CN109828460A - A kind of consistent control method of output for two-way heterogeneous multi-agent system - Google Patents
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Abstract
The invention discloses a kind of consistent control methods of output for two-way heterogeneous multi-agent system, construct the mathematical model of two-way heterogeneous multi-agent system, the overall topology and Laplacian matrix of system；The adaptive state observer of subsystems is constructed, the stable observation state of observer is obtained；The output for constructing subsystems adjusts equation, solves output and adjusts non trivial solution；The control law of each subsystem is constructed, so as to reach bidirectional output consistent for entire multi-agent system.The present invention is adaptive complete distributed control scheme, the Global Information of multi-agent system is not needed, as long as improving the flexibility of control program, the two-way multi-agent system of the isomery suitable for various structures obtaining the relative information between subsystems in practice.
Description
Technical field
The present invention relates to multi-agent system control technologies, and in particular to a kind of for two-way heterogeneous multi-agent system
Export consistent control method.
Background technique
The output-consistence research of complicated isomery multi-agent system is in satellite control, unmanned vehicle cooperation, traffic road
Line gauge stroke etc. is received significant attention and is got application.The general research only focuses on the cooperative relationship between system, but
It is for example social viewpoint dynamic system of some systems, the relationship of competition and cooperation is existed simultaneously between subsystems, in addition to
Need to pay close attention to the isomerism of subsystems itself, it is also necessary to pay close attention to the connection relationship between subsystems, i.e. isomery is two-way
Multi-agent system exports consensus.
It is found according to literature search, the two-way multi-agent system output-consistence research of isomery at present is all based on mostly intelligent
The global information of body topological structure, the mainly minimum real part of the characteristic value of the Laplacian matrix of topological structure.This is a kind of
Non-fully distributed control method, needs to be obtained ahead of time the Global Information of multi-agent system, significantly in design control law
Reduce the flexibility of control program in actual use.
Summary of the invention
The purpose of the present invention is to provide a kind of consistent control methods of output for two-way heterogeneous multi-agent system.
Realize the technical solution of foregoing invention purpose are as follows: a kind of output one for two-way heterogeneous multi-agent system
Cause control method, the specific steps are as follows:
The mathematical model of step 1, the two-way heterogeneous multi-agent system of building, the overall topology of system and
Laplacian matrix；
Step 2, the adaptive state observer for constructing subsystems obtain the stable observation state of observer；
Step 3, the output for constructing subsystems adjust equation, solve output and adjust non trivial solution；
The control law of step 4, each subsystem of building, so as to reach bidirectional output consistent for entire multi-agent system.
In step 1, the relevant knowledge of the related physical quantity that analysis subsystems need to pay close attention to, use state space is obtained
Following state-space expression:
Wherein AiFor the sytem matrix of subsystem, BiFor the control matrix of subsystem, CiFor the output matrix of subsystem, xi
For the state of subsystem, uiIt is inputted for the control of subsystem, yiFor the output of subsystem, N is the total number of subsystem.
The information exchange relationship between subsystems is analyzed, the overall topology of whole system is obtained, when two sons
When node is cooperative relationship, then the connection weight between them is positive number, conversely, be competitive relation between them, then connection weight
It is negative again；The Laplacian matrix L of whole system, building method are constructed according to topology diagram are as follows:
lij=-aij,i≠j；I, j=1,2 ..., N
Wherein lijFor each single item of L matrix, aijConnection weight between subsystems, N are total of subsystem
Number.
