CN110278571B - A Distributed Signal Tracking Method Based on Simple Prediction-Correction Link - Google Patents

Abstract

The invention discloses a distributed signal tracking method based on a simple prediction-correction link, comprising: constructing a network structure topology map of multi-agent; The change of the node state at time k and time k-1 is used as the prediction direction, and the predicted value of the node state at time k+1 of each node is obtained by substituting the prediction formula; Correction is performed to obtain the optimal estimated value of the node state of each node at time k+1; time update is performed to continue to calculate the optimal estimated value of the node state at the next moment, that is, time k+2. Compared with the prior art, the present invention can improve the robustness and self-adaptability of the system, reduce the computational complexity, improve the computational efficiency, and improve the real-time performance.

Description

A Distributed Signal Tracking Method Based on Simple Prediction-Correction Link

technical field

The invention relates to a distributed signal tracking method based on a simple prediction-correction link, belonging to the field of control and information technology.

Background technique

A multi-agent system is a collection of multiple coupled agent systems. Each agent system has a certain degree of autonomy and can communicate with other agents by sensing the surrounding environment. With the development in recent years, distributed cooperative control of multi-agent systems has become a hot research topic in the field of control. Compared with centralized control, distributed control has the advantages of low cost, high reliability, high flexibility and high scalability, and has a wide range of engineering background and application prospects. Distributed tracking methods are widely used to solve continuous time-varying global objective functions between different agents. With the continuous development of sensor technology, the sensor has been able to collect the changes of continuous time-varying signals well, and its essence is still discrete sampling. Therefore, we can discretize a continuous time-varying problem into a series of time-invariant problems. The current method to solve the time-invariant optimization problem is mainly based on the gradient descent method or the Newton method. Considering that some reference signals are constantly changing in the actual situation, the static gradient method or Newton method is used alone to calculate the optimal value at each moment. value is unrealistic. In recent years, the method of combining the dynamic optimization idea and adding the prediction link to the optimization algorithm can track the changing reference signal very well, solve the problem of increasing computing time cost, and at the same time, the addition of the prediction link improves the convergence of the optimization algorithm. Effect.

Compared with the centralized prediction-correction algorithm, each agent in the distributed prediction-correction algorithm only needs to use the information of its own neighbor agents, and does not need to know the information of all other agents in the entire network, which reduces the communication between agents. load, and can also improve the robustness and privacy of the system. However, for the existing distributed prediction-correction algorithms, the prediction link needs to invert the Hessian matrix of the cost function, which leads to high computational complexity in the prediction link, which reduces the computational efficiency of the algorithm and affects the real-time performance; and For multi-agent systems, if the Hessian matrix of the cost function does not perform additional processing on the matrix before inversion, the new matrix obtained by matrix inversion is often not an adjacency matrix, and it is impossible to directly design a distributed algorithm. Therefore, how to deal with the inverse operation of the matrix and simplify the prediction link in the distributed design of the algorithm is also a problem worthy of attention.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a distributed signal tracking method based on a simple prediction-correction link, which can at least solve one of the above technical problems.

In order to solve the above-mentioned technical problems, the present invention adopts the following technical scheme:

A distributed signal tracking method based on a simple prediction-correction link, comprising: step S1, constructing a multi-agent network structure topology map, the network structure topology map including n nodes, each node representing an agent respectively, And obtain the point set, edge set and neighbor information of each node of the network structure topology graph, where n is an integer and n≥2; Step S2, construct the cost function of the multi-agent system; Step S3, define the initial node state and set the sampling time interval h; step S4, use the change of the node state at time k of each node and the node state at time k-1 as the prediction direction, predict the change trend of the reference signal at time k+1 of each node, and substitute it into the prediction formula The predicted value of the node state at time k+1 of each node is obtained; in step S5, the predicted value of the node state at time k+1 is used as the initial value of the correction link, and the gradient descent method is used to calculate the predicted value of the node state at time k+1 of each node. The predicted value is corrected to obtain the optimal estimated value of the node state at time k+1 of each node; step S6, time update is performed, and steps S4 and S5 are repeated according to the information at time k+1 and time k, The optimal estimated value at moment k+2 of each node is obtained by calculation.

In the aforementioned distributed signal tracking method based on a simple prediction-correction link, in the step S1, the network structure topology diagram is expressed as G=(V, E), where V={1,...,n } denotes the set of nodes, E={(i,j)|j∈N ⁱ ,j=1...n} denotes the set of edges, N ⁱ denotes the set of neighbor nodes of node i, j∈N ⁱ , i ∈ N ^j , the network structure topology graph is an undirected connected graph, node j is a parent node, and node i is a child node.

