CN112180734A - Multi-agent consistency method based on distributed adaptive event triggering - Google Patents

Multi-agent consistency method based on distributed adaptive event triggering Download PDF

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CN112180734A
CN112180734A CN202011102462.6A CN202011102462A CN112180734A CN 112180734 A CN112180734 A CN 112180734A CN 202011102462 A CN202011102462 A CN 202011102462A CN 112180734 A CN112180734 A CN 112180734A
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CN112180734B (en
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刘丹复
黄娜
张健
郑小青
张尧
陈张平
赵晓东
孔亚广
张帆
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Hangzhou Dianzi University
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    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract

The invention discloses a multi-agent consistency method based on distributed self-adaptive event triggering. The invention improves the prior method, comprising the following steps: 1) simplifying the updating step of the controller protocol of the multi-agent control system; 2) each agent is updated only at the trigger moment, so that the updating frequency of event trigger control is effectively reduced. 3) Considering the influence of uncertainty factors existing in a multi-agent control system, an event trigger-based adaptive control strategy is proposed to overcome the influence. The invention does not need to carry out complex exponential operation, acquire global coordinate information and carry out complex data fusion operation, and the triggering of events is relatively independent and only depends on the triggering time of the event and the relative state of adjacent nodes. Meanwhile, the introduction of the self-adaptive parameter estimation method realizes the self-estimation and self-optimization of the parameters of the multi-agent control system, and overcomes the defect that the parameter estimation depends on the uncertainty of the global information during the design of the multi-agent control system.