In step 2, for undirected drawing system, subsystems construct following Adaptive Observer:
Wherein S is the state matrix of systems stabilisation, ρiFor the observation state of i-th of state observer, aijFor subsystem i with
The connection weight of subsystem j, θiFor adaptation coefficient, coefficient giWhether by that can obtain the information of frame of reference and determine, can should
Coefficient is equal to 1, it is not possible to which the coefficient is equal to 0, coefficient diIt is determined by group of the subsystem belonging to whole system, belongs to positive group and take
1, belong to negative sense group and take -1, Q, F, H are the feedback matrix of observer, and meeting (S, Q) is controllable, F=QTP, H=PQQTP, square
Battle array P meets following Riccati equation:
STP+PS+I-PQQTP=0 (4)
For oriented graph system, a monotonically increasing function is introduced in observer, to increase the freedom degree of design:
Wherein yi=(div-ρi)TP(div-ρi) it is monotonically increasing function, the feedback matrix definition of the observer and observer
(4) identical.When observer (4) and (5) tend to stablize, observation state meets:
In step 3, specific output adjusts equation are as follows:
Wherein Πi,ΓiTo need the solution found out, S is the state matrix of systems stabilisation, and E is the output matrix of systems stabilisation,
AiFor the sytem matrix of subsystem i, BiFor the control matrix of subsystem i, CiFor the output matrix of subsystem i, N is subsystem
Total number.
In step 4, the control law of building are as follows:
ui=Ki(xi-Πiρi)+ΓiρiI=1,2 ..., N (7)
Wherein uiIt is inputted for the control of subsystem i, KiFor the feedback matrix of control law, meet matrix Ai+BiKiFor
Hurwitz, AiFor the sytem matrix of subsystem i, BiFor the control matrix of subsystem i, subsystems can be under the control law
It is consistent to reach bidirectional output.
Compared with prior art, the present invention its remarkable advantage is: 1) present invention is adaptive distributed AC servo system side completely
Case does not need the Global Information of multi-agent system, as long as obtaining the relative information between subsystems in practice,
Improve the flexibility of control program；2) present invention provides the control method of non-directed graph and digraph simultaneously, has good suitable
Ying Xing, the two-way multi-agent system of isomery suitable for various structures.
Detailed description of the invention
Fig. 1 is the method flow diagram that the present invention is unanimously controlled for the output of two-way heterogeneous multi-agent system.
Fig. 2 is the topology controlment of connected undirected graph.
Fig. 3 is the topology controlment of the digraph comprising directed spanning tree.
Fig. 4 is the adaptation coefficient convergence curve figure for the observer of Fig. 2 topological structure.
Fig. 5 is the control effect figure of the subsystems of Fig. 2 topological structure.
Fig. 6 is the adaptation coefficient convergence curve figure for the observer of the topological structure of Fig. 3.
Fig. 7 is the control effect figure of the subsystems of Fig. 3 topological structure.
Specific embodiment
In the following with reference to the drawings and specific embodiments, the present invention program is further illustrated.
The bilateral system of balance is defined as: for a set V containing multinode, two nonempty sets can be divided into
Vp,Vq, and meet Vp∪Vq=V,And introduce a sign matrix D=diag { d1,…,dn|di∈
(1, -1) }, wherein diIf=1 ai∈Vp,diIf=- 1 ai∈Vq.The study found that for the bilateral system of balance, system can
It is consistent to reach bilateral output.The present invention is based on the bilateral systems of balance to carry out exporting consistent research.
The present invention is directed to the consistent control method of output of two-way heterogeneous multi-agent system, belongs to fully distributed adaptive
Should control, first to the two-way multi-agent system of isomery construct Adaptive Observer, then according to output adjust non trivial solution with
And the observation state of Adaptive Observer constructs control law, keeps the bidirectional output of two-way heterogeneous multi-agent system consistent.Such as Fig. 1
It is shown, specifically include following process:
Step 1: the relevant knowledge of the related physical quantity that analysis subsystems need to pay close attention to, use state space obtains
Following state-space expression:
Wherein AiFor the sytem matrix of subsystem, BiFor the control matrix of subsystem, CiFor the output matrix of subsystem, xi
For the state of subsystem, uiIt is inputted for the control of subsystem, yiFor the output of subsystem, N is the number of subsystem.
The information exchange relationship between subsystems is analyzed, the overall topology of whole system is obtained, can be nothing
It is that the connection of subsystems in digraph is that have direction to figure or digraph, the difference between digraph and non-directed graph
, therefore its topological structure is asymmetrical (non-directed graph and digraph difference is as shown in Figures 2 and 3).When two child nodes are
When cooperative relationship, then the connection weight between them is positive number, conversely, being competitive relation between them, then connection weight is negative.