其中，x_i表示第i个智能体的状态，xⁱ∈R^p；x∈R^np是每个智能体决策变量的堆叠；fⁱ(xⁱ；t)表示只与智能体自身有关的函数；g^i,j(xⁱ,x^j；t)表示网络结构拓扑图中相互通信的两个智能体所构成的函数；t表示时间；E表示边的集合；p是一个整数，表示向量的维度。In the aforementioned distributed signal tracking method based on a simple prediction-correction link, in step S2, the multi-agent cost function has the following form:

Among them, x _i represents the state of the ith agent, x ⁱ ∈ R ^p ; x ∈ R ^np is the stack of decision variables of each agent; f ⁱ ( ^xi ; t) represents the function only related to the agent itself ; g ^i,j (x ⁱ ,x ^j ; t) represents the function composed of two agents communicating with each other in the topology graph of the network structure; t represents time; E represents the set of edges; p is an integer, representing the vector dimension.

In the aforementioned distributed signal tracking method based on the simple prediction-correction link, the step S3 specifically includes: setting the initial state x(t ₀ ) of the agent,

In the aforementioned distributed signal tracking method based on a simple prediction-correction link, in the step S4, the prediction formula is: x _k+1|k =x _k +hp _k , where x _k+1|k is The predicted value of the node state at time k+1, x _k+1|k ∈R ^np , p _k represents the variable that predicts the direction of change of the reference signal,

校正环节的初始值为预测环节的输出值x_k+1|k，即

In the aforementioned distributed signal tracking method based on a simple prediction-correction link, in the step S5, the initial value of the correction link is set

The initial value of the correction part is the output value x _k+1|k of the prediction part, that is,

其中，γ为步长；第i个智能体关于xⁱ的梯度的表达式为

In the aforementioned distributed signal tracking method based on a simple prediction-correction link, in the step S5, the correction link of the ith agent is expressed as:

Among them, γ is the step size; the expression of the gradient of the ⁱ -th agent with respect to xi is

In the aforementioned distributed signal tracking method based on the simple prediction-correction link, in the step S5, the output value after n-step correction is obtained, and the output value of the algorithm is the optimal estimated value, that is,

Compared with the prior art, the present invention designs a distributed signal tracking method based on a simple prediction-correction link. This method only uses the teamwork of local neighbors, and each node only uses the information of the neighbor nodes, which improves the performance of the system. The robustness and adaptability of the whole system; at the same time, it also realizes the simplification of the prediction link, avoids the inverse calculation of the matrix and other complicated operation processes, greatly reduces the computational complexity of the prediction link, and the calculation amount is small , the real-time performance is good, and the convergence effect of the algorithm is guaranteed.

Description of drawings

FIG. 1 is a flowchart of a method provided by an embodiment of the present invention.

The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

Detailed ways

An embodiment of the present invention provides a distributed signal tracking method based on a simple prediction-correction link, as shown in FIG. 1 , including:

Step S1, construct a network structure topology map of multi-agents, the network structure topology map includes n nodes, each node represents an agent, and obtain the point set, edge set and neighbor information of each node of the network structure topology map , where n is an integer and n≥2;

This embodiment is directed to a multi-agent system with n agents.

In step S1, the network structure topology diagram includes n nodes, represented as G=(V, E), where V={1,...,n} represents a set of nodes, E={(i,j)| j∈N ⁱ , j=1...n} represents the set of edges, Ni represents the set of neighbor nodes of node ^{i, j∈N i ,} i∈N ^j , the network structure topology graph is an undirected connected graph, the node j is the parent node and node i is the child node.

Step S2, constructing the cost function of the multi-agent system;

As an optional implementation of this embodiment, the cost function of the multi-agent system in step S2 has the following form:

where x _i represents the state of the ith agent, x ⁱ ∈R ^p ; x∈R ^np is the stack of decision variables for each agent, for example, x=(x ^{1 T} ;...;x ^{n T} ) ^T ; f ⁱ ( ^xi ; t) represents the function only related to the agent itself; g ^i,j ( ^xi , x ^j ; t) represents the function composed of two agents communicating with each other in the topology diagram of the network structure ;∑· indicates the summation operation; T indicates the transpose operation of a matrix or vector; t indicates time; E indicates the set of edges; p is an integer, indicating the dimension of the vector.

Step S3, define the initial state of the node and set the sampling time interval h;

Step S3 specifically includes: setting the initial state x(t ₀ ) of the agent, and the initial state can be arbitrarily chosen,

In this embodiment, the sampling time interval generally needs to be less than 1, and the sampling time interval is usually adjusted according to the actual situation.