Description

Multi-agent consistency method based on distributed adaptive event triggering
Technical Field
The invention belongs to the field of computer science and control, and relates to a multi-agent consistency method based on distributed self-adaptive event triggering.
Background
The multi-agent system has wide application prospect, and related research results of the multi-agent system are widely applied to robot formation, vehicle traffic management, unmanned aerial vehicle driving, underwater vehicles and the like. The early multi-agent event trigger control is mostly distributed event trigger consistency algorithm; for linear multi-agent systems with/without input delay, implementation of the controller protocol in the algorithm requires interpretation of communication information received from other agents (i.e. the state of the neighbors) and exponential calculations involving the matrix, and requires access to and computation of state information sent by its neighboring agents through complex data fusion steps. Furthermore, all agents need to access some global information (which is unknown to the agent), such as eigenvalues of the network graph laplacian matrix, to implement the controller. In summary, the implementation of the control algorithm requires complex and obscure steps, which are not very user friendly for the algorithm. Based on this, how to design an efficient, reasonable and simple eventing controller protocol and eventing function has led more and more scholars to learn and study.
Disclosure of Invention
In view of the above problems in the prior art, the present invention provides a multi-agent consistency method based on distributed adaptive event triggering,
the invention ensures that all agents can reach consistency without Zeno triggering by a simple triggering mechanism. Compared with the traditional event trigger algorithm, the trigger behavior is improved mainly from three aspects: 1) simplifying the updating step of the controller protocol of the multi-agent control system and improving the control efficiency; 2) each agent is updated only at the trigger moment, so that the updating frequency of event trigger control is effectively reduced, and the calculation cost of each agent is reduced. 3) Considering the influence of uncertainty factors existing in a multi-agent control system, an event trigger-based adaptive control strategy is proposed to overcome the influence.
The technical scheme adopted by the invention is as follows: a linear multi-agent system consistency method based on distributed adaptive event trigger control comprises the following steps:
1) determining a multi-agent system set, establishing a communication network topological graph G of the multi-agent system, and describing the relation among agents by using a Laplace matrix L;
2) selecting a stable state space control model for each agent, and selecting a stable state control matrix (A, B) according to control requirements;
3) resolving an algebraic Riccati equation so as to design a multi-agent control system controller protocol;
4) designing a multi-agent control system controller protocol and introducing an adaptive estimation algorithm to solve the uncertainty problem of parameter dependence, wherein the multi-agent control system controller protocol is expressed as follows:
Figure BDA0002725856080000021
where c represents the forward gain of the multi-agent control system, K is the feedback gain matrix of the multi-agent control system,
Figure BDA0002725856080000022
represents the Kronecker product, IdIs d-dimensional unit matrix, xiRepresents the state quantity of the ith agent,
Figure BDA0002725856080000023
h representing agent iiA secondary trigger time;
5) defining the measurement error of the multi-agent control system, wherein the error adopts an error model based on PID;
6) defining an event-triggered auxiliary function of the multi-agent control system;
7) designing an event trigger function of the multi-agent control system based on the error defined in the step 5), and determining that no Zeno phenomenon exists in event trigger on the basis of ensuring the consistency and stability of the multi-agent control system;
8) the designed controller protocol and event trigger function of the multi-agent control system are programmed into each agent, and distributed information interaction among the agents is realized through the established communication topological graph, so that the consistency of all the agents is stable.
The invention has the beneficial effects that: the invention provides a new controller protocol and an event triggering mechanism based on the traditional distributed event triggering algorithm, and simultaneously provides a control protocol and an event triggering method based on the self-adaptive algorithm, so that the realization mechanism of the event triggering mechanism tends to be simplified under the condition of ensuring the consistency stability of the multi-agent control system and no Zeno action in event triggering; compared with the existing event triggering algorithm, the method has the advantages that the method is realized without complex exponential operation, global coordinate information acquisition and complex data fusion operation, the triggering of the event is relatively independent and only depends on the triggering time of the event and the relative state of the adjacent node. Meanwhile, the introduction of the self-adaptive parameter estimation method realizes the self-estimation and self-optimization of the parameters of the multi-agent control system, and overcomes the defect that the parameter estimation depends on the uncertainty of the global information during the design of the multi-agent control system.
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FIG. 1 is a flow chart of the present invention.
Detailed Description
The existing distributed event trigger consistency algorithm is implemented as follows: each agent needs to integrate the received communication information (i.e., the state of the neighbors) with the exponential calculations involving the matrix, as well as data fusion steps to access and calculate the state information sent by its neighboring agents. Furthermore, all agents need to access some global information, i.e. traverse the entire communication topology.
In order to solve the problems, the invention provides the following ideas:
1) on the basis of keeping the consistency of the multi-agent control system stable, a simplified controller protocol and an event trigger mechanism are provided to improve the control efficiency.
2) The trigger strategy of the decoupling multi-agent control system enables each agent to be updated only at the trigger moment, effectively reduces the update frequency of event trigger control, and simultaneously reduces the calculation cost of each agent.
3) Considering uncertainty factors existing in a multi-agent control system, such as uncertainty of global information of the system, an event trigger-based adaptive control strategy is proposed to avoid uncertainty problem in parameter selection.
Based on the above research thought, the flow chart of the distributed adaptive event triggering-based multi-agent consistency method of the present invention is shown in fig. 1, and comprises the following steps:
1) determining a set of multi-agent systems, where selection is made
Figure BDA0002725856080000031
n represents the number of agents; a communication topology G between agents is established and given a corresponding communication algorithm, the association between agents is described by a laplacian matrix L.
For multi-agent aggregation
Figure BDA0002725856080000032
Where d denotes that each agent is represented by d state quantities; the communication network between the agents is represented by the graph G (V, E), V ∈ RnRepresenting graph vertices (i.e., multi-agent set), E ∈ RmWhich represents the association between vertices, i.e. m communicable branches between agents.
