a vector
Figure BDA0001874563770000114
1-norm of (1); | x | is a vector
Figure BDA0001874563770000115
Taking an absolute value operation for each element of (1);
Figure BDA0001874563770000116
is a Kronecker product; sign (·) is a sign function.
Assume that 1: for the pilot flight node, no interference exists;
when there are multiple pilots, the Laplacian matrix can be written in the form of a block matrix as follows
Figure BDA0001874563770000117
Wherein
Figure BDA0001874563770000118
Order to
Figure BDA00018745637700001113
Figure BDA0001874563770000119
Figure BDA00018745637700001110
Then
Figure BDA00018745637700001111
Assume 2: for any follower, there is at least one pilot that has a directed path to the follower.
Assume that 3: presence of normal number MηLminSo that
0＜MηLmin≤min[||Mη1||,…||MηN+m||]。
Neural network technology has a strong ability to approximate non-linear equations, so it can be used to estimate non-linear uncertainties and external disturbances for this multi-flight node system. When a neural network is used to estimate the non-linear term f, f can be expressed as:
Figure BDA00018745637700001114
wherein w is a weight matrix; φ is an activation function, and can be selected generally as: a symbolic function, a hyperbolic tangent function, and a gaussian equation;
Figure BDA00018745637700001115
is a bounded estimation error. Non-linearAn estimate of the property term f is
Figure BDA00018745637700001112
Wherein,
Figure BDA0001874563770000121
is an estimate of w.
In the inventive method, an autoregressive neural network is selected to estimate the general perturbation of the system. Selecting a Gaussian equation as an activation function for an autoregressive neural network
Figure BDA0001874563770000122
Wherein x is [ x ]1,x2,…,xn]TIs an n-dimensional input vector, cjIs the center of the jth neuron, bjIs the width of the jth neuron. Definition of phi ═ phi1,φ2,…,φn]TThe output of the autoregressive neural network can be expressed as
ym＝w1φ1+w2φ2+…+wmφm (19)
The first step is as follows:
the following Lyapunov function is selected
Figure BDA0001874563770000123
In the formula:
Figure BDA0001874563770000124
and (5) obtaining the following by taking the derivative of (20):
Figure BDA0001874563770000125
substituting (8) and (10) - (15) into (21) can obtain:
Figure BDA0001874563770000126
make it
Figure BDA0001874563770000127
According to
Figure BDA0001874563770000128
And combining (22) to obtain the following relation.
Figure BDA0001874563770000129
By
Figure BDA00018745637700001210
To obtain
Figure BDA00018745637700001211
Can obtain
Figure BDA00018745637700001212
Thus variable
Figure BDA00018745637700001213
Is bounded, that is,
Figure BDA0001874563770000131
wherein
Figure BDA0001874563770000132
Is a normal number.
The second step is that:
the following Lyapunov function is selected
Figure BDA0001874563770000133
The derivation is carried out on (25) and further simplified to obtain
Figure BDA0001874563770000134
When in use
Figure BDA0001874563770000135
When, define
Figure BDA0001874563770000136
Delta is a smaller normal number, to
Figure BDA0001874563770000137
By selecting appropriatekSuch that for any i e vFAll are provided with
Figure BDA0001874563770000138
In this case, by selection
Figure BDA0001874563770000139
To obtain
Figure BDA00018745637700001310
According to the finite time theory, the multi-flight node system can converge to the terminal sliding mode surface s in finite timei＝0n。
When in use
Figure BDA00018745637700001311
Since delta is a small normal number, it can be reasonably assumed
Figure BDA00018745637700001312
For detailed analysis, first consider
Figure BDA00018745637700001313
In this case, the compound (8) can be used
Figure BDA00018745637700001314
Further analysis, Bu can be assumed for three reasonsi2-F i0. First, with ui1In contrast, ui2And is usually small. Second, since δ is a small normal number, region 2 in FIG. 1 is narrow, so this assumption has little impact on the overall performance of the multi-flight node system. Finally, ui2Has the effect of canceling the general disturbance term Fi. Thus, in conjunction with the three reasons listed above, assume Bui2-F i0 is true.
