CN116699989A - Non-linear multi-agent gradient-free optimization method based on edge event triggering - Google Patents
Non-linear multi-agent gradient-free optimization method based on edge event triggering Download PDFInfo
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Abstract
The invention discloses a non-linear multi-agent gradient-free optimal control method based on edge event triggering, which comprises the following steps: the method comprises the steps of carrying out online identification on unknown gradient items in a system by adopting a radial basis function neural network, introducing an edge event triggering communication strategy on the basis of the online identification to reduce communication resource loss, and then combining information of an intelligent agent node, reference model information and information of neighbor intelligent agent nodes thereof to design a distributed controller based on the neural network so as to enable multiple intelligent agents to achieve the optimal effect under the objective function and constraint. The invention realizes the online identification and constraint target optimization control of the nonlinear multi-agent optimization problem with unknown gradient, thereby solving the problem of multi-agent gradient-free optimization.
Description
Technical Field
The invention relates to the technical field of multi-agent control, in particular to a non-gradient optimization method for a nonlinear multi-agent based on edge event triggering.
Background
In recent years, the multi-agent system has wide application potential in the fields of micro-grids, unmanned aerial vehicles, sensors and the like, and the coordination control problem of the multi-agent system is widely studied. The problem of optimizing control of multiple intelligent agents is also receiving more and more attention, and the method is widely applied to the control fields of formation control, cluster control, gathered beehives and the like.
First, a definition of an agent is given, which is a device or machine that is autonomous, reactive, proactive, social, and evolutionary. The multi-agent system is a network composed of a plurality of agents, and the agents communicate through the topological rule of the network, so that the complex tasks are solved by cooperation.
With the deep research, the multi-agent system is also applied to more practical engineering, the problem to be solved is also more complex, and different from the simple consistency problem, the energy-saving factor is considered in practical application, and the multi-agent is often required to achieve a specific target, namely, multi-agent optimization. Aiming at the multi-agent optimization problem, not only the cooperation among the multi-agents but also whether the target requirement reaches the optimal or not are needed to be considered, so that the multi-agent optimization problem is more complex than the consistency problem, and the problem is more and more needed to be solved.
Multi-agent distributed optimization has been receiving much attention from communities, unlike centralized optimization, which solves some engineering problems in a distributed manner, i.e., each agent can only access local information about itself and neighbors, but not global information. Thus, in multi-agent systems, the goal of distributed optimization is typically to minimize the global goal that can only be achieved through cooperation between a single agent and its neighboring agents.
In a long period of time, the cost function of the multi-agent distributed optimization problem is obtained by assuming that the function gradient is available, but in the actual engineering background, there are many situations that the cost function gradient of the optimization target cannot be obtained normally or the gradient calculation is expensive. Therefore, the multi-agent distributed optimization problem with unknown research gradient has practical significance.
In general, communications between multiple agents are divided into continuous communications and discrete communications, where both communications may exist in which the states of the agents are not changed much over a period of time, and communications between agents are still implemented, resulting in wasteful use of communications resources, so that many students introduce event-triggered control, i.e., determining whether or not an agent communicates with all connected neighbors through events, where general event-triggered control determines whether or not an agent communicates with all connected neighbors through events related to the states of the agents, and edge event-triggered control determines whether or not two agents corresponding to an edge communicate by determining events related to the states of the edge, thereby using fewer communications resources.
Disclosure of Invention
The invention aims to provide a non-linear multi-agent gradient-free optimization method based on edge event triggering, so as to solve the problems in the background technology.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a non-linear multi-agent gradient-free optimization method based on edge event triggering comprises the following steps:
s1: the problem dynamics model and the optimization target are clearly researched;
s2: aiming at the gradient unknown item in the optimization target, an adaptive algorithm based on an RBF artificial neural network is adopted to identify the gradient unknown item on line so as to meet the requirements of system instantaneity and rapidity;
s3: introducing an edge event triggering control communication strategy, and determining whether two intelligent agents corresponding to an edge communicate or not by judging an event related to the edge state, so that fewer communication resources are used;
s4: combining S2 and S3, utilizing the information of the intelligent agent node and the information of the neighbor intelligent agent nodes, and designing a distributed controller under the Lyapunov stability theorem to ensure that non-linear multi-intelligent agent gradient-free optimization triggered based on side events is realized;
s5: and filling the unknown gradient identification strategy, the control algorithm and the edge event triggering communication mechanism into each multi-agent through programming.
