CN109828460B - Output consistency control method for bidirectional heterogeneous multi-agent system - Google Patents

Abstract

The invention discloses an output consistency control method for a bidirectional heterogeneous multi-agent system, which comprises the steps of constructing a mathematical model of the bidirectional heterogeneous multi-agent system, an integral topological structure of the system and a Laplacian matrix; constructing a self-adaptive state observer of each subsystem to obtain a stable observation state of the observer; constructing an output regulating equation of each subsystem, and solving the solution of the output regulating equation; and (3) constructing a control law of each subsystem, so that the whole multi-agent system achieves the two-way output consistency. The invention is a self-adaptive fully-distributed control scheme, does not need the whole information of a multi-agent system, only needs to obtain the relative information among all subsystems in practical application, improves the flexibility of the control scheme, and is suitable for heterogeneous bidirectional multi-agent systems with various structures.

Description

Output consistency control method for bidirectional heterogeneous multi-agent system

Technical Field

The invention relates to a multi-agent system control technology, in particular to an output consistency control method for a bidirectional heterogeneous multi-agent system.

Background

The output consistency research of the complex heterogeneous multi-agent system is widely concerned and applied in the aspects of satellite control, unmanned aerial vehicle cooperation, traffic route planning and the like. Generally, the research only focuses on the cooperative relationship among systems, but some systems, such as social viewpoint dynamic systems, have a competitive and cooperative relationship among subsystems, and need to focus on the connection relationship among the subsystems besides the heterogeneity of the subsystems, namely the problem of output consistency of heterogeneous bidirectional multi-agent systems.

According to literature retrieval, the output consistency research of the existing heterogeneous bidirectional multi-agent system is based on the global information of a multi-agent topological structure, and mainly is the minimum real part of the eigenvalue of a Laplacian matrix of the topological structure. The method is a non-completely distributed control method, and the whole information of the multi-agent system is required to be obtained in advance when a control law is designed, so that the flexibility of the control scheme in actual use is greatly reduced.

Disclosure of Invention

The invention aims to provide an output consistency control method for a bidirectional heterogeneous multi-agent system.

The technical solution for realizing the above purpose of the invention is as follows: an output consistency control method for a bidirectional heterogeneous multi-agent system comprises the following specific steps:

step 1, constructing a mathematical model of a bidirectional heterogeneous multi-agent system, an integral topological structure of the system and a Laplacian matrix;

step 2, constructing a self-adaptive state observer of each subsystem to obtain a stable observation state of the observer;

step 3, constructing output adjustment equations of all subsystems, and solving the solutions of the output adjustment equations;

and 4, constructing a control law of each subsystem, so that the whole multi-agent system achieves bidirectional output consistency.

In step 1, analyzing the relevant physical quantities of each subsystem which need to be concerned, and obtaining the following state space expression by using the relevant knowledge of the state space:

wherein A is_iSystem matrix being a subsystem, B_iIs a control matrix of the subsystem, C_iIs the output matrix of the subsystem, x_iIs the state of the subsystem, u_iIs a control input of the subsystem, y_iN is the total number of subsystems.

Analyzing the information exchange relationship among the subsystems to obtain the overall topological structure of the whole system, wherein when two child nodes are in a cooperative relationship, the connection weight between the two child nodes is positive, otherwise, the connection weight is negative if the two child nodes are in a competitive relationship; constructing a Laplacian matrix L of the whole system according to the topological structure chart, wherein the construction method comprises the following steps:

l_ij＝-a_ij,i≠j；i,j＝1,2,…,N

wherein l_ijFor each entry of the L matrix, a_ijAnd N is the total number of the subsystems.

