CN109884902B - Unmanned aerial vehicle formation system fault detection method based on interval observer - Google Patents

Unmanned aerial vehicle formation system fault detection method based on interval observer Download PDF

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CN109884902B
CN109884902B CN201910274124.1A CN201910274124A CN109884902B CN 109884902 B CN109884902 B CN 109884902B CN 201910274124 A CN201910274124 A CN 201910274124A CN 109884902 B CN109884902 B CN 109884902B
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印磊
刘剑慰
杨蒲
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention provides a fault detection method for an interval observer, which aims at an unmanned aerial vehicle formation system. Belonging to the technical field of safe reliability. First, when the formation of drones is in a fault-free state, a section observer is established based on known bounded disturbances and relative output errors. The residual error obtained by outputting the estimation error is used to detect actuator failure. The difference from the traditional fault detection is that the fault detection method based on the interval observer does not need a threshold value generator and a residual error evaluation function. The method mainly solves the problem of fault detection of the actuators of the unmanned aerial vehicle formation, has lower conservatism and stronger adaptability, and can well meet the requirement of fault detection of the actuators.

Description

Unmanned aerial vehicle formation system fault detection method based on interval observer
Technical Field
The invention relates to a fault detection method for an unmanned aerial vehicle formation system based on an interval observer, and belongs to the technical field of multi-agent systems.
Background
In recent years, with the development of technologies such as computers and communication networks, especially in the fields of resource exploration, earthquake rescue, environment monitoring, battlefield reconnaissance and the like, the application of unmanned aerial vehicle formation is more and more extensive. Compared with a single unmanned aerial vehicle, the unmanned aerial vehicle formation system has incomparable advantages in cost, robustness, redundancy and high efficiency.
The internal structure of the unmanned aerial vehicle is complex, and external interference needs to be considered, so that great challenges are caused to successful task completion of the unmanned aerial vehicle. When a certain unmanned aerial vehicle in a formation breaks down, the fault can be propagated to other healthy aircrafts in the formation network, which can cause performance degradation and even instability and other serious problems to the whole formation system. Therefore, unmanned aerial vehicle formation fault diagnosis becomes a hot problem in the control field of the present day.
For decades, observer-based fault diagnosis methods have been widely used on unmanned aerial vehicle formation systems. However, the fault diagnosis scheme based on the conventional observer has certain limitations. The Sims of the Swedish Imperial institute of technology, Sweden proposes a fault diagnosis method for an unknown input observer aiming at a second-order time-invariant multi-agent, and the feasibility of the scheme is analyzed through local measurement information. Professor Zhoutonhua of the university of Qinghua proposes that a distributed observer is designed for fault diagnosis of a sensor of a multi-machine formation system, and the method has the advantage of reducing calculation and communication loads. Teaching of Nanjing aerospace university is ginger and bin proposes to design an adaptive fault estimation observer for a multi-agent system of directed communication topology. In the existing research results, many assumed conditions need to be considered, such as ignoring uncertainty of system modeling, nonlinearity, observer matching conditions, and the like. Therefore, the method for diagnosing the faults of the unmanned aerial vehicle formation system based on the traditional observer needs to be further improved and has great conservation.
In order to break through the various limitations listed above, the interval observer fault detection scheme is not constrained by model uncertainty and observer matching conditions, adaptability to fault detection of a formation system is improved, conservation is reduced, and the method has very important theoretical and practical significance.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects of the prior art, the invention provides the fault detection method of the unmanned aerial vehicle formation system based on the interval observer, overcomes the defects of the traditional fault detection method, improves the adaptability of the fault detection method of the unmanned aerial vehicle formation system, and reduces the conservatism of the fault detection method.
The technical scheme is as follows: the invention provides an unmanned aerial vehicle formation fault detection method based on an interval observer, which does not need a residual error evaluation function and a threshold generator to carry out fault detection and comprises the following steps:
(1) modeling unmanned aerial vehicle formation system
Establishing communication connection topology among all unmanned aerial vehicles in a formation system through graph theory, a state equation and an output equation, expressing the communication connection topology by using a directionless topological graph, and simultaneously calculating a corresponding adjacency matrix A and a corresponding degree matrix D to obtain a Laplace matrix L;
(2) aiming at the established unmanned aerial vehicle formation system model, a fault detection interval observer based on a relative output estimation error is established;
(3) and obtaining a global estimation error equation of the unmanned aerial vehicle formation system through theoretical derivation, and performing stability verification on the global estimation error equation.