Compared with the prior art, the technical bright point of the invention is as follows: the self-adaptive algorithm based on the RBF artificial neural network can identify the unknown gradient of the system on line, so that the real-time performance of the system is met; meanwhile, the communication strategy of side event trigger control is considered, so that the communication resources among multiple agents in an actual system can be reduced better. In conclusion, the problem of gradient-free optimization of nonlinear multi-agent can be solved.
Drawings
Fig. 1 is a multi-agent communication topology diagram in the present embodiment.
Fig. 2 is a state response diagram of the multi-agent according to the method proposed herein in this embodiment.
Fig. 3 is an event-triggered timing diagram of the multi-agent in the side-event-triggered communication manner in this embodiment.
Detailed Description
The present invention will be described in further detail with reference to the drawings and embodiments, so that the objects, technical solutions and advantages of the present invention can be more clearly understood.
A non-linear multi-agent gradient-free optimization method based on edge event triggering comprises the following steps:
s1: a problem dynamics model is clearly researched;
the multi-agent dynamics model of the model comprises N agents, and the ith agent dynamics model is as follows:
wherein ,xi (t)∈R n ,u i (t)∈R n ,f i (x i ,t)∈R n Representing the position state, control inputs and nonlinear functions of the agent, respectively.
The optimization problem is considered to satisfy the following form:
in S1, the communication network topology of the agent is shown in fig. 1.
Assuming that the undirected connected graph G has m edges, defining a certain edge e j Connecting agent x i And x l ，Is the correlation matrix of graph G. Definition:
then there is l=dwd T 。Is an edge weight vector.
S2: optimizing item g for (1) i (x i (t)) and adopting an adaptive algorithm based on RBF artificial neural network to identify the gradient unknown condition on line so as toThe requirements of system instantaneity and rapidity are met;
order theIdeal case-> Ideal weight matrix for representing optimal RBF artificial neural network, G i (. Cndot.) represents RBF artificial neural network activation function, ε i And (t) represents an approximation error of the RBF artificial neural network.
The optimal weight matrix can be obtained according to the following formula:
wherein ,Gi (. Cndot.) is a Gaussian function.
Formula (3) is generally used for qualitative analysis, and is practically used
Approximation of an unknown function.
The update rate of the weight matrix is further given by combining an adaptive algorithm:
wherein ,ei (t)＝x i (t)-x ＊ ，x ＊ Representing a global optimum state, delta i > 0 is the designed control parameter Γ i ＝Γ i T ∈R ρ×ρ 。
S3: the communication strategy among the intelligent agents is designed based on the side event triggering mechanism, so that the purposes of saving energy consumption and improving operation time are achieved;
first defining the communication state of the first edge:
e l (t)＝x i (t)-x j (t) (6)
the edge event triggering conditions of the intelligent agent are designed as follows:
wherein ,at t k Agent x before the moment i And x j The latest edge event trigger time of the corresponding edge is 0 < { lambda ] p }＜1,{μ p P=1, 2, } > m is a constant sequence satisfying the condition. When the edge state violates the trigger condition (7), agent x i And x j Control is performed.
S4: in combination with the above method, the controller of agent i is designed to:
weight updatingAs shown in the above formula (5), and each control parameter is designed to satisfy the following formula:
η＞0,b＞0
s5: and filling the unknown model identification strategy and the control algorithm into each multi-agent through programming.
