阅读说明：本技术 二阶智能体系统连通性保持固定时间协同一致性控制方法 (Second-order intelligent system connectivity fixed time collaborative consistency control method ) 是由 黄攀峰 刘亚 张帆 张夷斋 孟中杰 于 2020-05-21 设计创作，主要内容包括：本发明涉及一种二阶多智能体系统连通性保持固定时间协同一致性控制方法,设计虚拟速度<Image he="63" wi="51" file="DDA0002502909040000011.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>和虚拟控制；设计固定时间微分器；设计多智能体系统连通性保持固定时间协同一致性控制器；将设计的控制器作用在系统上,实现多智能体系统连通性保持固定时间协同一致性控制。本发明基于势函数法和固定时间收敛理论,利用反步法设计思想和固定时间微分器,首次针对二阶多智能体系统连通性保持下的固定时间协同控制问题,提出了保证系统通讯连通性和固定时间内收敛的协同控制方法,确保多智能体系统收敛连通性必要条件的满足,同时收敛时间与系统初始状态无关。(The invention relates to a method for controlling connectivity of a second-order multi-agent system to maintain fixed time cooperative consistency, and designs a virtual speed)

1. A second-order intelligent system connectivity fixed time collaborative consistency control method is characterized by comprising the following steps:

step 1, designing virtual speedAnd virtual control

Wherein:as a virtual speedThe first derivative of (a) is,is the speed of the agent i and,is a control input to the agent i,representing an n-dimensional column vector;

virtual speed of the agent iComprises the following steps:

wherein β₁And β₂Is a normal number, and is,is the location, x, of agent i_jIs the location of agent j;

with potential function phi (| | x)_i-x_j| |) represents the strength of the communication between two agents;

step 2: designing virtual speed of agent iThe fixed time differentiator realizes the estimation of the differentiated signal within the fixed timeThe fixed time differentiator is:

wherein:andare state variables of differentiators, respectively estimate virtual velocitiesAnd its differential signalL and M are normal numbers, η_iI η - (i-1), where η∈ (1,1+), 0 < 1 is a normal number, and theta is the normal number₁，θ₂，The matrix A and the matrix B are selected to be Hurwitz matrixes;

and step 3: virtual control according to designVirtual speedThe fixed time differentiator is used for designing the connectivity of the multi-agent system to keep a fixed time cooperative consistency controller;

and 4, acting the designed controller on the system to realize the control of keeping fixed time cooperative consistency of the connectivity of the multi-agent system.

Technical Field

The invention belongs to the research of a distributed multi-agent system cooperative control technology, relates to a method for controlling connectivity of a second-order multi-agent system to maintain fixed time cooperative consistency, and particularly relates to a control technology for realizing distributed cooperative consistency in fixed time by the second-order multi-agent system under the condition of connectivity maintenance constraint.

Background

The connectivity of the communication link of the multi-agent system is a necessary condition for ensuring the realization of the system cooperative control technology. In an actual multi-agent system, the communication range between a single agent and a neighbor agent has physical limitation, in order to ensure the connectivity of the communication link of the system, the communication link of the system at the initial moment is generally provided with connectivity, and a controller with reasonable design is designed to ensure that the communication of the system is kept in the operation process.

The convergence rate is an important index for evaluating the performance of the control system, and when an actual engineering task is completed, the timeliness of the completed task is always required to be considered. Therefore, on the basis of the gradual convergence, a limited-time convergence control theory is proposed by scholars. The upper bound of the convergence time of the finite time convergence control estimation is related to the state of the initial time of the system, and the state of the initial time is usually difficult to accurately obtain, or when the initial time is far away from the balance point, the convergence time is not estimated or the estimation time is over conservative, so that the application value is lost. In order to solve the problem of finite time convergence, some researchers have proposed a fixed time convergence control method. So-called fixed time convergence, i.e. the estimated system convergence time is independent of the initial state and depends only on parameters set in advance by the controller. Therefore, the system under the control of fixed time convergence will achieve convergence within certain limited bounds.

Currently, there are three main approaches to the problem of connectivity maintenance constraints for multi-agent systems: potential function methods, error conversion methods, and model prediction methods. There are two main methods for solving the fixed time cooperative control of the multi-agent system: the method is based on the homogeneity principle and on nonsingular terminal sliding mode control. The research results of the existing literature mainly aim at connectivity maintenance under cooperative control of gradual convergence and limited time convergence, and the research on the problem of cooperative control of fixed time connectivity maintenance is little.

Disclosure of Invention

Technical problem to be solved

In order to avoid the defects of the prior art, the invention provides a second-order multi-agent system connectivity maintaining fixed-time cooperative consistency control method, which aims at realizing the communication link connectivity maintaining of a multi-agent system under the condition that the communication range of the second-order multi-agent system is limited and realizing the distributed cooperative consistency control in a fixed time. The method can ensure the connectivity of the communication link of the system and simultaneously realize the rapid distributed cooperative consistency of the multi-agent system in a fixed time.