The Laplacian matrix L of whole system, building method are constructed according to topology diagram are as follows:
lij=-aij,i≠j；I, j=1,2 ..., N
Wherein lijFor each single item of L matrix, aijConnection weight between subsystems, N are total of subsystem
Number.
Step 2: systems stabilisation is observed to non-directed graph or digraph building subsystems adaptive state observer, surely
Determine the state expression formula of system are as follows:
Wherein S is the state matrix of systems stabilisation, and E is the output matrix of systems stabilisation, and v is the state of systems stabilisation, and w is
The output of systems stabilisation.
For undirected drawing system, subsystems construct following Adaptive Observer:
Wherein ρiFor the observation state of state observer, aijFor the connection weight of system, coefficient θiFor adaptation coefficient, it is
Number giBy that whether can obtain the information of frame of reference and determine, can the coefficient be equal to 1, it is not possible to the coefficient is equal to 0, coefficient di
It is determined by group of the subsystem belonging to whole system, belongs to positive group and take, 1, which belongs to negative sense group, takes -1.The feedback matrix Q of observer
Meeting (S, Q) is controllable, feedback matrix F, H satisfaction of observer: F=QTP, H=PQQTP, and matrix P satisfaction is as follows
Riccati equation:
STP+PS+I-PQQTP=0 (4)
Observer is improved due to the asymmetry of its Laplacain matrix for oriented graph system,
A monotonically increasing function is introduced in observer, to increase the freedom degree of design:
Wherein yi=(div-ρi)TP(div-ρi) it is monotonically increasing function.The feedback matrix of the observer defines and observer
(4) identical.When observer (4) and (5) tend to stablize, observation state meets:
Step 3: the output consensus in order to solve heterogeneous system needs to construct output and adjusts equation, finds out output and adjusts
The solution of modal equation can solve adjusting equation by the correlation function packet of matlab software.Specific output adjusts equation are as follows:
Wherein Πi,ΓiTo need the solution found out, S is the state matrix of systems stabilisation, and E is the output matrix of systems stabilisation,
AiFor the sytem matrix of subsystem i, BiFor the control matrix of subsystem i, CiFor the output matrix of subsystem i, N is subsystem
Total number.
Step 4: after obtaining the stable observation state of observer and output adjusting non trivial solution, control law is constructed:
ui=Ki(xi-∏iρii)+ΓiρiI=1,2 ..., N (7)
The wherein feedback matrix K of control lawiMeet matrix Ai+BiKiFor Hurwitz.The subsystems under the control law
Output can be with the bidirectional output for reaching following form is consistent:
Wherein y*For continuous output trajectory.
Embodiment
In order to verify effectiveness of the invention, it is real that this part carries out emulation to the topological structure based on Fig. 2 and Fig. 3 respectively
It tests.For the structure of Fig. 2 and Fig. 3, the parameter of subsystems are as follows:
C1=[1 1], C2=[1 0], C3=[2 1], C4=[1 0.5]
The parameter of frame of reference are as follows:
Corresponding output adjusts non trivial solution are as follows:
Γ1=[- 1.4-0.2], Γ2=[- 1.5-0.5], Γ3=[- 0.53-0.27], Γ4=[- 0.94-
0.24].
Feelings consistent with output for the convergence situation of the adaptation coefficient of the Adaptive Observer of the first topology diagram
Condition is respectively shown in Fig. 4 and Fig. 5.For the convergence situation of the adaptation coefficient of the Adaptive Observer of second of topology diagram
Situation consistent with output is respectively shown in Fig. 6 and Fig. 7.From simulation result as can be seen that Adaptive Observer can be in the short time
Interior convergence, system can reach that bidirectional output is consistent under the action of control protocol, demonstrate the correctness of the method for the present invention.