Further, in the step (1), the undirected switching topological graph adopts G ═ { V, E, a } to represent a communication topological structure of the unmanned aerial vehicle formation system; wherein the node set V ═ { V ═ V1，...VNDenotes all drones, node ViDenotes the ith drone, i ═ 1, 2.. N; the edge set E represents the communication connection relationship between the drones, and the element E in E is (v ═ v)i，vj) Representing unmanned aerial vehicle viCan transmit to drone vjWherein i, j ═ 1, 2.., N; n is a radical ofi＝{vj∈V|(vi，vj) E | } denotes viA set of neighbors of, i.e. all can and viA node set of interactive information; adjacency matrix a ═ aij]N×N(aij≧ 0), wherein if (v) isi，vj) E is E, then aij1, otherwise aij0; degree matrix
Figure GSB0000193169270000011
Wherein
Figure GSB0000193169270000012
If (v)i，vj) E and (v)j，vi) E, G is an undirected graph;
the topology description matrix is specifically:
defining Laplace matrix L ═ D-A
Further, the dynamic equation of each drone of the formation system is as follows:
Figure GSB0000193169270000021
yi(t)＝Cxi(t)
wherein,
Figure GSB0000193169270000022
represents the state vector of the ith drone,
Figure GSB0000193169270000023
is the control input vector for the ith drone,
Figure GSB0000193169270000024
represents the output vector of the ith drone,
Figure GSB0000193169270000025
which is representative of an external disturbance,
Figure GSB0000193169270000026
the fault of an actuator of the ith unmanned aerial vehicle is shown, wherein s is more than or equal to q and is less than n;
Figure GSB0000193169270000027
a system matrix representing the ith drone,
Figure GSB0000193169270000028
an input matrix representing the ith drone,
Figure GSB0000193169270000029
an output matrix representing the ith drone,
Figure GSB00001931692700000210
a state interference matrix representing the ith drone,
Figure GSB00001931692700000211
a fault matrix representing the ith drone, where the D and E matrices are both known column full rank matrices.
For a long machine in a formation system, it is marked as 0, and the dynamic equation is as follows:
Figure GSB00001931692700000212
y0(t)＝Cx0(t)
wherein,
Figure GSB00001931692700000213
represents the state vector of the long machine,
Figure GSB00001931692700000214
representing the output vector of the long machine.
Figure GSB00001931692700000215
A system matrix representing a long machine,
Figure GSB00001931692700000216
representing the output matrix of the long machine. In fig. G, long machines are directly observed by a small percentage of drones. If the i-th unmanned aerial vehicle can directly acquire the information of the long aircraft, an edge (v) exists in the graph G0，vi) And controlling the weight giAnd > 0, the unmanned plane is a controlled node in the graph G.
Further, the fault detection observer in step (2) is as follows:
Figure GSB00001931692700000217
Figure GSB00001931692700000218
wherein,
Figure GSB00001931692700000219
and
Figure GSB00001931692700000220
representing the upper and lower bounds of a state vector in an observer, respectively，
Figure GSB00001931692700000221
And
Figure GSB00001931692700000222
respectively representing the upper and lower bounds of the external disturbance, matrix A1Is the larger of matrix A and matrix 0, A2＝A-A1In the same way, D+The larger of matrix D and matrix 0, D-＝D-D+And K is the observer gain matrix,
Figure GSB00001931692700000223
and
Figure GSB00001931692700000224
respectively representing the upper and lower bounds of the relative output estimation error of the ith drone, given the definition as follows:
Figure GSB00001931692700000225
Figure GSB00001931692700000226
wherein,
Figure GSB00001931692700000227
to the ith unmanned aerial vehicle, define its upper and lower bounds of error, do respectively:
Figure GSB0000193169270000031
then
Figure GSB0000193169270000032
Figure GSB0000193169270000033
Can be rewritten as:
Figure GSB0000193169270000034
Figure GSB0000193169270000035
under the condition of no fault, defining dynamic equations of upper and lower bounds of errors for the ith unmanned aerial vehicle respectively:
Figure GSB0000193169270000036
Figure GSB0000193169270000037
for ease of reading, some of the symbols are simplified as follows:
Figure GSB0000193169270000038
then the following results are obtained:
Figure GSB0000193169270000039
Figure GSB00001931692700000310
further, the global estimation error equation of the unmanned aerial vehicle formation system in step (3) is as follows:
Figure GSB00001931692700000311
Figure GSB00001931692700000312
wherein,
Figure GSB00001931692700000313
Figure GSB00001931692700000314
Figure GSB00001931692700000315
Figure GSB00001931692700000316
INis an identity matrix of dimension N,
Figure GSB00001931692700000317
representing the kronecker product of the matrix. This allows to carry out a fault detection study of the formation system of drone based on longplane-bureaucratic planes from a global point of view.