For communication exchange among the multi-agent systems, the communication exchange is described by an algebraic graph theory method; g (V, E) is an undirected graph, and defines an adjacency matrix W of G (V, E), where W is the value of (i, j) ∈ Ei，j1, otherwise w i，j0; constructing a degree matrix D ═ diag (D) of G (V, E)1，d2，..di，..dn)，diThe number of neighbors for each vertex i; a laplace matrix L ═ D-W for G (V, E) can be obtained, and the correlation matrix H defining G (V, E) represents the relationship between graph vertices and edges, and H is the case when the kth edge starts at vertex ikiWhen the kth edge ends at vertex i, h ═ 1ki1, otherwise h ki0; from the knowledge of algebraic graph theory, we can get:
rank(L)＝n-1，null(L)＝span{1n}，L＝HTH
2) selecting a stable state space control model for each agent, and selecting a stable state control matrix (A, B) according to control requirements; the linear governing equation for each agent is expressed as:
Figure BDA0002725856080000048
xirepresenting the state quantity of the i-th agent, where uiI.e. the controller protocol that needs to be designed.
3) Resolving an ARE equation according to an optimization theory: a. theTP+PA-PBBTP + Q is 0, Q is InSolving for P, K ═ BTP, for the design of the multi-agent control system controller protocol. It should be noted that the ARE equation refers to an algebraic ricati equation, which is a matrix equation used to solve the optimal quadratic form.
4) A controller protocol of a multi-agent control system is designed, and an adaptive estimation algorithm is introduced to solve the problem of uncertainty of parameter dependence.
The coherence protocol for a conventional continuous system can be expressed as:
Figure BDA0002725856080000041
c represents the forward gain of the multi-agent control system, and K is a feedback gain matrix of the multi-agent control system; for the event trigger mechanism, the transmission and sampling of data are represented in a discrete non-periodic form:
Figure BDA0002725856080000042
wherein
Figure BDA0002725856080000043
H representing agent iiThe time of the secondary trigger. The implementation of the controller protocol involves exponential calculation and requires complex steps such as global information fusion.
In view of the above existing limitations, for uiCertain simplification and improvement are carried out to obtain a simplified event controller protocol:
Figure BDA0002725856080000044
here, the
Figure BDA0002725856080000045
Represents the Kronecker product, IdIs a d-dimensional unit matrix; at the moment, the event trigger of each single agent is only related to the trigger moment of the single agent, so that the calculation cost is greatly saved.
Further, on the basis of the above-mentioned controller protocol, the forward gain c is adjustedi(t) performing adaptive estimation means: will uiThe modification is as follows:
Figure BDA0002725856080000046
the adaptive update rule is:
Figure BDA0002725856080000047
ηifor selecting constant gain parameters, i.e. uncertainty parameter c for each agent while the controller is updatingiSelf-adjustment is carried out according to a self-adaptive algorithm, and the problem that the controller protocol carries out global information when the state of each intelligent agent is updated is overcomeReal-time access and uncertainty factor.
5) And defining the measurement error of the multi-agent control system, wherein the error adopts a PID-based error model.
Designing a representation form of the measurement error of the multi-agent control system according to the control requirement:
Figure BDA0002725856080000051
based on this, a PID-based error model is proposed:
Figure BDA0002725856080000052
where k isp，ki，kdRepresenting a given pid parameter, may be given in conjunction with the actual freedom.
6) Defining event-triggered auxiliary functions for multi-agent control systems
Figure BDA0002725856080000053
Introducing auxiliary functions
Figure BDA0002725856080000054
Can be selected according to the following:
Case1：p∈[1，∞)，
Figure BDA0002725856080000055
Case2：p∈(0，1)，
Figure BDA0002725856080000056
and is
Figure BDA0002725856080000057
Representing auxiliary function bounded
Case3：
Figure BDA0002725856080000058
And is
Figure BDA0002725856080000059
7) Designing an event trigger function of the multi-agent control system based on the error defined in the step 5), and determining that no Zeno phenomenon exists in event trigger on the basis of ensuring the consistency and stability of the multi-agent control system.
The Zeno phenomenon refers to that: if an event is triggered an infinite number of times within a finite time, this phenomenon is referred to as the Zeno phenomenon. In the study of event-driven mechanisms, one key task is to exclude Zeno behavior; a reasonable event trigger function needs to be designed. In event-triggered control, the measurement error of the state by the agent determines whether the agent is triggered.
For non-adaptive controller protocols:
Figure BDA00027258560800000510
designing a corresponding event trigger function:
Figure BDA00027258560800000511
Figure BDA00027258560800000512
an auxiliary function, representing an event trigger, controls the error threshold. When f isiWhen (t) is 0, SiReset to zero, agent i event triggers and updates the controller.
Further, checking the consistency of the multi-agent control system refers to: detecting the consistency stability of the multi-agent control system by designing a Lyapunov function of the system; the Lyapunov function of the system is expressed as:
Figure BDA0002725856080000061
further, it is possible to obtain:
Figure BDA0002725856080000062
let β ═ λmin(P-1Q)
Figure BDA0002725856080000063
To obtain
Figure BDA0002725856080000064
I.e. limt→∞V(t)＝0
Meaning that multi-agent control system consistency is asymptotically stable: x is the number of0(∞)＝x1(∞)＝…＝xn(∞)
Further determining that the multi-agent control system has no Zeno phenomenon, specifically: by calculating the rate of change of the error function we obtain:
Figure BDA0002725856080000065
wherein N isiIs the number of neighbors of agent i,
Figure BDA0002725856080000066
further deducing when piiWhen t is 0, it is easily obtained
Figure BDA0002725856080000067
If | | | Si(t) | | 0 means that
Figure BDA0002725856080000068
Constantly have fi(t) < 0. Namely, it is
Figure BDA0002725856080000069
In the time period, the event cannot be triggered again, and the Zeno phenomenon can be eliminated; II typeiWhen (t) ≠ 0, it can be integrated to obtain:
Figure BDA00027258560800000610
it is further possible to demonstrate the existence of a constant positive time constant
Figure BDA00027258560800000611
Figure BDA00027258560800000612
This means that there is a certain time difference between the trigger times of every two events, i.e. the Zeno phenomenon can also be excluded.
For the adaptive controller protocol:
Figure BDA00027258560800000613
the event trigger function is rewritten as: arbitrarily take a positive number xii∈R
Figure BDA00027258560800000614
According to the Zeno detection method and the consistency analysis, the modified distributed adaptive event-triggered controller protocol can meet the requirement of system consistency and has no Zeno behavior. Meanwhile, the proposal of the controller protocol overcomes the defect of uncertainty dependence on global information in the process of estimating the forward gain parameters during system design, and improves the stability of the system.
8) Writing the protocol of the distributed self-adaptive event trigger controller obtained in the step 7) and the corresponding event trigger function into each intelligent agent through programming, realizing distributed information interaction among the intelligent agents through the established communication topological graph, realizing stable consistency of all the intelligent agents, determining the trigger time of each intelligent agent by the starting function, and when the trigger time is determined by the starting function, writing the protocol of the distributed self-adaptive event trigger controller and the corresponding event trigger function into each intelligent agent through programming, wherein the trigger time is determined by the starting function
Figure BDA0002725856080000071
When S is presentiReset to zero, agent i all events trigger and update controller protocol ui。
The parameters may be selected at will, and are not intended to limit the invention in any way, allowing flexibility in designing the system model and selecting the parameters without exceeding the scope of the claims.

