多智能体系统分布式跟踪控制问题研究
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摘要
近十多年来,多智能体系统的分布式控制问题是控制理论中的一个热门研究课题,吸引了许多研究人员的关注,其在许多学科和领域,如计算机科学、生物学等有着广泛的应用背景。分布式趋同控制问题是多智能体系统研究的一个中心问题,其目标是设计分布式控制器以使得所有智能体的状态或输出信息达到一致。根据系统中是否带有领导者,此问题可以分为两类：无领导者的趋同(或一致)控制问题以及带有领导者的分布式跟踪控制问题。本文主要研究多智能体系统的分布式跟踪控制算法设计与分析,主要研究内容以及贡献包括以下几个方面。
一、研究了二阶非线性多智能体系统的分布式跟踪控制问题。首先,在有向图下分别考虑了二阶积分器型和二阶严格反馈型非线性多智能体系统的分布式跟踪控制问题。同时,在领导者的控制输入等于零时,研究了系统的逆最优自适应分布式跟踪控制问题。其次,在无向图下考虑了带有扰动的二阶非线性多智能体系统的分布式跟踪控制问题,并分别设计了状态反馈控制器和动态输出反馈控制器。与已有文献相比,我们并不要求系统中的非线性函数满足全局Lipschitz条件,并且所设计的控制器不依赖于通信拓扑图对应拉普拉斯矩阵以及各个智能体系统自身的状态等。因此,所设计控制器为严格意义上的分布式控制。
二、利用前面处理非线性多智能体系统的方法,研究了一般线性多智能体系统在有向图下的分布式跟踪控制问题。首先,研究了一类高阶积分器型的线性多智能体系统的分布式跟踪控制问题。与已有结果相比,所设计的控制器不需要利用通信拓扑图对应拉普拉斯矩阵的特征值信息。为此,所设计的控制器为非线性的而非常见的线性控制器。对于任意的含有一个以领导者对应节点为根节点的有向生成树的有向图,此控制器均可使得所有跟踪者状态渐近跟踪领导者状态。其次,利用线性系统理论,将一般线性多智能体系统的分布式跟踪控制问题分解为多个高阶积分器型多智能体系统的分布式跟踪控制问题,进而得到其分布式控制器。
三、研究了一类输出反馈型非线性多智能体系统在有向图下的分布式跟踪控制问题。通过设计一类新颖的分布式观测器,并利用反步设计法,构造了一类只依赖于相对输出信息的分布式自适应控制器。所设计的控制器可在任意的含有一个以领导者对应节点为根节点的生成树的有向图下,解决系统的分布式跟踪控制问题。
四、在无向通信拓扑图下,研究了一类带有扰动和不确定函数的非线性多智能体系统的半全局分布式跟踪控制问题。首先利用鲁棒误差符号积分方法,对一类高阶积分器型非线性多智能体系统进行了控制器设计。所设计的控制器可使得系统达到半全局鲁棒跟踪。其次,将此方法推广到了一类更为广泛的不确定非线性系统。与已有文献相比,所设计的控制器为连续型的,而非常见的为达到系统状态渐近趋于一致所设计的非连续型控制器。
五、在Markov切换拓扑图下,研究了二阶异构非线性多智能体系统的分布式跟踪控制问题以及带有扰动的二阶非线性多智能体系统的分布式逆最优增益设计问题。由于Markov切换拓扑图带来的困难,相应的稳定性分析更具有挑战性,而不是平行的推广。为了更为清晰地讨论多智能体系统的分布式逆最优增益设计问题,首先讨论了Markov跳跃系统的逆最优增益设计问题,并给出此问题可解的两个充分条件。针对二阶非线性多智能体系统,利用两个充分条件设计了两类分布式控制器来解决系统的分布式逆最优增益设计问题。
During the past decade, as one of the central problems in control theory, the dis-tributed control of multi-agent systems has gained much attention due to its broad appli-cation backgrounds in many disciplines, such as computer sciences and biology. One main fundamental problem in multi-agent systems is the consensus problem that aims to design distributed control laws such that the states or outputs of all agents reach an agree-ment. It contains the consensus problem without a leader (i.e., leader-less consensus) and consensus problem with a leader, which is generally called leader-following consen-sus or distributed tracking problem. This dissertation focuses on the leader-following consensus problem of multi-agent systems. The main contents and contributions are summarized as follows.
