多智能体系统一致性若干问题的研究
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摘要
近年来,随着应用的需要和技术的发展,多智能体系统的协调控制在世界范围内掀起了研究热潮。作为多智能体系统协调控制的基础,一致性问题主要是研究如何基于多智能体系统中个体相互之间有限的信息交换,来设计合适的算法,使得所有智能体的状态达到某同一值的问题。本文以多智能体系统为研究背景,以图论为工具,重点分析了快速一致性算法和有限时间一致性问题,并研究了基于一致性理论的水下智能体群的运动稳定性问题。
在多智能体系统的一致性控制中,系统收敛速度的分析非常重要。许多工程系统都要求保证一定的收敛速度。因此,如何提高系统的收敛性能显得十分必要。给定一个系统,其收敛速度是由该系统通讯网络拓扑结构的代数连通度决定的。在不改变网络的拓扑结构,并且不需要额外增加个体间通讯的情况下,本文针对如何提高一阶系统和二阶系统的收敛速度分别给出了相应的解决方法。针对一阶多智能体系统,设计了PI控制器,使系统在不增加最大控制能量的条件下能够比使用标准一致性算法更快的达到一致。在这种方法中,通过利用控制系统中更多的有效信息,来确定智能体的下一步状态。应用频域中的分析方法,得到了加快系统收敛速度的充分条件。由于通讯网络中不可避免的存在个体本身和其它个体之间的时滞问题,本文进一步分析了在具有输入时滞和通信时滞的条件下,系统使用所提出的快速一致性算法的稳定性问题。针对二阶多智能体系统,首先在无向网络下设计了PI控制器,基于给定的条件,分析得到了系统能够快速的达到静态一致和动态一致的充分条件。随后,在有向网络下,提出了一类基于智能体当前状态和过去状态的一致性控制算法,分析了系统在该控制算法作用下的稳定性问题,并得到了系统实现快速静态一致性和快速动态一致性的充分条件。进一步,将提出的算法在多智能体系统的快速编队控制中进行了应用。以上理论分析的结果表明系统能否实现快速一致与Laplacian矩阵的特征值,网络的结构和连通性密切相关。仿真结果表明所提出的几类快速一致性控制算法能大大提高系统的收敛性能。
目前已有的大多数一致性算法都是使得多智能体系统状态达到渐近稳定,但是,实际上系统的状态变量是不能在有限的时间内达到平衡状态。所以使得系统在有限时间内达到稳定是非常必要和必需的。本文利用Lyapunov有限时间稳定性理论和矩阵理论,分析了多智能体系统的有限时间一致性问题。针对存在通信约束的多智能体系统有限时间一致性问题,提出了一类连续的非线性一致性算法,分析表明当系统个体间的通信网络拓扑结构为连通图的情况时,该算法使得系统具有通信约束时能够在有限时间内达到一致。进一步给出了系统收敛时间的上界,该时间上界由选取的Lyapunov函数,无向图的Laplacian矩阵以及系统的初始状态决定。随后,研究了基于一般非线性函数的有限时间一致性算法,并且给出了该算法使得系统在有限时间内收敛的非线性函数项必须满足的条件。本文针对不忽略智能体质量的情况,也给出了系统有限时间一致性算法的设计方法。随后研究了多智能体系统的有限时间跟踪控制问题。针对领导者状态是时变的情况,提出了一类非线性有限时间跟踪控制算法,在固定网络拓扑结构下,分析得到了该算法使得系统中跟随者状态在有限时间内与领导者状态达到一致的充分条件；在切换网络拓扑结构下,提出了一类有限时间跟踪控制算法,在领导者的状态是时不变的情况下,给出了该算法使得系统实现有限时间跟踪控制的充分条件。
受一致性理论的启发,基于领导-跟随者模型,针对三类不同的通信情况分别提出了相应的水下智能体群的队形控制和群运动控制模型。在所提出模型的基础上,使用一致性理论,给出了使得所有跟随者能够跟随领航者在水中以规定的队列沿着指定的运动方式前行的系统条件。进一步,在具有通信约束的情况下,对每一个水下智能体设计一个分布式控制器,使得水下智能体间的通信时滞在一定范围内,所有的水下智能体仍然能够全局渐近地收敛至期望速度和期望队形。由于该时滞上界是依赖于网络参数的,所以具有更低的保守性。
最后,对全文的研究工作做了总结,并对需要进一步开展的研究工作进行了展望。
In recent years, distributed coordination of multi-agent systems has attracted great attention due to several technological advances in the fields of communication and computation. As a fundamental problem in distributed coordination of networks of dynamic agents, the consensus problem is to design appropriate protocols such that the group of vehicles can reach consensus on the shared information in the presence of limited and unreliable information exchange and dynamically changing interaction topologies. Based on garph theory, the fast consensus protocols, finite-time consensus problems and the group motion stability problems of autonomous underwater vehicle (AUV) systems are studied in this dissertation, the main work and research results lie in the following.
