CN115016539A - Multi-aircraft fully-distributed disturbance-resistant cooperative enclosure control method - Google Patents

Multi-aircraft fully-distributed disturbance-resistant cooperative enclosure control method Download PDF

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CN115016539A
CN115016539A CN202210812262.2A CN202210812262A CN115016539A CN 115016539 A CN115016539 A CN 115016539A CN 202210812262 A CN202210812262 A CN 202210812262A CN 115016539 A CN115016539 A CN 115016539A
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aircraft
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董朝阳
姚翔
楼朝飞
李泓宇
冉茂鹏
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    • G05D1/104—Simultaneous control of position or course in three dimensions specially adapted for aircraft involving a plurality of aircrafts, e.g. formation flying
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Abstract

The invention provides a fully distributed disturbance-resistant cooperative trapping control method for multiple aircrafts, which comprises the following steps: establishing an aircraft kinematic model, and determining a multi-aircraft cooperative capture mode and a capture formation; step two: building a multi-aircraft distributed extended state observer; step three: acquiring a communication topological relation among multiple aircrafts to obtain corresponding data information; step four: and implementing the fully distributed disturbance-resistant cooperative trapping of the multiple aircrafts according to all data information which can be acquired by the aircrafts and the proposed multi-aircraft cooperative trapping control algorithm. The multi-aircraft cooperative trapping control algorithm designed by the invention not only has lower requirement on communication between the aircrafts, but also has a certain inhibiting effect on external disturbance suffered by the aircrafts, and improves the reliability and the practicability of the multi-aircraft cooperative trapping.

