CN108508914A - A kind of formation control method of discrete multi-agent system - Google Patents

Abstract

The invention discloses a kind of formation control methods of discrete multi-agent system, the described method comprises the following steps：Utilize the correspondence between the knowledge description intelligent body of graph theory；With networking forecast Control Algorithm, Active Compensation communicates time lag；It is proposed the design method of the distributed formation control agreement of discrete multi-agent system；The consistency of multi-agent system is analyzed using matrix theory and Lyapunov Theory of Stability, and realizes the formation control of multi-agent system on this basis；Numerical simulation, the validity of proof theory result are carried out with MATLAB.The present invention solves the problems, such as the formation control problem of the formation control and the discrete time isomery multi-agent system with identical permanent communication delay of the discrete time isomery multi-agent system of no communication delay, has highly application value.

Description

A Formation Control Method for Discrete Multi-Agent System

technical field

The invention relates to a formation control method of a discrete multi-agent system.

Background technique

Multi-agent systems became the main research object in distributed artificial intelligence research in the late 1980s. The main purpose of studying multi-agent systems is to perform distributed cooperation and coordination control between agents with relatively simple functions, and finally complete complex tasks. Compared with a single agent, multi-agent systems, especially distributed multi-agent systems, have many obvious advantages. For example: distributed perception and executors, and inherent parallelism; greater redundancy, better fault tolerance and robustness than a single agent, and can complete tasks more efficiently; complete the same task The multi-agent system is generally low in cost, and it is more economical than a single agent with excellent performance but expensive cost. Therefore, in recent years, multi-agent systems have developed into an important research direction in the field of control and robotics.

In the multi-agent distributed coordination and cooperation control problem, the consistency problem is the basis of cooperation and coordination control among agents, which has important theoretical value and practical significance. The so-called consistency means that as time goes by, a certain state of all agents in a multi-agent system tends to be consistent. The consensus protocol is a rule for the interaction and transmission of information between agents, which describes the information exchange process between each agent and its adjacent agents. Consensus research focuses on the design analysis of the consensus protocol model, the convergence, equilibrium state and application analysis of the consensus protocol. At present, the matrix theory method and the Lyapunov method are mainly used to analyze the convergence of the consensus protocol, and the graph theory is used to analyze the equilibrium state. The research on consistency issues develops rapidly, and various fields, including biological science, physical science, system and control science, computer science, etc., have carried out analysis and research on consistency issues at different levels.

In recent years, with the in-depth research on consistency issues in multi-agent systems, many research directions have been derived. Among them, formation control, as an important application of multi-agent system consistency problem, has become a hot issue in the current control discipline. Formation control refers to the control problem that a team composed of multiple agents maintains a predetermined collective shape (ie formation) with each other while moving towards a specific goal or direction, and at the same time adapts to environmental constraints (such as obstacle avoidance). . Formation control has a wide range of applications and has good prospects in the fields of industry, military, aviation, and society. In the military field, the coordinated control of unmanned fighter jets has effectively enhanced the combat capability, offensive and defensive capabilities of the troops; in the aerospace field, the system's flexibility has been effectively improved by using satellite groups instead of a single satellite to image the surface of the star. Imaging accuracy and quality. It is this broad application prospect that attracts more and more researchers to study the formation control of multi-agent systems, which also makes the research on formation control of multi-agent systems have great theoretical value and Guiding significance.

This topic is based on the understanding of the research status of the multi-agent system consistency problem and the formation control problem based on the consensus protocol, using the relevant knowledge of graph theory, using the networked predictive control method, to design the consensus protocol and put it into It is used in formation control to solve the problem of multi-agent system formation control.

Contents of the invention

The purpose of the present invention is to provide a formation control method of a discrete multi-agent system to solve the problems raised in the above-mentioned background technology.

To achieve the above object, the present invention provides the following technical solutions:

A formation control method for a discrete multi-agent system, the method comprising the following steps:

Step (1), using the knowledge of graph theory to describe the communication relationship between agents;

Step (2), using the network predictive control method to actively compensate the communication time lag;

Step (3), propose the design method of the distributed formation control protocol of discrete multi-agent system;

Step (4), using matrix theory and Lyapunov stability theory to analyze the consistency of the multi-agent system, and on this basis to realize the formation control of the multi-agent system;

In step (5), use MATLAB to carry out numerical simulation to verify the validity of the theoretical results.

As a further solution of the present invention: in step (2), there is a constant time lag τ existing in the communication network; where τ>0 is a known constant.

As a further solution of the present invention: in step (4), the system is formed by a mixture of first-order and second-order dynamic models, if N agents include m first-order individuals and n-m second-order individuals, then The kinetic model is described as follows:

First-order kinetic model:

x _i (t+1)= _xi (t)+Tu _i (t)i=1,2,...,m,

Second-order kinetic model:

x _i (t+1)= _xi (t)+Tv _i (t)i=m+1,m+2,...,N,

v _i (t+1)=v _i (t)+Tu _i (t)

In the formula: x _i represents the displacement of agent i, u _i represents the control input of agent i, v _i represents the velocity of agent i; t is the discrete time, and T is the sampling cycle.

