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:
where c represents the forward gain of the multi-agent control system, K is the feedback gain matrix of the multi-agent control system,
represents the Kronecker product, I
dIs d-dimensional unit matrix, x
iRepresents the state quantity of the ith agent,
h representing agent i
iA secondary trigger time;
5) defining the measurement error of the multi-agent control system, wherein the error adopts a PID-based error model;
6) defining an event triggering 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.
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 multi-agent consistency method based on distributed adaptive event triggering of the invention is shown in fig. 1, and comprises the following steps:
1) determining a set of multi-agent systems, where selection is made
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
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 ∈ R
nRepresenting graph vertices (i.e., multi-agent set), E ∈ R
mAnd the relation between vertexes is represented, namely m communicable branches between the intelligent agents are provided.
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:
x
irepresenting the state quantity of the i-th agent, where u
iI.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:
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:
wherein
H representing agent i
iThe 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:
here, the
Represents the Kronecker product, I
dIs 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:
the adaptive update rule is:
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 influences of real-time access of a controller protocol on global information and uncertainty factors when the state of each intelligent agent is updated are overcome.
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:
based on this, a PID-based error model is proposed:
where k isp,ki,kdRepresenting a given pid parameter, a knotAnd is freely given in practice.
6) Defining event-triggered auxiliary functions for multi-agent control systems
Introducing auxiliary functions
Can be selected according to the following:
Case2:p∈(0,1),
and is
Representing auxiliary function bounded
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 unlimited number of times within a limited 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:
designing a corresponding event trigger function:
an auxiliary function, representing an event trigger, controls the error threshold. When f is
iWhen (t) is 0, S
iReset 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:
further, it is possible to obtain:
let β ═ λ
min(P
-1Q)
To obtain
I.e. lim
t→∞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:
wherein N is
iIs the number of neighbors of agent i,
further deducing when pi
iWhen t is 0, it is easily obtained
If | | | S
i(t) | | 0 means that
Constantly have f
i(t) < 0. Namely, it is
In the time period, the event cannot be triggered again, and the Zeno phenomenon can be eliminated; II type
iWhen (t) ≠ 0, it can be integrated to obtain:
it is further possible to demonstrate the existence of a constant positive time constant
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:
the event trigger function is rewritten as: arbitrarily take a positive number xi
i∈R
According to the Zeno detection method and the consistency analysis, the modified protocol of the distributed adaptive event-triggered controller can be provedThe system consistency requirement can be met and no Zeno action is taken. 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, and determining the trigger time of each intelligent agent by the starting function when the protocol of the distributed self-adaptive event trigger controller and the corresponding event trigger function are programmed
When S is present
iReset to zero, agent i all events trigger and update controller protocol u
i。
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.