1. The leader-following consensus problem of second-order nonlinear multi-agent systems is investigated. First, the leader-following consensus problem of second-order integrator type nonlinear multi-agent systems and second-order strict-feedback nonlin-ear multi-agent systems are studied under directed communication topology. Under the assumption that the control input of the leader agent is equal to zero, the inverse opti-mal adaptive distributed tracking control problem is also studied. Second, the leader-following consensus problem of second-order nonlinear multi-agent systems with un-known but bounded disturbances is considered. Both state feedback and dynamic output feedback control laws are designed. Compared with the existence literatures, the nonlin-ear functions are not required to satisfy any globally Lipschitz growth or Lipschitz-like growth condition. Moreover, the adaptive consensus protocol is in a distributed fashion without using any global information such as the eigenvalues of the Laplacian matrix of underly topology and the agent's own state. Therefore, the proposed control laws are in a fully distributed fashion.
2. According to the methods developed for nonlinear multi-agent systems, the leader-following consensus problem of general linear multi-agent systems is investi-gated. First, the leader-following consensus problem of a class of high-order integrator type multi-agent systems is studied. Compared with the existing works, the proposed control law is independent of the eigenvalues of the Laplacian matrix of underly topol-ogy. Due to the complexity caused by the directed graph, the proposed protocol is nonlinear rather than the conventional linear protocol. It is proved that, for any directed communication graph that contains a spanning tree with the root node being the leader agent, the proposed control law solves the leader-following consensus problem. Sec-ond, by using linear system theory, we convert the leader-following consensus problem of general linear multi-agent systems into the leader-following consensus problem of some high-order integrator type multi-agent systems.
3. The leader-following consensus problem of a class of nonlinear multi-agent systems in strict feedback form is studied. By introducing a novel distributed observer and employing the backstepping methodology, a distributed adaptive nonlinear control law is constructed using the relative output information between neighboring agents. For any directed communication graph that contains a spanning tree with the root node being the leader agent, the proposed control law solves the leader-following consensus problem.
4. The robust leader-following consensus problem of a class of multi-agent sys-tems with unknown nonlinear dynamics and unknown but bounded disturbances under undirected communication topology is studied. First, by employing the robust inte-gral of the sign of the error technique, a distributed control law is designed for a class of high-order integrator type nonlinear multi-agent systems. The proposed protocol achieves semiglobally leader-following consensus. Second, the approach is extended to study a class of more general uncertain multi-agent systems. It is worth pointing out that the proposed distributed control law is continuous rather than discontinuous.
5. The leader-following consensus problem of a class of heterogeneous second-order nonlinear multi-agent systems and the inverse optimal gain assignment distribut-ed control of a class of second-order multi-agent systems under Markovian switching topology are investigated. It is more difficult to design distributed control laws due to the complexity caused by Markovian switching topology. To study the inverse optimal gain assignment distributed control problem of multi-agent systems, the inverse opti-mal gain assignment problem of Markovian jump nonlinear systems is introduced. Two sufficient conditions are given for the solvability of this problem. Based on those two sufficient conditions, two distributed control laws are designed, which solve the inverse optimal gain assignment distributed control problem of multi-agent systems.
一、研究了二阶非线性多智能体系统的分布式跟踪控制问题。首先,在有向图下分别考虑了二阶积分器型和二阶严格反馈型非线性多智能体系统的分布式跟踪控制问题。同时,在领导者的控制输入等于零时,研究了系统的逆最优自适应分布式跟踪控制问题。其次,在无向图下考虑了带有扰动的二阶非线性多智能体系统的分布式跟踪控制问题,并分别设计了状态反馈控制器和动态输出反馈控制器。与已有文献相比,我们并不要求系统中的非线性函数满足全局Lipschitz条件,并且所设计的控制器不依赖于通信拓扑图对应拉普拉斯矩阵以及各个智能体系统自身的状态等。因此,所设计控制器为严格意义上的分布式控制。
二、利用前面处理非线性多智能体系统的方法,研究了一般线性多智能体系统在有向图下的分布式跟踪控制问题。首先,研究了一类高阶积分器型的线性多智能体系统的分布式跟踪控制问题。与已有结果相比,所设计的控制器不需要利用通信拓扑图对应拉普拉斯矩阵的特征值信息。为此,所设计的控制器为非线性的而非常见的线性控制器。对于任意的含有一个以领导者对应节点为根节点的有向生成树的有向图,此控制器均可使得所有跟踪者状态渐近跟踪领导者状态。其次,利用线性系统理论,将一般线性多智能体系统的分布式跟踪控制问题分解为多个高阶积分器型多智能体系统的分布式跟踪控制问题,进而得到其分布式控制器。
三、研究了一类输出反馈型非线性多智能体系统在有向图下的分布式跟踪控制问题。通过设计一类新颖的分布式观测器,并利用反步设计法,构造了一类只依赖于相对输出信息的分布式自适应控制器。所设计的控制器可在任意的含有一个以领导者对应节点为根节点的生成树的有向图下,解决系统的分布式跟踪控制问题。
四、在无向通信拓扑图下,研究了一类带有扰动和不确定函数的非线性多智能体系统的半全局分布式跟踪控制问题。首先利用鲁棒误差符号积分方法,对一类高阶积分器型非线性多智能体系统进行了控制器设计。所设计的控制器可使得系统达到半全局鲁棒跟踪。其次,将此方法推广到了一类更为广泛的不确定非线性系统。与已有文献相比,所设计的控制器为连续型的,而非常见的为达到系统状态渐近趋于一致所设计的非连续型控制器。