Compared with the prior art, the beneficial effect of the present invention is: in the case that the displacement state of the multi-agent body is unmeasurable and the output is measurable, a control protocol with state feedback is proposed, and finally, through mathematical derivation, the realization of the multi-agent body is demonstrated. Formation control (the final state displacement and speed tend to be consistent), through numerical simulation to illustrate the validity of the theoretical results; when the state of the agent is unpredictable and has a constant communication time delay, based on a networked predictive control method, a state feedback control method is proposed. Finally, through mathematical derivation, it is demonstrated that the formation control of multi-agents is realized (the final state displacement and speed tend to be consistent), and the validity of the theoretical results is proved by numerical simulation results.

In summary, the formation control method of the discrete multi-agent system solves the formation control problem of the discrete-time heterogeneous multi-agent system without communication delay and the discrete-time heterogeneous multi-agent system with the same constant communication delay The formation control problem of the system has a very high promotion and application value.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some of the embodiments of the present invention, but not all of them. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

This application refers to the relevant research at home and abroad, combines their respective advantages, and on the basis of a large amount of previous work, studies the formation problem of the discrete-time multi-agent system in the two cases of communication time delay and no communication time delay. The networked predictive control method actively compensates the communication time lag, based on the consensus protocol of the multi-agent system, optimizes its deformation, designs the formation control protocol, and gives the multi-agent system to form a certain formation, such as: speed, relative Displacement, etc. reach a consistent criterion.

In an embodiment of the present invention, a formation control method of a discrete multi-agent system, the method includes the following steps:

Step (1), using the knowledge of graph theory to describe the communication relationship between agents;

Step (2), using the network predictive control method to actively compensate the communication time lag;

Step (3), propose the design method of the distributed formation control protocol of discrete multi-agent system;

Step (4), using matrix theory and Lyapunov stability theory to analyze the consistency of the multi-agent system, and on this basis to realize the formation control of the multi-agent system;

In step (5), use MATLAB to carry out numerical simulation to verify the validity of the theoretical results.

Considering a heterogeneous system, this heterogeneous system is composed of a mixture of first-order and second-order dynamic models. If N agents contain m first-order individuals and n-m second-order individuals, the dynamic model is described as follows:

First-order kinetic model:

x _i (t+1)= _xi (t)+Tu _i (t)i=1,2,...,m,

Second-order kinetic model:

x _i (t+1)= _xi (t)+Tv _i (t)i=m+1,m+2,...,N,

v _i (t+1)=v _i (t)+Tu _i (t)

In the formula: x _i represents the displacement of agent i, u _i represents the control input of agent i, v _i represents the velocity of agent i; t is the discrete time, and T is the sampling cycle. Assume that there is a constant time delay τ in the communication network between agents, where τ>0 is a known constant.

1) Formation control problem of discrete-time heterogeneous multi-agent systems without communication delay. In the case where the displacement state of the multi-agent is not measurable and the output is measurable, a control protocol with state feedback is proposed, and finally through mathematical derivation, it is demonstrated that the formation control of the multi-agent (the final state displacement and speed tend to be consistent) is realized through mathematical derivation. Simulations are performed to illustrate the validity of the theoretical results. 2) Formation control problem of discrete-time heterogeneous multi-agent systems with the same constant communication delay. When the state of the agent is unpredictable and has a constant communication time delay, based on the networked predictive control method, a control protocol with state feedback is proposed, and finally through mathematical derivation, the realization of multi-agent formation control (final state displacement, velocity trend) is demonstrated. In agreement), the numerical simulation results are used to prove the effectiveness of the theoretical results.

The above are only preferred embodiments of the present invention, and it should be pointed out that for those skilled in the art, some modifications and improvements can be made without departing from the concept of the present invention, and these should also be regarded as protection of the present invention. None of these will affect the effect of implementing the present invention and the practicability of the patent.

Claims (3)

1. a kind of formation control method of discrete multi-agent system, which is characterized in that the described method comprises the following steps：

Step (1) utilizes the correspondence between the knowledge description intelligent body of graph theory；

Step (2), with networking forecast Control Algorithm, Active Compensation communicates time lag；

Step (3) proposes the design method of the distributed formation control agreement of discrete multi-agent system；

Step (4) analyzes the consistency of multi-agent system using matrix theory and Lyapunov Theory of Stability, and basic herein The upper formation control for realizing multi-agent system；

Step (5) carries out numerical simulation, the validity of proof theory result with MATLAB.

2. the formation control method of discrete multi-agent system according to claim 1, which is characterized in that in step (2) In, permanent time lag τ present in communication network；Wherein, τ>0 is known constant.

3. the formation control method of discrete multi-agent system according to claim 1, which is characterized in that in step (4) In, this system is mixed by single order, second-order dynamic model, if N number of intelligent body includes m single order individual, n-m second order Individual, then kinetic model be described as follows：

Single order kinetic model：

x_i(t+1)=x_i(t)+Tu_i(t) i=1,2 ..., m,

Second-order dynamic model：

x_i(t+1)=x_i(t)+Tv_i(t) i=m+1, m+2 ..., N,

v_i(t+1)=v_i(t)+Tu_i(t)

In formula：x_iIndicate the displacement of intelligent body i, u_iIndicate the control input of intelligent body i, v_iIndicate the speed of intelligent body i；T be from The moment is dissipated, T is sampling week.