Description

Multi-aircraft fully-distributed disturbance-resistant cooperative enclosure control method
Technical Field
The invention belongs to the field of multi-aircraft cooperative control, and particularly relates to a fully distributed disturbance-resistant cooperative enclosure control method for multiple aircrafts.
Background
Cooperative control of multiple aircraft systems is a research hotspot in the control field at present, and is widely applied in the fields of scientific research and engineering. Such as: the method comprises the following steps of mixed cooperative combat of a manned/unmanned aerial vehicle, cooperative detection of a spacecraft, cooperative guidance of a missile and the like. The cooperative trapping technology of the multiple aircrafts is used as important research content in the field of cooperative control of the multiple aircrafts, and plays a vital role in improving the national air defense capability and establishing an omnibearing and multilevel air defense system. At present, a consistency-based control method has great advantages, but the control protocol of the method still has certain dependence on some global information. Furthermore, the aircraft is inevitably affected by external disturbances, such as atmospheric disturbances, while in flight, posing a threat to both flight safety and reliability. And a multi-aircraft cooperative capture control method based on a completely distributed architecture and considering the external disturbance of the aircraft is relatively few at present.
In order to meet the background requirements, the invention provides a fully distributed disturbance-resistant collaborative trapping control method for multiple aircrafts, which is characterized in that an extended state observer is used for estimating the speed and the disturbance of a trapping aircraft, the sum of the speed, the disturbance and unknown control input of the aircraft to be trapped is estimated, a consistency theory is combined with a self-adaptive method, and a fully distributed control protocol for the multi-aircraft disturbance-resistant collaborative trapping is further provided, so that the aircraft to be trapped can be trapped in the geometric center of a time-varying formation of the aircraft by the trapping aircraft within a short time, and the method has high practicability and reliability.
Disclosure of Invention
The invention aims to provide a fully distributed disturbance-resistant cooperative trapping control method for multiple aircrafts to solve the problems that communication resources are limited and external interference influence exists during cooperative trapping of the multiple aircrafts.
The technical scheme adopted by the invention is as follows:
the invention provides a fully distributed disturbance-resistant cooperative trapping control method for multiple aircrafts, which comprises the following steps:
the method comprises the following steps: establishing an aircraft kinematic model, and determining a multi-aircraft cooperative capture mode and a capture formation;
step two: building a multi-aircraft distributed extended state observer;
step three: acquiring a communication topological relation among multiple aircrafts to obtain corresponding data information;
step four: and implementing the fully distributed disturbance-resistant cooperative trapping of the multiple aircrafts according to all data information which can be acquired by the aircrafts and the proposed multi-aircraft cooperative trapping control algorithm.
The invention has the advantages that:
(1) the method for controlling the complete distributed disturbance-resistant collaborative trapping of the multiple aircrafts is provided, and the reliability and the practicability of the collaborative trapping of the multiple aircrafts are improved.
(2) The designed multi-aircraft cooperative capture control algorithm has low requirement on communication between the aircrafts and has a certain inhibiting effect on external disturbance on the aircrafts.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart illustrating an embodiment of the present invention;
FIG. 2 is a schematic illustration of the cooperative encirclement of multiple aircraft according to the present invention;
FIG. 3 is a diagram of a communication topology between multiple aircraft according to an embodiment of the present invention;
FIG. 4 is a frame diagram of a fully distributed disturbance-rejection cooperative trapping control method for multiple aircrafts according to the present invention;
fig. 5 is a schematic diagram of a motion trajectory of a multi-aircraft cooperative trapping t-7 s according to an embodiment of the present invention;
fig. 6 is a schematic diagram of a motion trajectory of a multi-aircraft cooperative capture t-15 s according to an embodiment of the present invention;
FIG. 7 is a time-varying fleet tracking of a portion of a state of an aircraft according to an embodiment of the present invention;
FIG. 8 is an observer view of a portion of the state of an aircraft according to an embodiment of the invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Fig. 1 is a specific flowchart of the present invention, and as shown in fig. 1, the method includes:
the method comprises the following steps: establishing an aircraft kinematic model, and determining a multi-aircraft cooperative capture mode and a capture formation;
first, symbols to be used in steps one to four of the present invention will be explained:
Figure BDA0003741127290000021
represents a set of real numbers and a real number,
Figure BDA0003741127290000022
representing a complex set.
Figure BDA0003741127290000023
Means that a > 0 and
Figure BDA0003741127290000024
represents an n-dimensional real vector space,
Figure BDA0003741127290000025
representing an n x n-dimensional real vector space
Figure BDA0003741127290000026
Vectors whose representative elements are all 1, I N Representing an nxn dimensional identity matrix. X T The upper right hand symbol of (a) is a transposed symbol,