The following reasoning was used:
consider the following continuous system:
Figure GSB0000193169270000041
wherein the matrix A is a MerSigle matrix,
Figure GSB0000193169270000042
and is
Figure GSB0000193169270000043
If the system initial state x (0) ≧ 0, then x (t) ≧ 0 holds constantly when t ≧ 0.
The following theorem is drawn therefrom:
for a given communication topology, if
Figure GSB0000193169270000044
Both mertseller and herwitz matrices, then when the drone formation system is fault-free, it is a section observer and makes it possible to obtain a complete set of unmanned aerial vehicles
Figure GSB0000193169270000045
This is true.
Theorem proves that: consider the global estimation error equation:
Figure GSB0000193169270000046
Figure GSB0000193169270000047
if it is not
Figure GSB0000193169270000048
Both Merzsler and Helverz matrices, then for t ≧ 0, the following inequality holds:
Figure GSB0000193169270000049
then can obtain
Figure GSB00001931692700000410
This is true.
The certification is complete.
When the unmanned aerial vehicle formation system does not have actuator faults, the output of the interval observer is defined as:
Figure GSB00001931692700000411
then output y of the ith dronei(t) should satisfy:
Figure GSB00001931692700000412
thus, when the formation system is in a healthy state, the following inequality should hold:
Figure GSB00001931692700000413
otherwise, a fault is indicated, and the fault should be alarmed.
Has the advantages that: in the field, the observer corresponding to each unmanned aerial vehicle is designed, so that each observer can achieve the purpose of performing actuator fault detection on the corresponding unmanned aerial vehicle. The invention designs a design scheme of the fault detection interval observer, and greatly reduces the conservatism of the traditional observer design.
Description of the drawings:
FIG. 1 is a flow chart of the method of the present invention;
fig. 2 is a communication topology diagram of a formation system of 5 drones according to an embodiment of the present invention;
fig. 3 is an upper bound of the output residual error of the first drone in accordance with an embodiment of the present invention;
fig. 4 shows an upper bound of the output residual error of the second drone according to an embodiment of the present invention.
Detailed Description
The invention is further described with reference to the accompanying drawings and specific examples.
Compared with the traditional fault detection method, the fault detection method does not need a threshold generator and a residual evaluation function, and greatly reduces the conservatism of observer design.