The analysis of convergence rate is very important in the consensus control of multi-agent systems. In most engineering systems, a fast convergence rate is necessary. Based on the local information, agents automatically converge to a common consensus state and the convergence rate is determined by the algebraic connectivity of the communication network. Without changing the network topology and without requiring extra communication, this dissertation proposes solutions to fast consensus of first-order systems and second-order systems. Aimed at first-order systems, the PI controller is used in fast consensus. With out increasing the maximum control effort, the systems using the PI controller can reach a faster consensus than using the standard consensus protocol. The main idea is to employ a more useful package of information to make sure the agents' next state. Based on the frequency-domain analysis, the sufficient condition to guarantee a faster consensus convergence has been obtained. The disturbance of communication delay is unavoidable and might cause multi-agent systems to diverge or oscillation, the stability analyses of the systems using the proposed protocol with input delays and communication delays are also given. Aimed at second-order systems, a PI controller is used in undirected topologies; the sufficient conditions for the multi-agent systems converging to a fast stationary consensus and a fast dynamical consensus are obtained. Under directed topologies, a fast consensue protocol using both current states and outdated states is proposed. The stability analysis of the systems using the protocol is given, and the sufficient conditions for the system converging to a fast stationary consensus and a fast dynamical consensus are obtained, respectively. What's more, the consensus protocols are applied to the formation control of the multi-vehicle system. The theoretic results show that the fast consensus of the systems is related to the eigenvalues of the Laplacian matrix, the structure of the network and the interconnection topology of the network. Simulations show that the proposed fast protocols can improve the convergence rate significantly.
Most of the existing protocols (including those appeared in the aforementioned works) can not result in state consensus in a finite time, that is, consensus is only achieved asymptotically. Hence, finite-time consensus is more appealing and there are a number of settings where finite-time convergence is a desirable property. Based on the theory of finite-time Lyapunov stability and matrix theory, the finite-time consensus problems are studied in this dissertation. Finite-time consensus protocol for continuous multi-agent systems with communication constraints is proposed. The sufficient conditions which guarantee the multi-agent systems to reach a consensus in finite time are given, provided that the undirected network is connected. Moreover, the settling time for the system to reach a consensus is given, it is important to know that the settling time depends on the Lyapunov function, the Laplacian matrix of the undirected graph and the initial state of the system. In order to identify general criteria for solving finite-time consensus problems of multi-agent systems with communication constraints, we show that under protocols satisfying our conditions, the states of agents reach a consensus in finite time when the interaction topology is connected. The methods to design finite-time consensus protocols for systems consider mass are given. The finite-time tracking problems of multi-agent systems with leader-follower models are studied. To track a time-varying leader, a nonlinear finite-time tracking control protocol is proposed for multi-agent systems under fixed network topologies. The sufficient conditions which guarantee the system to reach a finite-time tracking are obtained. Moreover, for the system under switching network topologies, another tracking control protocol is proposed. We show that the followers can track the time-invariant leader in finite time. Simulation results demonstrate that designed protocols can make the system reach consensus in finite time and meeting corresponding performance.
Motivated by recent advances in consensus theory of multi-agent systems, based on the leader-follower model, we present corresponding motion model about the formation control and group motion control of AUVs for three different communication conditions. Based on the models and the consensus theory, the conditions for the followers to track the leader steadily are presented and proved. For the systems with communication constraints, a distributed consensus controller for each AUV is designed. It is proved that if the communication time delay between two AUVs is smaller than a certain upper bound, then the velocity vectors of all AUV and the group formation converge to the same desired velocity vector and the desired formation globally asymptotically, and the commen upper bound of the time delay is dependent on the parameters of the network, so it can reduce the conservatism.