Figure BDA0003741127290000027
representing the kronecker product. λ (M) represents the eigenvalues of matrix M. Lambda [ alpha ] max (Q) and lambda min (Q) respectively represent the maximum and minimum eigenvalues of the matrix Q. | | · | represents the euclidean norm.
Secondly, the aircraft to be captured is numbered as N, and N-1 surrounding aircraft are numbered from 1 to N-1. Together they form a system with N agents. In order to increase the reliability of the cooperative entrapment control method while consuming as little communication resources as possible, it is assumed that the interaction topology among the individual aircraft is directional and each aircraft can only obtain information of its neighbor aircraft. Furthermore, global information in any form is not available. At the same time, the external disturbances to which the aircraft to be arrested is subjected and the control inputs of the aircraft to be arrested are also unknown. The aircraft to be captured needs to be enclosed in a three-dimensional space in the time-varying formation center as fast as possible, and has the capability of continuously tracking the aircraft to be captured, and the schematic diagram is shown in fig. 2.
Then, a kinematic model of the captive aircraft is established as follows (i ∈ F, F ═ 1, 2, …, N-1 }):
Figure BDA0003741127290000031
wherein the content of the first and second substances,
Figure BDA0003741127290000032
and x i (t)＝[x ix (t)，x iv (t)] T Respectively representing the output vector and the state vector of the aircraft.
Figure BDA0003741127290000033
And
Figure BDA0003741127290000034
respectively representing the control inputs of the aircraft i (i e F) and the unknown external disturbances experienced.
The kinematic model of the aircraft to be captured is as follows:
Figure BDA0003741127290000035
wherein the content of the first and second substances,
Figure BDA0003741127290000036
and
Figure BDA0003741127290000037
respectively representing the output vector and the state vector of the aircraft to be arrested.
Figure BDA0003741127290000038
And
Figure BDA0003741127290000039
respectively, an unknown control input of the aircraft to be caught and an external disturbance experienced.
For each aircraft, if only the position and velocity of the catch formation are of interest, the overall control task can be split into two parts, an inner ring part and an outer ring part. The purpose of the outer ring portion is to allow the aircraft to reach the desired position at the desired speed, while the inner ring functions to track the attitude. Therefore, it is reasonable to describe the aircraft as a particle system and use a second order integrator, depending on the actual requirements of the enclosure. Meanwhile, for convenience of analysis and expression, the spatial dimension is set to 1 at the time of description. It is emphasized that the multi-aircraft cooperative containment problem analyzed by the present invention occurs in three-dimensional space, but the theoretical modeling analysis is not necessarily so complex, as the dimensionality can be extended using the kronecker product. Therefore, the theoretical results of the subsequent correlation still hold in three-dimensional space.
Then, let the desired trapping formation of the trapping aircraft be:
Figure BDA00037411272900000310
wherein h is i (t)＝[h ix (t)，h iv (t)] T (i∈F)，
Figure BDA00037411272900000311
Finally, the aircraft cooperative trapping is determined to aim at the geometric center of the time-varying formation where the aircraft to be trapped can be trapped by the trapping unmanned aerial vehicle, that is, the state of the aircraft satisfies the following equation:
Figure BDA00037411272900000312
Figure BDA00037411272900000313
in order to prevent the aircraft to be arrested from escaping, a predetermined enclosure formation is satisfied
Figure BDA00037411272900000314
By substituting this formula for formula (5), we can obtain formula (4). That is, the final goal of the design of the aircraft in cooperation with the entrapment control algorithm is to make the state of the aircraft satisfy equation (5).
And finishing the step I, and determining the kinematics model, the cooperative capture formation and the capture mode of the aircraft clearly.
Step two: building a multi-aircraft distributed extended state observer;
the following expansion states are first defined:
Figure BDA0003741127290000041
for an captive aircraft i, i ∈ F, the following distributed ESO is designed:
Figure BDA0003741127290000042
the ESO design for the aircraft N to be arrested is as follows:
Figure BDA0003741127290000043
wherein the content of the first and second substances,
Figure BDA0003741127290000044
it is the state of observation that the state,
Figure BDA0003741127290000045
and
Figure BDA0003741127290000046
is a parameter of ESO, and E is Hurwitz matrix.
Figure BDA0003741127290000047
Error of observation of ESO
Figure BDA0003741127290000048
Comprises the following steps:
Figure BDA0003741127290000049
the dynamic equation is as follows:
Figure BDA00037411272900000410
and at this moment, the construction of the multi-aircraft distributed extended state observer is finished.
Step three: acquiring a communication topological relation among multiple aircrafts to obtain corresponding data information;
first, one directed graph G (v (G)), e (G)) is composed of an edge e (G) and a node v (G). An edge may consist of a pair of nodes (v) i ，v j ) And (4) showing. In this set of nodes, the parent node is v i Child node is v j . Side (v) j ，v i ) Weight w of ij Is an element of the adjacency matrix W of the graph G. If (v) j ，v i ) E (G), then w ij ≥0。
Figure BDA00037411272900000411
And
Figure BDA00037411272900000412
respectively represent nodes v i In-degree and out-degree. If the in-degree is equal to the out-degree for each node in the graph, it is called a balanced graph. The diagonal elements of the in-degree matrix D of the graph are the in-degree of each node, and the laplacian matrix L of the graph is D-W. For a directed graph G, if at least one node has a directed path to any node, the graph is called as having a spanning tree.
