Cooperative Control of Dynamical Systems With Application to Autonomous Vehicles

Qu Z.; Wang J.; Hull R. A.

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Cooperative Control of Dynamical Systems With Application to Autonomous Vehicles

机译：动态系统的协同控制及其在自动驾驶汽车中的应用

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In this paper, a new framework based on matrix theory is proposed to analyze and design cooperative controls for a group of individual dynamical systems whose outputs are sensed by or communicated to others in an intermittent, dynamically changing, and local manner. In the framework, sensing/communication is described mathematically by a time-varying matrix whose dimension is equal to the number of dynamical systems in the group and whose elements assume piecewise-constant and binary values. Dynamical systems are generally heterogeneous and can be transformed into a canonical form of different, arbitrary, but finite relative degrees. Utilizing a set of new results on augmentation of irreducible matrices and on lower triangulation of reducible matrices, the framework allows a designer to study how a general local-and-output-feedback cooperative control can determine group behaviors of the dynamical systems and to see how changes of sensing/communication would impact the group behaviors over time. A necessary and sufficient condition on convergence of a multiplicative sequence of reducible row-stochastic (diagonally positive) matrices is explicitly derived, and through simple choices of a gain matrix in the cooperative control law, the overall closed-loop system is shown to exhibit cooperative behaviors (such as single group behavior, multiple group behaviors, adaptive cooperative behavior for the group, and cooperative formation including individual behaviors). Examples, including formation control of nonholonomic systems in the chained form, are used to illustrate the proposed framework.

机译：在本文中，提出了一种基于矩阵理论的新框架，用于分析和设计一组个体动力系统的协作控制，这些动力系统以间歇，动态变化和局部的方式感知或传达给他人。在该框架中，感测/通信通过时变矩阵进行数学描述，时变矩阵的维数等于组中动力系统的数量，并且其元素采用分段恒定和二进制值。动力系统通常是异构的，可以转换为不同，任意但相对有限度的规范形式。该框架利用关于不可约矩阵的扩充和可约矩阵的较低三角剖分的一组新结果，使设计人员能够研究通用的局部和输出反馈协作控制如何确定动力学系统的组行为，并了解如何感测/交流的变化会随着时间的推移影响小组的行为。明确推导了可约化行随机（对角正）矩阵的乘法序列收敛的充要条件，并通过在合作控制律中简单选择增益矩阵，表明整个闭环系统表现出合作性行为（例如单组行为，多组行为，该组的自适应合作行为以及包括个人行为在内的合作形成）。实例（包括链形式的非完整系统的结构控制）用于说明所提出的框架。

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《IEEE Transactions on Automatic Control》 |2008年第4期|p.894-911|共18页
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Qu Z.; Wang J.; Hull R. A.;
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Cooperative Control of Dynamical Systems With Application to Autonomous Vehicles

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