Finally, a summary has been done for all discussions in the dissertation. The research works in future study are presented.
在多智能体系统的一致性控制中,系统收敛速度的分析非常重要。许多工程系统都要求保证一定的收敛速度。因此,如何提高系统的收敛性能显得十分必要。给定一个系统,其收敛速度是由该系统通讯网络拓扑结构的代数连通度决定的。在不改变网络的拓扑结构,并且不需要额外增加个体间通讯的情况下,本文针对如何提高一阶系统和二阶系统的收敛速度分别给出了相应的解决方法。针对一阶多智能体系统,设计了PI控制器,使系统在不增加最大控制能量的条件下能够比使用标准一致性算法更快的达到一致。在这种方法中,通过利用控制系统中更多的有效信息,来确定智能体的下一步状态。应用频域中的分析方法,得到了加快系统收敛速度的充分条件。由于通讯网络中不可避免的存在个体本身和其它个体之间的时滞问题,本文进一步分析了在具有输入时滞和通信时滞的条件下,系统使用所提出的快速一致性算法的稳定性问题。针对二阶多智能体系统,首先在无向网络下设计了PI控制器,基于给定的条件,分析得到了系统能够快速的达到静态一致和动态一致的充分条件。随后,在有向网络下,提出了一类基于智能体当前状态和过去状态的一致性控制算法,分析了系统在该控制算法作用下的稳定性问题,并得到了系统实现快速静态一致性和快速动态一致性的充分条件。进一步,将提出的算法在多智能体系统的快速编队控制中进行了应用。以上理论分析的结果表明系统能否实现快速一致与Laplacian矩阵的特征值,网络的结构和连通性密切相关。仿真结果表明所提出的几类快速一致性控制算法能大大提高系统的收敛性能。
目前已有的大多数一致性算法都是使得多智能体系统状态达到渐近稳定,但是,实际上系统的状态变量是不能在有限的时间内达到平衡状态。所以使得系统在有限时间内达到稳定是非常必要和必需的。本文利用Lyapunov有限时间稳定性理论和矩阵理论,分析了多智能体系统的有限时间一致性问题。针对存在通信约束的多智能体系统有限时间一致性问题,提出了一类连续的非线性一致性算法,分析表明当系统个体间的通信网络拓扑结构为连通图的情况时,该算法使得系统具有通信约束时能够在有限时间内达到一致。进一步给出了系统收敛时间的上界,该时间上界由选取的Lyapunov函数,无向图的Laplacian矩阵以及系统的初始状态决定。随后,研究了基于一般非线性函数的有限时间一致性算法,并且给出了该算法使得系统在有限时间内收敛的非线性函数项必须满足的条件。本文针对不忽略智能体质量的情况,也给出了系统有限时间一致性算法的设计方法。随后研究了多智能体系统的有限时间跟踪控制问题。针对领导者状态是时变的情况,提出了一类非线性有限时间跟踪控制算法,在固定网络拓扑结构下,分析得到了该算法使得系统中跟随者状态在有限时间内与领导者状态达到一致的充分条件；在切换网络拓扑结构下,提出了一类有限时间跟踪控制算法,在领导者的状态是时不变的情况下,给出了该算法使得系统实现有限时间跟踪控制的充分条件。
受一致性理论的启发,基于领导-跟随者模型,针对三类不同的通信情况分别提出了相应的水下智能体群的队形控制和群运动控制模型。在所提出模型的基础上,使用一致性理论,给出了使得所有跟随者能够跟随领航者在水中以规定的队列沿着指定的运动方式前行的系统条件。进一步,在具有通信约束的情况下,对每一个水下智能体设计一个分布式控制器,使得水下智能体间的通信时滞在一定范围内,所有的水下智能体仍然能够全局渐近地收敛至期望速度和期望队形。由于该时滞上界是依赖于网络参数的,所以具有更低的保守性。
最后,对全文的研究工作做了总结,并对需要进一步开展的研究工作进行了展望。
In recent years, distributed coordination of multi-agent systems has attracted great attention due to several technological advances in the fields of communication and computation. As a fundamental problem in distributed coordination of networks of dynamic agents, the consensus problem is to design appropriate protocols such that the group of vehicles can reach consensus on the shared information in the presence of limited and unreliable information exchange and dynamically changing interaction topologies. Based on garph theory, the fast consensus protocols, finite-time consensus problems and the group motion stability problems of autonomous underwater vehicle (AUV) systems are studied in this dissertation, the main work and research results lie in the following.