For the communication topological relation between the aircrafts in the invention needs to satisfy the condition that the spanning tree exists in the directed graph G, and the specific form is determined according to the actual problem requirement, a specific embodiment will be given to explain the invention. According to the output of the aircraft kinematic model in the first step of the invention, and by means of the observation of the extended state observer in the second step of the invention, the data information required by the multi-aircraft cooperative trapping control method in the fourth step of the invention can be obtained, and the whole framework is shown in fig. 4.
And determining the communication topological relation of the multiple aircrafts, and finishing the acquisition of the corresponding data information.
Step four: and implementing the fully distributed disturbance-resistant cooperative trapping of the multiple aircrafts according to the data information which can be obtained by the aircrafts and the proposed multi-aircraft cooperative trapping control algorithm.
First, the external disturbances to which the aircraft is subjected, the desired formation of the enclosure formation and the control inputs to the aircraft should satisfy the following assumptions:
assume that 1: external disturbances d to the aircraft i (t) and derivatives thereof
Figure BDA0003741127290000051
Is bounded.
Assume 2:
Figure BDA0003741127290000052
and the desired formation h (t) are bounded.
Assume that 3: each-order state, unknown control input u for an aircraft N (t) and derivatives thereof
Figure BDA0003741127290000053
Is bounded.
Second, a fully distributed control protocol is constructed that encloses aircraft i (i ∈ F) as follows:
Figure BDA0003741127290000054
wherein
Figure BDA0003741127290000055
Figure BDA0003741127290000056
Is a symmetric positive definite matrix, tau i (. cndot.) is a monotonically increasing function that satisfies τ when s > 0 i (s)≥1，c i Is a coupling weight function satisfying c i (0)≥1。
Clipping the aircraft control inputs in view of aircraft actuator limitations:
u i ＝sat(u i ) (13)
wherein sat (u) i )＝min{U i ，|u i |}·sign(u i )，i∈F，(U i ＞0)。
Finally, the parameter setting method of the multi-aircraft cooperative trapping control method provided by the invention comprises the following steps:
step 1: solving the following linear matrix inequality to obtain a matrix P:
AP+PA T -2BB T ＜0 (14)
step 2: the feedback gain matrix K is obtained by:
K＝-B T P -1 (15)
step 3: the matrix xi is obtained by the following equation:
Ξ＝P -1 BB T P -1 (16)
step 4: determining a monotonically increasing function τ i (. is):
τ i (ξ i T P -1 ξ i )＝(1+ξ i T P -1 ξ i ) 3 ，i∈F (17)
so far, the method for controlling the fully distributed disturbance-resistant cooperative trapping of the multiple aircrafts is given, and for the system formed by the formula (1) and the formula (2), if the system is saturated, the amplitude is limited by U i And the containment control protocol formula (12) is reasonably set according to a parameter setting method, so that for any bounded initial condition:
Figure BDA0003741127290000057
Figure BDA0003741127290000061
and meanwhile, the complete distributed disturbance resistance and cooperative trapping of the multiple aircrafts are realized.
Wherein the content of the first and second substances,
Figure BDA0003741127290000062
Figure BDA0003741127290000063
examples
A specific example of the present invention is given below to verify the validity of the proposed control method. The specific implementation steps of this example are as follows:
(1) multi-aircraft system and enclosure configuration
Consider that 3 containment aircraft with external disturbances in three-dimensional space contain an aircraft with unknown control inputs. The formation of the enclosure is as follows (N ═ 4):
Figure BDA0003741127290000064
it can be verified that the requirement of hypothesis 2 is met.
In addition, each aircraft is subjected to a value of d for the x, y and z directions i External perturbation i sin (t) + (5-i) cos (t), unknown control input setting for the captive drone is u 4 ＝-3 sin(t)-4 cos(t)-2/3，U i 80. The initial position of the aircraft to be caught is set to [200, 200%] T 。
(2) Multi-aircraft distributed extended state observer establishment and parameter selection
Aiming at the multi-aircraft distributed extended state observers (7) and (8) built in the step two, the parameter l is led to 1 ＝3，l 2 ＝3，l 3 1, epsilon is 0.01. It can be verified that formula (9) in step two is satisfied.
(3) Communication topological structure among multiple aircrafts and collaborative capture control algorithm parameter setting
The multi-aircraft communication topology, as shown in fig. 3, may verify that the conditions in step three are met. Aiming at the control algorithm of the formula (12), according to the proposed parameter setting method, the parameters are set as:
Figure BDA0003741127290000065
K＝[-1，-2]，
Figure BDA0003741127290000066
(4) analysis of results
By applying the theoretical results, the motion locus diagrams of the multi-aircraft cooperative enclosure capture t-7 s and t-15 s are shown in fig. 5 and 6, and the time-varying formation tracking condition of the partial aircraft state is shown in fig. 7. From the above three figures, it can be seen that both the desired multi-aircraft capture formation and the continuous tracking of the aircraft to be captured can be achieved under the effect of the proposed control method, i.e. equation (19) holds. As can be seen from fig. 8, the extended state observer converges and equation (18) also holds. Therefore, the multiple aircrafts realize complete distributed disturbance-resistant cooperative enclosure, and the effectiveness of the control method is verified through the experiment.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (5)