The model of the embodiment of the invention refers to a text entitled "Adaptive observer-based fast estimation" taught by ginger and bin of university of aerospace, Nanjing, and is specifically as follows:
Figure GSB0000193169270000051
yi(t)＝Cxi(t)
wherein x isi(t)＝[Vh Vv q θ]TFor each unmanned aerial vehicle, where Vh，VvQ, theta respectively represent the horizontal component, the vertical component, the pitch angle speed and the pitch angle of the flying speed of the unmanned aerial vehicle along the axis of the unmanned aerial vehicle; u. ofi(t)＝[δc δl]TRepresenting the input vector of each drone, where δcAnd deltalRespectively representing a total distance variable and a longitudinal periodic variable; y isi(t)＝[VhVv θ]TIs the output vector of each drone, where Vh，VvTheta respectively represents a horizontal component, a vertical component and a pitch angle of the flying speed of the unmanned aerial vehicle along the axis of the unmanned aerial vehicle;
Figure GSB0000193169270000052
which is representative of an external disturbance,
Figure GSB0000193169270000053
the actuator of each unmanned aerial vehicle has faults, wherein s is more than or equal to q and is less than n. Each matrix is represented as follows:
Figure GSB0000193169270000054
Figure GSB0000193169270000055
Figure GSB0000193169270000056
D＝[0.01 0.01 0.01 0.01]T。
assuming that an actuator fault occurs in the unmanned aerial vehicle formation system, the actuator fault occurs in an input channel, and therefore a fault matrix E is set as B;
as shown in fig. 1, 1-5 indicate that the undirected graph has 5 drone nodes, 0 indicates a long machine in formation, and the undirected graph indicates that each edge in the connection graph of the formation system has no connection direction, so that the undirected graph is less conservative compared with the directed graph. From fig. 1, it can be derived that the laplacian matrix L and the self-loop matrix G are respectively:
Figure GSB0000193169270000057
for a long machine in a formation system, it is marked as 0, and the dynamic equation is as follows:
Figure GSB0000193169270000058
y0(t)＝Cx0(t)
wherein,
Figure GSB0000193169270000061
represents the state vector of the long machine,
Figure GSB0000193169270000062
representing the output vector of the long machine.
Figure GSB0000193169270000063
A system matrix representing a long machine,
Figure GSB0000193169270000064
representing the output matrix of the long machine. In fig. G, long machines are directly observed by a small percentage of drones. If the i-th unmanned aerial vehicle can directly acquire the information of the long aircraft, an edge (v) exists in the graph G0，vi) And controlling the weight giAnd > 0, the unmanned plane is a controlled node in the graph G.
Further, the fault detection observer described in step 2 is as follows:
Figure GSB0000193169270000065
Figure GSB0000193169270000066
wherein, the first and second guide rollers are arranged in a row,
Figure GSB0000193169270000067
and
Figure GSB0000193169270000068
representing the upper and lower bounds of the state vector in the observer,
Figure GSB0000193169270000069
and
Figure GSB00001931692700000610
respectively representing the upper and lower bounds of the external disturbance, matrix A1Is the larger of matrix A and matrix 0, A2＝A-A1In the same way, D+The larger of matrix D and matrix 0, D-＝D-D+And K is an observer gain matrix, wherein,
Figure GSB00001931692700000611
Figure GSB00001931692700000612
and
Figure GSB00001931692700000613
respectively representing the upper and lower bounds of the relative output estimation error of the ith drone, given the definition as follows:
Figure GSB00001931692700000614
Figure GSB00001931692700000615
wherein,
Figure GSB00001931692700000616
to the ith unmanned aerial vehicle, define its upper and lower bounds of error, do respectively:
Figure GSB00001931692700000617
then
Figure GSB00001931692700000618
Figure GSB00001931692700000619
Can be rewritten as:
Figure GSB0000193169270000071
Figure GSB0000193169270000072
under the condition of no fault, defining dynamic equations of upper and lower bounds of errors for the ith unmanned aerial vehicle respectively:
Figure GSB0000193169270000073
Figure GSB0000193169270000074
for ease of reading, some of the symbols are simplified as follows:
Figure GSB0000193169270000075
then the following results are obtained:
Figure GSB0000193169270000076
Figure GSB0000193169270000077
further, the global estimation error equation of the unmanned aerial vehicle formation system in step 3 is as follows:
Figure GSB0000193169270000078
Figure GSB0000193169270000079
wherein,
Figure GSB00001931692700000710
Figure GSB00001931692700000711
Figure GSB00001931692700000712
Figure GSB00001931692700000713
INis an identity matrix of dimension N,
Figure GSB00001931692700000714
kronecker product of representative matrix. This allows to carry out a fault detection study of the formation system of drone based on longplane-bureaucratic planes from a global point of view.
When the unmanned aerial vehicle formation system does not have actuator faults, the output of the interval observer is defined as:
Figure GSB00001931692700000715
then output y of the ith dronei(t) should satisfy:
Figure GSB00001931692700000716
thus, when the formation system is in a healthy state, the following inequality should hold:
Figure GSB00001931692700000717
otherwise, a fault is indicated, and the fault should be alarmed.