Technical scheme

A second-order intelligent system connectivity fixed time collaborative consistency control method is characterized by comprising the following steps:

step 1, designing virtual speedAnd virtual control

Wherein:as a virtual speedThe first derivative of (a) is,is the speed of the agent i and,is a control input to the agent i,representing an n-dimensional column vector;

virtual speed of the agent iComprises the following steps:

wherein β₁And β₂Is a normal number, and is,is the location, x, of agent i_jIs the location of agent j;

with potential function phi (| | x)_i-x_j| |) represents the strength of the communication between two agents;

step 2: designing virtual speed of agent iThe fixed time differentiator realizes the estimation of the differentiated signal within the fixed timeThe fixed time differentiator is:

wherein:andare state variables of differentiators, respectively estimate virtual velocitiesAnd its differential signalL and M are normal numbers, η_iI η - (i-1), where η∈ (1,1+), 0 < 1 is a normal number, and theta is the normal number₁，θ₂，The matrix A and the matrix B are selected to be Hurwitz matrixes;

and step 3: virtual control according to designVirtual speedThe fixed time differentiator is used for designing the connectivity of the multi-agent system to keep a fixed time cooperative consistency controller;

and 4, acting the designed controller on the system to realize the control of keeping fixed time cooperative consistency of the connectivity of the multi-agent system.

Advantageous effects

The invention provides a control method for maintaining fixed time cooperative consistency of connectivity of a second-order multi-agent system, which designs virtual speedAnd virtual control; designing a fixed time differentiator; designing a multi-agent system connectivity maintaining fixed time cooperative consistency controller; the designed controller acts on the system, and the control of keeping fixed time cooperative consistency of the connectivity of the multi-agent system is realized.

Compared with the prior art, the invention has the following positive effects:

Detailed Description

The invention will now be further described with reference to the examples:

in order to achieve the purpose, the technical scheme adopted by the invention comprises the following steps:

1) designing virtual speedAnd virtual control;

2) designing a fixed time differentiator;

3) designing a multi-agent system connectivity maintaining fixed time cooperative consistency controller;

4) the designed controller acts on the system, and the control of keeping fixed time cooperative consistency of the connectivity of the multi-agent system is realized.

In the step 1, virtual speed is introduced by using the thought of a back stepping method for referenceAnd introducing a potential function according to the limit condition of the communication range of the intelligent agent.

Assuming that a second-order multi-agent system is composed of N agents, the kinetic equation of the ith (i ═ 1,2, …, N) agent is:

whereint represents the position, first derivative of position, velocity, first derivative of velocity, control input, and time of agent i, respectivelyAnd (3) removing the solvent.Representing an n-dimensional column vector. For convenience of representation, the following variables represent the omission time t.

By using the thought of the backstepping method, virtual speed is introduced into the speed channel of the intelligent agent iDefining a virtual tracking error e_iAnd virtual controlThe variables are as follows:

whereinAs a virtual speedThe first derivative of (a). The kinetics (1) of agent i are further transformed according to equations (2) - (3) into:

introducing potential function phi (| | x)_i-x_j| |) defines the strength of connectivity between agents, which is defined as:

wherein x_jIndicating the location, x, of agent j_i(t₀) And x_j(t₀) Respectively representing initial time t of agents i and j₀Position of, | | x_i-x_jI represents the vector x_i-x_jThe vector of (a) is a two-norm,is a normal number, R represents the radius of the agent's communication range, the symbol ∩ represents the intersection of the sets, ∈ (0,1) is a normal number₀The distance is smaller than the radius R of the communication range, and when the distance at the next moment becomes larger and approaches to R, the potential function approaches infinity, namely infinite attraction is generated between the two intelligent agents, so that the two intelligent agents approach to each other, and the communication link is prevented from being interrupted; when the distance between two agents is larger than R at the initial moment, then when the distance between the two agents is smaller than R, the two agents realize communication, and once the distance between the two agents is larger than R, the communication between the two agents is immediately interrupted.

To ensure convergence within a fixed time of the virtual tracking error, virtual control of agent i is designedThe following were used:

wherein α₁And α₂Is a normal number, v_jIs the speed of the agent j,for the virtual velocity of agent j, μ > 1 is a normal number. Defining an n-dimensional vectorSign operations sign (y) and sig^μ(y) is defined as sign (y) or [ sign (y)₁),…,sign(y_n)]^T，sig^μ(y)＝[sign(y₁)|y₁|^μ,…,sign(y_n)|y_n|^μ]^TWherein sign (#) is a standard symbol operation, whichIs defined as:

designing virtual speed of agent iThe following were used:

β therein₁And β₂Is a normal number.

In the step 2, because unavoidable signals such as noise exist in an actual system, in order to avoid singularity caused by differentiating the virtual speed, the design adopts the principle of a differentiator, designs a fixed-time virtual speed differentiator, differentiates the virtual speed, and effectively avoids the singularity problem.

Designing virtual speed of agent iThe fixed time differentiator realizes the estimation of the differentiated signal within the fixed timeThe fixed time differentiator is designed as follows:

whereinAndare state variables of differentiators, respectively estimate virtual velocitiesAnd its differential signalL and M are normal numbers, η_iI η - (i-1), where η∈ (1,1+), is the smallest possible normal number₁，θ₂，Are chosen such that matrices a and B are Hurwitz matrices. Matrices a and B are defined as follows:

in the step 3, virtual control according to designVirtual speedAnd a fixed time differentiator for designing the connectivity of the multi-agent system to maintain a fixed time cooperative consistency controller.

Designing control input u for agent i_i：

In the step 4, each agent can detect other agents within the radius R, each agent and the adjacent agent satisfying the distance relation (5) can mutually transmit and receive state quantity information and virtual speed information of each other, the agent calculates the virtual speed and potential function according to the self and received state information, then calculates the virtual control according to the agent self and received state information and virtual speed, meanwhile, uses the self virtual speed as the input of the fixed time differentiator to estimate the differential signal of the virtual speed, and finally estimates the control quantity acting on the agent according to the virtual control and the differential estimation of the virtual speed, thereby realizing the purpose that the multi-agent system maintains the connectivity of the fixed time cooperative consistency control.