1. A multi-aircraft fully distributed disturbance-resistant cooperative enclosure control method is characterized by comprising the following steps:
the method comprises the following steps: establishing an aircraft kinematic model, and determining a multi-aircraft cooperative capture mode and a capture formation;
step two: building a multi-aircraft distributed extended state observer;
step three: acquiring a communication topological relation among multiple aircrafts to obtain corresponding data information;
step four: and implementing the fully distributed disturbance-resistant cooperative trapping of the multiple aircrafts according to all data information which can be acquired by the aircrafts and the proposed multi-aircraft cooperative trapping control algorithm.
2. The method according to claim 1, wherein the step of establishing the aircraft kinematic model and the multi-aircraft cooperative trapping mode comprises:
the kinematic model of the captive aircraft is as follows (i ∈ F, F ═ 1, 2, …, N-1 }):
Figure FDA0003741127280000011
wherein the content of the first and second substances,
Figure FDA0003741127280000012
and x i (t)＝[x ix (t)，x iv (t)] T Respectively representing the output vector and the state vector of the aircraft.
Figure FDA00037411272800000110
And
Figure FDA00037411272800000111
respectively representing the control inputs of the aircraft i (i e F) and the unknown external disturbances experienced.
The kinematic model of the aircraft to be captured is as follows:
Figure FDA0003741127280000013
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00037411272800000114
and x N (t)＝[x Nx (t)，x Nv (t)] T Respectively representing the output vector and the state vector of the aircraft to be arrested.
Figure FDA00037411272800000113
And
Figure FDA00037411272800000112
respectively, an unknown control input of the aircraft to be caught and an external disturbance experienced.
The expected interception formation for enclosing the aircraft is as follows:
Figure FDA0003741127280000014
wherein h is i (t)＝[h ix (t)，h iv (t)] T (i∈F)，
Figure FDA0003741127280000015
The goal of the cooperative trapping of the aircrafts is to enable the aircraft to be trapped by the trapping unmanned aerial vehicle to be trapped in the geometric center of the time-varying formation thereof, i.e. the state of the aircraft satisfies the following equation:
Figure FDA0003741127280000016
Figure FDA0003741127280000017
furthermore, the predetermined enclosure formation should satisfy
Figure FDA0003741127280000018
3. The method according to claim 1, wherein the multi-aircraft distributed extended state observer building process of the second step is as follows:
aircraft expansion state definition:
Figure FDA0003741127280000019
the distributed ESO of the captive aircraft i, i belongs to F is as follows:
Figure FDA0003741127280000021
the ESO of the aircraft N to be caught is:
Figure FDA0003741127280000022
wherein the content of the first and second substances,
Figure FDA0003741127280000027
it is the state of observation that the state,
Figure FDA0003741127280000028
and
Figure FDA0003741127280000029
is a parameter of the ESO, and E is a Hurwitz matrix to be satisfied:
Figure FDA0003741127280000023
。
4. the method according to claim 1, wherein the step three of determining the communication topology between multiple aircraft and obtaining the corresponding data information according to the step two comprise:
the communication topological relation between the aircrafts needs to meet the requirement that a spanning tree exists in a directed graph G, and the specific form is determined according to the actual problem requirement. According to the output of the aircraft kinematic model in the first step of the invention, the data information required by the multi-aircraft cooperative trapping control method is obtained by means of the observation of the extended state observer in the second step of the invention, and the whole framework is shown in fig. 4.
5. The method according to claim 1, wherein step four comprises a fully distributed disturbance-resistant cooperative trapping control algorithm and a parameter setting process of the multi-aircraft:
the external disturbance to the aircraft, the expected form of the formation of the enclosure and the control input of the aircraft should satisfy the following assumptions:
assume that 1: external disturbances d to the aircraft i (t) and derivatives thereof
Figure FDA00037411272800000210
Is bounded.
Assume 2:
Figure FDA00037411272800000211
and the desired contour h (t) are bounded.
Assume that 3: each-order state, unknown control input u for an aircraft N (t) and derivatives thereof
Figure FDA00037411272800000212
Is bounded.
The fully distributed control protocol for the captive aircraft i (i e F) is:
Figure FDA0003741127280000024
wherein
Figure FDA0003741127280000025
Figure FDA0003741127280000026
Is a symmetric positive definite matrix, tau i (. cndot.) is a monotonically increasing function satisfying τ when s > 0 i (s)≥1，c i Is a coupling weight function satisfying c i (0)≥1。
Clipping the aircraft control inputs in view of aircraft actuator limitations:
u i ＝sat(u i )
wherein sat (u) i )＝min{U i ，|u i |}·sign(u i )，i∈F，(U i ＞0)。
The parameter setting method of the multi-aircraft cooperative trapping control method comprises the following steps:
step 1: solving the following linear matrix inequality to obtain a matrix P:
AP+PA T -2BB T ＜0 (14)
step 2: solving the following formula to obtain a feedback gain matrix K:
K＝-B T P -1 (15)
step 3: solving the following equation to obtain a matrix xi:
Ξ＝P -1 BB T P -1 (16)
step 4: monotonically increasing function tau i (. is):
τ i (ξ i T P -1 ξ i )＝(1+ξ i T P -1 ξ i ) 3 ，i∈F (17)
for the multi-aircraft system of the present invention, clip U if saturated i And the trapping control protocol formula is reasonably set according to the parameter setting method, so that for any bounded initial condition:
Figure FDA0003741127280000031
Figure FDA0003741127280000032
the two modes are simultaneously established, and the complete distributed disturbance resistance and cooperative trapping of the multiple aircrafts are realized.
Wherein the content of the first and second substances,
Figure FDA0003741127280000033
Figure FDA0003741127280000034
CN202210812262.2A 2022-07-12 2022-07-12 Multi-aircraft fully-distributed disturbance-resistant cooperative enclosure control method Pending CN115016539A (en)

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115826416A (en) * 2023-02-20 2023-03-21 北京航空航天大学 Multi-airship cooperative control method and system in network rejection environment

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115826416A (en) * 2023-02-20 2023-03-21 北京航空航天大学 Multi-airship cooperative control method and system in network rejection environment

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