Simulation example:
defining a reference input ui(t)＝[0.5 0.5]TExternal disturbance wi＝0.1sin(t)
Let t0Consider the following failure mode at 0:
unmanned aerial vehicle 1: f. of1(t)＝[f11(t) f12(t)]T
Unmanned aerial vehicle 2: f. of2(t)＝[f21(t) f22(t)]T
Wherein,
Figure GSB0000193169270000081
Figure GSB0000193169270000082
unmanned aerial vehicle 3, unmanned aerial vehicle 4 and unmanned aerial vehicle 5 do not break down.
In order to verify the effect of the fault detection method, simulation experiments are carried out by applying a Simulink module in Matlab, and if the fault of the constant-value actuator occurs in the unmanned aerial vehicle 1, the fault of the time-varying actuator occurs in the unmanned aerial vehicle 2, and other unmanned aerial vehicles keep normal flight states. When the formation system fails, the upper bound curve of the residual error output by the first unmanned aerial vehicle is shown in fig. 2, and the upper bound curve of the residual error output by the second unmanned aerial vehicle is shown in fig. 3.
According to the simulation result, when one or more unmanned aerial vehicles in the unmanned aerial vehicle formation system have actuator faults, the fault detection scheme of the interval observer can detect the nodes with the faults, a threshold generator and a residual evaluation function are not needed, the conservatism is reduced to a great extent, and the method has strong adaptability. The method has important applicable reference value for the fault detection of the unmanned aerial vehicle formation system under the condition of actuator fault.
The above specific implementation mode is a specific support for the technical idea of the interval observer-based unmanned aerial vehicle formation fault detection method, and the protection scope of the present invention cannot be limited thereby, and any modification made on the basis of the technical scheme of the present invention according to the technical idea of the present invention still belongs to the protection scope of the technical scheme of the present invention.

Claims (1)

1. The unmanned aerial vehicle formation fault detection method based on the interval observer is characterized in that fault detection is carried out without a residual error evaluation function and a threshold value generator, and the method comprises the following steps:
(1) modeling unmanned aerial vehicle formation system
Establishing communication connection topology among all unmanned aerial vehicles in a formation system through graph theory, a state equation and an output equation, expressing the communication connection topology by using a directionless topological graph, and simultaneously calculating a corresponding adjacency matrix A and a corresponding degree matrix D to obtain a Laplace matrix L; undirected handover topology graph adoption
Figure FSB0000194060240000011
Communication topology structure for representing unmanned aerial vehicle formation system(ii) a Wherein the node sets
Figure FSB0000194060240000012
Representing all drones, nodes
Figure FSB0000194060240000013
Denotes the ith drone, i ═ 1, 2.. N; the edge set epsilon represents the communication connection relation among all unmanned aerial vehicles, and the element epsilon in epsilon is (v)i，vj) Representing unmanned aerial vehicle viCan transmit to drone vjWherein i, j ═ 1, 2, …, N;
Figure FSB00001940602400000127
denotes viA set of neighbors of, i.e. all can and viA node set of interactive information; adjacency matrix
Figure FSB0000194060240000014
Wherein if (v)i，vj) E is epsilon, then aij1, otherwise aij0; degree matrix
Figure FSB0000194060240000015
Wherein
Figure FSB0000194060240000016
If (v)i，vj) E is epsilon and (v)j，vi) E is epsilon, G is an undirected graph; the topology description matrix is specifically:
defining a Laplace matrix
Figure FSB0000194060240000017
(2) Aiming at an unmanned aerial vehicle formation system model, establishing a fault detection interval observer based on a relative output estimation error;
the dynamic equations for drones in a formation system as follows:
Figure FSB0000194060240000018
yi(t)＝Cxi(t)
wherein,
Figure FSB0000194060240000019
represents the state vector of the ith drone,
Figure FSB00001940602400000110
is the control input vector for the ith drone,
Figure FSB00001940602400000111
represents the output vector of the ith drone,
Figure FSB00001940602400000112
which is representative of an external disturbance,
Figure FSB00001940602400000113