The analysis of convergence rate is very important in the consensus control of multi-agent systems. In most engineering systems, a fast convergence rate is necessary. Based on the local information, agents automatically converge to a common consensus state and the convergence rate is determined by the algebraic connectivity of the communication network. Without changing the network topology and without requiring extra communication, this dissertation proposes solutions to fast consensus of first-order systems and second-order systems. Aimed at first-order systems, the PI controller is used in fast consensus. With out increasing the maximum control effort, the systems using the PI controller can reach a faster consensus than using the standard consensus protocol. The main idea is to employ a more useful package of information to make sure the agents' next state. Based on the frequency-domain analysis, the sufficient condition to guarantee a faster consensus convergence has been obtained. The disturbance of communication delay is unavoidable and might cause multi-agent systems to diverge or oscillation, the stability analyses of the systems using the proposed protocol with input delays and communication delays are also given. Aimed at second-order systems, a PI controller is used in undirected topologies; the sufficient conditions for the multi-agent systems converging to a fast stationary consensus and a fast dynamical consensus are obtained. Under directed topologies, a fast consensue protocol using both current states and outdated states is proposed. The stability analysis of the systems using the protocol is given, and the sufficient conditions for the system converging to a fast stationary consensus and a fast dynamical consensus are obtained, respectively. What's more, the consensus protocols are applied to the formation control of the multi-vehicle system. The theoretic results show that the fast consensus of the systems is related to the eigenvalues of the Laplacian matrix, the structure of the network and the interconnection topology of the network. Simulations show that the proposed fast protocols can improve the convergence rate significantly.
Most of the existing protocols (including those appeared in the aforementioned works) can not result in state consensus in a finite time, that is, consensus is only achieved asymptotically. Hence, finite-time consensus is more appealing and there are a number of settings where finite-time convergence is a desirable property. Based on the theory of finite-time Lyapunov stability and matrix theory, the finite-time consensus problems are studied in this dissertation. Finite-time consensus protocol for continuous multi-agent systems with communication constraints is proposed. The sufficient conditions which guarantee the multi-agent systems to reach a consensus in finite time are given, provided that the undirected network is connected. Moreover, the settling time for the system to reach a consensus is given, it is important to know that the settling time depends on the Lyapunov function, the Laplacian matrix of the undirected graph and the initial state of the system. In order to identify general criteria for solving finite-time consensus problems of multi-agent systems with communication constraints, we show that under protocols satisfying our conditions, the states of agents reach a consensus in finite time when the interaction topology is connected. The methods to design finite-time consensus protocols for systems consider mass are given. The finite-time tracking problems of multi-agent systems with leader-follower models are studied. To track a time-varying leader, a nonlinear finite-time tracking control protocol is proposed for multi-agent systems under fixed network topologies. The sufficient conditions which guarantee the system to reach a finite-time tracking are obtained. Moreover, for the system under switching network topologies, another tracking control protocol is proposed. We show that the followers can track the time-invariant leader in finite time. Simulation results demonstrate that designed protocols can make the system reach consensus in finite time and meeting corresponding performance.
Motivated by recent advances in consensus theory of multi-agent systems, based on the leader-follower model, we present corresponding motion model about the formation control and group motion control of AUVs for three different communication conditions. Based on the models and the consensus theory, the conditions for the followers to track the leader steadily are presented and proved. For the systems with communication constraints, a distributed consensus controller for each AUV is designed. It is proved that if the communication time delay between two AUVs is smaller than a certain upper bound, then the velocity vectors of all AUV and the group formation converge to the same desired velocity vector and the desired formation globally asymptotically, and the commen upper bound of the time delay is dependent on the parameters of the network, so it can reduce the conservatism.
Finally, a summary has been done for all discussions in the dissertation. The research works in future study are presented.
引文
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