In step 2, aiming at the undirected graph system, each subsystem constructs the following self-adaptive observer:

where S is the state matrix, ρ, of the stable system_iIs the observed state of the i-th state observer, a_ijIs the connection weight of subsystem i and subsystem j, θ_iFor adaptive coefficients, coefficient g_iDepending on whether information of the reference system is available, it is possible for the coefficient to be equal to 1, it is not possible for the coefficient to be equal to 0, and the coefficient d_iThe feedback matrix of the observer is determined by the group of the subsystems in the whole system, wherein the group belongs to a positive group of 1, the group belongs to a negative group of-1, Q, F, H, and the feedback matrix satisfies that (S, Q) is controllable, and F is Q^TP,H＝PQQ^TP, matrix P satisfies the following Riccati equation:

S^TP+PS+I-PQQ^TP＝0 (4)

for a directed graph system, a monotonically increasing function is introduced in the observer to increase the degree of freedom of design:

wherein y is_i＝(d_iv-ρ_i)^TP(d_iv-ρ_i) The feedback matrix of the observer is defined as the observer (4) for a monotonically increasing function. When the observers (4) and (5) tend to be stable, the observation state satisfies:

in step 3, the specific output adjustment equation is as follows:

II therein_i,Γ_iFor the solution to be solved, S is the state matrix of the stable system, E is the output matrix of the stable system, A_iSystem matrix being subsystem i, B_iIs the control matrix of subsystem i, C_iAnd N is the total number of the subsystems.

In step 4, the constructed control law is as follows:

u_i＝K_i(x_i-Π_iρ_i)+Γ_iρ_i i＝1,2，...,N (7)

wherein u is_iFor control input of subsystem i, K_iSatisfies matrix A as the feedback matrix of the control law_i+B_iK_iIs Hurwitz, A_iSystem matrix being subsystem i, B_iThe control matrix of the subsystem i can achieve the bidirectional output consistency of each subsystem under the control law.

Compared with the prior art, the invention has the remarkable advantages that: 1) the invention is a self-adaptive fully distributed control scheme, does not need the overall information of a multi-agent system, and only needs to obtain the relative information among subsystems in the actual application, thereby improving the flexibility of the control scheme; 2) the invention provides the control method of the undirected graph and the directed graph at the same time, has good adaptability and is suitable for heterogeneous bidirectional multi-agent systems with various structures.

Drawings

FIG. 1 is a flow chart of a method of consistent control of output for a bi-directional heterogeneous multi-agent system of the present invention.

FIG. 2 is a topology model of a connected undirected graph.

FIG. 3 is a topology model of a directed graph containing a directed spanning tree.

Fig. 4 is a graph of the convergence of the adaptive coefficients of the observer for the topology of fig. 2.

Fig. 5 is a control effect diagram of the various subsystems of the topology of fig. 2.

FIG. 6 is a plot of the convergence of the adaptive coefficients of an observer for the topology of FIG. 3.

Fig. 7 is a control effect diagram of various subsystems of the topology of fig. 3.

Detailed Description

The invention is further illustrated by the following examples in conjunction with the accompanying drawings.

The definition of a balanced bidirectional system is: for a set V containing multiple nodes, the method can be divided into two non-empty sets V_p,V_qAnd satisfy V_p∪V_q＝V，

And introduces a sign matrix D ═ diag { D ═ D₁,…,d_n|d_iE (1, -1) }, where d _i1 if a_i∈V_p,d _i1 if a_i∈V_q. Research has found that for a balanced bi-directional system, the system can achieve bilateral output consistency. The invention carries out output consistency research based on a balanced bilateral system.

The invention relates to an output consistency control method for a bidirectional heterogeneous multi-agent system, which belongs to completely distributed self-adaptive control. As shown in fig. 1, the method specifically includes the following steps:

the method comprises the following steps: analyzing the relevant physical quantity which needs to be concerned by each subsystem, and obtaining the following state space expression by using the relevant knowledge of the state space:

wherein A is_iSystem matrix being a subsystem, B_iIs a control matrix of the subsystem, C_iIs the output matrix of the subsystem, x_iIs the state of the subsystem, u_iIs a subsystemControl input of the system, y_iN is the number of subsystems.