五、在Markov切换拓扑图下,研究了二阶异构非线性多智能体系统的分布式跟踪控制问题以及带有扰动的二阶非线性多智能体系统的分布式逆最优增益设计问题。由于Markov切换拓扑图带来的困难,相应的稳定性分析更具有挑战性,而不是平行的推广。为了更为清晰地讨论多智能体系统的分布式逆最优增益设计问题,首先讨论了Markov跳跃系统的逆最优增益设计问题,并给出此问题可解的两个充分条件。针对二阶非线性多智能体系统,利用两个充分条件设计了两类分布式控制器来解决系统的分布式逆最优增益设计问题。
During the past decade, as one of the central problems in control theory, the dis-tributed control of multi-agent systems has gained much attention due to its broad appli-cation backgrounds in many disciplines, such as computer sciences and biology. One main fundamental problem in multi-agent systems is the consensus problem that aims to design distributed control laws such that the states or outputs of all agents reach an agree-ment. It contains the consensus problem without a leader (i.e., leader-less consensus) and consensus problem with a leader, which is generally called leader-following consen-sus or distributed tracking problem. This dissertation focuses on the leader-following consensus problem of multi-agent systems. The main contents and contributions are summarized as follows.
1. The leader-following consensus problem of second-order nonlinear multi-agent systems is investigated. First, the leader-following consensus problem of second-order integrator type nonlinear multi-agent systems and second-order strict-feedback nonlin-ear multi-agent systems are studied under directed communication topology. Under the assumption that the control input of the leader agent is equal to zero, the inverse opti-mal adaptive distributed tracking control problem is also studied. Second, the leader-following consensus problem of second-order nonlinear multi-agent systems with un-known but bounded disturbances is considered. Both state feedback and dynamic output feedback control laws are designed. Compared with the existence literatures, the nonlin-ear functions are not required to satisfy any globally Lipschitz growth or Lipschitz-like growth condition. Moreover, the adaptive consensus protocol is in a distributed fashion without using any global information such as the eigenvalues of the Laplacian matrix of underly topology and the agent's own state. Therefore, the proposed control laws are in a fully distributed fashion.
2. According to the methods developed for nonlinear multi-agent systems, the leader-following consensus problem of general linear multi-agent systems is investi-gated. First, the leader-following consensus problem of a class of high-order integrator type multi-agent systems is studied. Compared with the existing works, the proposed control law is independent of the eigenvalues of the Laplacian matrix of underly topol-ogy. Due to the complexity caused by the directed graph, the proposed protocol is nonlinear rather than the conventional linear protocol. It is proved that, for any directed communication graph that contains a spanning tree with the root node being the leader agent, the proposed control law solves the leader-following consensus problem. Sec-ond, by using linear system theory, we convert the leader-following consensus problem of general linear multi-agent systems into the leader-following consensus problem of some high-order integrator type multi-agent systems.
3. The leader-following consensus problem of a class of nonlinear multi-agent systems in strict feedback form is studied. By introducing a novel distributed observer and employing the backstepping methodology, a distributed adaptive nonlinear control law is constructed using the relative output information between neighboring agents. For any directed communication graph that contains a spanning tree with the root node being the leader agent, the proposed control law solves the leader-following consensus problem.
4. The robust leader-following consensus problem of a class of multi-agent sys-tems with unknown nonlinear dynamics and unknown but bounded disturbances under undirected communication topology is studied. First, by employing the robust inte-gral of the sign of the error technique, a distributed control law is designed for a class of high-order integrator type nonlinear multi-agent systems. The proposed protocol achieves semiglobally leader-following consensus. Second, the approach is extended to study a class of more general uncertain multi-agent systems. It is worth pointing out that the proposed distributed control law is continuous rather than discontinuous.
5. The leader-following consensus problem of a class of heterogeneous second-order nonlinear multi-agent systems and the inverse optimal gain assignment distribut-ed control of a class of second-order multi-agent systems under Markovian switching topology are investigated. It is more difficult to design distributed control laws due to the complexity caused by Markovian switching topology. To study the inverse optimal gain assignment distributed control problem of multi-agent systems, the inverse opti-mal gain assignment problem of Markovian jump nonlinear systems is introduced. Two sufficient conditions are given for the solvability of this problem. Based on those two sufficient conditions, two distributed control laws are designed, which solve the inverse optimal gain assignment distributed control problem of multi-agent systems.
引文
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