In the present embodiment, preferably, x i (t)∈R,u i (t)∈R，f i (x i (t))∈R,g i (x i (t))∈R。
The optimal problem is considered as follows:
it is easy to know that the globally optimal solution is x ＊ ＝30。
The laplace corresponding to the multi-agent communication topology in this embodiment is as follows:
preferably, the control parameters of the system are designed as follows:
η＝2.4,b＝0.35,λ i ＝0.85,μ i =1.2, i=1, …, m, the remaining corresponding parameters can be calculated from the known information. The initial value of each agent is set as x= [ -2,4,12, -8,8]。
According to fig. 2, it can be seen that, within the allowable error, the state of each agent can reach the optimal state, that is, the algorithm can realize the optimal control of the multi-intelligent system with unknown gradient, and according to fig. 3, the respective event trigger time and times of each side can be seen, that is, the distributed event trigger control is realized, the energy consumption of the system is reduced, and the running duration of the system is prolonged.
The above examples are only preferred embodiments of the present invention, and it should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, and these should also be regarded as the scope of the invention, which does not affect the effect of the implementation of the invention and the practical applicability of the patent.
Claims (7)
1. The non-linear multi-agent gradient-free optimization method based on edge event triggering has the following characteristics:
s1: the problem dynamics model and the optimization target are clearly researched;
s2: aiming at the gradient unknown item in the optimization target, an adaptive algorithm based on an RBF artificial neural network is adopted to identify the gradient unknown item on line so as to meet the requirements of system instantaneity and rapidity;
s3: introducing an edge event triggering control communication strategy, and determining whether two intelligent agents corresponding to an edge communicate or not by judging an event related to the edge state, so that fewer communication resources are used;
s4: combining S2 and S3, utilizing the information of the intelligent agent node and the information of the neighbor intelligent agent nodes, and designing a distributed controller under the Lyapunov stability theorem to ensure that non-linear multi-intelligent agent gradient-free optimization triggered based on side events is realized;
s5: and filling the unknown gradient identification strategy, the control algorithm and the edge event triggering communication mechanism into each multi-agent through programming.
2. The non-linear multi-agent gradient-free optimal control method based on edge event triggering as claimed in claim 1, wherein the method is characterized by comprising the following steps: in S1:
the multi-agent dynamics model for defining a model comprises N agents, and the ith agent dynamics model is as follows:
wherein ,xi (t)∈R n ,u i (t)∈R n ,f i (x i ,t)∈R n Representing the position state, control inputs and nonlinear functions of the agent, respectively.
The optimization problem is considered to satisfy the following form:
s.t.x i ＝x j
3. the non-linear multi-agent gradient-free optimal control method based on edge event triggering as claimed in claim 1, wherein the method is characterized by comprising the following steps: the communication network of the intelligent agent is in an undirected communication topology, and a feasible input for realizing the control target exists in the system.
4. The non-linear multi-agent gradient-free optimal control method based on edge event triggering as claimed in claim 1, wherein the method is characterized by comprising the following steps: in S2: for unknown itemsAn RBF artificial neural network-based adaptive algorithm is adopted to identify the RBF artificial neural network on line, which comprises the following steps:
defining a tracking error:
e i (t)＝x i (t)-x ★ ,i＝1,…,N
approximation of unknown functions:
wherein ,δi > 0 is the control parameter of the design.
5. The non-linear multi-agent gradient-free optimal control method based on edge event triggering as claimed in claim 1, wherein the method is characterized by comprising the following steps: in S3: introducing an edge event trigger control communication policy comprising:
first defining the communication state of the first edge:
e l (t)＝x i (t)-x j (t)
the edge event triggering conditions of the intelligent agent are designed as follows:
wherein ,at t k Agent x before the moment i And x j The latest edge event trigger time of the corresponding edge is 0 < { lambda ] p }＜1,{μ p P=1, 2, …, m is a constant sequence satisfying the condition. When the edge state violates the trigger condition, agent x i And x j Control is performed.
6. The non-linear multi-agent gradient-free optimal control method based on edge event triggering as claimed in claim 1, wherein the method is characterized by comprising the following steps: in S4:
the controller of the design agent i is designed as follows:
weight updatingAs shown in claim 4, and the control parameters are designed to satisfy the following equation:
η＞0,b＞0
7. the non-linear multi-agent gradient-free optimal control method based on edge event triggering as claimed in claim 1, wherein the method is characterized by comprising the following steps: in S5:
and filling the unknown model identification strategy and the control algorithm into each multi-agent through programming.
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