the fault of an actuator of the ith unmanned aerial vehicle is shown, wherein s is more than or equal to q and is less than n;
Figure FSB00001940602400000114
a system matrix representing the ith drone,
Figure FSB00001940602400000115
an input matrix representing the ith drone,
Figure FSB00001940602400000116
an output matrix representing the ith drone,
Figure FSB00001940602400000117
a state interference matrix representing the ith drone,
Figure FSB00001940602400000118
a fault matrix representing the ith drone, wherein the D and E matrices are both known column full rank matrices; for a long machine in the formation system, marking the long machine as 0;
aiming at the unmanned aerial vehicle dynamic equation, the fault detection observer is designed as follows:
Figure FSB00001940602400000119
Figure FSB00001940602400000120
wherein,
Figure FSB00001940602400000121
and
Figure FSB00001940602400000122
representing the upper and lower bounds of the state vector in the observer,
Figure FSB00001940602400000123
and
Figure FSB00001940602400000124
respectively representing the upper and lower bounds of the external disturbance, matrix A1Is the larger of matrix A and matrix 0, A2＝A-A1In the same way, D+The larger of matrix D and matrix 0, D-＝D-D+And K is the observer gain matrix,
Figure FSB00001940602400000125
and
Figure FSB00001940602400000126
respectively representing the upper and lower bounds of the relative output estimation error of the ith drone, given the definition as follows:
Figure FSB0000194060240000021
Figure FSB0000194060240000022
wherein,
Figure FSB0000194060240000023
if the ith unmanned plane can directly acquire the information of the long plane, controlling the weight giIs greater than 0; if information for drone i can be communicated to drone j, i, j ═ 1, 2, …, N, then aij1, otherwise aij＝0；NiRepresenting a neighbor set of the ith unmanned aerial vehicle, namely all other unmanned aerial vehicles capable of interacting information with the ith unmanned aerial vehicle;
to the ith unmanned aerial vehicle, define its upper and lower bounds of error, do respectively:
Figure FSB0000194060240000024
then
Figure FSB0000194060240000025
Can be rewritten as:
Figure FSB0000194060240000026
Figure FSB0000194060240000027
under the condition of no fault, defining dynamic equations of upper and lower bounds of errors for the ith unmanned aerial vehicle respectively:
Figure FSB0000194060240000028
Figure FSB0000194060240000029
for ease of reading, some of the symbols are simplified as follows:
Figure FSB00001940602400000210
then the following results are obtained:
Figure FSB00001940602400000211
Figure FSB00001940602400000212
(3) obtaining a global estimation error equation of the unmanned aerial vehicle formation system through theoretical derivation, carrying out stability verification on the global estimation error equation and finally obtaining a fault detection algorithm;
the global estimation error equation is as follows:
Figure FSB00001940602400000213
Figure FSB00001940602400000214
wherein,
Figure FSB0000194060240000031
Figure FSB0000194060240000032
Figure FSB0000194060240000033
Figure FSB0000194060240000034
INis an identity matrix of dimension N,
Figure FSB0000194060240000035
representing the kronecker product of the matrix, L is a Laplace matrix, and G is a calibration matrix;
consider the following continuous system:
Figure FSB0000194060240000036
wherein the matrix A is a MerSigle matrix,
Figure FSB0000194060240000037
and is
Figure FSB0000194060240000038
If the system initial state x (0) is more than or equal to 0, then x (t) is more than or equal to 0 when t is more than or equal to 0;
the following theorem is drawn therefrom:
for a given communication topology, if
Figure FSB0000194060240000039
Both mertseller and hevrz matrices, then when the drone formation system is fault-free, the fault detection observer is a section observer and makes it possible to operate the drone formation system without fault
Figure FSB00001940602400000310
If true;
when the unmanned aerial vehicle formation system does not have actuator faults, the output of the interval observer is defined as:
Figure FSB00001940602400000311
then output y of the ith dronei(t) should satisfy:
Figure FSB00001940602400000312
thus, when the formation system is in a healthy state, the following inequality should hold:
Figure FSB00001940602400000313
otherwise, a fault is indicated, and the fault should be alarmed.
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