Analyzing the information exchange relationship among the subsystems to obtain the overall topological structure of the whole system, which can be an undirected graph or a directed graph, wherein the difference between the directed graph and the undirected graph is that the connections of the subsystems in the directed graph are directed, so that the topological structures are asymmetric (the undirected graph and the directed graph are respectively shown in fig. 2 and fig. 3). When two sub-nodes are in a cooperative relationship, the connection weight between the two sub-nodes is positive, otherwise, the connection weight is negative when the two sub-nodes are in a competitive relationship.

Constructing a Laplacian matrix L of the whole system according to the topological structure chart, wherein the construction method comprises the following steps:

l_ij＝-a_ij,i≠j；i,j＝1,2,…,N

wherein l_ijFor each entry of the L matrix, a_ijAnd N is the total number of the subsystems.

Step two: constructing an observation stable system of the self-adaptive state observer of each subsystem for an undirected graph or a directed graph, wherein the state expression of the stable system is as follows:

wherein S is a state matrix of the stable system, E is an output matrix of the stable system, v is a state of the stable system, and w is an output of the stable system.

For an undirected graph system, each subsystem constructs an adaptive observer as follows:

where ρ is_iBeing observations by state observersState a of_ijFor the connection weight of the system, coefficient θ_iFor adaptive coefficients, coefficient g_iDepending on whether information of the reference system is available, it is possible for the coefficient to be equal to 1, it is not possible for the coefficient to be equal to 0, and the coefficient d_iThe group of the subsystem belongs to the positive group, and 1 belongs to the negative group, namely-1. The observer feedback matrix Q is controllable, satisfying (S, Q), the observer feedback matrix F, H satisfying: f ═ Q^TP，H＝PQQ^TP, and matrix P satisfies the following Riccati equation:

S^TP+PS+I-PQQ^TP＝0 (4)

for a directed graph system, due to the asymmetry of a Laplacain matrix, an observer is improved, and a monotone increasing function is introduced into the observer to increase the degree of freedom of design:

wherein y is_i＝(d_iv-ρ_i)^TP(d_iv-ρ_i) Is a monotonically increasing function. The feedback matrix definition of the observer is the same as the observer (4). When the observers (4) and (5) tend to be stable, the observation state satisfies:

step three: in order to solve the problem of output consistency of the heterogeneous system, an output regulation equation needs to be constructed, the solution of the output regulation equation is solved, and the regulation equation can be solved through a related function package of matlab software. The specific output adjustment equation is:

II therein_i,Γ_iFor the solution to be solved, S is the state matrix of the stable system, E is the output matrix of the stable system, A_iSystem for subsystem iMatrix, B_iIs the control matrix of subsystem i, C_iAnd N is the total number of the subsystems.

Step four: after obtaining the stable observer state and the solution of the output governing equation, a control law is constructed:

u_i＝K_i(x_i-∏_iρi_i)+Γ_iρ_i i＝1,2，...,N (7)

in which the feedback matrix K of the control law_iSatisfies matrix A_i+B_iK_iIs Hurwitz. Under the control law, the output of each subsystem can reach the following two-way output consistency:

wherein y is^*Is a continuous output trace.

Examples

To verify the effectiveness of the present invention, this section performs simulation experiments on topologies based on fig. 2 and 3, respectively. For the structures of fig. 2 and 3, the parameters of each subsystem are:

C₁＝[1 1]，C₂＝[1 0],C₃＝[2 1],C₄＝[1 0.5].

the parameters of the reference system are:

the solution to the corresponding output adjustment equation is:

Γ₁＝[-1.4 -0.2],Γ₂＝[-1.5 -0.5],Γ₃＝[-0.53 -0.27],Γ₄＝[-0.94 -0.24].

the convergence condition and the output consistency condition of the adaptive coefficients of the adaptive observer for the first topology structure diagram are shown in fig. 4 and fig. 5, respectively. The convergence condition and the output consistency condition of the adaptive coefficients of the adaptive observer for the second topology structure diagram are shown in fig. 6 and fig. 7, respectively. The simulation result shows that the adaptive observer can be converged in a short time, the system can achieve bidirectional output consistency under the action of the control protocol, and the correctness of the method is verified.