Based on the above analysis, can be simplified to
Figure BDA0001874563770000141
Bringing (12) in to obtain
Figure BDA0001874563770000142
Consider that
Figure BDA0001874563770000143
It can be known that
Figure BDA0001874563770000144
In fact, for some j e {1, …, n }, the current time is
Figure BDA0001874563770000145
Is formed in a way that
Figure BDA0001874563770000146
Then, according to the form of the control law (12), the method can obtain
Figure BDA0001874563770000147
When s isij> 0 and sijWhen less than 0, can be respectively obtained
Figure BDA0001874563770000148
And
Figure BDA0001874563770000149
this means that
Figure BDA00018745637700001410
Not an attractor. Therefore, the temperature of the molten metal is controlled,
Figure BDA00018745637700001411
there is a neighborhood satisfaction
Figure BDA00018745637700001412
(delta is a small positive constant), in this region,
Figure BDA00018745637700001413
and
Figure BDA00018745637700001414
this is true. Therefore, the states of the system may traverse the region in a limited time
Figure BDA00018745637700001415
When in use
Figure BDA00018745637700001416
According to (28) and finite-time theory, the multi-flight node system will converge to the terminal sliding-mode surface s in finite timei＝0n. Thus, for any initial condition, the system converges to the terminal sliding-form surface s within a limited timei＝0n. Fig. 1 shows the phase trajectory of the system.
According to the finite time theory, each state converges to the terminal sliding mode surface si＝0nAfter that, they will haveReaching the origin within a limited time, i.e.
Figure BDA00018745637700001417
When in use
Figure BDA00018745637700001418
When, from the error variable (6), there is
Figure BDA00018745637700001419
From (32), can be obtained
Figure BDA00018745637700001420
Writing (33) in the form of a column vector to obtain
Figure BDA00018745637700001421
Due to L1Is reversible, has
Figure BDA00018745637700001422
By configuration inclusion definition, it is understood
Figure BDA0001874563770000151
Is a convex hull composed of pilot flight nodes.
Under the action of the control law (11), when a propeller fault exists, the follower flight nodes converge into a convex hull surrounded by the pilot flight nodes within limited time, and therefore the multi-flight-node limited-time fault-tolerant inclusion control is achieved.
Comparison with the prior art solution
There are now many control schemes for the AUV, and four schemes are briefly described below and compared with the present invention.
Trajectory tracking scheme
An unified rolling horizon optimization strategy is designed for path planning and tracking control of AUVs aiming at a single AUV system in a unified recording horizon optimization approach (Shen, C., Shi, Y., Buckham, B.: Integrated path planning and tracking control an AUV). Considering that the effective sensing range of the sensor on the AUV is actually short, a path template is used for customizing the path planning as a rolling time domain optimization problem, and then the planned path is regarded as a state track of a virtual reference system with the same motion and dynamic characteristics as the AUV. By constructing a proper error dynamic model, as shown in formula (36), AUV tracking control is equivalent to the regulation problem of an error dynamic system, so as to deduce the theoretical result of the nonlinear model-based predictive control technology.
Figure BDA0001874563770000152
However, compared with the method, the control method only considers the situation of a single AUV, and the multi-AUV system has high flexibility, strong adaptability, low operation and maintenance cost and wider application in actual engineering. Therefore, the invention designs a control method aiming at the AUV system such as a plurality of ocean bottom seismic wave detection flight nodes, and realizes distributed control.
Multiple AUV path tracking scheme
The Formation learning control of multiple AUVs is a new concept of Formation learning control introduced to the Formation control problem of multiple AUVs and also points to a common goal of distributed Formation tracking control and nonlinear AUV dynamic learning/identification.
Compared with the existing method, the key characteristics of the proposed new formation learning control scheme can be summarized as follows: first, the multi-AUV system under consideration has heterogeneous nonlinear uncertainty dynamics. Secondly, the formation control strategy can be completely realized by each local AUV agent in a distributed mode design, and global information is not required. Thirdly, besides the formation control performance, the distributed control strategy can also accurately identify heterogeneous nonlinear uncertain dynamics of the AUV, and improve the formation control performance by using experience.