Claims (4)

1. A distributed adaptive event triggering-based multi-agent consistency method comprises the following steps:
1) determining a multi-agent system set, establishing a communication network topological graph G of the multi-agent system, and describing the relation among agents by using a Laplace matrix L;
2) selecting a stable state space control model for each agent, and selecting a stable state control matrix (A, B) according to control requirements;
3) resolving an algebraic Riccati equation so as to design a multi-agent control system controller protocol;
4) designing a multi-agent control system controller protocol and introducing an adaptive estimation algorithm to solve the uncertainty problem of parameter dependence, wherein the multi-agent control system controller protocol is expressed as follows:
Figure FDA0002725856070000011
where c represents the forward gain of the multi-agent control system, K is the feedback gain matrix of the multi-agent control system,
Figure FDA0002725856070000012
represents the Kronecker product, IdIs d-dimensional unit matrix, xiRepresents the state quantity of the ith agent,
Figure FDA0002725856070000013
h representing agent iiA secondary trigger time;
5) defining the measurement error of the multi-agent control system, wherein the error adopts an error model based on PID;
6) defining an event-triggered auxiliary function of the multi-agent control system;
7) designing an event trigger function of the multi-agent control system based on the error defined in the step 5), and determining that no Zeno phenomenon exists in event trigger on the basis of ensuring the consistency and stability of the multi-agent control system;
8) the designed controller protocol and event trigger function of the multi-agent control system are programmed into each agent, and distributed information interaction among the agents is realized through the established communication topological graph, so that the consistency of all the agents is stable.
2. The distributed adaptive event triggering-based multi-agent coherence method as recited in claim 1, wherein: the method also comprises the following steps of carrying out self-adaptive updating on the forward gain of the system, wherein the updating process is as follows:
Figure FDA0002725856070000014
wherein etaiTo select a constant gain parameter.
3. The distributed adaptive event triggering-based multi-agent coherence method as recited in claim 1, wherein: the event-triggered auxiliary function is
Figure FDA0002725856070000015
The selection of the auxiliary function is based on the following:
case 1:
Figure FDA0002725856070000016
case 2:
Figure FDA0002725856070000021
and is
Figure FDA0002725856070000022
Representing auxiliary function bounded
Case 3:
Figure FDA0002725856070000023
and is
Figure FDA0002725856070000024
4. The distributed adaptive event triggering-based multi-agent coherence method as recited in claim 1, wherein: and detecting the consistency stability of the multi-agent control system through the Lyapunov function.
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