Step S4, using the change of the node state at the time of each node k and the node state at the time of k-1 as the prediction direction, predict the change trend of the reference signal at the time of each node k+1, and substitute it into the prediction formula to obtain the time of each node k+1. The predicted value of the node state;

As an optional implementation of this embodiment, in step S4, the prediction formula is: x _k+1|k =x _k +hp _k , where x _k+1|k is the prediction of the node state at time k+1 value, x _k+1|k ∈ R ^np , p _k represents the variable of the direction of change of the prediction reference signal,

Step S5, take the predicted value of the node state at time k+1 as the initial value of the correction link, and use the gradient descent method to correct the predicted value of the node state at time k+1 of each node, and obtain the node at time k+1 of each node. the best estimate of the state;

校正环节的初始值为预测环节的输出值x_k+1|k，即

In step S5, the initial value of the correction link is set

The initial value of the correction part is the output value x _k+1|k of the prediction part, that is

The correction link of the i-th agent is expressed as:

Among them, γ is the step size. The step size is adjusted according to the actual application model. Usually, it should not be adjusted too large to prevent the iteration from not converging. , 0.00003, 0.0001, 0.0003, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3... and then fine-tune after determining the range.

The expression for the gradient of the ^ith agent with respect to xi is:

The output value after n-step correction is obtained, and the output value of the algorithm is the optimal estimated value, namely

Step S6, time update is performed, and steps S4 and S5 are sequentially repeated according to the information at time k+1 and time k, and the optimal estimated value of each node at the next time, that is, time k+2, is obtained by calculation.

The method described in this embodiment only uses the team cooperation of local neighbors, and each node only uses the information of neighbor nodes, which improves the robustness and adaptability of the entire system; at the same time, it also simplifies the prediction process and avoids the need for The inverse calculation of the matrix and other complex operation processes greatly reduce the computational complexity of the prediction link, the calculation amount is small, the real-time performance is good, and the convergence effect of the algorithm is guaranteed.

The above are only preferred embodiments of the present invention, and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the inventive spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims (7)

1. A distributed signal tracking method based on a simple prediction-correction link is characterized by comprising the following steps:

s1, constructing a network structure topological graph of the multi-agent, wherein the network structure topological graph comprises n nodes, each node represents an agent, and a point set, an edge set and neighbor information of each node of the network structure topological graph are obtained, wherein n is an integer and is more than or equal to 2;

step S2, constructing a cost function of the multi-agent system; the cost function of the multi-agent system has the form:

wherein x isⁱIndicating the state of the i-th agent, xⁱ∈R^p；x∈R^npIs a stack of each agent decision variable; f. ofⁱ(xⁱ(ii) a t) represents a function related only to the agent itself; g^i,j(xⁱ,x^j(ii) a t) represents a function formed by two agents which are communicated with each other in the topological graph of the network structure; t represents time; v represents a set of nodes; e represents a set of edges; p is an integer representing the dimension of the vector;

step S3, defining the initial state of the node and setting a sampling time interval h;

step S4, predicting the variation trend of the reference signal of each node at the k +1 moment by using the variation of the node state of each node at the k moment and the variation of the node state at the k-1 moment as the prediction direction, and substituting the variation trend into a prediction formula to obtain the prediction value of the node state of each node at the k +1 moment;

step S5, taking the predicted value of the node state at the moment k +1 as the initial value of a correction link, and correcting the predicted value of the node state at the moment k +1 of each node by using a gradient descent method to obtain the optimal estimated value of the node state at the moment k +1 of each node;

and step S6, updating time, repeating the step S4 and the step S5 according to the information of the time k +1 and the time k, and calculating to obtain the optimal estimated value of each node at the time k + 2.

2. The simple predictor-corrector link-based distributed signal tracking method as claimed in claim 1, wherein in the step S1, the network topology is represented by G ═ (V, E), where V ═ 1.. multidot.n } represents a set of nodes, and E { (i, j) | j ∈ NⁱN represents a set of edges, NⁱSet of neighbor nodes representing node i, j ∈ Nⁱ，i∈N^jThe network structure topological graph is an undirected connected graph, the node j is a father node, and the node i is a child node.

3. The simple predictor-corrector based distributed signal tracking method according to claim 1 or 2, wherein the step S3 specifically comprises:setting an initial state x (t) of an agent₀)，

4. The simple predictor-corrector based distributed signal tracking method of claim 1 or 2, wherein in the step S4, the prediction formula is: x is the number of_k+1|k＝x_k+hp_kWherein x is_k+1|kIs a predicted value, x, of the node state at time k +1_k+1|k∈R^np，p_kA variable indicating a direction of change of the prediction reference signal,

5. the simple predictor-corrector-based distributed signal tracking method as claimed in claim 1 or 2, wherein in step S5, an initial value of the corrector is set

The initial value of the correction link is the output value x of the prediction link_k+1|kI.e. by

6. The distributed signal tracking method based on simple prediction-correction link according to claim 5, wherein in step S5, the correction link of the ith agent is expressed as:

wherein gamma is the step length; ith agent about xⁱThe expression of the gradient of (c) is:

7. the distributed signal tracking method based on simplified prediction-correction procedure as claimed in claim 6, wherein in step S5, the output value corrected by η step is obtained, and the output value is the optimal estimation value

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