However, compared with the present invention, this control method realizes multi-AUV cooperative control, but is not inclusive control, and in actual engineering, a distributed inclusive control with a plurality of pilots is more widely used. Particularly for the multi-seabed seismic wave detection flight node system, the whole system can jointly go to a target area by adopting the control when only part of flight nodes (pilots) receive information of a mother ship, so that only the pilots are provided with equipment capable of carrying out long-distance communication with the mother ship, and only the followers need to carry equipment for carrying out communication with close followers or pilots, and the cost of the equipment is reduced. Therefore, the invention designs an inclusion control method aiming at the AUV system such as a plurality of ocean bottom seismic wave detection flight nodes.
Multiple AUV Inclusion control scheme
A description of a networked autonomous Underwater DSC design (Peng, Z., Wang, D., Wang, W., Liu, L.: description of a networked autonomous Underwater DSC design. ISA Trans.59, 160-2015171 (R)) studies the problem of multi-AUV inclusion control in the presence of model uncertainty and unknown marine disturbances. A neural dynamic surface control design method based on a predictor is provided to develop a distributed self-adaptive inclusion controller, and in the system, the tracks of follower AUVs are converged into a dynamic convex hull formed by a plurality of pilot AUVs. The neural adaptation law is updated by prediction error instead of tracking error, which is independent of tracking error dynamics, so two time scalars are used to control the entire system. The transient characteristics of the proposed predictor-based neurodynamic surface control method are demonstrated to be better than the normal neurodynamic surface control method, and the L2 norm of the neural weight derivative of the proposed method is smaller.
However, compared with the method of the present invention, although the control method realizes multi-AUV inclusion control, the fault tolerance problem is not considered, and for the AUV, due to the complexity of the marine environment, during the sailing process, the propeller may malfunction to reduce the efficiency, and it needs to be ensured that the multi-AUV system can still sail to the target sea area under such a condition. Therefore, the method of the invention designs a fault-tolerant inclusion control method aiming at the AUV system such as a plurality of ocean bottom seismic wave detection flight nodes.
Multi-AUV fault-tolerant control scheme
Model predictive and non-cooperative dynamic fault recovery control protocols for interactive work of indirect lower vehicles (Sedaghati, S., Abdollahi, F., Khorasani, K.: Model predictive and non-cooperative dynamic fault recovery control protocols for interactive work of indirect lower vehicles (2017)) solves the problem of control and fault recovery of multiple AUVs in the presence of propeller faults. Two different fault recovery control strategies based on a model prediction control technology and a dynamic game theory are provided and designed. Two control recovery schemes are provided by considering two conditions of centralized type and semi-decentralized type so as to ensure the track tracking and formation of the multi-AUV system when the propeller fails. The results show that the proposed semi-distributed fault recovery control scheme can keep the population with good degraded performance while being less constrained to communication and computation than centralized.
Compared with the method of the invention, although the method realizes fault-tolerant control, the problem of limited time is not considered, and the convergence time is an important performance index for inclusion control, for example, when avoiding danger, a follower needs to enter a convex hull surrounded by a pilot as soon as possible. Therefore, the method of the invention designs a finite time fault-tolerant inclusion control method aiming at the AUV system such as a plurality of ocean bottom seismic wave detection flight nodes.
Examples
In order to verify the effectiveness of the multi-flight-node distributed finite-time fault-tolerant controller, the multi-flight-node system consisting of 8 followers (numbers 1, … and 8) and 5 pilots (numbers 9, … and 13) is selected for simulation verification.
The dynamic and kinematic model of the follower flight node may be described as
Figure BDA0001874563770000171
The dynamic and kinematic model of the pilot flight node can be described as
Figure BDA0001874563770000172
FIG. 2 is a communication topology diagram between a pilot flight node and a follower flight node;
model uncertainty
In order to represent the model uncertainty, a model error of 30% is taken in the simulation process, i.e. the nominal value of the dynamic model in the controller is 70% of the actual value.
Disturbance of ocean currents
In the method, a first-order Gauss-Markov process is selected to simulate the ocean current interference, and the method comprises the following steps
Figure BDA0001874563770000173
In the formula, VcRepresenting the size of ocean current under a fixed coordinate system, wherein omega is Gaussian white noise with the mean value of 1 and the variance of 1; mu is 3.
