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首页> 外文期刊>IEEE Transactions on Automatic Control >Scaling in Bidirectional Platoons With Dynamic Controllers and Proportional Asymmetry
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Scaling in Bidirectional Platoons With Dynamic Controllers and Proportional Asymmetry

机译：具有动态控制器和比例不对称性的双向排缩放

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摘要

We consider platoons composed of identical vehicles with an asymmetric nearest-neighbor interaction. We restrict ourselves to intervehicular coupling realized with dynamic arbitrary-order onboard controllers such that the coupling to the immediately preceding vehicle is proportional to the coupling to the immediately following vehicle. Each vehicle is modeled using a transfer function and we impose no restriction on the order of the vehicle. The only requirement on the controller and vehicle model is that the platoon is stable for any number of vehicles. The platoon is described by a transfer function in a convenient product form. We investigate how the H-infinity norm and the steady-state gain of the platoon scale with the number of vehicles. We conclude that if the open-loop transfer function of the vehicle contains two or more integrators and the second smallest eigenvalue of the graph Laplacian is uniformly bounded from below, the norm scales exponentially with the growing distance in the graph. If there is just one integrator in the open loop, we give a condition under which the norm of the transfer function is bounded by its steady-state gain-the platoon is string-stable. Moreover, we argue that in this case it is always possible to design a controller for the extreme asymmetry-the predecessor following strategy.
机译：我们考虑由不对称的近邻交互作用的相同车辆组成的排。我们将自己限制在使用动态任意阶车载控制器实现的车辆间耦合上，以使得与前一车辆的耦合与与后一车辆的耦合成比例。每辆车都是使用传递函数建模的，我们对车的顺序没有任何限制。对控制器和车辆模型的唯一要求是，排对于任何数量的车辆都是稳定的。排以方便的产品形式通过传递函数进行描述。我们研究了H-无穷大范数和排的稳态增益与车辆数量的关系。我们得出的结论是，如果车辆的开环传递函数包含两个或多个积分器，并且图拉普拉斯算子的第二最小特征值从下方均匀地有界，则范数会随着图中距离的增加而按指数比例缩放。如果开环中只有一个积分器，我们给出一个条件，在该条件下，传递函数的范数受其稳态增益的约束-排是字符串稳定的。而且，我们认为在这种情况下，总是有可能设计一种用于极端不对称的控制器-先前的跟随策略。

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