Claims (1)

1. An output consistency control method for a bidirectional heterogeneous multi-agent system is characterized by comprising the following specific steps:

step 1, constructing a mathematical model of a bidirectional heterogeneous multi-agent system, an integral topological structure of the system and a Laplacian matrix;

step 2, constructing a self-adaptive state observer of each subsystem to obtain a stable observation state of the observer;

step 3, constructing output adjustment equations of all subsystems, and solving the solutions of the output adjustment equations;

step 4, constructing a control law of each subsystem to enable the whole multi-agent system to achieve bidirectional output consistency;

in step 1, analyzing the relevant physical quantities of each subsystem which need to be concerned, and obtaining the following state space expression by using the relevant knowledge of the state space:

wherein A is_iSystem matrix being a subsystem, B_iFor control of subsystemsMatrix, C_iIs the output matrix of the subsystem, x_iIs the state of the subsystem, u_iIs a control input of the subsystem, y_iN is the total number of the subsystems;

step 1, analyzing information exchange relations among subsystems to obtain an overall topological structure of the whole system, wherein when two child nodes are in a cooperative relation, the connection weight between the two child nodes is positive, otherwise, the connection weight is negative if the two child nodes are in a competitive relation; constructing a Laplacian matrix L of the whole system according to the topological structure chart, wherein the construction method comprises the following steps:

l_ij＝-a_ij,i≠j；i,j＝1,2,…,N

wherein l_ijFor each entry of the L matrix, a_ijThe connection weight among the subsystems is defined, and N is the total number of the subsystems;

in step 2, aiming at the undirected graph system, each subsystem constructs the following self-adaptive observer:

where S is the state matrix, ρ, of the stable system_iIs the observed state of the i-th state observer, a_ijIs the connection weight of subsystem i and subsystem j, θ_iFor adaptive coefficients, coefficient g_iDepending on whether information of the reference system is available, v is the state of the stable system, coefficient d may be equal to 1, not equal to 0_iIs determined by the group of the subsystem in the whole system, which belongs to the positive group 1, the negative group-1, Q, F,H is the feedback matrix of the observer, and satisfies that (S, Q) is controllable, and F is equal to Q^TP,H＝PQQ^TP, matrix P satisfies the following Riccati equation:

S^TP+PS+I-PQQ^TP＝0 (4)

for a directed graph system, a monotonically increasing function is introduced in the observer to increase the degree of freedom of design:

wherein y is_i＝(d_iv-ρ_i)^TP(d_iv-ρ_i) The feedback matrix of the observer is defined as the observer (4) as a monotone increasing function; when the observers (4) and (5) tend to be stable, the observation state satisfies:

in step 3, the specific output adjustment equation is as follows:

II therein_i,Γ_iFor the solution to be solved, S is the state matrix of the stable system, E is the output matrix of the stable system, A_iSystem matrix being subsystem i, B_iIs the control matrix of subsystem i, C_iAn output matrix of the subsystem i is obtained, and N is the total number of the subsystems;

in step 4, the constructed control law is as follows:

u_i＝K_i(x_i-∏_iρ_i)+Γ_iρ_i i＝1,2，...,N (7)

wherein u is_iFor control input of subsystem i, K_iSatisfies matrix A as the feedback matrix of the control law_i+B_iK_iIs Hurwitz, A_iSystem matrix being subsystem i, B_iThe control matrix of the subsystem i can achieve the bidirectional output consistency of each subsystem under the control law.

Images