Propeller failure
In the simulation process, it is assumed that only the T1 propeller fails, and a case where the propeller failure suddenly occurs is considered. The expression for propeller failure is shown in (37)
Figure BDA0001874563770000181
The control parameter is selected as alpha1＝1.8，β1＝0.01，α2＝2，β2＝1，k＝175。
For neural networks, the activation function in simulation is selected as
φi(zi)＝[φi1(zi),…,φi11(zi)]T，i＝1,…,8
Wherein phi isij(zi) Is a Gaussian equation
Figure BDA0001874563770000182
In the formula
Figure BDA0001874563770000183
The activation function of the neural network is assumed to be the same for all follower flight nodes. Center of neuron cijIs evenly distributed in the area [ -0.1,0.1 [)]6The above. Width b of the gaussian equationijIs selected as bij60. Other parameters are: lambda1＝Λ2＝Λ3＝Λ4＝Λ5＝Λ6＝Λ7＝Λ8＝0.2，
Δ1＝Δ2＝Δ3＝Δ4＝Δ5＝Δ6＝Δ7＝Δ8＝0.2，
Figure BDA0001874563770000184
The initial position and velocity of the follower flight nodes are shown in tables 1 and 2.
TABLE 1 initial position (Angle) of follower flight node
Figure BDA0001874563770000185
TABLE 2 initial (angular) velocity of follower flight node
Figure BDA0001874563770000186
The parameters relating to the flight nodes are shown in tables 3 and 4.
TABLE 3 inertial parameters of flight nodes
Figure BDA0001874563770000191
TABLE 4 hydrodynamic coefficients of flight nodes
Figure BDA0001874563770000192
The position (angle) trajectory of the pilot flight nodes is shown in table 5.
TABLE 5 position (Angle) trajectory of the Pilot flight node
Figure BDA0001874563770000193
Fig. 3 to 12 show the control effect of the distributed finite time fault-tolerant controller with multiple flight nodes.
Without loss of generality, the method of the present invention illustrates the output of the controller by way of example of a follower flight node 5. The simulation results are shown in fig. 13 and 18.
As can be seen from fig. 3 to 8, under the action of the control law (11), the pilot flight node can implement the finite-time fault-tolerant inclusion control on the follower flight node system. As can be seen from fig. 9 to 12, when t is 0s, all the follower flight nodes are located outside the convex hull enclosed by the pilot flight node system. When t is 20s, all the follower flight nodes enter a convex hull enclosed by the pilot flight node system. When t is 50s and t is 80s, all follower flight nodes are still positioned in a convex hull enclosed by the pilot flight nodes. Therefore, the distributed limited time containing control is reasonably realized under the action of the control law (11). Fig. 13 to 18 show that the follower flight node requires a relatively large force and torque output for an initial period of time, and after t is 10s, the control force amplitude is reduced to a range of 60N and the control torque amplitude is reduced to a range of 100 Nm. Since the propeller T1 affects the longitudinal and yaw motions of the flight node, as can be seen from fig. 3 and 8, before 20s, the follower flight node follows the pilot and the yaw angle has converged to 0, and after 20s, the follower flight node still follows the pilot and the yaw angle floats, but the amplitude is small and the influence on the overall performance is small. Therefore, under the action of the control law (11), the multi-flight node system realizes distributed finite-time fault-tolerant containment control.