Claims (6)
1. a kind of consistent control method of output for two-way heterogeneous multi-agent system, which is characterized in that specific step is as follows:
The mathematical model of step 1, the two-way heterogeneous multi-agent system of building, the overall topology and Laplacian square of system
Battle array；
Step 2, the adaptive state observer for constructing subsystems obtain the stable observation state of observer；
Step 3, the output for constructing subsystems adjust equation, solve output and adjust non trivial solution；
The control law of step 4, each subsystem of building, so as to reach bidirectional output consistent for entire multi-agent system.
2. the output consistent control method according to claim 1 for two-way heterogeneous multi-agent system, feature exist
In in step 1, the related physical quantity that analysis subsystems need to pay close attention to, the relevant knowledge in use state space obtains as follows
State-space expression:
Wherein AiFor the sytem matrix of subsystem, BiFor the control matrix of subsystem, CiFor the output matrix of subsystem, xiFor subsystem
The state of system, uiIt is inputted for the control of subsystem, yiFor the output of subsystem, N is the total number of subsystem.
3. the output consistent control method according to claim 1 for two-way heterogeneous multi-agent system, feature exist
In, in step 1, analyze subsystems between information exchange relationship, the overall topology of whole system is obtained, when two
When child node is cooperative relationship, then the connection weight between them is that positive number then connects conversely, being competitive relation between them
Weight is negative；The Laplacian matrix L of whole system, building method are constructed according to topology diagram are as follows:
lij=-aij,i≠j；I, j=1,2 ..., N
Wherein lijFor each single item of L matrix, aijConnection weight between subsystems, N are the total number of subsystem.
4. the output consistent control method according to claim 1 for two-way heterogeneous multi-agent system, feature exist
In in step 2, for undirected drawing system, subsystems construct following Adaptive Observer:
Wherein S is the state matrix of systems stabilisation, ρiFor the observation state of i-th of state observer, aijFor subsystem i and subsystem
The connection weight of system j, θiFor adaptation coefficient, coefficient giIt, can the coefficient by that whether can obtain the information of frame of reference and determine
Equal to 1, it is not possible to which the coefficient is equal to 0, coefficient diIt is determined by group of the subsystem belonging to whole system, belongs to positive group and take 1, belong to
- 1 is taken in negative sense group, Q, F, H are the feedback matrix of observer, and meeting (S, Q) is controllable, F=QTP, H=PQQTP, matrix P are full
The following Riccati equation of foot:
STP+PS+I-PQQTP=0 (4)
For oriented graph system, a monotonically increasing function is introduced in observer, to increase the freedom degree of design:
Wherein yi=(div-ρi)TP(div-ρi) it is monotonically increasing function, feedback matrix definition and observer (4) of the observer
It is identical.When observer (4) and (5) tend to stablize, observation state meets:
5. the output consistent control method according to claim 1 for two-way heterogeneous multi-agent system, feature exist
In in step 3, specific output adjusts equation are as follows:
Wherein Πi,ΓiTo need the solution found out, S is the state matrix of systems stabilisation, and E is the output matrix of systems stabilisation, AiFor
The sytem matrix of subsystem i, BiFor the control matrix of subsystem i, CiFor the output matrix of subsystem i, N is total of subsystem
Number.
6. the output consistent control method according to claim 1 for two-way heterogeneous multi-agent system, feature exist
In, in step 4, the control law of building are as follows:
ui=Ki(xi-∏iρi)+ΓiρiI=1,2 ..., N (7)
Wherein uiIt is inputted for the control of subsystem i, KiFor the feedback matrix of control law, meet matrix Ai+BiKiFor Hurwitz, Ai
For the sytem matrix of subsystem i, BiFor the control matrix of subsystem i, subsystems be can achieve two-way under the control law
Output is consistent.
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| CN110609469B (en) * | 2019-06-30 | 2022-06-24 | 南京理工大学 | Consistency control method of heterogeneous time-lag multi-agent system based on PI |
| CN114114905A (en) * | 2021-10-25 | 2022-03-01 | 南京理工大学 | Optimal tracking control method for data-driven carrier-based rocket launcher launching device |
| CN114114905B (en) * | 2021-10-25 | 2023-02-28 | 南京理工大学 | Optimal tracking control method for data-driven carrier-based rocket launcher launching device |
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