Claims (7)

1. A finite time configuration inclusion control method for a ocean bottom geophone flight node that accounts for propeller faults, comprising the steps of:
step 1, establishing a dynamics and kinematics equation of a multi-ocean bottom seismic wave detection flight node system;
the ocean bottom seismic wave detection flight node comprises a pilot flight node and a follower flight node;
the influence caused by propeller damage is represented as the change of a thrust distribution matrix, defined as delta B, and the thrust or moment actually acting on the flight node is changed from tau to tau + delta tau;
step 2, selecting an error function and a finite time sliding mode variable based on a dynamics and kinematics equation of a flight node and thrust or moment on the flight node corresponding to damage of a propeller; selecting a nonsingular rapid terminal sliding mode surface;
step 3, designing a controller according to the selected error function, the finite time sliding mode variable and the nonsingular rapid terminal sliding mode surface, thereby realizing the finite time configuration inclusion control of the submarine seismic demodulation flight node;
the specific process of step 1 is as follows:
establishing a dynamics and kinematics equation of a multi-ocean bottom seismic wave detection flight node system:
Figure FDA0002984334290000011
in the formula: the corner mark i represents that the parameter is a parameter for a flight node i; mηi＝MiJi -1，JiFor transformation matrix from body coordinate system to inertial coordinate system, MiAn inertial matrix including an additional mass;
Figure FDA0002984334290000012
Figure FDA0002984334290000013
is JiFirst derivative of, CRBiA rigid body Coriolis centripetal force matrix which is a flight node i; cAηi＝CAi(νri)Ji -1，CAiIs an additional mass coriolis centripetal force matrix; dηi＝Di(νri)Ji -1，DiA damping coefficient matrix; gηi＝gi(ηi)，gi(ηi) Is a restoring force vector generated by gravity and buoyancy;
Figure FDA0002984334290000014
νriis the velocity of the flight node relative to the ocean current; v isi＝[ui vi wi pi qi ri]TThe velocity-related vector, ν, is defined for the flight node i in the body coordinate systemri＝νi-νci，νciThe speed of the ocean current under a fixed coordinate system;
Figure FDA0002984334290000015
for vectors, x, defined in an inertial coordinate system with respect to position and orientationi、yi、ziRespectively longitudinal displacement, transverse displacement and vertical displacement;
Figure FDA0002984334290000016
θi、ψirespectively a rolling angle, a pitching angle and a yawing angle; tau isiThrust or moment acting on the flight node;
the ocean bottom seismic wave detection flight node comprises a pilot flight node and a follower flight node;
for the pilot flight node, no interference exists; for i ∈ vLIs provided with
Figure FDA0002984334290000017
vLRepresenting a set of pilot flight nodes; tau isLiA controller representing a pilot flight node;
the influence caused by propeller damage is represented as the change of a thrust distribution matrix, defined as delta B, and the thrust or moment actually acting on the flight node is changed from tau to tau + delta tau;
τ+Δτ＝(Bz-KB)u＝(Bz+ΔB)u (3)
wherein, BzIs an estimate of the thrust distribution matrix; u is the control input of the propeller; k is a diagonal matrix, element Kii∈[0,1]Indicating the magnitude of the corresponding propeller fault; Δ τ is the variation of thrust or torque;
according to (3), converting (1) into
Figure FDA0002984334290000021
In the formula, subscript z is defined as an estimated value corresponding to each parameter; fiFor general uncertainty, i.e. general disturbance, expressed as
Figure FDA0002984334290000022
Wherein,
Figure FDA0002984334290000023
representing the influence of the ocean current disturbance; Δ Mηi、ΔBi、ΔCRBηi、ΔCAηi、ΔDηi、ΔgηiRespectively represent Mηi、Bi、CRBηi、CAηi、Dηi、gηiRespective corresponding uncertainty values;
step 2, the process of selecting the error function and the finite time sliding mode variable and selecting the nonsingular fast terminal sliding mode surface is as follows:
selecting an error function and a finite time sliding mode variable:
the following error function is defined:
Figure FDA0002984334290000024
Figure FDA0002984334290000025
wherein v isFRepresenting a set of follower flight nodes; a isijElements related to the flight node i and the flight node j in the weighted adjacency matrix of the directed graph are shown;
from (4) and (7), it is possible to obtain
Figure FDA0002984334290000026
The error function is defined as (6), (7) and (8), and according to finite time theory, the following nonsingular fast terminal sliding mode surfaces are selected:
Figure FDA0002984334290000031
in the formula: alpha is alpha1、α2、β1、β2Are all constants, 1 < alpha1＜2，
Figure FDA0002984334290000032
q1、q2Is a positive odd integer, α2＞α1，β1＞1，β2＞0；
According to
Figure FDA0002984334290000033
And
Figure FDA0002984334290000034
to obtain
Figure FDA0002984334290000035
And
Figure FDA0002984334290000036
according to (9) obtaining
Figure FDA0002984334290000037
And arranged into the following forms:
Figure FDA0002984334290000038
wherein: enIs an n × n unit array.
2. The method of claim 1, wherein the step 3 of designing the controller to achieve the finite time configuration of ocean bottom geophone flight nodes comprises the steps of:
the control law is designed as follows:
ui＝ui1+ui2 (11)
Figure FDA0002984334290000039
Figure FDA00029843342900000310
wherein k is a normal number, sign (·) is a sign function;
Figure FDA00029843342900000311
is the intermediate variable(s) of the variable,
Figure FDA00029843342900000312
Figure FDA00029843342900000313
is wiEstimated value of, wiIs a weight matrix; phi is aiIs an activation function;
Figure FDA00029843342900000314
is composed of
Figure FDA00029843342900000315
Is determined by the estimated value of (c),
Figure FDA00029843342900000316
represents an intermediate quantity;
therefore, the finite time configuration containing control of the ocean bottom seismic wave detection flight node is realized.
3. The propeller fault consideration ocean bottom geophone flight node finite time configuration containment control method of claim 2, wherein u isi2For compensating general disturbances FiBy using neural network techniques to correct general disturbances FiAnd estimating the upper bound of the data, wherein the specific process is as follows:
design of
Figure FDA00029843342900000317
For general disturbance FiEstimating and then providing
Figure FDA00029843342900000318
Estimating error for neural network
Figure FDA00029843342900000319
Estimating the upper bound of (c);
wherein, for
Figure FDA0002984334290000041
Design a neural network estimation law as
Figure FDA0002984334290000042
Wherein, ΛiIs a normal number;
estimating errors for neural networks
Figure FDA0002984334290000043
To the upper bound of
Figure FDA0002984334290000044
Design the adaptive law as
Figure FDA0002984334290000045
Wherein, DeltaiIs a normal number and is defined
Figure FDA0002984334290000046
4. The ocean bottom geophone flight node finite time configuration under consideration of propeller faults of claim 3 comprises a control method, characterized in that the neural network is an autoregressive neural network, the activation function of which is a gaussian equation.
5. The propeller fault consideration ocean bottom geophone flight node finite time configuration containment control method of claim 1, wherein said controller of step 3 is designed such that the process of containment control according to the control law ocean bottom geophone flight node finite time configuration containment control is as follows:
the control law is designed as follows:
ui＝ui1+ui2
Figure FDA0002984334290000047
Figure FDA0002984334290000048
wherein k is a normal number, sign (·) is a sign function;
Figure FDA0002984334290000049
is the intermediate variable(s) of the variable,
Figure FDA00029843342900000410
Figure FDA00029843342900000411
is wiEstimated value of, wiIs a weight matrix; phi is aiIs an activation function;
Figure FDA00029843342900000412
is composed of
Figure FDA00029843342900000413
Is determined by the estimated value of (c),
Figure FDA00029843342900000414
represents an intermediate quantity;
therefore, the finite time configuration containing control of the ocean bottom seismic wave detection flight node is realized.
6. The propeller fault consideration ocean bottom geophone flight node finite time configuration containment control method of claim 5, wherein u isi2For compensating general disturbances FiBy using neural network techniques to correct general disturbances FiAnd estimating the upper bound of the data, wherein the specific process is as follows:
design of
Figure FDA00029843342900000415
For general disturbance FiEstimating and then providing
Figure FDA00029843342900000416
Estimating error for neural network
Figure FDA00029843342900000417
Estimating the upper bound of (c);
wherein, for
Figure FDA0002984334290000051
Design a neural network estimation law as
Figure FDA0002984334290000052
Wherein, ΛiIs a normal number;
estimating errors for neural networks
Figure FDA0002984334290000053
To the upper bound of
Figure FDA0002984334290000054
Design the adaptive law as
Figure FDA0002984334290000055
Wherein, DeltaiIs a normal number and is defined
Figure FDA0002984334290000056
7. The ocean bottom geophone flight node finite time configuration under consideration of propeller faults of claim 6 comprises a control method, characterized in that the neural network is an autoregressive neural network, the activation function of which is a gaussian equation.
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